The Final Piece Of The Puzzle!

[Doctordick]

Right, um, you are referring to measuring how fast something is receding from us via measuring a Doppler effect of some light source.

Could be, that works; however, I was thinking of the clock controlling the communication system on the Pioneer; I presume its frequency is a pretty well known thing.

 

Okay I'm trying to be a bit careful here because it's easy to get confused... When you say "solving for orbital motion", do you mean the standard procedure here is to measure the velocity and direction of the object (I have no idea how...

They are sending the thing out of our solar system and thus have given it a trajectory yielding “orbital motion” which has an infinite aphelion or something quite large anyway. Now, the very fact that they are disturbed by their observations implies that they have actually calculated the expected path. I am not aware of exactly what calculations they did; however, I am quite sure that, if they didn't use a Newtonian calculation, that they perhaps used Einstein's theory. It makes no difference how they calculated the result, what they have is where they think the satellite is and how fast it should be moving at that position. Certainly they are taking into account GR effects or they wouldn't be upset by the observed slower speed.

 

As I showed, the Einstein calculation should yield a radial velocity which can be written as a function of r.

[math]

v_E = \frac{dr}{dt}= F( r )

[/math]

 

Because of the similarity of my solution to the same problem, I can guarantee that my calculation will yield a radial velocity such that

[math]

v_{DD}\sqrt{1-\frac{2\kappa M}{c^2 r}} = \frac{dr}{dt}\sqrt{1-\frac{2\kappa M}{c^2 r}}= F( r )

[/math]

 

where that function “F” is exactly the same function obtained from Einstein's theory. This means that I can write

[math]

v_E = v_{DD}\sqrt{1-\frac{2\kappa M}{c^2 r}}

[/math]

 

Since that square root factor is less than one, it should be clear that the radial velocity obtained from my calculation (for the same radius: i.e., the same path) must be slightly larger than the radial velocity obtained from their calculation. (This can also be interpreted to imply they should have started with a larger radial velocity to begin with; if they wanted the thing to be where their plots show it.) But let's get back to my original argument. They think they know where the Pioneer is; however, the actual velocity being observed is a more accurate measurement than is the actual radius to the Pioneer.

 

Think about the following analysis very carefully. Consider two universes: one where Einstein is right and one where DD is right. If we concern ourselves with the position where the radial velocities are identical, exactly the same result will occur if one is “measuring the Einstein velocity at one radius and the DD velocity at a different radius” (such as to make the two velocities identical).

 

Now, since the DD velocity is greater at the same radius and velocities are both declining as we proceed away from the solar system, the radius where the DD velocity was measured must be smaller than the radius where the Einstein velocity was measured. We can immediately conclude that, when the velocity was measured, the DD Pioneer is feeling a stronger gravitational field (it is actually closer to the sun than the observers think it is) and its de-acceleration is thus greater than what is expected.

 

Now I'm confused, I think I misunderstood something because in my mind, if the future of the object was predicted by figuring out its orbit, and if your result generated an orbit where the radius was increasing more rapidly, then I would have said Schwarzschild would presume to object to be closer than you would. But with my lacking knowledge, there are just few too many unknowns in what you said, so maybe you could clarify a bit...

The whole thing revolves around which measurement is more accurate and what issues the calculator is taking for granted. Most scientists work with “known information” and presume that the “known information” is indeed known.

 

Yeah the so-called Pioneer anomaly. I'm wondering if the anomalous orbital speeds of large galaxies could be affected by the same issue:

http://en.wikipedia.org/wiki/Galaxy_rotation_curve

 

I really don't know how the associated parameters are measured so it's a bit difficult to judge.

Yeah, we have to know exactly how the significant parameters are measured and exactly what kind of errors exist in those specific measurements. Essentially, as I said a long time ago, the difference between my results and Einstein's results is a correction in the energy due to radial motion on the same order of magnitude as the correction in energy due to angular motion between Newton's solution and Einstein's solution. It is well known that the angular effect is what causes the precession of the aphelion of Mercury. Now that effect has to be looked at for quite a while before it can be observed so it certainly should be clear that the radial effect would also be extremely small.

 

The consequences would only show up after a long time of continuous application in the same direction. Now, the Pioneer's path could definitely be a case to examine. Your comment concerning a higher velocity with the DD solution is quite accurate; however, as I said above, that would suggest that they should have started with a higher velocity than they did to get the path they wanted. You should see that this perspective yields exactly the same effect I discussed above: the thing is moving too slow. Their question is, Why? Their answer is “Dark Matter”. My answer is, “they are doing their calculations incorrectly”.

