What are the implications of a Euclidean interpretation of special relativity?

[jcsd]

You don't need GR to handle curved worldlines...


What is the point of #57? I think you're still trying to describe how to go from 3+1-space to 4+1-space... but I think it's much easier than you're making it.

When we're working in 3+1-space, if we pick any pointed worldline, we already know how to assign a proper-time to any point on that worldline. Then, IMHO it's straightforward to lift that worldline into 4+1-space simply by making the new coordinate to be equal to the proper time at that point.

(If I've misunderstood your intent, let me know)

This is precisely how it seems to be and my beef is that 5 coordinates does not necessarily mean 5 dimensions, 5 independent coordinates mean 5 dimensions.

For example in a Cartesin coordinate system describing a Euclidena plane you could insert an extra axis say 45 degrees to the other two axis and assign every point in the plane 3 coordinates. These 3 coordinates are not indepent though, knowing any two coordinates describing a point will allow you to work out the third one.

(Unless I've too misunderstood the intentions) that is precisely what is being done here. In this case the extra axis is the worldline of the object we're descrbing and knowing any four cooridnates of an event will allow you to calculate the fifth.

It seems to me we don't have a 5 dimensional structure, instead we've got a 4 dimensional structure being described by a quirky coordinate system that uses 5 coordinates.

 

[CarlB]

This is precisely how it seems to be and my beef is that 5 coordinates does not necessarily mean 5 dimensions, 5 independent coordinates mean 5 dimensions.
...
In this case the extra axis is the worldline of the object we're descrbing and knowing any four cooridnates of an event will allow you to calculate the fifth.

It seems to me we don't have a 5 dimensional structure, instead we've got a 4 dimensional structure being described by a quirky coordinate system that uses 5 coordinates.

Your complaint is that any single world line does not fully utilize all 5 dimensions. But the set of all possible worldlines uses them, so they are fully utilized.

Consider a 3 dimensional substance, with one dimension curled up, which carries quantized waves that all happen to travel at the same speed c. If you know the speed of the particle in two of those dimensions you can compute the speed in the third dimension, so by your argument, there are actually only two dimensions.

What I'm saying here is just because you can mathematically eliminate a redundant piece of information from the description of a physical object certainly does not prove that that piece of information is not a part of the physical object. And eliminating these things can bring you a world of hurt in terms of making your physical intuition more difficult and your mathematics more complicated.

At the moment, if you are unfamiliar with the hundreds of papers written under the assumption of Euclidean relativity, you are not in a position to pass judgement on the efficacy of the technique. If you are not intimately familiar with both techniques you are not in a position to judge one against the other.

You can see that there are people who have studied this thing carefully for years and thought about it deeply, made calculations, rewrote the foundations of physics to fit the new assumption, etc. Having done this, we tell you that the grass is greener on this side of the fence.

To see the world from this side you will have to relearn the relativity that you already learned once. I admit that this is a mountain to climb. I admit that the only reason I had the time available to waste on this was because the economy turned down and it looked like a good time to take a vacation from my usual employment. Maybe you don't have this luxury. Life is short.

However, if you do decide to make the effort, the view from up here is beautiful and the weather is fine. The road was very difficult, more especially for a particle physicist than most, because it required that I rethink almost everything I thought I knew about particle physics. It looked like a real stupid idea many times to me, but eventually I worked out new ways of explaining the contradictions and they were simpler and more beautiful than the paradoxes that I was taught before.

Having arrived here at great effort, and experiencing great enjoyment, I will never leave, but I recognize that the effort to get here is beyond the capability of most at this time. To leave the fields where 99.99% of physicists live will give you solitude that may be unwelcome for most, and the path will require a nose for elegance that will evade most. It just ain't easy.

In the example of bringing 3 dimensions down to 2 in an unphysical way, one would notice that in 2 dimensions, there actually are two different choices for that undetermined 3rd velocity coordinate. The corresponding choice in Euclidean relativity is the choice of going forwards and backwards in time, as in the Feynman description of antiparticles. See Hans Montanus for a description of this in classical relativity.

Carl

 

[Mortimer]

You can see that there are people who have studied this thing carefully for years and thought about it deeply, made calculations, rewrote the foundations of physics to fit the new assumption, etc. Having done this, we tell you that the grass is greener on this side of the fence.
To see the world from this side you will have to relearn the relativity that you already learned once.

Although my experience and probably also the effort done in the field so far is only a fraction of Carl's yet, I can only fully agree! Euclidean special relativity has really opened my eyes.

