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Some Subtle Aspects Of Relativity.


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#1 Doctordick

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Posted 04 August 2008 - 02:08 PM

Will,
I am sorry for being unable to present my thoughts in a clear concise manner but I apparently have a somewhat strange way of looking at things. No one seems to comprehend that what I have done is to set up a logical structure designed to provide a representation of any and all epistemological constructs such that they are guaranteed to be flaw free with regard to what is known (what is known being undefined). Everyone presumes I am putting forth a theory of some sort. This is not a theory; it is a logical structure designed to provide a factual guarantee that all expectations expressed in that form are factually flaw free. Surprisingly, the constraint that the epistemological construct be flaw free turns out to have a rather simple representation: the expectations from any flaw free epistemological construct are given by solutions of my fundamental equation: i.e., the probability that a set of ontological elements will be part of the universe of possibilities is given by the squared magnitude of [math]\vec{\Psi}[/math]. That is a fact, not a conjecture! If one were to follow my proof carefully, they would discover the truth of that statement. But no one takes the trouble to do such a thing. I am instead confronted with two classes of people, those who cannot follow my proof because the lack the education in formal logic and mathematics and those who, though they have the education to do so, refuse to examine that proof because they “full well know that it can not possibly be correct”. Well, life is tough all over.

Nonetheless, I will attempt to answer the complaints I received from Erasmus00 on my presentation of relativity. At his suggestion I am starting a new thread devoted to clearing up some subtle issues which concern him. The following are my answers to some of his complaints.

What you are doing (essentially re-plotting world lines parameterized by x,y,z and tau instead of x,y,z,t, yielding a Euclidean type metric) isn't incorrect, but I think it has one big problem- t is not invariant under coordinate transformation, so this isn't really observer independent.

It turns out that, when the entirety of the deduction is taken into account, it is indeed invariant under such coordinate transformation but that fact is not easy to demonstrate until the full nature of the representation is understood. If you look at the development of solutions so far presented, “distance” has not been defined. Measure of x, tau and time are free to be defined (plotting arbitrary numerical references to a coordinate system does not define these measures).

If you doubt that assertion, consider the “plotting of the evolution of primates”. We can do this on a piece of paper, assigning a specific point on the paper to represent a specific primate (where, for the fun of it, we can put drawings of the specific primate being referred to). We can then draw lines between various points which specify the evolution of those primates. I have, in fact, seen just such drawings in many books discussing the issue of evolution, yet no effort is put forth on the idea that such a plot implies a “measure”. Oh, the geometric mechanism of the presentation may have a measure but one can not presume that measure carries over to the plot. A “measure” of the ontological elements being represented by these numerical references must be established in the epistemological construct being represented: i.e., it is possible that some measure might be defined which can be represented by the measure of the geometry, but this is certainly not a necessity.

I have defined time, but not the measure of time. I have defined position (as using those numerical references as a set of coordinates in that x,tau space) but I have not defined the measure of that position. I have defined Energy, Momentum and Mass; as specific differential terms of that fundamental equation. And, oh yes, I have also defined one's expectations in terms of the solution of that equation. Unless I have missed something here, I haven't defined anything else!

Now one might be tempted to say that I have defined these measures by identifying the Schroedinger equation as an approximation to my equation. But have I? Aren't these “measures”, used by modern physics, defined elsewhere? I don't think these measures are defined by the Schroedinger equation itself at all; they are defined by other arguments and are then presumed to be the correct measures to be used in the Schroedinger equation. Until your epistemological construct defines those measures, they are free variables of the presentation. This leads to some interesting observations, some of which I will lay out for you at the end of this post.

Meanwhile, I will return to your complaints:

By reparameterizing, you obscure the invariant- i.e. the metric you introduce isn't a true metric because different observers cannot agree on the value of t for a given event. Also, z,y,z,tau aren't true vectors for the same reason.

It seems possible that you have a different meaning for the word “metric of the geometry” than I was taught so, in the interest of communication, let us instead call what I mean “path length”. Other than that, it seems, once again, that you totally miss what I am doing. First of all, different observers have nothing at all to do with this parametric analysis.

To reiterate, it is presumed that we have a specific valid solution to a problem which is expressed in a general relativistically correct representation of reality (using a specific Einsteinian “space-time” representation). We can use a parameterized representation of the paths of every entity involved (having also included a hypothetical clock attached to each and every entity). This leads to five algebraic expressions for values associated with every point in every path of every entity in that specific Einsteinian plot. Einstein's picture only uses four of those for the geometric representation and the fifth becomes a measure of path length (Einstein's invariant interval or “proper time”: i.e., the reading on the clocks themselves).

We have here the (specific; correct; valid; unquestioned) solution to a specific problem expressed in a parametric form. All I am doing is re-plotting exactly the same numerical values, which were plotted in the original Einsteinian space time geometry, but in a different geometry. This is no more than an alternate plot of exactly the same information. I plot those paths (which constitute the correct valid solution to the given problem) given by the parametric expressions in a four dimensional geometry consisting of the coordinates x,y,z and tau exactly as given by the explicit parametric expressions yielding the known correct solution. By the way, tau is a real number as used here; I use tau, the time representation of the invariant interval, as the parameter because, in Einstein's picture, the invariant interval along the path of any entity is always imaginary when expressed in spacial terms.

That leaves me with the fifth parametric expression associated with every point in every path, [math]t_i=f_{t_i}(\alpha_i)[/math].

Now think about what this variable expresses. It is time in the representation which was used by whoever it was that correctly solved that general relativistic problem, and found that specific; correct; valid; unquestioned solution. This surface in his Einsteinian representation represents simultaneity from his perspective. Time has exactly the old fashioned meaning: i.e., things can interact when they exist at the same place and time (forces at a distance can be seen as virtual entities which, through exchange, interact with the primary entities when the entities being exchanged are at the same place and time as those primary entities). This is a concept entirely consistent with the Newtonian perspective. Newton used this variable “time” as a dynamic parameter of mechanical evolution of the structure being examined. Under the assumption that one could set all clocks to agree, Newton represented dynamic evolution in space time diagrams setting space and time orthogonal to one another. Einstein continued this representation in spite of the fact that he knew full well that one could not set all clocks to agree.

What I think Einstein missed was the fact that time could still be used as a parameter of the dynamic evolution of his structure (as that evolution is very dependent upon the actual path being taken by each specific entity making up any structure). In view of that fact, how about we use this fifth parameter [imath]t_i[/imath] as a parameter of evolution just as Newton did (and, I might comment, just as it is used in quantum mechanics). Our parameterized representation of the correct valid solution to our problem assigns a value of t to every point of every path of every entity.

Note that this value continually increases along the paths specified in our geometry. Would it not be convenient that this parameter be path length in our geometry? Can we conceive of a geometry where t might be at least proportional to our path length? Does it not seem reasonable to match the relationship between the five variables already expressed in the Einsteinian picture (which we know to be the physically “correct” solution? How about we just rearrange the terms in his expression, [math]c\tau_i =i\sqrt{dx_i^2+dy_i^2+dz_i^2-c^2dt_i^2}[/math] into [math]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c^2d\tau_i^2}[/math] implying exactly the same relationship? O'migod, that's the path length in a Euclidean geometry! :doh: Who would have thunk it! Boy, it sure makes for a convenient geometry to consider doesn't it. ;)

The second thing is that the concept of momentum in the tau direction being equal to mass seems to obscure the invariant nature of mass- you would think a coordinate transformation should mix the coordinates of momentum, but the mass is fixed. The traditional view has the value of having the mass be the invariant "length" of the momentum vector.

But who cares about the traditional view? The point here is that we are merely looking at a correct valid solution plotted in a different geometry. The purpose of our analysis here is to understand that a correct valid solution as seen in that specific plot.

So I guess what I'm saying is that I can't see the use of your formulation because I think it hides the very properties a good formalism should emphasize.

Oh does it now! I suspect a strong prejudiced towards supporting Einstein's picture as the only possible picture. I would like you to consider some things about this representation. It has one very striking aspect which, from the perspective of quantum mechanics, I believe the Einsteinian perspective hides. Notice that, in this alternate geometric representation (of this correct valid general relativistic solution) interactions occur when x,y,z and t are the same, but tau (which happens to be exactly the reading on the different entities hypothetical clocks) need not be the same: i.e., these “clocks” do not measure time! I think I have commented about this a number of times elsewhere. As far as I am concerned, Einstein's perspective hides the fact that clocks do not in fact measure time.

Since tau, one of the coordinates of this geometry (a coordinate which, by the way, is exactly what is read on clocks attached to the entities) has no bearing upon the whether or not an interaction can take place it should be clear that, in this geometry, we need some kind of mechanism to project out the differences in the tau coordinate as they bear upon interactions. An excellent mechanism comes to mind: i.e., the uncertainty principal. If the value of this coordinate has an infinite uncertainty (i.e., it is projected out as not a necessary part of our world view) then the momentum in that direction can have zero uncertainty (it can be a quantized variable).

And what quantized variable do you think comes to my mind? Well from doing calculations of half lives on unstable particles it becomes quite clear to me that the uncertainty principal relates the uncertainty in rest mass to the uncertainty in tau in exactly the way the uncertainty in position is related to uncertainty in momentum in modern quantum mechanics. Add to this the fact that, for massless entities, the magnitude of momentum is essentially the magnitude of energy (exactly as the magnitude of rest mass relates to energy) and I simply can not comprehend the total refusal to relate rest mass to the momentum of an entity in the tau direction (except that do do so is inconvenient ot Einstein's picture).

Look at the similarities. Momentum can be converted into energy; but only when the conversion conserves momentum (a body with momentum cannot covert that momentum into energy without interacting with another body). It's a simple kinematic thing. Likewise mass by itself with nothing to interact with cannot convert that mass into energy because of exactly the same kinds of kinematic constraints. People fail to see the possibility of such a perspective because they all work in laboratories made of mass quantized entities with equipment they use to record these phenomena built entirely of mass quantized entities. So who is hiding what?

I have a thought experiment you really need to perform. Suppose, for the fun of it, that I am an individual from a technologically advanced society and I meet with you to show you a couple of devices we have invented. I can't show you why it works the way it does because I, personally, don't know the science behind it; but I do know exactly what it does. The first device looks exactly like what you would see as an old fashion analog pocket watch. It has a dial with three hands which show hours, minutes and seconds, and has a knurled stem at the top which would appear to be for setting and/or winding the watch.

But I tell you it is not a watch; it is a one way time machine. When the stem is turned it will move the holder (and the holder only) into the future. When the stem is not turned, the reading on the time machine will read exactly the correct time (we won't worry about relativistic effects here, just assume that, for practical purposes, we live in a Newtonian universe). When the stem is turned, the reading on the face can be advanced. When the reading is advanced, the holder will be moved to exactly the time indicated on the face. The reverse is not possible. It is my understanding that one can not move to the past because doing so would cause paradoxes, but moving to the future will cause no such problems.