 

Notice that the effect is much stronger inside the solar system than it is out on the edge. This implies that the “higher velocity” required would be very little different from the Newtonian requirement (undetectable at a small radius and short times). Now, exactly how accurately was that original velocity established? Given the small error in acceleration implied by my equation and the number of months that effect was applied, how large a difference in the effective radius does one expect. I haven't made the calculation but I suspect it isn't a very large number. The velocity, on the other hand, is easy to measure very accurately and I think that is where the discrepancy would, and did, show up.

 

Now, if you want to talk about the galactic problem, it seems to me that we once again have the same issues in play: i.e., velocities are easy to measure via Doppler effects and we need to know exactly how the radial terms are established. Notice that the masses of the entities in these circumstances are calculated under the assumption that the Newtonian equations are correct (at least they were fifty years ago). We are talking about some very small differences here and they could arise from many different directions. That is one reason why I would like some to the professionals to make some calculations based upon my representation of the data.

 

And, yes, I would be fun to see what Qfwfq might have to say on the subject.

 

In the latest issue of “Scientific American” there is an article entitled, “The (Elusive) Theory of Everything”. One of the authors is apparently that great “genius” of modern physics, Stephen Hawking. In the summary they refer to Hawking's and Mlodinow's new book, “The Grand Design”.

 

Hawking and Caltech physicist Leonard Miodinow now argue that the quest to discover a final theory may in fact never lead to a unique set of equations. Every scientific theory, they write, comes with its own model of reality, and it may not make sense to talk about what reality actually is.

Even Qfwfq must admit that I have come up with one rather general and powerful “unique equation” (at least compared to the sets of equations they already have). Gee they seem to see the problem, why does no one in the professional community have any interest in solving that problem? I wrote Hawking a letter maybe twenty years ago and I didn't even receive an acknowledgment that he received my letter. At least Feynman answered me and offered to discuss the issue; but he up and died on me. With geniuses like these leading the physics community, it most probably will be another 1400 years before someone takes the trouble to actually look at the underlying problem: i.e., treat reality as a mathematical unknown.

 

Sorry about that; I think I have the right to rave occationally! :doh:

 

Have fun – Dick

[Doctordick]

I’m assuming that the converse is also true in this case, that is any solution to the Euler-Lagrange equation is a minimizing path and there are no stationary paths. Actually the idea of a stationary path doesn’t make much sense as it would imply the existence of a path that any infinitesimal change in would result in the path having the same length, at least in the limiting case.

What you mean when you bring up “stationary paths” is not entirely clear to me. I suspect you have little experience with finding solutions to differential equations.

 

So after we have defined the initial conditions, is the shortest path and hence the solution to the equation that you have derived define a unique path in the geometry that you have defined. Or is there some further requirements needed to define a unique path for an object to follow? That is, will the differential equation you have derived on its own define a unique equation or is some further constraint needed to insure uniqueness.

If you consider the general set of Euler-Lagrange equations, I can assure you say that there can exist solutions which differ from one another (at some point in the path) by a differential measure. That would amount to an “unstable” circumstance and either path would suffice to connect to that point. We are talking here of very subtle aspects of the characteristics of differential equations and their solutions of only peripheral interest here. You need a course in solving differential equations in order to understand the subtleties here.

 

Also I am wondering if we can expect this equation to be solvable and if it is are we more likely to learn more from studying the equation itself then we would from actually solving it?

Which equation are you talking about? I have just solved the Euler-Lagrange equation for the boundary conditions consisting of a point source for the gravitational attraction. The solution is an equation which tells you how changes in r must be related to changes in theta. Now, if you want to solve that equations for solutions (for r as a function of theta) you need to specify the boundary conditions imposed on that solution. Some solutions are quite trivial. One is r equals a constant (that is a circle) where r' vanishes. Set r' equal to zero and solve the equation for that constant (h over cl) and use the original Euler-Lagrange relationship on the rate of change of theta. That will depend upon what r you choose.

 

But mostly solutions are somewhat difficult to find and the quickest and easiest is to start from a specific boundary condition (position and velocity) and calculate the path via numerical methods on a computer. Differential equations is not a trivial subject.