 

[bda]

jcsd

It seems to me we don't have a 5 dimensional structure, instead we've got a 4 dimensional structure being described by a quirky coordinate system that uses 5 coordinates.

You are right in saying that we have a 4 dimensional structure. By imposing a null displacement condition in 5D we are reducing by 1 the number of independent dimensions. The advantage is that we are left with a choice for describing this 4D structure in either Minkowski or Euclidean geometry and we have the mathematical machinery to translate between the two geometries.

The advantage of starting off in 5D will be even bigger when we consider quantum behaviour, which we are neglecting for the moment.
Jose

 

[Sheyr]

Hi and hallo to all enthusiasts of Euclidean Relativity. I’ve read the whole post and some papers of some of you – those of Rob and Jose. Although I don’t understand some of your thesis and ideas I’m an enthusiastic supporter of the ER concept.

Studding the geometry based on the equation (ct)^2 = s^2 + x^2 + y^2 +z^2 , I found it possible to derivate the Lorentz transformation, equation of time dilatation and Lorentz contraction that are identical in comparison to those of Special Relativity. Also the composition of velocities equivalent to SR makes no problem. Unfortunately I have no drawing that can be posted here, but if you “play” more with the geometry you should have no problem with adding velocities. BTW, I don’t like the term “adding velocities”. It is rather looking for the answer to the question: “what is the velocity of a moving body measured by the observer, who is moving with a known velocity with respect to us, if we also know the velocity of the moving body in our reference frame. If we ask this way it is obvious why the “sum” can not exceed ‘c’.

Cheers
Martin

 

[Mortimer]

Hello Martin,
You are very welcome. I'm glad you are enthousiastic about Euclidean relativity. It may be my wishful thinking but it seems like Euclidean relativity is beginning to attract more attention in widening circles, thanks amongst others to the efforts of Jose Almeida, Hans Montanus and Carl Brannen who recently brought the topic on the agenda of some physics conferences.

Rob

 

[CarlB]

One of the social difficulties of Euclidean relativity is that few physicists are ready to accept an alternative to the special theory of relativity. But perhaps things are changing. Here are some quotes from Lee Smolin's new book, "The Trouble With Physics -- The Rise of String Theory, the Fall of a Science, and What Comes Next":

(p. 218) When the ancients declared the circle the most perfect shape, they meant that it was the most symmetric: Each point on the orbit is the same as any other. The principles that are hardest to give up are those that appeal to our need for symmetry and elevate and observed symmetry to a necessity. Modern physics is based on a collection of symmetries, which are believed to enshrine the most basic principles. No less than the ancients, many modern theorists believe instinctively that the fundamental theory must be the most symmetric possible law. Should we trust this instinct, or should we listen to the leson of history which tells us that (as in the example of the planetary orbits) nature becomes less rather than more symmetric the closer we look?

(p 221) These events [i.e. AGASA events over GZK limit] may be a signal that special relativity is breaking down at extreme energies.

(p 226) I mentioned at the beginning of this chapter that there were two possiblities. We have already discussed one, which is that the principle of the relativity of motion is wrong -- meaning that we could indeed distinguish absolute motion from absolute rest. This would reverse a principle that has been the linchpin of physics since Galileo. I personalll find this possibility abhorrent, but as a scientist I must acknowledge that it is a real possibility.

(p 256) What could that wrong assumption be? My guess is that it involves two things: the foundations of quantum mechanics and the nature of time. We have already discussed the first; I find it hopeful that new ideas about quantum mechanics have been proposed recently, motivated by studies of quantum gravity. But I strongly suspect that the key is time. More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the origin of physics.

(p 314) Fine, you might say, but who are the seers? They are by definition highly independent and self-motivated individuals who are so committed to science that they will do it even if they can't make a living at it. There should be a few out there, even though our professionalized academy is unfriendly to them. Who are they and what have they managed to do to solve the big problems?

They are hiding in plain sight. They can be recognized by their rejection of assumptions that most of the rest of us believe in. Let me introduce you to a few of them.

I have a lot of trouble believing that special relativity is false; if it is, then there is a preferred state of rest and both the direction and speed of motion must be ultimately detectable. But there are a few theorists around who have no trouble with this concept. Ted Jacobson ... Joao Maguiejo ... Robert Laughlin ... Grigori Vilovik ... Xiao-Gang Wen ...

(p 354) To put it more bluntly: If you are someone whose first reaction when challenged on your scientific beliefs is "What does X think?" or "How can you say that? Everybody good knows that ...," then you are in danger of no longer being a scientist. ...