The question is, if I operate my time machine, what do you see? If you think about it a little, you should realize that, as I turn the stem, I move to whatever time is indicated on the face: i.e., I don't disappear and then reappear at the new time, I instead move through each and every time indicated on the dial. If you look at the face of the device while I am turning the stem, you will simply see the correct time as, whatever time you are at, I am there too (the second hand will appear to advance just as it did when I wasn't touching the stem). You will see me standing very still with my hand on the stem. If I advance the dial one hour while I take one breath (during the breath I turn the minute hand entirely around the face), you will see that breath as taking the entire hour. If my pulse were sixty beats a minute, you could perhaps detect my heart as beating once or twice during that hour (depending of course on how fast I personally am turning the stem). We won't worry about other effects; you could push me but I don't think either of us would like the results.

My second device is a toy we make for our children. It appears to be a standard baseball but it is not. It contains exactly the same time machine which I just demonstrated for you; however, it has no stem. Within the ball is a second device which, via internal dynamic effects enables it to know exactly where it is (remember, for practical effects of this thought experiment, we live in a Newtonian universe). When it is moved, the time machine (it and the ball within which it is contained) is advanced in time proportional to the distance it is moved. It is advanced exactly one second for every foot it is moved. Such a ball will display some rather interesting dynamic effects. (For the sake of simplicity, we won't consider rotation; the system is not designed to be rotated as rotation brings up some very complex effects.)

Consider two children ten feet apart playing catch with such a ball. From the children's perspective, how long does the ball take to cross the room? Suppose you replace the children with professional baseball pitchers? Then try firing it out of a canon. If you cannot figure out the logical consequences let me know and I will explain (and justify) the results. Another thing you might look at is tying a string to the ball and swinging it is a circle. I think you will find the consequences are quite interesting.

Now to a portion of the observations which arise from the measure issue I talked about earlier.

My fundamental equation was derived from the necessity of shift symmetry. There is another symmetry inherent in idea of using arbitrary numerical references to the undefined ontological elements on which the flaw free epistemological construct is to be built. That is the existence of scale symmetry: if a given epistemological construct can be deduced from a certain set of numerical labels then the same epistemological construct must be perfectly consistent with those same numbers multiplied by some arbitrary constant. If our expectations are to be given by [imath]\vec{\Psi}[/imath] as a function of those references (those numbers) then the solution must be scale invariant. Note that, in the original derivation, my fundamental equation is valid only in a frame of reference where the sum of the differentials vanish: however, I show this is not a serious issue because any [imath]\vec{\Psi}[/imath] is easily transformed to a frame where the differentials do not vanish.

However, this constraint on a valid frame still leads to one very significant conundrum. If we have a portion of the universe which can be considered as totally independent of another portion and, if the differentials of the two portions do not vanish in the same frame of reference, the resultant fundamental equations can not be asserted to be valid in all three of the possible reference frames. It turns out that this problem is easily solved. If you look at my fundamental equation, is is (sans the Dirac delta function) a simple many body wave equation in four dimensions with a wave velocity of 1/K. The problem is actually identical to problem Maxwell's equation presented to the physics Community. It was solved by what is essentially a scale transformation related to the two different reference frames and exactly the same methods may be used here (in order for all three reference frames to see the same fundamental equation as valid, they must all see it as describing an expanding sphere). This presents a simple algebraic problem which is quite easy to solve. If you need me to do this; let me know and I will show the explicit solution. The most important part of the solution is what is commonly referred to as Lorentz-Fitzgerald contraction. There must be exactly that scale transformation between the two frames (if the two portions of the universe can be considered as totally independent). If they are not totally independent, then the fundamental equation cannot be applied to them separately: i.e., they can not be handled as if they are independent. Seems quite reasonable to me.

Also, please notice that the actual “measure” here is still determined elsewhere by some method within the epistemological construct. Notice further that this method, whatever it happens to be is determined independently in each of the three frames (if it isn't then the two portions referred to are not totally independent). My arguments above are only setting a required scale relationship between these portions required by the validity of my fundamental equation.

Notice that, in my representation, time is a mere parameter characterizing the evolution of the system: i.e., 1/K is a constant but totally arbitrary factor. In order to relate this to what physicists call time, it is necessary to design a clock in my representation. You can find a specific design of an ideal clock in the physicsforum thread, posts #64 and #66 (again the post is a bit long and required two parts. I apologize for the diagrams being url references and not images. For convenience, I will post the relevant images here:

A picture of the ideal clock.
clock.gif

A tau,y cut at the midpoint of the oscillator perpendicular to the x,z plane.
restcloc.gif

An identical moving clock.
movecloc.gif

Vector representation of the clock
clocvect.gif

Analysis of the embedded geometry
showdiog.gif

Note that, in that presentation, I use “c” as the evolution velocity. Essentially the presentation goes through exactly the same if you use 1/K. The apparent speed of light is actually the ratio of the units used to define tau and the units used to define x,y and z (these are set by the methods used to define them in your “valid” epistemological construct). As I said, the value of 1/K is actually totally arbitrary and though clocks may seem to measure time, the actual “time” (the evolution parameter) is an unmeasurable variable. The apparent velocity of light is set by the methods used to measure x,y,z and tau. It is the assumption that tau along the path of an object is the same as the evolution parameter which yields our standard result of “c”.

Note that the real issue in this analysis is that there exists no way to guarantee that your frame of reference is the frame of reference where the differentials vanish (which, by the way, would define a rest simultaneous frame). This is a tad different from Einstein's statement that the physics is independent of that frame of reference (which, I would also comment, we know full well is false). If you doubt that assertion, consider the microwave background radiation from the supposed big bang. So my approach allows one to define a unique frame of reference (in fact, it is valid only in the frame where the sum over those differentials vanish) which simply takes care of the problems inherent in non local collapse of the wave function and some of the other difficulties between relativity and quantum mechanics.

Another strange and interesting phenomena arises. Suppose we change the sign of the “space” variables. Since the sum of the differential for the whole of the universe must vanish (or my fundamental equation is invalid), this can make no change in the fundamental equation. If the ontological elements invented to defend the epistemological construct yield a non zero contribution from the Dirac delta functions (which I am convinced is a distinct possibility), the same is not true of t. If the sign of t is changed, the whole equation can be returned to the initial form by multiplying through by minus one except for the fact that the Dirac delta function then changes sign, as the Dirac delta function is defined to be positive even when the arguments change sign. Any place the integrals involved in the transformation to the Schroedinger equation produced an attractive potential, they will now produce a repulsive potential. This fact makes for some other rather important consequences.

Have fun -- Dick

 


Edited by Doctordick, 01 February 2016 - 03:31 AM.


#2 Doctordick

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Posted 05 August 2008 - 09:54 PM

Well, I have just read an interesting article in July's “Scientific American”. My complaint with Einstein's theory of relativity is that he mishandles the issue of time and that this is the very issue which has been blocking their attempts to cast general relativity into quantum mechanics. Well, it seems that some European physicists have discovered a subtle trick around that shortcoming. I wouldn't be surprised to hear that they manage to accomplish the task of casting GR into QM, at least they are dealing with exactly the problem in Einstein's theory.

I found a couple of the things they say to be very revealing.

... Hawking and others taking this approach have said that “time is imaginary” in both a mathematical sense and a colloquial one. Their hope was that causality would emerge as a large-scale property from microscopic quantum fluctuations that individually carry no imprint of a causal structure.

Their hope was apparently dashed by computer simulations. Why am I not surprised? Einstein did not use time as an evolutionary parameter so why should they expect it to be consistent with cause and effect.

I do have one complaint with one comment in their article

The distinction between cause and effect is fundamental to nature, rather than a derived property

It certainly isn't a derived property but neither is it fundamental to nature. What it is, is a necessary component of any explanation of anything. If you don't use “cause” and “effect” how can you possibly expect to get from your axioms to your expectations. How they could continue to miss that issue is simply beyond me.

At any rate, they get around the difficulty with time by making differential elements of their space time agree with the direction of time. This at least inserts an evolutionary aspect to their computer analysis. But it also leads them to the idea of “atoms of space time” (which I suppose are regions where one need not worry about being careful with your definition of time. But it does look like a trick which will work.

Have fun -- Dick

#3 modest

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Posted 08 August 2008 - 01:35 PM

Forgive me for playing catch-up. I have a sincere desire to understand your results Dr. D. It's sounds like you advocate a 5D Euclidean geometry over Minkowski's:

Can we conceive of a geometry where t might be at least proportional to our path length? Does it not seem reasonable to match the relationship between the five variables already expressed in the Einsteinian picture (which we know to be the physically “correct” solution? How about we just rearrange the terms in his expression, [imath]c\tau_i =i\sqrt{dx_i^2+dy_i^2+dz_i^2-c^2dt_i^2}[/imath] into [imath]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c^2d\tau_i^2}[/imath] implying exactly the same relationship? O'migod, that's the path length in a Euclidean geometry! :doh: Who would have thunk it! Boy, it sure makes for a convenient geometry to consider doesn't it. ;)


My first question is, can you verify that this does indeed represent a geometry or metric that you advocate, rather than simply pointing out it's a Euclidean equation of motion.

Secondly, it would help me if you could summarize what t and tau are meant to represent here. I have a feeling you intend them meaning something quite different than I'm used to.

Actually, if you used the above to describe the motion of a photon and a massive particle that would be very helpful. Is tau zero for the photon and not zero for the not photon?

~modest

#4 Doctordick

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Posted 09 August 2008 - 12:18 PM

Hi modest, it was a pleasure to read your post as it seems to display an honest interest in understanding what I am saying.

It's sounds like you advocate a 5D Euclidean geometry over Minkowski's:

I think the phrase “over Minkowski's” over states the issue a bit. Plus that my geometry is a four dimensional Euclidean geometry (connecting ct to the path length makes it Euclidean) My position is that various geometries exist which yield insights to different aspects of physics. What I am adamantly against is the idea that there is only one way to skin a cat (so to speak) a position which I have found to be absolutely demanded by the physics community when it comes to relativity.

My first question is, can you verify that this does indeed represent a geometry or metric that you advocate, rather than simply pointing out it's a Euclidean equation of motion.

This question makes no sense to me. I have presented a Euclidean geometry consisting of four orthogonal coordinates, x.y.z and tau and asked you to plot certain information in that geometry. What could you possibly mean by asking if this indeed represents a geometry. Why on earth do you think it not a geometry?

Secondly, it would help me if you could summarize what t and tau are meant to represent here. I have a feeling you intend them meaning something quite different than I'm used to.