 

Doesn’t this imply that there is a limit to the mass per radius that is allowed otherwise the term in the square root could equal zero for large masses which would seem to imply an infinite radial velocity limit? Or a negative under the square root which seems no less problematic.

That is the existence of “black holes” a radius and mass within which escape velocity is greater than the speed of light.

 

Also is this the only place that a difference between your equation and the Schwarzschild solution exists or is there other differences that exist?

That is the only difference; however, I think you may be missing the point that Schwarzschild's solution for a single point source of a gravitational field is a rather specific problem. Many more problems may be proposed, most of which will probably be much more difficult to solve. As I said, solving differential equations is not a trivial problem.

 

Have fun -- Dick

[Rade]

Doctordick. In all seriousness....

 

If you are claiming that your fundamental equation solution for the radial velocity related to the Pioneer Anomaly (that you give in above post) yields a more accurate prediction of measurements than the Einstein Equation, then, does it not make sense that you write a note to Science or Nature journals about this significant discovery--rather than continue your two + year rants that professional physicists do not have any interest in the topic you discuss ? I mean, -- is not the "past" for professional physicists what they know about your equation ? And, is it not true that less than 0.1 % of professional physicists know anything about it, that it is still in their "future" ?

 

==

 

So--my request. Please, please, please--put together a draft Note to Science -- here -- on this forum. Forum members will serve as the first draft "peer" review of your claim and the soundness of your mathematics. You will need to format the presentation as required by the journal. Then, good luck and perhaps your approach becomes part of the "past" of science--what is known.

 

==

 

In my mind--this action is the final piece of the puzzle--until you put this final puzzle piece in place (submit a manuscript) you have no puzzle--only a bunch of ideas and assumptions and mathematics that signify nothing of scientific value. I am not trying to be rude--only logical and to the point because I think it possible you may be correct, and the Einstein approach may be in error. And please, do not claim you already tried this--you have not submitted anything for publication of this sort, a very specific application to show that the Einstein approach lacks a fundamental fine tuning that your approach corrects.

[AnssiH]

They are sending the thing out of our solar system and thus have given it a trajectory yielding “orbital motion” which has an infinite aphelion or something quite large anyway. Now, the very fact that they are disturbed by their observations implies that they have actually calculated the expected path. I am not aware of exactly what calculations they did; however, I am quite sure that, if they didn't use a Newtonian calculation, that they perhaps used Einstein's theory. It makes no difference how they calculated the result, what they have is where they think the satellite is and how fast it should be moving at that position. Certainly they are taking into account GR effects or they wouldn't be upset by the observed slower speed.

 

As I showed, the Einstein calculation should yield a radial velocity which can be written as a function of r.

[math]

v_E = \frac{dr}{dt}= F( r )

[/math]

 

Because of the similarity of my solution to the same problem, I can guarantee that my calculation will yield a radial velocity such that

[math]

v_{DD}\sqrt{1-\frac{2\kappa M}{c^2 r}} = \frac{dr}{dt}\sqrt{1-\frac{2\kappa M}{c^2 r}}= F( r )

[/math]

 

where that function “F” is exactly the same function obtained from Einstein's theory. This means that I can write

[math]

v_E = v_{DD}\sqrt{1-\frac{2\kappa M}{c^2 r}}

[/math]

 

Since that square root factor is less than one, it should be clear that the radial velocity obtained from my calculation (for the same radius: i.e., the same path) must be slightly larger than the radial velocity obtained from their calculation. (This can also be interpreted to imply they should have started with a larger radial velocity to begin with; if they wanted the thing to be where their plots show it.)

 

Right okay, here's where I had made a hidden assumption in my mind, and right now I'm backtracking a bit, trying to convince myself of your thoughts.

 

The assumption I had made was that, once a measurement of the speed of the satellite has been made, your expectation of higher radial velocity implied a larger path. So what I had in my mind when writing the previous post was that your solution would yield the expectations of the satellite moving along a path that goes farther away from the sun than the path of Schwarzschild's expectations.

 

So now I'm focused on that bit, I see the point is that the radial velocity is a function of "r", i.e. the radial velocity is higher at any given point of the orbit, and that is seen to essentially imply a shorter turnaround time for the same path?( (i.e. the satellite is just plain moving faster)

 

I can see that in that case, making a measurement of velocity and figuring out the radius from that, would give Schwarzschild the impression that the satellite is farther away than you'd figure it is. And yes in that case they would see unexpectedly large slow-down.

