A rather unorthodox view of relativity.

I have spent a considerable amount of time in composing this post because, in close to fifty years, I have been totally unable to communicate the rationality of my position to any professional physicists. They invariably turn a blind eye to my arguments. I am trying here to put the issue down in as clear a manner as I can. I hope my efforts yield some success.

I personally find it quite difficult to comprehend why the physics community puts such absolute faith in the validity of Einstein's theory of relativity. If you go into the derivation of that theory, you will find that it is fundamentally based upon the null result of the Michelson-Morley experiments. This null result was first explained by the Lorentz-FitzGerald contraction hypothesis: the hypothesis that physical structures contracted in the direction of motion according to the equation $L'= L \sqrt{1-\left(\frac{v}{c}\right)^2}$ . Einstein came up with the idea of simply postulating the null result of the Michelson-Morley experiment and deducing the Lorentz-FitzGerald contraction as a consequence of that postulate. But that was not the central issue of his theory. The central issue of his theory was that he replaced the “aether” with a “space-time continuum”.

Quoting Wikipedia, “Physics theories of the late 19th century postulated that, just as water waves must have a medium to move across (water), and audible sound waves require a medium to move through (air or water), so also light waves require a medium, the 'luminiferous aether' or the 'ethereal aether'. Because light can travel through a vacuum, it was assumed that the vacuum must contain the medium of light.” Einstein instead hypothesized that they were “??waves??” (which he called distortions in geometric curvature) in the very “fabric” of his space-time continuum. I personally see little difference between his theory and the ethereal aether theory other than the geometry involved and Einstein's removal of the concept “time” as an interaction parameter. By that very removal (making it a dimension of his space-time continuum) he created a rather static description of reality. Calling one of his coordinates “time”, does little to remove the rock hard nature of his description of the universe as absolute fixed paths in a four dimensional space; no matter what geometry he uses.

What I want everyone here to comprehend is that, as soon as you accept Lorentz-FitzGerald contraction as experimentally correct, the clock settings (the standard relativistic clock adjustments) follow exactly as they do in Einstein's theory so it is only the mental image of reality we are discussing here. Most physicists seem to lose sight of that fact. Now there is one important fact which should be kept in mind: the Lorentz-FitzGerald contraction was originally based upon Maxwell's equation; that is, the contraction is a clearly deduced consequence of electromagnetic phenomena (electromagnetic interactions) and not necessarily binding on other type interactions. On the other hand, from the perspective of Einstein's geometric explanation (his space-time continuum) all interactions should obey the same rules.

With that in mind, let us go back to some earlier comments I have made. I made a very important observation in post #42 of the thread “What can we know of reality”. In that post, I showed exactly how the four fundamental constraints I had developed from logical considerations could be expressed in a single equation (what I have come to call my fundamental equation). All I did was demonstrate that the four constraints would be obeyed by any solution to that equation and likewise, that any solution to the fundamental constraints would obey that equation (in the form zero plus zero equals zero). The most important observation occurs in the very end of that post and has to do with the fact that

$\sum_q \frac{\partial}{\partial x_q}\vec{\psi} = 0$

is valid in only one specific frame of reference.

Quote:

Originally Posted by Doctordick

This means that the fundamental equation is only valid in in one specific Euclidean coordinate system: that would be the coordinate system where $\sum_i \frac{\partial}{\partial x_i}\vec{\psi} = 0.$ . This can be seen as quite analogous to Newton's “inertial” coordinate system in that his equations simplify to F=ma in that coordinate system. Likewise, my fundamental equation is much simpler in the particular coordinate system where $\sum_i \frac{\partial}{\partial x_i}\vec{\psi} = 0.$ . Thus this is a constraint on the coordinate system to be used, not actually a problem with achieving the represented deduced constraints.

The problem is that my equation is not valid unless the entire universe is included (i.e., absolutely all relevant information is expressed in terms of those numerical labels we have indexed) and that makes the issue non trivial.