They “mean” exactly the same thing that they mean in the “space-time” representation proposed by the modern physics community when they speak of “space time paths” describing physical reality from a classical perspective: i.e., in the absence of QM effects. However, I would not use the term “Minkowski” as that is not really a representation of Einstein's GR geometry even though it may have the same signature.

Actually, if you used the above to describe the motion of a photon and a massive particle that would be very helpful. Is tau zero for the photon and not zero for the not photon?

First of all, in the classical perspective (i.e., no QM effects), the path of a massive particle would have a component in the tau direction whereas the photon would be moving on a path orthogonal to tau (mass, being momentum in the tau direction is zero). Both of them would have a t attached to that path which would measure the path length in this geometry (not tau as tau is the path length in Einstein's picture).

Suppose both the photon and the massive particle were being sent from Earth to Alpha Centauri (which I will take to be exactly four light years away). For the sake of this discussion, I will presume the massive particle is moving (from the conventional perspective) at a velocity of ten percent the speed of light (I just pulled that out of my hat). Now, the frame of reference I intend to use is a rest frame with respect to Alpha Centauri and Earth. So, in order to make things easy, let us define the “x” axis as being the line from the Earth to Alpha Centauri where Earth is taken to be at zero.

To quote my opening post to this thread:

To reiterate, it is presumed that we have a specific valid solution to a problem which is expressed in a general relativistically correct representation of reality (using a specific Einsteinian “space-time” representation).

In this case, that “specific Einsteinian 'space-time' representation” is the rest frame of Alpha Centauri and Earth with x=0 being the position of the earth and x= 4 light years being the position of Alpha Centauri. Clearly GR is unimportant in this particular problem and special relativity is the only issue of note.

Since, in my four dimensional frame, tau is what a clock attached to the entity under discussion would read, the photon (who's “invariant interval” along this path is zero) would travel parallel to the “x” axis (the trip does not change its tau value). The massive particle, on the other hand would appear to be moving at ten percent the speed of light so the actual direction of its movement would would have to have a tau component (tau, the clock attached to that entity would have a non zero reading by the time it got to Alpha Centauri). But hey, I'm not there; so suppose I had previously told my partner, now at Alpha Centauri, to return both entities to me at the same velocities and the same momentum with which he receives them (I will presume the time lag for him to accomplish this is zero for all practical purposes. When they get back, I will have enough information to describe their apparent paths. (If I look only at the one way trip, I have to make assumptions which I can not prove.)

So let us look at the photon first. It has made a round trip of distance eight light years, so t (its evolution parameter, time in Einstein's picture; in that static frame defined by the Earth and Alpha Centauri) has changed by eight years. The photon is now at the position x=0, y=0, z=0 and tau=0 but t has changed by eight years. I personally have been sitting in my chair on Earth at the position x=0, y=0, z=0 and some tau position. Since my “evolution parameter”,t, my change in position in this four dimensional Euclidean space is given by ct, my tau position must have changed by eight light years (proportional to what the clock attached to me reads). Since the photon and I have exactly the same x,y,z and t we can interact: i.e., the reading on those clocks attached to us or the photon (which yields tau) has nothing to do with our being able to interact.

So we will see the photon as going from Earth to Alpha Centauri and back in eight years. What about the massive particle? Well, we have already said that it appears to be going at ten percent the speed of light. That being the case, when it gets back, we will have seen it as taking eighty years: i.e., we will have moved in the tau direction eighty light years. The massive particle is also back to x=0, y=0, z=0 and tau= some value (again remember that tau has nothing to do with our ability to interact) and the path length it has traveled must be eighty light years long. Being a massive particle, we know it's change in tau position is not zero nor is it eighty light years, it has traveled a total of eighty light years in some diagonal direction (forty years out and forty years back) where [math]\sqrt{4^2 +\tau^2}=40[/math] (again, its path length being given by ct). Solve that for tau and one has [math]\tau=\sqrt{40^2-4^2}=39.8[/math] years. So an ideal clock attached to the massive particle will read 79.6 years for the round trip. Note that, in Einstein's picture, the massive particles “clock” runs slow by a factor [math]t'=t\sqrt{1-(v/c)^2}=t\sqrt{1-.1^2}=.995t[/math] or exactly 79.6 years for the round trip.

The above analysis is essentially the analysis I was trying to get Erasmus00 to perform when I gave him the thought experiment below.

My second device is a toy we make for our children. It appears to be a standard baseball but it is not. It contains exactly the same time machine which I just demonstrated for you; however, it has no stem. Within the ball is a second device which, via internal dynamic effects enables it to know exactly where it is (remember, for practical effects of this thought experiment, we live in a Newtonian universe). When it is moved, the time machine (it and the ball within which it is contained) is advanced in time proportional to the distance it is moved. It is advanced exactly one second for every foot it is moved. Such a ball will display some rather interesting dynamic effects. (For the sake of simplicity, we won't consider rotation; the system is not designed to be rotated as rotation brings up some very complex effects.)

Consider two children ten feet apart playing catch with such a ball.

Essentially, the issue here is that entities advance in time when they are moved (when they are not moved, they also advance but at some fixed rate). The thought experiment deals with the two components of temporal advance as if they are unrelated and thus actually don't give the correct answer (the results are not exactly consistent with correct relativistic effects); however, the physical consequences do, nonetheless, provide a superb mimicry of relativistic effects where the maximum velocity is one foot per second. You even get the apparent mass going to infinity as the velocity approaches one foot per second. To get exactly the correct relativistic effects, one needs the advancement in time to be proportional to distance in the four dimensional geometry, not just the three dimensional distance moved.

As I have said, all we need is a mechanism to project out the tau dimension and the results become absolutely identical to standard relativity. Quantize the momentum in the tau direction and “wallah” the uncertainty principal performs the projection and the two pictures give exactly the same results for any conceivable circumstance, Since the picture is of quantized massless entities in a four dimensional Euclidean universe, it turns out that all exchange forces (even those mediated by massive exchange particles) are ruled by exactly the same factors demanded by Maxwell's equation in three dimensions (i.e., photon exchange) so one also obtains exactly the same Lorentz-Fitzgerald contraction for any stable structure concievable.

So it is just a different way of looking at exactly the same thing; however, it has some very powerful advantages over Einstein's picture. First of all, time has become a parameter of the dynamics, not a dimension of the geometry (we are back to Newton's use of time as an evolution parameter) a perspective which is one hundred percent compatible with quantum mechanics from the get go. Secondly, we are dealing with a Euclidean universe where every entity travels at exactly the same speed. This has some important subtle consequences. According to established authority, Einstein proved that "a reduction of gravitational theory to geodesic motion in an appropriate geometry could be carried out only in the four-dimensional space-time continuum of Einstein's relativity theory". If that statement were actually true then he certainly has strong support that his picture is worth the effort (I don't think anyone would refer to GR as a trivial intellectual exercise); but, the real question is: is it true?

Maupertuis is credited with the proof no such transformation existed in a Euclidean universe; however, that proof revolved around the fact that different initial velocities yielded different trajectories: i.e., different geodesics. In the picture above, which is totally in conformance with all conventional experiments, this difficulty does not exist as “different velocities” do not exist. General Relativistic transformations yielding gravitational geodesics are relatively easy to deduce in this picture and once again, they are entirely consistent with quantum mechanics from the get go.

Last, but not least, my fundamental equation (which is deduced entirely from fundamental definitions and symmetry principals) results in exactly the picture given. What more can one ask?

I hope you found that presentation clear. If you have any questions you know how to reach me.

Have fun -- Dick

 


Edited by Doctordick, 01 February 2016 - 03:36 AM.


#5 Bombadil

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Posted 11 August 2008 - 08:05 PM

Note that this value continually increases along the paths specified in our geometry. Would it not be convenient that this parameter be path length in our geometry? Can we conceive of a geometry where t might be at least proportional to our path length? Does it not seem reasonable to match the relationship between the five variables already expressed in the Einsteinian picture (which we know to be the physically “correct” solution? How about we just rearrange the terms in his expression, [imath]c\tau_i =i\sqrt{dx_i^2+dy_i^2+dz_i^2-c^2dt_i^2}[/imath] into [imath]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c^2d\tau_i^2}[/imath] implying exactly the same relationship? O'migod, that's the path length in a Euclidean geometry! Who would have thunk it! Boy, it sure makes for a convenient geometry to consider doesn't it.


If I understand this correctly the equation [imath]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c_i^2d\tau _i^2}[/imath] is a measure of total distance that has been traveled in time t . That is, we always travel tc distance where dx dy and dz are the infinitesimal change along that axis in a three dimensional plane and [imath]c^2d\tau [/imath] is the distance traveled along the [imath]\tau [/imath] axis which is also experienced as time.
I’m not sure but the statement that [imath]\tau[/imath] is what a clock will measure still has not been proven?

Since tau, one of the coordinates of this geometry (a coordinate which, by the way, is exactly what is read on clocks attached to the entities) has no bearing upon the whether or not an interaction can take place it should be clear that, in this geometry, we need some kind of mechanism to project out the differences in the tau coordinate as they bear upon interactions. An excellent mechanism comes to mind: i.e., the uncertainty principal. If the value of this coordinate has an infinite uncertainty (i.e., it is projected out as not a necessary part of our world view) then the momentum in that direction can have zero uncertainty (it can be a quantized variable).


Does this mean that we can never know the [imath]\tau[/imath] coordinate of an object, or that no mater what the [imath]\tau[/imath] coordinate is that the object having it will always act like it is at the same [imath]\tau[/imath] coordinate as the object it is interacting with?

Also, [imath]\tau[/imath] corresponded to mass so does this mean that there is no uncertainty in the mass of an object?

Also, I’m not quite sure what you mean by Quantize the movement in the [imath]\tau[/imath] dimension?

However, this constraint on a valid frame still leads to one very significant conundrum. If we have a portion of the universe which can be considered as totally independent of another portion and, if the differentials of the two portions do not vanish in the same frame of reference, the resultant fundamental equations can not be asserted to be valid in all three of the possible reference frames. It turns out that this problem is easily solved. If you look at my fundamental equation, is is (sans the Dirac delta function) a simple many body wave equation in four dimensions with a wave velocity of 1/K. The problem is actually identical to problem Maxwell's equation presented to the physics Community. It was solved by what is essentially a scale transformation related to the two different reference frames and exactly the same methods may be used here (in order for all three reference frames to see the same fundamental equation as valid, they must all see it as describing an expanding sphere). This presents a simple algebraic problem which is quite easy to solve. If you need me to do this; let me know and I will show the explicit solution. The most important part of the solution is what is commonly referred to as Lorentz-Fitzgerald contraction. There must be exactly that scale transformation between the two frames (if the two portions of the universe can be considered as totally independent). If they are not totally independent, then the fundamental equation cannot be applied to them separately: i.e., they can not be handled as if they are independent. Seems quite reasonable to me.