 

These brings up few questions to my mind, like whether the conservation of angular momentum is still valid in your solution and where did we get it when it was used in the derivation of this result. I'm not really sure because I'm not very good at reading the actual mechanisms of those equations :I

 

Well at any rate, it would be quite interesting to get in touch with someone who knows the measured data of Pioneer and could analyze the situation in terms of your solution. Should be fairly trivial since they don't even have to know where your equation came from...

 

The consequences would only show up after a long time of continuous application in the same direction. Now, the Pioneer's path could definitely be a case to examine. Your comment concerning a higher velocity with the DD solution is quite accurate; however, as I said above, that would suggest that they should have started with a higher velocity than they did to get the path they wanted. You should see that this perspective yields exactly the same effect I discussed above: the thing is moving too slow. Their question is, Why? Their answer is “Dark Matter”. My answer is, “they are doing their calculations incorrectly”.

 

Well yeah, the dark matter thing feels very much like a text-book example of how Kuhn describes things before a paradigm shift. I.e. adding complexity in terms of old terminology, until a new terminology washes it away as unnecessary.

 

Now, if you want to talk about the galactic problem, it seems to me that we once again have the same issues in play: i.e., velocities are easy to measure via Doppler effects and we need to know exactly how the radial terms are established. Notice that the masses of the entities in these circumstances are calculated under the assumption that the Newtonian equations are correct (at least they were fifty years ago). We are talking about some very small differences here and they could arise from many different directions. That is one reason why I would like some to the professionals to make some calculations based upon my representation of the data.

 

Indeed. That would be interesting.

 

Btw, I don't know if you are aware of it, but there are attempts to modify the laws of gravity to explain the galaxy rotation problem, i.e. MOND and later TeVes;

http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics

 

I guess there has been few different flavours to it from day one (it's mostly based on guessing and error and trial), and it seems to be modifying somewhat different parameters than what your analysis shows (at least as far as I can understand that), but maybe you can tell whether they happen to be landing onto similar modifications as your analysis reveals, in any sense at all...

 

In the latest issue of “Scientific American” there is an article entitled, “The (Elusive) Theory of Everything”. One of the authors is apparently that great “genius” of modern physics, Stephen Hawking. In the summary they refer to Hawking's and Mlodinow's new book, “The Grand Design”.

Hawking and Caltech physicist Leonard Miodinow now argue that the quest to discover a final theory may in fact never lead to a unique set of equations. Every scientific theory, they write, comes with its own model of reality, and it may not make sense to talk about what reality actually is.

 

Well, it's interesting that they are saying that, because in my mind at least Hawking has been talking of things in terms of ontological correctedness a lot (like concerning himself with the possibility of time travel due to relativity etc), but at the same time I realize a lot of that is something he does with his "popular science" hat on, i.e. over simplification of things, and saying things that sell to general public. But, if they are now starting to say things like "it may not make sense to talk about what reality actually is.", my only problem is with the word "may" in there ;)

 

Anyway, I do see physicists occasionally make comments about that issue, which is always nice. And perhaps the time would be ripe for Hawking to pay attention to your analysis now. If it was just made clear from the word go that your analysis is exactly concerning the issue non-sensibility of talking about reality itself, and the sensibility of talking about valid models.

 

Even Qfwfq must admit that I have come up with one rather general and powerful “unique equation” (at least compared to the sets of equations they already have). Gee they seem to see the problem, why does no one in the professional community have any interest in solving that problem?

 

Right now, judging by the recent discussion between me and Qfwfq, it seems physicists have somewhat different levels of understanding how deep that issue really goes. Qfwfq has been saying for a long time that he understands what I mean by reality being ontologically unknown, but he was still assuming all that time that the reality must bear some likeness to our everyday perception, which is essentially where all his comments about phenomological observations were coming from (and in my mind most of his misinterpretation of our commentary).

 

I think in his mind, allowing for the possibility that the everyday perception is just an interpretation of something entirely unknown (i.e. that there may not be any likeness there), is exactly the same as letting go of the only way to get any information about reality, so the first reaction to your analysis would be either "1. you are assuming idealism" or "2. you cannot be in connection with physics at all"

 

Also, when I say something like "no, there may not be any likeness", I know exactly how he reads that; he immediately starts to think about something like "but it's not possible to just interpret my kitchen table away".

