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! 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.

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

An identical moving clock.

Vector representation of the clock

Analysis of the embedded geometry

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.**