I’m not quite sure what it is that we are looking for. Are we looking for a transformation that will allow us to use the result of one frame in another, or are we looking for a way of modifying the differentials in the fundamental equation in such a way that it remains the same no matter what frame they are measured in? Ether way I think that the equation that you solve in the thread “is time a measurable variable” is what you are talking about.

If I understand this correctly it is the second one that is correct. That is, we want a function that both sides of the fundamental equation can be multiplied by, so that no matter what the sum of the differentials sum to, we get the same equation. It seems that due to shift symmetry that such a function can’t be a function of the variables. But how do we know that such a function is a constant and is not a function of the differentials?

So we will see the photon as going from Earth to Alpha Centauri and back in eight years. What about the massive particle? Well, we have already said that it appears to be going at ten percent the speed of light. That being the case, when it gets back, we will have seen it as taking eighty years: i.e., we will have moved in the tau direction eighty light years. The massive particle is also back to x=0, y=0, z=0 and tau= some value (again remember that tau has nothing to do with our ability to interact) and the path length it has traveled must be eighty light years long. Being a massive particle, we know it's change in tau position is not zero nor is it eighty light years, it has traveled a total of eighty light years in some diagonal direction (forty years out and forty years back) where [LaTeX Error: Syntax error] (again, its path length being given by ct). Solve that for [imath]\tau[/imath] and one has [imath]\tau=\sqrt{40^2-4^2}=39.8[/imath] years. So an ideal clock attached to the massive particle will read 79.6 years for the round trip. Note that, in Einstein's picture, the massive particles “clock” runs slow by a factor [imath]t'=t\sqrt{1-(v/c)^2}=t\sqrt{1-.1^2}=.995t[/imath] or exactly 79.6 years for the round trip.


I can’t be sure because some of your latex didn’t show up but did you come to your number without the use of the Lorenz transformation?

#6 Doctordick

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Posted 13 August 2008 - 02:45 PM

If I understand this correctly the equation [math]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c_i^2d\tau _i^2}[/math] is a measure of total distance that has been traveled in time t .

Within the x,y,z,tau frame of reference I have set forth.

I’m not sure but the statement that [math]\tau[/math] is what a clock will measure still has not been proven?

My tau is exactly what standard relativistic models refer to as “proper time” and the fact that clocks measure exactly proper time on their specific space-time paths is a central tenet of both special and general relativity.

Does this mean that we can never know the [math]\tau[/math] coordinate of an object, or that no mater what the [math]\tau[/math] coordinate is that the object having it will always act like it is at the same [math]\tau[/math] coordinate as the object it is interacting with?

In a sense, yes as the uncertainty principal insures that the quantum mechanical wave function which describes the object is smeared out from plus to minus infinity; however, the self same wave function need not be spread out over x,y and z: i.e., that means that the object may be localized in the x,y,z space. A subtle consequence of this fact is that the change in position in tau can be a calculated quantity; the “change in tau” is directly inferable from the change in x,y and z from the constraint that the total distance traveled is given by c tau [error here, sorry guys, correct statement should be “total distance traveled is given by ct]. This is totally analogous to the fact that, in standard relativity, the absolute value of tau is not a knowable thing while the changes in tau between physical events is indeed a calculable value; it is exactly what Einstein called the “invariant interval”. That is to say, there is nothing here which is not in standard relativity; it is no more than a different way of looking at exactly the same information.

Also, [math]\tau[/math] corresponded to mass so does this mean that there is no uncertainty in the mass of an object?

Only if the half life of that mass is infinite. If the half life is finite, then the uncertainty in tau is not infinite and the uncertainty in mass cannot be zero; however, even in this case, the fact that our measuring instruments are built from mass quantized entities, still prevents us from establishing an absolute value on tau. Exactly the same thing happens in standard relativity though the effect is sort of hidden from view in the standard presentation.

Also, I’m not quite sure what you mean by Quantize the movement in the [math]\tau[/math] dimension?

The “momentum” is quantized, not the “movement”. You need to understand quantum mechanics to understand that aspect of the presentation.

I’m not quite sure what it is that we are looking for. Are we looking for a transformation that will allow us to use the result of one frame in another, or are we looking for a way of modifying the differentials in the fundamental equation in such a way that it remains the same no matter what frame they are measured in? Ether way I think that the equation that you solve in the thread “is time a measurable variable” is what you are talking about.

The answer is neither. The issue here is the validity of my fundamental equations. I have proved that the equation is valid in the coordinate system where the sum of the momentum vanishes and shown that the solution may be transformed to a solution in the frame where the momentum does not vanish; however, if we have a portion of the universe which can be considered as totally independent of another portion a difficulty arises. You need to understand the mathematical transformation just mentioned in order to comprehend that a problem exists.

In essence the problem arises because of the fact that there exists no mechanism to prove you are in a frame where the velocity of light is the same in both directions. This is exactly the problem brought up my Maxwell's equations and the null result of the Michelson-Morley experiments; the conundrum which lead to the solution proposed by Einstein (actually it is the Lorentz-Fitzgerald contraction which solves the problem; the issue Einstein explained was, “why the Lorentz-Fitzgerald contraction was universally necessary”). I show that scale symmetry together with my fundamental equation demands that Lorentz-Fitzgerald contraction is universally necessary.

But how do we know that such a function is a constant and is not a function of the differentials?

I do not know what this question means. The only thing important here is that the transformation between those two frames of reference above must leave my fundamental equation unaltered “if we have a portion of the universe which can be considered as totally independent of another portion”. If that constraint is false then the constraint on my fundamental equation is also false. There is a subtle but very important issue embedded in that observation: it is our demand (in the construction of our epistemological constructs to explain our expectations) that these subsets be totally independent of one another which imposes the constraint, it is not a requirement of reality. That is an issue worth thinking about.

I can’t be sure because some of your latex didn’t show up but did you come to your number without the use of the Lorenz transformation?

I fixed the problem; I had left out the “t” in the LaText tag “sqrt”. And you are absolutely correct; I did not use the Lorentz transformation at all. That transformation is only required if you are going to change to a new frame of reference and everything I did was done in the rest frame of the Earth and Alpha Centauri.

Notice that what the standard relativistic picture sees as "time distortion" in the moving object just doesn't exist in my picture because I regard time as an "unmeasurable" variable. Go look at my ideal clock in that earlier post; so long as acceleration is not included, it measures change in tau exactly (just as does an ideal clock in Einstein's relativity). If one goes to GR, life gets a little more complicated because no ideal clock can be designed with no physical extent; however, the issue is still solved in a very simple manner.

I notice that you have not commented on my geometric proof. I assume you now understand the proof but there are a few important aspects of that proof to be pointed out; hope you haven't decided there is nothing more to be said.

Have fun -- Dick


Edited by Doctordick, 01 February 2016 - 03:42 AM.


#7 Bombadil

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Posted 19 August 2008 - 07:03 PM

My tau is exactly what standard relativistic models refer to as “proper time” and the fact that clocks measure exactly proper time on their specific space-time paths is a central tenet of both special and general relativity.


Then what is it that t is representing? Is it simply a total distance moved along an axis that we cannot effect?

The answer is neither. The issue here is the validity of my fundamental equations. I have proved that the equation is valid in the coordinate system where the sum of the momentum vanishes and shown that the solution may be transformed to a solution in the frame where the momentum does not vanish; however, if we have a portion of the universe which can be considered as totally independent of another portion a difficulty arises. You need to understand the mathematical transformation just mentioned in order to comprehend that a problem exists.


I don’t think that you have shown this to be true yet. If you have I don’t know where. Also, I’m not sure how such a transformation is performed. I suspect that it may be as simple as adding a constant to both sides of the equation to change to a reference frame with a constant momentum and in so doing removing the nonzero momentum term from one side of the equation but I’m really not sure if this is the case.

Now I’m wondering if this has any connection with the effect that the [imath]\vec{\alpha }_I[/imath] and [imath]\beta _{ij}[/imath] operators have when on there own in the fundamental equation.

Notice that what the standard relativistic picture sees as "time distortion" in the moving object just doesn't exist in my picture because I regard time as an "unmeasurable" variable. Go look at my ideal clock in that earlier post; so long as acceleration is not included, it measures change in tau exactly (just as does an ideal clock in Einstein's relativity). If one goes to GR, life gets a little more complicated because no ideal clock can be designed with no physical extent; however, the issue is still solved in a very simple manner.


I’m not sure what you mean by time distortions. Are you talking about inconsistencies in the time coordinate of where objects are interacting?

Would I be correct in understanding that the equation that you are using is arrived at by modifying an equation from special relativity and you have simply rearranged it into a more convenient form for what you are doing with it?

#8 Erasmus00

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Posted 19 August 2008 - 09:54 PM

Because the initial post is quite long, I'm attempting to comment things I think get to the heart of my objections rather than discuss all the ideas presented- if you feel I've missed something crucial, please highlight it for me.

Would it not be convenient that this parameter be path length in our geometry? Can we conceive of a geometry where t might be at least proportional to our path length? Does it not seem reasonable to match the relationship between the five variables already expressed in the Einsteinian picture (which we know to be the physically “correct” solution? How about we just rearrange the terms in his expression, [imath]ctau_i =isqrt{dx_i^2+dy_i^2+dz_i^2-c^2dt_i^2}[/imath] into [imath]ct_i=sqrt{dx_i^2+dy_i^2+dz_i^2+c^2dtau_i^2}[/imath] implying exactly the same relationship? O'migod, that's the path length in a Euclidean geometry! :doh: Who would have thunk it! Boy, it sure makes for a convenient geometry to consider doesn't it. ;)


I know that you have said that this has nothing to do with multiple observers- but relativity is a theory more about coordinates/coordinate systems than anything else, so I still feel the most cogent way to express my objection is by looking at different observers.

The problem with this, as I've tried to get at, is that path length needs to be observer independent- in a good geometry everyone agrees on how long paths are. Einstein's equation says "invariant" = "invariant". To rearrange it, you have moved subtracted something not invariant from each side, so your equation is "variable" = "variable." Its still true, but neither side should be used as a path length as two observers cannot agree on the length. Do you see at all what I'm saying? If each observer in an Einstein world did this reparameterization, no one would agree on the path lengths.

The whole point of Einstein's physics program is to try to use coordinate free notation wherever possible- because philosophically the coordinates shouldn't matter. In your rearrangement this is no longer possible.

But who cares about the traditional view? The point here is that we are merely looking at a correct valid solution plotted in a different geometry.


Its a valid PLOT and a valid solution, but its not a geometry in the mathematical sense, as your path lengths aren't observer independent.

Also, considering mass the canonical variable to tau leaves you with a momentum vector in your geometry (p_x,p_y,p_z,m). do you agree? But the lengths of vectors, like path lengths, needs to be invariant in your geometry- everyone should agree on a vectors magnitude. However, no invariant can be formed from these, so this cannot be a geometry, though it is perfectly plotable.