 

Well, I'll be writing a response to the other thread, and as I said, I believe I know how he is thinking about this, and I'm just trying very hard to think about what would be a good way to communicate this issue in ways that would get around those few mental blocks that almost everyone seems to collide with head-on... The key thing here seems to be that there exists an interpretation to your analysis, that most physicists intuitively make, and it makes them convinced that they read you correctly, when they don't. Certainly a short version of it would be "they are not working exclusively with your definitions", but it would be nice to understand why exactly they find it so incredibly impossible to do that, or what are the things that spark them to make the wrong interpretation, so that could perhaps be avoided in the communication...

 

Easier said than done, I know!

 

-Anssi

[Bombadil]

What you mean when you bring up “stationary paths” is not entirely clear to me. I suspect you have little experience with finding solutions to differential equations.

 

What I mean is if we define

 

[imath]I(\mu) = \int_U L(d\mu,\mu,x)dx [/imath]

 

Then we can set [imath] i(\tau)=I[\mu+\tau v] [/imath] , by finding the constraints placed on [imath] \mu [/imath] needed for [imath] i'(0)=0 [/imath] for an arbitrary choice of v we can derive the Euler-Lagrange equation. This will show that any minimum path must satisfy the Euler-Lagrange equation. However it is the converse that I am interested in here in particular. Have sufficient constraints been placed on the Euler-Lagrange equation so that the solution to [imath] i'(0)=0 [/imath] must also satisfy the requirement that [imath] i(0)=\underset{\mu}{min} I(\mu)[/imath]. By a “stationary paths” I mean any path that is a solution to the Euler-Lagrange equation that won’t also satisfy the equation [imath] i(0)=\underset{\mu}{min} I(\mu)[/imath].

 

Which equation are you talking about? I have just solved the Euler-Lagrange equation for the boundary conditions consisting of a point source for the gravitational attraction. The solution is an equation which tells you how changes in r must be related to changes in theta. Now, if you want to solve that equations for solutions (for r as a function of theta) you need to specify the boundary conditions imposed on that solution. Some solutions are quite trivial. One is r equals a constant (that is a circle) where r' vanishes. Set r' equal to zero and solve the equation for that constant (h over cl) and use the original Euler-Lagrange relationship on the rate of change of theta. That will depend upon what r you choose.

 

I was referring to the equation that gives r as a function of theta, which it sounds like is not in general solvable, at least not easily. But it sounds like it doesn’t really matter since it could be approximated by numerical methods if we needed a solution to it.

 

That is the only difference; however, I think you may be missing the point that Schwarzschild's solution for a single point source of a gravitational field is a rather specific problem. Many more problems may be proposed, most of which will probably be much more difficult to solve. As I said, solving differential equations is not a trivial problem.

 

Wouldn’t any further situation be a combination of multiple cases of the current problem? That is the current problem is a one body example of what is in general a many body problem. In other words further problems would be just generalizations of this problem? Or is there some other possibility issue that you are suggesting?

 

There is another thing that I keep wondering, that is shouldn’t it be possible to go back to the fundamental equation and map this path into a two body equation using the definition of mass that you have derived and derive a differential equation of the interference pattern of two elements. With the goal of deriving a sort of quantum view of gravity? That is a quantum interpretation of the solution to the Euler-Lagrange equation that you derived much as the Schrödinger equation could be looked at as a quantum interpretation of Newtonian physics.

[Rade]

I will post here, hoping the information reaches the most interested in this topic.

 

There is a very nice new book (2010) that has as its theme to "explain information". Now, this is very close to the goal of Doctordick, to "explain undefined information". I find as I read this book, the ideas Doctordick is trying to explain come into new understanding.

 

Here is the title: Decoding Reality, the Universe as Quantum Information, by Vlatko Vedral. 2010. Oxford University Press.

[Doctordick]

There is a very nice new book (2010) that has as its theme to "explain information". Now, this is very close to the goal of Doctordick, to "explain undefined information". I find as I read this book, the ideas Doctordick is trying to explain come into new understanding.

I am sorry Rade, but I think you are reading something into my work which simply isn't there. I am NOT "trying to explain" anything at all! I am trying to discover the constraints on "an explanation" which are solely required by the "definition of an explanation". This cannot by any stretch be thought of as an attempt to explain anything. Explaining is left to others; all I am trying to do is see what constraints can be put on the issue without saying anything at all about what is being explained or what the explanation might be.