This brings up a very interesting conundrum regarding relativity. Newton's “inertial” system was quite easy to identify: i.e., if you were in an inertial frame, pseudo forces could not be present. But identifying the fact that you are in the frame where the sum of the momentum of the universe is zero is not such an easy task. That brings up a unappreciated fact about conventional physics normally ignored by the physics professionals. In standard conventional physics, they will tell you that the speed of light is c but, if you are a reasonable person, you should comprehend that this statement can not be logically defended. There exists absolutely no way to measure the actual speed of light because, to do so would require setting two clocks to agree (one at each end of the path) and every procedure I am aware of for accomplishing that task makes the assumption that the speed of light is c. What most physicists are talking about when they say that the speed of light is c is that the round trip distance divided by the time to make the trip is c. There exists no way to prove that the speed of light in one direction is the same as the speed of light in the opposite direction (that is in fact the very essence of the Michelson-Morley null result). What is important here is the fact that they are making a very significant assumption. That assumption being that there exists no way to establish a unique frame of reference. An assumption by the way which is in clear violation of their experimental analysis of reality: if your frame of reference were to get very far from the rest frame of our galaxy the microwave background of the universe would become quite Doppler shifted and this very fact is actually being used today to talk about the velocity of the earth through the universe.

What I want you to do is keep in mind is the fact that Lorentz-FitzGerald contraction is the central experimental result of significance here. If that issue is indeed a fact then all of special relativity (the transformation equations of interest) fall out as required. All I am trying to do is to get you to look at relativity from a slightly different perspective. The two issues I want to build upon are, first, if a paradigm yields the proper contraction, all of relativity can be deduced and, second, there is nothing in relativity to preclude a single preferred reference frame (the real issue of relativity being that there exists no way to “locally” prove you are in that specific frame: a direct consequence of Lorentz-FitzGerald contraction).

So, moving on to my fundamental equation, I would like to point out that the equation is scale invariant. Notice that the term I have referred to as the “interaction term” is entirely built of Dirac delta function interactions. These functions only have value when the argument is zero. It follows that the scale of the arguments is of no consequence. If you were to multiply every numerical index by some fixed number “a”, all the arguments I made for that fundamental equation go through exactly as they did before the scale adjustment. You should see that as quite a reasonable fact. The length measurements to be used in your description of your world view must arise out of the data supporting that world view and is not given a-priori as some kind of information above and beyond all other things. This is no more than another symmetry embedded in the problem which you have solved with your flaw-free epistemological construct and it must be embedded in your solution.

This fact brings up a rather important possible inconsistency. If you have found a solution to that equation for some subset of all the information available to you, your frame of reference must be at rest with respect to that subset of information (think in terms of a universe where there is no information outside that subset). Suppose you then find a solution for some different subset of information. That solution must reside in a frame of reference at rest with respect to that second subset of information. Now, if you try to combine those two solutions you are confronted by the fact that they may well be in different reference frames. The question arises as to how both solutions can be consistent with that fundamental equation since the equation is only valid in a specified rest frame. There is only one answer to the question: the form of the equation cannot change in going from one frame to the other.

If you have the specific solution in each frame, it is a trivial issue to discover the motion of the origin of one frame in the other reference frame and thus establish the velocity of that frame as seen from the other. The only question is, what change in our arguments will make those two problems identical. The solution is quite simple; all we need is a method of transforming the equation from one frame to the other. And here we are quite lucky as others have already found the required transformation many many years ago. If you look at my equation and temporarily ignore the “interaction terms” which are totally scale invariant, the similarity between

$\left\{\sum_i \vec{\alpha}_i \cdot \nabla_i + \sum_{i neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\psi} = K\frac{\partial}{\partial t}\vec{\psi} = iKm\vec{\psi}$

and Maxwell's equation for the propagation of photons should be obvious. All we need do to make this equation the same in both frames is exactly the same Lorentz-FitzGerald contraction required by the Michelson-Morley experiment. Since my equation is scale invariant, this merely says that the epistemological constructs of your flaw-free solution must obey special relativity. What you need to recognize here is that this is no statement about reality, it is merely a statement about your expectations and the method you use to achieve them.

As a statement about reality, it makes the assumption that separate pieces of the information known to you can be regarded as independent of one another; an assumption which could be false. But it is not a statement about reality; it is a statement about your expectations, quite another matter. If your expectations are based upon the fact that other information available to you can be ignored then, in order to be flaw-free, your explanation must conform to special relativity.

Please, if you believe you can see an error in my arguments, let me know about it.

Have fun -- Dick

A rather unorthodox view of relativity.

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