If our expectations are to be given by [imath]vec{Psi}[/imath] as a function of those references (those numbers) then the solution must be scale invariant.


But don't we know that the universe itself isn't scale invariant? Doesn't this predict that our universe (or at least the explanation we develop) should be?
-Will

#9 Doctordick

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Posted 21 August 2008 - 07:40 PM

Then what is it that t is representing? Is it simply a total distance moved along an axis that we cannot effect?

I don't exactly know what you mean by that. It is a measure of the path length of an entity in our personal rest frame of reference, the frame in which we are describing the circumstances.

I don’t think that you have shown this to be true yet. If you have I don’t know where. Also, I’m not sure how such a transformation is performed. I suspect that it may be as simple as adding a constant to both sides of the equation to change to a reference frame with a constant momentum and in so doing removing the nonzero momentum term from one side of the equation but I’m really not sure if this is the case.

It is a common transformation used in quantum mechanics to change the wave function to a new function having momentum with respect to the first: i.e., the momentum operator is a differential operator and the differential of a product, [math]\frac{d}{dx}[\Psi(x)\phi(x)]=\Psi'(x)\phi(x)+\Psi(x)\phi'(x)[/math], adds a term related to the function [math]\phi(x)[/math]. Since the definition of the momentum operator is [math]-i\hbar \frac{\partial}{\partial x}[/math], setting [math]\phi(x)= Ae^{i\frac{ Kx}{\hbar}}[/math] will add the factor K to the result of application of the momentum operator. If we have n arguments [math]x_i[/math] we can do this n times (once for every argument and add nK to the total momentum. At that point, one is no longer in the frame of reference where [math]\sum_i \frac{\partial}{\partial x_i}\vec{\Psi}[/math] vanishes.

Now I’m wondering if this has any connection with the effect that the [math]vec{alpha }_I[/math] and [math]beta _{ij}[/math] operators have when on there own in the fundamental equation.

No, all it does is shift the reference frame to one where the momentum of the total is not zero.

I’m not sure what you mean by time distortions.

The distortions normally appearing in the time coordinate of conventional space-time coordinate system when you look at a moving observers measuring equipment. That isn't in my representation because it isn't a measurable parameter; it is an evolution parameter associated with the entity following the specified path. Now a clock is a designed device made to measure time. When you actually sit down and design a clock (in what one might refer to as a Lorentz-Fitzgerald coordinate system), it turns out that it does not succeed. What it actually measures is the change in tau along the path of the object. Which just happens to be exactly what a clock does in Einstein's picture; it measures Einstein's invariant interval , exactly both in special and general relativity.

Are you talking about inconsistencies in the time coordinate of where objects are interacting?

No, there are no inconsistencies in time in my picture as time is an unmeasureable evolution parameter unique to each entity. He normally sets that evolution parameter to whatever the reading on his local clock happens to be and he sees interactions occurring totally consistent with that parameter; however, because a moving observer (moving relative to him sets his evolution parameter in accordance to his personal clock (which also happens to measures changes in tau exactly) they will not agree about the correct time to attach to these events.

Would I be correct in understanding that the equation that you are using is arrived at by modifying an equation from special relativity and you have simply rearranged it into a more convenient form for what you are doing with it?

No you would not. My equation is deduced from my definition of “an explanation” via ordinary symmetry arguments.

Since my earlier explanations of that procedure seems to be rather unclear to most people, I will try to present the central issues here again for you.

The fundamental issue is that no one knows what reality is: i.e., your world view is acquired via an unexplained procedure. (I could waste a lot of time talking about philosophers unsuccessful attempts to attack this problem but I won't.) The philosophic world has made a rather powerful devision of the issues involved here; that division comes down to “ontology” and “epistemology” and I will make rather extensive use of that division (google the terms if you don't know what they mean). Ontology is the issue of “what exists” and epistemology is the issue of the nature of knowledge. In rather broad terms, scientific theories are epistemological constructs and scientists seldom concern themselves with ontology (sometimes they invent “new” entities). Science generally proceeds by what I call the “by guess and by golly” attack. They say, “suppose this existed” (they guess an ontology), “what kind of predictions could you make” (they look at the epistemological constructs they can make under the assumption of that ontology). They get a good answer (the experiments work out) and they say “by golly, that must be the right answer”.

A major problem with that attack is what is called “infinite regression”. There is no way to be sure that the fundamental elements of your ontology are in fact fundamental; there might be a lower level ontology which will yield (as an epistemological construct) the ontology you thought was fundamental. The fundamental problem here is the need to guess the ontology. Since the only defense of that guessed ontology is the success of the epistemology it seemed to me that some analytical analysis would be valuable. (Consider the attack used to solve the problem of black body radiation; take a bunch of unknowns and look for a solution which defines those unknowns and what do you get but the black body spectrum).

Well, let us take an arbitrary undefined fundamental ontology. (Remember, the only defense of that ontology is success of the epistemological construct based on it.) Since the ontology is totally undefined, we certainly cannot describe any element therein (without having that epistemological construct) so I will just use numerical labels to refer to those elements. For the moment, I will simply call those true elements of reality (thus defining reality). I often refer to that entire set of elements as set “A”. Now, there are two important issues embedded in that perspective. First, there is no way for me to be sure that I am even aware of all the elements of set “A” and, second, my epistemological construct may very well include hypothetical elements not in A (think philogestin). With regard to the first, my analysis must include the possibility of changes of that which I am aware. To accommodate this possibility, I will introduce set “B” which constitutes elements of “A” I become newly aware of. Since I can not be aware of an infinite number of references, changes in the set I am aware of must be finite, they can be ordered. I will use the index “t” to indicate which change I am talking about.

The entire set of ontological elements that I am aware of (and from which I build my epistemological construct) must consist of a collection of sets Bt. I will refer to the true elements in that collection as set “C” but I must admit of another component, the set of elements I think are true which are required by that epistemological construct. This second set I will refer to as set “D”. There is an interesting dichotomy here. These two sets obey different rules; the first is real and cannot change but the second is merely necessary to support the presumed epistemological construct; on the other hand, there cannot be any way (under that epistemological construct) to tell the difference between the two sets. This turns out to have some very profound consequences.

Now you need to remember, these are no more than massive sets of numbers divided into subsets indexed by t; mere references to the ontological elements which stand behind that epistemological construct. Meanwhile, exactly what purpose does that epistemological construct serve? I say that it serves the purpose of yielding to you a set of expectations which are consistent with your experiences (those true ontological elements referred to as “C”). What is important is that the set of expectations can be represented by “the probability of experiencing some supposed new set Bt”: i.e., another set of those self same references to elements of what you believe to be reality. That is, a number who's value is dependent upon another set of numbers. That is the definition of a mathematical function and that mathematical function is defined by the specific epistemological construct.

The central issue of my original proof (that any flaw-free epistemological construct must obey my fundamental equation) resides on the fact that the assignment of those numeric references has utterly no impact upon the situation at all. That is to say, if in my first description of that epistemological construct uses a specific number to represent one of those ontological elements in all sets Bt making up the sets “D” and “C” and in the functional representation of your expectations, then, using a different number in all cases cannot yield a different result. That lone fact results in some very profound consequences.

I will explain (and have explained) that proof in detail but, unless one understands the basis of that proof, explaining the proof is a total waste of time. If what I have just said makes any sense to you, I will cover the details of the proof again; however, this thread is concerned with other issues.

Thanks for your attention -- Dick


Edited by Doctordick, 01 February 2016 - 03:46 AM.


#10 Doctordick

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Posted 21 August 2008 - 08:45 PM

I know that you have said that this has nothing to do with multiple observers- but relativity is a theory more about coordinates/coordinate systems than anything else, so I still feel the most cogent way to express my objection is by looking at different observers.

I think I understand your objection; you would like to believe Einstein's solution is the only possibility and are coming up with the reasons you like it. Fine, I have no complaint with that except for the fact that it is preventing you from looking at this thing from another perspective which has some very interesting consequences. If you go back to the problems confronting physics by the null result of the Michelson-Morley experiments, you will discover that the solution to the difficulty was presented by both Lorentz and Fitzgerald prior to Einstein (commonly referred to as “Lorentz-Fitzgerald contraction”). They even defended this contraction as a result of the fact that their measuring devices were physical objects who's structure was defined by stable states of physical bonds mediated by electromagnetic effects: i.e., Maxwell's equations.

The central point being that there is absolutely no way to prove that the speed of light is the same in both directions. The real issue here between the Lorentz and Fitzgerald solution and Einstein's solution is, “why is this true?” (By the way, you are aware of the fact that the “Lorentz-Fitzgerald contraction” is sufficient to explain the time differences also aren't you?)

Einstein's solution provided what a lot of people thought was a better “why” (which everyone likes) via his axiom that the speed of light is a constant. With this axiom, he guaranteed the speed of light to be “the same in both directions”. What people fail to note is that this is a grand assumption which absolutely can not be defended. The real issue of relativity is that it tells one how to convert the measurements in one frame of reference to those in another frame of reference.

The problem with this, as I've tried to get at, is that path length needs to be observer independent- in a good geometry everyone agrees on how long paths are. Einstein's equation says "invariant" = "invariant".

Just exactly why does the path length need to be observer independent, other than the fact that Einstein's theory says so? Could it not be that Lorentz and Fitzgerald were right? Their solution yielded a change in physical measurements for observers moving with respect to one another exactly the same as Einstein's theory; if the measurements of individual components establishing the geometry presumed by the observers change, why would you not expect the path lengths to change (other than believing Einstein was infallible).

By the way, if you look at my work, you will find that I prove that the standard relativistic transformation equations must be valid if the outcome of the experiment is taken to be independent of the rest of the universe: i.e., limited to the local bodies of interest. No axioms necessary here at all. And add to that the fact that Einstein's theory is based on the idea that there is no preferred coordinate system in direct contradiction to the fact of the existence of the microwave background radiation. Come on Will, take a look at another possibility. It's the relativistic transformations which are important here not the lack of existence of a preferred coordinate system.

To rearrange it, you have moved subtracted something not invariant from each side, so your equation is "variable" = "variable." Its still true, but neither side should be used as a path length as two observers cannot agree on the length. Do you see at all what I'm saying? If each observer in an Einstein world did this reparameterization, no one would agree on the path lengths.

I just don't buy this as an important issue at all as t is not a measurable variable; in my picture, it is an evolution parameter and, as such, is totally dependent upon the observer's frame of reference. They would still agree exactly on the transformations between their measurements and the other observer's measurements.

The whole point of Einstein's physics program is to try to use coordinate free notation wherever possible- because philosophically the coordinates shouldn't matter. In your rearrangement this is no longer possible.