 

In the old days, you could say, "well, the explanation cannot contradict itself". That is a constraint. All I have done is examined the general question of finding constraints a little closer. What I am "trying to explain" is exactly what I have deduced from my thoughts about the issue.

 

In particular, I am not trying "to explain undefined information". I am merely trying to represent such a thing consistent with the common definition of "an explanation" so that I can make a logical analysis of the situation and discover issues which clearly imply a specific explanation "has to be wrong" in a decent and exact manner!.

 

See if you can rap your head around that.

 

Have fun -- Dick

[LaurieAG]

Hi Doctordick,

 

In particular, I am not trying "to explain undefined information". I am merely trying to represent such a thing consistent with the common definition of "an explanation" so that I can make a logical analysis of the situation and discover issues which clearly imply a specific explanation "has to be wrong" in a decent and exact manner!.

 

See if you can rap your head around that.

 

Yes, very clear now. Undefined information is the sum total collection of all that exists and all that does not exist..

 

Yes it is very clear that there is only one place where this undefined information can become defined, at the very end of your universe. So from that discrete point in the process (and probably even at the beginning), where you invoke any undefined information, the state of all universal locations are already known, including those that don't exist.

 

If you want to see a practical experiment that shows what happens when you apply an all knowing definition at discrete points along a continuum you should have a look at optical feedback loops.

[Rade]

I am sorry Rade, but I think you are reading something into my work which simply isn't there. I am NOT "trying to explain" anything at all! I am trying to discover the constraints on "an explanation" which are solely required by the "definition of an explanation". This cannot by any stretch be thought of as an attempt to explain anything. Explaining is left to others; all I am trying to do is see what constraints can be put on the issue without saying anything at all about what is being explained or what the explanation might be.

 

Good Doctor--please excuse me--but how do you expect me to understand what you are claiming when you here claim you are NOT trying to explain--when just a few days ago on the other thread you told me this, and it is what you see below in large font that I was referring to in reference to the book I cited:

 

Hi Rade,...I have a few comments which I think you should consider carefully...We are interested in “explaining” what is “undefined”. That is the central issue of what I have discovered.

 

I post this here so as this thread is up-to-date, and I will post also on the Laying out the Representation thread where you can "explain" yourself. Again, I am not trying to be a troll--but I am no fool--and either you are interesting in explaining OR you are not, you cannot have it both ways.

 

===

 

OK, so you claim you "are trying to discover", and not "to explain". You have no interest in trying to discover |undefined information|, but you try to discover "constraints on an explanation" [of the undefined information] which are required by the "definition of an explanation" that you use. Sure, makes sense, first you must define then you look for the constraints that follow.

[Doctordick]

I post this here so as this thread is up-to-date, and I will post also on the Laying out the Representation thread where you can "explain" yourself. Again, I am not trying to be a troll--but I am no fool--and either you are interesting in explaining OR you are not, you cannot have it both ways.

This is exactly the kind of cavils I sincerely desire to avoid. I have no interest in creating or discovering explanations; however, the fundamental issue of explaining things, the issue which no philosopher talks about, is that in the total absence of an explanation (which is exactly where the whole problem of explaining begins) everything is “undefined”. Thus the very basic problem of creating explanations assumes the “undefined” can “be explained”.

 

But it's a big secret no one talks about. If such a thing can be done (and apparently it can as science is chock full of explanations) then it appears to me that “guessing possibilities” is the only route. That certainly justifies the billions of years required for “life” to come up with “explanations”.

 

My position is that, if all we can do is “guess” it would behoove us to guess intelligently: i.e., one should it interesting to find the constraints implied by the definition of an explanation.

 

And yes, WE (as a life form) are interested in “explaining” what is “undefined”. And furthermore, what I have discovered (which will become clear down the road) is that all of our scientific discoveries appear to be no more than ways of mathematically expressing “the constraints implied by the definition of an explanation”. If I am correct (and I really have aquired a lot of confidence in that assertion over the years), then that is a very profound discovery.

 

But it is a consequence of my proof; not the goal of my proof.

 

I hope you can come to understand the difference.

 

Have fun -- Dick

[Qfwfq]

But it's a big secret no one talks about.

Of course! That's because the ones who are the most fully aware of it are cryptanalysts; their very trade is handling secrets! You can't very well expect them to let the cat out of the bag.