Carl

 

[Mortimer]

I would like to mention that the article "Dimensions in Special Relativity Theory", that was presented to initiate this thread will be published in the Jan/Feb 2007 issue of the peer-reviewed journal Galileon Electrodynamics. Not a top-rated journal like e.g. Physical Review, but nevertheless encouraging for an amateur without any affiliations.

Rob

 

[Mortimer]

A discussion is going on in thread https://www.physicsforums.com/showthread.php?t=232693, "Prove that 4 vector potential is really a 4 vector?". The conclusion of samalkhaiat in message #13 is that it is not a 4-vector.
Remarkably, this is also the conclusion I got, reasoning from principles of Euclidean special relativity. Section 6 of the article "http://www.euclideanrelativity.com/4vectors/node6.html" " suggests that the classical potential 4-vector is in fact an Euclidean 4-vector instead of a Minkowski 4-vector.

 

[robphy]

A discussion is going on in thread https://www.physicsforums.com/showthread.php?t=232693, "Prove that 4 vector potential is really a 4 vector?". The conclusion of samalkhaiat in message #13 is that it is not a 4-vector.
Remarkably, this is also the conclusion I got, reasoning from principles of Euclidean special relativity. Section 6 of the article "http://www.euclideanrelativity.com/4vectors/node6.html" " suggests that the classical potential 4-vector is in fact an Euclidean 4-vector instead of a Minkowski 4-vector.

samalkhaiat's conclusion is that there is a gauge-related term in the transformation.

 

[Cuetek]

As CarlB suggests, the fact that Mortimer's theory suggests changes to GR may well be an attractive aspect. I think we are at a point in physics that is similar to the transition between the Ptolemaic view and the post-Copernican view. The Ptolemaic model was an exquisitely complicated system that, while remarkably functional, turned out not only to be more complicated than necessary but flawed exactly where it was most complicated. It was dramatically simplified by Copernican models explanations of retrograde aspects. I think the same thing will happen to string theory (and perhaps inflation, too) in the near future by the recognition of a more plausible broad-scale disposition of the material universe.

But what it won't be is a unified theory of everything. It will be a temporary consolidation and simplification that will continue to evolve into more complicated theories just like the Copernican model continued to evolve. Young Kmarinas' perspective kind of speaks to the point.

I had the same idea. I have a theory of a fractal universe (so far mostly qualitative) which agrees with these statements, which proposes that our visible universe of galaxies and stars is a boson (specifically a gluon) and that by looking at the "edge of the universe" we may be looking at the surfaces of very large black holes (specificially the surfaces of fermions (quarks)).

Presuming a fractal symmetry in the universe is, in my estimate, an area rich in potential for evolving the standard model because it suggests and ongoing hierarchy. But to presume that hierarchy to be identically repeating (ie, the quark can be identically found at both extra-visible-universe scales and sub-nuclear scales, etc, etc) is similar in many ways to a common failing found in most of our prior cosmologies.

Trying to limit the scalar diversity of the universe to what we humans can see of it at any given time is typically where our prior cosmologies were corrected by their succeeding cosmologies. The Copernican crystal sphere terminus was expanded by Milky Way island universe terminus, which was expanded by the contemporary "finite but unbounded" space/time model, which is less egregiously mitigated by an infinite presumption of the cosmological principle. All of these terminating criteria try to depict a universe that can be completely characterized (if not examined) using only the data at hand. With the exception of the most recent version of an infinitely homogeneous universe, they all failed in precisely the extent to which they strived to to limit the scalar diversity of the universe as it might evolve beyond our ability to examine at any given time. We should presume that the universe cannot be completely depicted from the perspective of something stuck inside it.

In kmarinas' fractal disposition above, I would suggest that the fractal symmetry he depicts as absolute and repeating represents this same type of effort to have the universe conform completely to the data at hand. The fractal behavior of the universe is more likely to be only locally transmitted up and down the scale before evolving into new symmetries across an ongoing, open-ended material hierarchy.

That is, if the enigmatic obits of electrons around the atomic nucleus is only loosely reflected by the very deterministic obits of the planets around stars, so too might the fractal symmetry kmarinas suggests as identically repeating be found evolve its symmetry across any scalar interval. (the black hole may be only vaguely "quark-like" at even greater mega-scales beyond.)

Change is permanent, evolution is inherent. But change is also symmetrical and continuous across all spectra. So while we will always be able to expand our knowledge, we will probably never be able to assert a final deposition and should formally recognize this prospect in our models. It might seem very depressing, but imagine how we'd feel if one day we found out we'd figured it all out and there was nothing left to discover. Now, that would be depressing.

-Mike