Oh, I admit that Einstein's attack is very nice for determining the form those local interactions must obey but it is a convenience for determining what is and is not allowed, not a requirement. It provides a simple mechanism for producing the correct relationships, which are required to obey the proper transformations, and corresponds to my work in much the same way as Ptolomy's celestial spheres are related to Newton's work, they give essentially the same answers. You know that Newton differed in a few places and he originally said that he might have made some errors, thus giving preference to the old charts and I obtain some slightly different results in GR which may also be due to errors on my part though I could be right as some aspects of this “dark matter” yield deviations in the same direction. And by the way, in my head, the solid fixed nature of the two pictures, Einstein's and Ptolomy's, is actually quite astounding.

As far as doing physics is concerned, the physics community could just as well adopt the frame at rest with respect to the microwave background radiation as a preferred frame, use the proper interactions and truck on, no problems would actually arise so long as the relativistic impact on the interactions was properly accounted for. In fact, that is the central issue of “relativity”, any frame can be used as a basis of your calculations if your interactions are correct. Lay that Einsteinian brain clamp aside for a moment and do a little good old fashion physics.

Its a valid PLOT and a valid solution, but its not a geometry in the mathematical sense, as your path lengths aren't observer independent.

Now wait a minute here. Are you implying that the Euclidean geometry Newton used in his work “was not a geometry in the mathematical sense”? The path length of a cannon shot in a frame at rest with respect to the cannon is quite different from the path length of the same cannon shot in a frame at rest with respect to the x motion of the cannon shot itself. “Not a geometry in the mathematical sense?” Exactly what do you mean by that classification?

Also, considering mass the canonical variable to tau leaves you with a momentum vector in your geometry (p_x,p_y,p_z,m). do you agree? But the lengths of vectors, like path lengths, needs to be invariant in your geometry- everyone should agree on a vectors magnitude.

Again, riding in your car (as observer #1 doing calculations in your frame) and someone else standing on the street (as observer #2 doing calculations in his frame) would agree on the magnitude of the momentum of a golf ball you just dropped? Come on Will, you are so bound up in the absolute validity of Einstein's representation that you are blocking out everything I say without thinking about it at all.

However, no invariant can be formed from these, so this cannot be a geometry, though it is perfectly plotable.

Apparently, you and I have a very different definition of “a geometry”. I would truly like to see your definition of “a geometry”.

But don't we know that the universe itself isn't scale invariant?

Oh do we now? I would love to see your proof of that. I am afraid you are just wrong and I believe I can prove it in detail.

Doesn't this predict that our universe (or at least the explanation we develop) should be?

Yes it does; however, every experiment anyone has ever done has presumed the scale of the universe (outside the actual rather limited parameters used as variables in the experiment) is correctly determined (in order to prove scale effects, you will have to first prove that assumption is correct). The only way to do the problem correctly is to include every entity in the universe and then find the coherent solution which details everything. If you had that, you could perhaps begin to understand the problem of scale. And by the way, if you had that solution, exactly how would you go about setting the scale? You should be able to comprehend that there is no information not already included in that explanation to set this scale; the “universe” (defined to be everything) is a closed system so the scale has to be set by the internal relations themselves. Now that is not a detailed proof but I think it still carries a lot of weight.

“Ptolomy was the last of the great ancient astronomers, his ideas and descriptions of the planetary system lasted more than 1000 years.” I suppose Einstein's ideas and description of the universe could last a thousand years too before the physics community thinks about any alternative simpler explanations, but does the idea of that really appeal to you?

Try those thought experiments I gave you -- Dick

#11 Erasmus00

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Posted 22 August 2008 - 01:09 AM

I think I understand our sticking point- we have very different notions of a geometry, and I'll try to highlight the problem.

Just exactly why does the path length need to be observer independent, other than the fact that Einstein's theory says so?


Actually, its not a requirement of Einstein's theory, its a mathematical requirement for a consistent geometry. The length of lines in any geometry cannot depend on the coordinates used to describe those lines. In my mind, the fundamentally nice thing about Einstein's relativity is that its a geometrical theory- we can describe everything with geometric objects and never have to specify coordinates. A metric, by definition, must produce invariants. These are mathematical requirements. A geometry is simply a space equipped with a valid metric. Einstein interpreted by Minkowski is a metric space, yours is not.

Again, my problem isn't that your construct is WRONG, its not. Its that its not as useful. I'm not saying Einstein's is the only right solution, rather that your solution uses the utility of Einstein's.

Come on Will, take a look at another possibility. It's the relativistic transformations which are important here not the lack of existence of a preferred coordinate system.


My complain has nothing to do with a preferred frame- some geometries have preferred frames, some don't. My complaint is that coordinates don't matter (your own admission is that the coordinate system shouldn't matter, the labels are arbitrary anyway). Hence, our formalism should emphasize this fact by describing things by geometric objects, NOT objects tied to coordinates.

The utility of Einstein really only comes with Minkowski's addition to the theory- special relativity describes a very nice metric space i.e. a geometry, and so we can get rid of coordinates entirely and describe things in terms of geometric invariants.

Now, as to scale invariance, lets start with an observation:

On a large scale (mega parsecs), the universe is quite regular, and IS roughly scale invariant, see the sloan digital sky survey. However, as you zoom in, it becomes clumpy and is no longer scale invariant- the universe is only roughly scale invariant. (to be scale invariant, things must be homogenous- compare the contents of the room you are in to the contents of a pocket of space 3 light minutes away). On our telescope scales, its observationally trivial that things aren't scale invariant.
-Will

#12 Doctordick

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Posted 23 August 2008 - 08:47 PM

Sorry Will but I think you just have that Einsteinian brain clamp screwed on just a little bit too tight; I think it is cutting off the blood flow to your brain.

I think I understand our sticking point- we have very different notions of a geometry, and I'll try to highlight the problem. Actually, its not a requirement of Einstein's theory, its a mathematical requirement for a consistent geometry. The length of lines in any geometry cannot depend on the coordinates used to describe those lines.

The whole object of the issue of relativity is the transformation of measurements in one observers geometry to the same phenomena as seen in a second observers geometry. Geometry is, “the branch of mathematics concerned with points, lines, curves, and surfaces and the method of representing them”.

In my mind, the fundamentally nice thing about Einstein's relativity is that its a geometrical theory- we can describe everything with geometric objects ...

This is a direct consequence of that Einsteinian brain clamp.

A geometry is simply a space equipped with a valid metric.

You have the issue backwards if I ever saw such a thing. A metric is “a geometric function that describes the distances between pairs of points in a space”. The metric is defined by the geometry and there is nothing in the definition which says that “different representations of the same phenomena” need to yield identical value for the effective length of the path: i.e., identical metrics. The value of their metrics along the path of the entity need not be the same, they are a function of the geometry used by the specific observer.

The path length of a cannon shot in a frame at rest with respect to the cannon is quite different from the path length of the same cannon shot in a frame at rest with respect to the x motion of the cannon shot itself.


Einstein interpreted by Minkowski is a metric space, yours is not.

Here's that brain clamp again. Einstein interpreted the metric to be the central issue of the physics. Without that brain clamp, the metric would be a way of measuring the path of an object in the given geometry.

Again, my problem isn't that your construct is WRONG, its not. Its that its not as useful.

So you manage to dismiss my work without examining it; right? I am sorry but I cannot hold that as a valid issue; how can you seriously say it is not useful without examining the consequences of such a view is beyond me. It certainly sounds like a closed mind.

I'm not saying Einstein's is the only right solution, rather that your solution uses the utility of Einstein's.

Now that is an outright lie. My solution makes utterly no use of Einstein's solution. My construction was designed to show that the Einstein solution was exactly the same as mine. I came up with it long before I had even a glimmer of Einstein's work. It is perhaps founded on Lorentz and Fitzgerald's work but not because I read their work but rather because the same solution to the Michelson-Morley conundrum which occurred to them occurred to me.

My complain has nothing to do with a preferred frame- some geometries have preferred frames, some don't. My complaint is that coordinates don't matter (your own admission is that the coordinate system shouldn't matter, the labels are arbitrary anyway). Hence, our formalism should emphasize this fact by describing things by geometric objects, NOT objects tied to coordinates.

Using a geometry to describe the evolution of structures is not “tying objects to coordinates”. In fact, “describing things as geometric objects” could much more be described as tying those objects to coordinates. Put that brain clamp aside and think about things a bit.

The utility of Einstein really only comes with Minkowski's addition to the theory- special relativity describes a very nice metric space i.e. a geometry, and so we can get rid of coordinates entirely and describe things in terms of geometric invariants.

"One geometry can not be more true than another; it can only be more convenient." by Henri Poincareé. Einstein's is more convenient to his perspective, mine is more convenient to an absolutely objective perspective; a perspective which presumes there are no axioms to define the “correct geometry”.

On a large scale (mega parsecs), the universe is quite regular, and IS roughly scale invariant, see the sloan digital sky survey. However, as you zoom in, it becomes clumpy and is no longer scale invariant- the universe is only roughly scale invariant. (to be scale invariant, things must be homogenous- compare the contents of the room you are in to the contents of a pocket of space 3 light minutes away). On our telescope scales, its observationally trivial that things aren't scale invariant.

Again, there is utterly no thought in that statement. “Belief is easy, thought is not. That is why so many people would rather believe than think.” Scale invariance on a universal scale has absolutely nothing to do with the smoothness or clumpy nature of the solution. It has to do with the solutions themselves. If you have an equation which defines the possible solutions to “the universe” and that equation is scale invariant, it means that changing the scale of that specific solution yields an equally valid solution. Use your head, if you had a complete description of the universe which satisfied a specific equation (a scale invariant equation) and you doubled every measurement in the entire description, that new description would also be a valid solution to the equation. In no way does such a thing require the solution be smooth in any way. Scale invariance and smoothness are not the same thing.

The problem here is that you are so bound up with compartmentalizing your thinking that you cannot comprehend the possibilities inherent in a total solution. The physics community is so stuck on the idea that a many body equation cannot be solved that they never even consider the possibilities represented by such an equation. Just as Ptolemaic authorities could not comprehend a dynamic solution to the motion of the planets and had to conceptually attach them to celestial spheres, modern physicists cannot comprehend that the universe might satisfy a simple many body equation and have to conceptually tie their solutions to Einsteins space-time geometry. I had proved the validity of my fundamental equation ten years before I found the first solution. During that period, I held no expectations from that equation other than "solving it might be of value". I only saw its significance when I saw the solutions.

However, if you are adamant in your belief that my attack is useless, we can just part ways; I am not going to fight your prejudices. Try taking off that brain clamp and examine my thought experiments. You might learn something.