[Rade]

...the fundamental issue of explaining things, the issue which no philosopher talks about, is that in the total absence of an explanation (which is exactly where the whole problem of explaining begins) everything is “undefined”. Thus the very basic problem of creating explanations assumes the “undefined” can “be explained”.

First, thank you for your attempt to explain that "we" but not "you" have an interest in explaining. Also, I agree with you, if I understand you correctly, that everything must be undefined until such time that some explanation comes to be. Therefore, everything must be unexplained until such time that there is a mutual interaction between |information| with potential to be defined and the entity that has a need to define. However, definition is meaningless if what is explained has no expectation of communication outside the entity explaining, for there is no need to define that which has already been explained to the self.

[giorgiofontana]

The main problem is going to be: The Return of Euclidean Geometry

(sounds like a B-series movie sequel, I know)

 

Well, it is indeed euclidean geometry in four space dimensions plus an adimensional time.

 

Now what you should understand is that 4 space dimensions means that there must exist four dimensional objects of which we suppose to perceive a three space dimensional slice or brane.

This concept implies a hyper-cylindrical symmetry of static objects in the four space dimensional euclidean space. This 4D euclidean space is another beast respect to Galilean space.

But we like to explore new concepts and try new ways, like this 4D gravitoelectromagnetism:

 

http://www.scribd.com/doc/24069210/On-the-Foundations-of-Gravitation-Inertia-and-Gravitational-Waves

 

Like all of you normally do, all comments will be ignored. :) :) :)

[Doctordick]

The main problem is going to be: The Return of Euclidean Geometry

(sounds like a B-series movie sequel, I know)

Euclidean Geometry has never left. It is central to almost every objective analysis of any experimental data to be analyzed.

 

Well, it is indeed euclidean geometry in four space dimensions plus an adimensional time.

“It is”? What is? You should be a little clearer with your references.

 

Now what you should understand is that 4 space dimensions means that there must exist four dimensional objects of which we suppose to perceive a three space dimensional slice or brane.

No, what four space dimensions means is that one is considering four independent variables where the four independent measurements are assumed to be free to take on any value over the entire range of real numbers: i.e., no assumptions are being made concerning the character of the data being analyzed.

 

The use of a non-euclidean geometry presumes there is a known relationship between the measurements being analyzed. If one is to begin with the presumption of a non-euclidean geometry, one is certainly not beginning without presumptions. I think you have misinterpreted the thrust of this entire thread.

 

Like all of you normally do, all comments will be ignored. :) :) :)

Why do you post if you are going to ignore all comments?

 

Have fun -- Dick

[sigurdV]

Excuse me for asking an ELEMENTAry question: "Euclidean" coordinate systems ...Don´t you mean Cartesian?

[Doctordick]

If you google “cartesian” you will discover that the ideas of Euclid stood long before the introduction of algebra. As a matter of fact, Descartes used Euclidean geometry in his presentation. Essentially “Cartesian coordinates” are direct representations of Euclidean geometry. My complaint is that “modern, non-Euclidean geometry” can not be constructed without making assumptions concerning the relationships between various coordinates.

 

If I may quote the results of the above google:

 

The invention of Cartesian coordinates in the 17th century by Rene' Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.

 

Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory, and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering, and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design, and other geometry-related data processing.

Of course I use the power of analytic geometry, essential to any modern physics, but as my interest is in making “no assumptions”, I see non-Euclidean (non-orthogonal) coordinate systems as presumptive.

 

Yes, Descartes' “cartesian” coordinate system is quite correctly thought of as orthogonal, but in modern physics (particularly in Einstein's theory of relativity) Descartes concepts of a coordinate system are taken directly over to non-Euclidean geometries so, in my mind, the orthogonal issue could be quite easily lost.

 

Essentially you bring up a semantic issue, not really relevant to my presentation.

 

Have fun -- Dick

[Rade]

I would like to activate this old thread to see if there have been any experiments conducted to test the claim made by DoctorDick stated below.

 

Seems to me it would be a revolutionary finding if the equation of DD (with the extra term) predicted gravity more precisely than the equation of Einstein. So my question, are there any experiments where the equation of DD could be compared to that of Einstein (side by side) concerning the strength of a gravitational field ? Which equation comes closer to the experimental measurement of gravitational field strength ?

 

QUOTE OF DOCTORDICK: it appears (at least to me at the moment) that the effect of that extra term in my solution is to make the gravitational field appear to be slightly stronger than estimated via Einstein's field theory.