Have fun -- Dick

#13 Erasmus00

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Posted 26 August 2008 - 09:02 AM

Doctordick, you wonder why you have trouble getting your ideas across, but in the last page you have responded to my criticism by telling me to take off my brain clamp, and I still feel you are missing my point. If you wish to communicate ideas to other people, you really need to try to understand what they are saying. I will rephrase my objection to your relativity framework in as clear a way as I can:

You and Einstein BOTH agree that the coordinates should be irrelevant because ultimately they are just labels. Einstein's response was to formulate a language to talk about physics that is coordinate invariant, and doesn't need coordinates at all to describe its fundamental entities.

By reparameterizing Einstein, your new relativity formalism loses this coordinate independence- so in a sense while you are asserting that coordinates are meaningless you are then defining your physics to rely on these meaningless numbers. Further, your Euclidean metric isn't actually a metric. This isn't an Einstein thing, its a MATHEMATICS thing. Metrics are properties of spaces NOT coordinates. You can't turn a Minkowski space into a Euclidean space by reparametrizing, its still a Minkowski space (just like you can't flatten a beach ball by using square coordinates on top of a mercator projections).


Now, as to scale invariance- if your equation is scale invariant your solution ought to also be scale invariant. The solution is the universe. Now, on a large scale the universe is isotropic and homogenous (see the sloan digital sky survey). However, on a small scale, the universe is extremely lumpy, i.e. it is different at a light minute scale then at a megaparsec scale. Also, I cannot think of an interaction that is scale invariant (QCD is strongly coupled at large scales, weakly at small scales. QED is the opposite, etc). What observations do you have to support your scale invariance?
-Will

#14 Doctordick

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Posted 26 August 2008 - 06:02 PM

Doctordick, you wonder why you have trouble getting your ideas across, but in the last page you have responded to my criticism by telling me to take off my brain clamp, and I still feel you are missing my point. If you wish to communicate ideas to other people, you really need to try to understand what they are saying. I will rephrase my objection to your relativity framework in as clear a way as I can:

I think I have a very clear idea as to why you have objections and that is because you have utterly no comprehension at all of what I am doing.

Since my earlier explanations of that procedure seems to be rather unclear to most people, I will try to present the central issues here again for you.

The fundamental issue is that no one knows what reality is: i.e., your world view is acquired via an unexplained procedure. (I could waste a lot of time talking about philosophers unsuccessful attempts to attack this problem but I won't.) The philosophic world has made a rather powerful devision of the issues involved here; that division comes down to “ontology” and “epistemology” and I will make rather extensive use of that division (google the terms if you don't know what they mean). Ontology is the issue of “what exists” and epistemology is the issue of the nature of knowledge. In rather broad terms, scientific theories are epistemological constructs and scientists seldom concern themselves with ontology (sometimes they invent “new” entities). Science generally proceeds by what I call the “by guess and by golly” attack. They say, “suppose this existed” (they guess an ontology), “what kind of predictions could you make” (they look at the epistemological constructs they can make under the assumption of that ontology). They get a good answer (the experiments work out) and they say “by golly, that must be the right answer”.

A major problem with that attack is what is called “infinite regression”. There is no way to be sure that the fundamental elements of your ontology are in fact fundamental; there might be a lower level ontology which will yield (as an epistemological construct) the ontology you thought was fundamental. The fundamental problem here is the need to guess the ontology. Since the only defense of that guessed ontology is the success of the epistemology it seemed to me that some analytical analysis would be valuable. (Consider the attack used to solve the problem of black body radiation; take a bunch of unknowns and look for a solution which defines those unknowns and what do you get but the black body spectrum).

Well, let us take an arbitrary undefined fundamental ontology. (Remember, the only defense of that ontology is success of the epistemological construct based on it.) Since the ontology is totally undefined, we certainly cannot describe any element therein (without having that epistemological construct) so I will just use numerical labels to refer to those elements. For the moment, I will simply call those true elements of reality (thus defining reality). I often refer to that entire set of elements as set “A”. Now, there are two important issues embedded in that perspective. First, there is no way for me to be sure that I am even aware of all the elements of set “A” and, second, my epistemological construct may very well include hypothetical elements not in A (think philogestin). With regard to the first, my analysis must include the possibility of changes of that which I am aware. To accommodate this possibility, I will introduce set “B” which constitutes elements of “A” I become newly aware of. Since I can not be aware of an infinite number of references, changes in the set I am aware of must be finite, they can be ordered. I will use the index “t” to indicate which change I am talking about.

The entire set of ontological elements that I am aware of (and from which I build my epistemological construct) must consist of a collection of sets Bt. I will refer to the true elements in that collection as set “C” but I must admit of another component, the set of elements I think are true which are required by that epistemological construct. This second set I will refer to as set “D”. There is an interesting dichotomy here. These two sets obey different rules; the first is real and cannot change but the second is merely necessary to support the presumed epistemological construct; on the other hand, there cannot be any way (under that epistemological construct) to tell the difference between the two sets. This turns out to have some very profound consequences.

Now you need to remember, these are no more than massive sets of numbers divided into subsets indexed by t; mere references to the ontological elements which stand behind that epistemological construct. Meanwhile, exactly what purpose does that epistemological construct serve? I say that it serves the purpose of yielding to you a set of expectations which are consistent with your experiences (those true ontological elements referred to as “C”). What is important is that the set of expectations can be represented by “the probability of experiencing some supposed new set Bt”: i.e., another set of those self same references to elements of what you believe to be reality. That is, a number who's value is dependent upon another set of numbers. That is the definition of a mathematical function and that mathematical function is defined by the specific epistemological construct.

The central issue of my original proof (that any flaw-free epistemological construct must obey my fundamental equation) resides on the fact that the assignment of those numeric references has utterly no impact upon the situation at all. That is to say, if in my first description of that epistemological construct uses a specific number to represent one of those ontological elements in all sets Bt making up the sets “D” and “C” and in the functional representation of your expectations, then, using a different number in all cases cannot yield a different result. That lone fact results in some very profound consequences.

I will explain (and have explained) that proof in detail but, unless one understands the basis of that proof, explaining the proof is a total waste of time. If what I have just said makes any sense to you, I will cover the details of the proof again; however, this thread is concerned with other issues.

My proof shows that there is always an interpretation of any explanation which must satisfy my fundamental equation (which is directly cast into a Euclidean geometry).

You keep wanting to cast it in Einstein's perspective and it is just simply a very different perspective. The only purpose of that parameterization was to point out that exactly the same entities used in the Einsteinian perspective can be directly translated into my perspective.

You and Einstein BOTH agree that the coordinates should be irrelevant because ultimately they are just labels. Einstein's response was to formulate a language to talk about physics that is coordinate invariant, and doesn't need coordinates at all to describe its fundamental entities.

I am not even describing fundamental entities; I am intentionally leaving the issue entirely and absolutely open. My fundamental equation is valid no matter what those “fundamental entities” might be. I use geometry for one purpose and one purpose only: I use it as a mechanism to display humongous volumes of information parameterized via numerical references to ontological elements and nothing else. These “ontological elements” are totally undefined things: i.e., unknowns. I display these numerical references as points in a Euclidean geometry and I use the definition of a “Euclidean metric” as given in “Wolfram MathWorld”

By reparameterizing Einstein, your new relativity formalism loses this coordinate independence- so in a sense while you are asserting that coordinates are meaningless you are then defining your physics to rely on these meaningless numbers.

This is exactly what I mean by that “Einsteinian brain clamp” (you tell me what I am defining without ever even looking at my definitions). And that reference to “doing good old fashion physics”, what I mean is, take down your data, plot it and look at the implied relationships. For example, take a look at the thought problem I gave you (it is entirely non-relativistic and requires no knowledge of relativity). Work out how that would appear and then we can talk. If that is beyond your analytical abilities, I am totally wasting my time.

I have a thought experiment you really need to perform. Suppose, for the fun of it, that I am an individual from a technologically advanced society and I meet with you to show you a couple of devices we have invented. I can't show you why it works the way it does because I, personally, don't know the science behind it; but I do know exactly what it does. The first device looks exactly like what you would see as an old fashion analog pocket watch. It has a dial with three hands which show hours, minutes and seconds, and has a knurled stem at the top which would appear to be for setting and/or winding the watch.

But I tell you it is not a watch; it is a one way time machine. When the stem is turned it will move the holder (and the holder only) into the future. When the stem is not turned, the reading on the time machine will read exactly the correct time (we won't worry about relativistic effects here, just assume that, for practical purposes, we live in a Newtonian universe). When the stem is turned, the reading on the face can be advanced. When the reading is advanced, the holder will be moved to exactly the time indicated on the face. The reverse is not possible. It is my understanding that one can not move to the past because doing so would cause paradoxes, but moving to the future will cause no such problems.

The question is, if I operate my time machine, what do you see? If you think about it a little, you should realize that, as I turn the stem, I move to whatever time is indicated on the face: i.e., I don't disappear and then reappear at the new time, I instead move through each and every time indicated on the dial. If you look at the face of the device while I am turning the stem, you will simply see the correct time as, whatever time you are at, I am there too (the second hand will appear to advance just as it did when I wasn't touching the stem). You will see me standing very still with my hand on the stem. If I advance the dial one hour while I take one breath (during the breath I turn the minute hand entirely around the face), you will see that breath as taking the entire hour. If my pulse were sixty beats a minute, you could perhaps detect my heart as beating once or twice during that hour (depending of course on how fast I personally am turning the stem). We won't worry about other effects; you could push me but I don't think either of us would like the results.

My second device is a toy we make for our children. It appears to be a standard baseball but it is not. It contains exactly the same time machine which I just demonstrated for you; however, it has no stem. Within the ball is a second device which, via internal dynamic effects enables it to know exactly where it is (remember, for practical effects of this thought experiment, we live in a Newtonian universe). When it is moved, the time machine (it and the ball within which it is contained) is advanced in time proportional to the distance it is moved. It is advanced exactly one second for every foot it is moved. Such a ball will display some rather interesting dynamic effects. (For the sake of simplicity, we won't consider rotation; the system is not designed to be rotated as rotation brings up some very complex effects.)

Consider two children ten feet apart playing catch with such a ball. From the children's perspective, how long does the ball take to cross the room? Suppose you replace the children with professional baseball pitchers? Then try firing it out of a canon. If you cannot figure out the logical consequences let me know and I will explain (and justify) the results. Another thing you might look at is tying a string to the ball and swinging it is a circle. I think you will find the consequences are quite interesting.

If you refuse to look at that problem, I will henceforth ignore your posts on the assumption that you are scientifically incompetent.

You can't turn a Minkowski space into a Euclidean space by reparametrizing, its still a Minkowski space (just like you can't flatten a beach ball by using square coordinates on top of a mercator projections).

But I can plot the information in a Euclidean geometry if I wish! What the devil do you think a Mercator projection is. The fact that the measurements on the Mercator projection (a Euclidean geometry) must be scaled to obtain the measurements in reality has nothing to do with the metric of that Euclidean geometry and everything to do with measurements taken from your data. Any competent physicist would recognize that fact. And their “theory” would “explain” those scaling factors: i.e., in this case the two dimensional information being represented is actually a sphere in a three dimensional Euclidean geometry and not that spherical geometry is the only geometry applicable to the situation. Likewise, Einstein's space time is a rather limited interpretation of the circumstance. A valid quantized interpretation of a four dimensional Euclidean universe (my fundamental equation) yields exactly the same results and that is the central issue here.

Now, as to scale invariance- if your equation is scale invariant your solution ought to also be scale invariant.

What you are totally avoiding is the issue of solving a many body equation. Your entire mental image is from the perspective of a one body problem (or at best, a two body problem). My equation is an n body equation and the solutions can be quite complex. You keep looking at those one body solutions. If you look at it from the perspective of a many body problem, the boundary conditions on that one body solution are fixed by the solution for the rest of the universe. If that solution has lumps in it, the local solutions can be quite different.

Just for the sake of argument, look at a coherent solution of an infinite surface which can support wave motion. The equation can be perfectly scale invariant and yet a possible solution could be as lumpy as you desire (think of the initial water level in an infinite pool). And the a specific micro solution in a disturbed area could be quite different from a similar micro solution in a similar disturbed area with a significantly different size. You need to learn how to do physics.

Have fun -- Dick

#15 Erasmus00

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Posted 26 August 2008 - 11:43 PM

Doctordick, I don't enjoy being insulted, and if your method of addressing complaints is to insult the asker, then I can see why you have trouble getting people to look at your work. I am done with this conversation, but leave you with this question: you claim the universe is scale invariant, but what empirical evidence do you have? No fundamental force we've measured is scale invariant. Every wave we've seen has dispersion, etc.
-Will

#16 Bombadil

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Posted 27 August 2008 - 07:43 PM

I don't exactly know what you mean by that. It is a measure of the path length of an entity in our personal rest frame of reference, the frame in which we are describing the circumstances.


The way I understand it is that the right side of the equation [imath]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c_i^2d\tau _i^2}[/imath] is the distance in your x,y,z,tau coordinate system but this coordinate system is inside of a x,y,z,tau,t system. Now, the movement on any of the x,y,z,tau axis’s can be changed by moving along a different axis as long as the total distance traveled remains the distance changed on your t axis but is there any way to change the distance moved along the t axis or for that matter, does it even make sense to talk about the t axis for anything but a way of keeping tract of the elements in the equation?

It is a common transformation used in quantum mechanics to change the wave function to a new function having momentum with respect to the first: i.e., the momentum operator is a differential operator and the differential of a product, [imath]\frac{d}{dx}[\Psi(x)\phi(x)]=\Psi'(x)\phi(x)+\Psi(x)\phi'(x)[/imath], adds a term related to the function [imath]\phi(x)[/imath]. Since the definition of the momentum operator is [imath]-i\hbar \frac{\partial}{\partial x}[/imath], setting [imath]\phi(x)= Ae^{i\frac{ Kx}{\hbar}}[/imath] will add the factor K to the result of application of the momentum operator. If we have n arguments [imath]x_i[/imath] we can do this n times (once for every argument and add nK to the total momentum. At that point, one is no longer in the frame of reference where [imath]\sum_i \frac{\partial}{\partial x_i}\vec{\Psi}[/imath] vanishes.


Am I correct in saying that the only effect that adding momentum to the fundamental equation has on the derivation of the schrodinger equation is adding a waited alpha term to the function after the first integration? In fact the only effect that adding momentum appears to have on the fundamental equation seems to be adding a waited alpha term to the equation. But how I understand the alpha term, it is in a totally different vector space then the rest of the terms in the equation. So adding this should have no effect on the propagation speed of the wave which I understand to be 1/k. Although it seems that this may not be the case and that the added momentum has an effect on the value of the right side of the equation. If so, is the task to find a scaling factor that leaves the value of the constants on the right side of the fundamental equation the same no matter the momentum added?

Now, will mass and energy eventually be added to the equation in the same way only with the mass or energy operators in place of the momentum operator?

No you would not. My equation is deduced from my definition of “an explanation” via ordinary symmetry arguments.

Since my earlier explanations of that procedure seems to be rather unclear to most people, I will try to present the central issues here again for you.


I suspect that I was not entirely clear as to the equation that I was referring to as the remainder of the post while quite interesting seems to be the basic idea for the derivation of the fundamental equation while what I was referring to was the equation [imath]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c_i^2d\tau _i^2}[/imath]

I will explain (and have explained) that proof in detail but, unless one understands the basis of that proof, explaining the proof is a total waste of time. If what I have just said makes any sense to you, I will cover the details of the proof again; however, this thread is concerned with other issues.


What you are saying does make sense to me, previously I have managed to find some of your derivation of that equation from links that you have put in different threads although I don’t know how much of it so I would be interested in seeing the proof. But as you say this is clearly not the place to go into the issues involved so I won’t go into commenting on the remainder of your post here.

#17 Doctordick

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Posted 30 August 2008 - 09:24 AM

The way I understand it is that the right side of the equation [math]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c_i^2d\tau _i^2}[/math] is the distance in your x,y,z,tau coordinate system but this coordinate system is inside of a x,y,z,tau,t system.

Think about that a bit. Exactly what do you mean by the phrase, “inside of a x,y,z,tau,t system.” I am not using t as a dimensional axis here. I am merely using t as an evolution parameter. How do you propose to plot the changes in a physical configuration of interest by using t as an axis and at the same time attempt to include all four physical axes (x,y,z and tau). We can only actually plot two dimensions against one another on a sheet of paper. It may be true that we can create a picture which the brain will interpret as a three dimensional image; however, even that only allows us to plot two physical dimensions against that evolution parameter. Furthermore, those three dimensional images can sometimes be difficult to interpret as illusions can sometimes arise in such a picture.

... for that matter, does it even make sense to talk about the t axis for anything but a way of keeping tract of the elements in the equation?

For the moment, forget that equation. The issue here is keeping tract of the position of entities in the x,y,z,tau coordinate system. Those entities follow paths in that geometry and the value of t tells you where on that path the entity is at time t. I am using t as an evolution parameter in exactly the same way Newton used time.

That is one of my major complaints about Einstein's picture. He also sees objects as following paths through his four dimensional “space-time” geometry and uses the concept of time to talk about evolution of structures along those paths. In essence he simultaneously uses time as a coordinate of his geometry and as a concept of position along those paths (essentially he is confusing two very different issues).

Am I correct in saying that the only effect that adding momentum to the fundamental equation has on the derivation of the schrodinger equation is adding a waited alpha term to the function after the first integration?

Perhaps I should not have put that issue forward in this thread as I am afraid it is confusing you (that is why I changed the title of the post to “Answers to Bombadil's questions!”. The central issue here is that my equation “is just not valid” if the total sum of all momentum of all entities being described by that equation does not vanish. However, in spite of that fact, if I do have a specific solution [imath]\vec{\Psi}[/imath] to that equation, quantum mechanics does provide me with a mathematical mechanism for transforming that solution to a solution where that sum is not zero (this is a subtly a very different issue). Please note my definition of momentum; there is no alpha term in the definition. A secondary issue here is that, in deriving Schroedinger's equation, I am clearly stating that Schroedinger's equation is an approximation to my fundamental equation and is thus only valid when those approximations are valid. It is a well known fact that Schroedinger's equation is not in conformance with special relativity so, technically speaking, any shift in reference frame can be seen as invalidating Schroedinger's equation: i.e., the mathematical mechanism discussed above does not technically give the correct answer; it only yields an approximately correct answer.

If so, is the task to find a scaling factor that leaves the value of the constants on the right side of the fundamental equation the same no matter the momentum added?

The scaling factor occurs directly as a consequence of the fact that the “form of the equation” must be exactly the same in all three relevant frames even when each is moving with respect to the other. The Dirac delta functions are of no consequence in that analysis as they are not influenced at all by a scale change. Omitting them, the remainder of the equation has the time evolution of an expanding sphere. Actual events described by that equation must conform to that self same expanding sphere. The only way that can be true is if observers who go to use that equation in those different frames use a different coordinate system. The solution to that problem is exactly the same solution required to make Maxwell's equation valid in everyone's frame (they must all see a flash bulb as producing an expanding sphere). This problem was solved years before Einstein published his theory and is exactly the changes which his theory was concocted to explain. The scaling solution is simple high school algebra and I will show it to you if you wish. The problem is exactly the same in four dimensions as it was in three dimensions.

Now, will mass and energy eventually be added to the equation in the same way only with the mass or energy operators in place of the momentum operator?

I don't understand your question at all. I have already defined the mass and energy operators in terms of the fundamental equation itself. They are not added to the equation, they are already there; I have done no more than define what aspects of the equation I am referring to when “I” use the terms “momentum”, “mass” and “energy”.

... what I was referring to was the equation [math]ct_i=\sqrt{dx_i^2+dy_i^2+dz_i^2+c_i^2d\tau _i^2}[/math]

That falls directly out of my fundamental equation and is essentially a differential description of that expanding sphere I just mentioned above.

I would be interested in seeing the proof. But as you say this is clearly not the place to go into the issues involved so I won’t go into commenting on the remainder of your post here.

The central idea of the proof can be found in my paper, “A Universal Analytical Model of Explanation Itself” which I posted in 2006; however, a number of things I said in that paper seem to have confused people and I have made some real changes in the way I express those issues since then (including a subtle, but very important change in my definition of Bt). I think I now know a little more about how I should have put the thing but, as far as I know, I no longer have FTP access to those web pages (actually I am quite surprised to find that they still exist on the web as it seems to me they could disappear at any moment). If you want to catch up on the current situation, you might read some of the posts on the thread “What can we know of reality?”

This is a thread started to discuss a serious problem deeply embedded in the whole fabric of philosophical thought.

Don't waste a lot of time there unless it really interests you. But, if you do get into reading that thread, I would suggest you read the opening post, referred to above, and then start with post #33 which gives essentially my background discussion with Anssi over on “physicsforums”. From that point forward I think you would hit the most important issues if you looked at the posts by “Qfwfq”, “Buffy” and “Anssi” plus my direct answers to them. That should pretty well cover most of the things people seem to misunderstand. If you have any questions, post to that thread, with a quote of the particular post you are referring to, and I will do my best to make the issues clear (there are a lot of things I could put quite differently). That is one of the reasons I think I am right; there are six ways from Sunday to attack all these things.

Meanwhile, not to put too much on your plate, you might check out the post I am composing for this thread. I have decided to expound on that thought experiment which I was trying to get Erasmas00 interested in working out. He either had no interest in the problem or found it beyond his abilities. Either way, I will present a solution for everyone's examination.

Have fun -- Dick


Edited by Doctordick, 01 February 2016 - 03:52 AM.