Comparison of Special Relativity with a Galilean "preferred frame" theory

I'm not convinced we should dismiss what we would observe as being trivial; Science is ALL about observation.

 

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Not exactly, read below

I didn't mean absolute position but rather relative position; this would account for your toy example. So is translation invariance of the rate of clocking sufficient to imply SR's first postulate?

 

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Nobody is saying what we observe is trivial. We're just saying that Terrell rotation is not really analogous to the projection of a 3D object along different planes that are rotations of one another. Terrell rotation is a result of relativistic length contraction combined with a second visual time-delay effect that you could well have anyway independently of relativity. The relativistic length of a moving object is also in principle measurable anyway (standing in one place and just looking at an object isn't the only way of 'measuring' it) and is the quantity that will determine e.g. whether a pole gets through in the "pole-barn paradox", similar to the way that projections of a 3D object will determine whether it will fit through a doorway.

 

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Przyk beat me to it. I was going ask who said it was trivial, and mention that measurement is how we verify whether observation is actual or apparent. Terrell rotation is definitely the latter. Even though an approaching object would be subject to length contraction, the Terrell effect describes the visual effect of being elongated, as the light from the leading edge would meet our eye at the same time as older light from the trailing edge (further away at the time of emission).

 

How do you define "relative position" invariance as opposed to "absolute position" invariance?

How does my toy example violate your principle of proper time invariance? How does Newtonian mechanics + electromagnetism violate your principle of proper time invariance?

Translation invariance in general doesn't imply SR's first postulate. They're just different symmetries. The only logical 'constraint' on symmetries is that the set of all possible symmetries should form a group (meaning things like the composition of two symmetries is also a symmetry, and so on). The set of all translations already forms a group, so it is impossible to derive further symmetries from it.

 

You may not have recognized it (or perhaps you do, however you seemed to be dismissive of the idea), but you are basically reiterating what I said earlier about foreshortening.

Foreshortening (minus parallax) is a projection. Take the pole-barn paradox and replace the barn with a hole in the ground which is shorter than the pole; now there can be no question about whether doors are open/shut at the same time. However, we will find that all parties agree that the pole still fits in the hole because (depending on the frame of measurement) the pole is either length contracted or rotated.

 

You've misunderstood my response. I am saying the idea is fine just left at length contraction; you don't need to complicate it with Penrose-Terrell effects to make it "more correct". A Lorentz boost is much more closely analogous to a rotation than a collective transform describing a Lorentz boost combined with Penrose-Terrell effects. This isn't denying Penrose-Terrell effects or dismissing them as trivial or anything; it's just saying that they're best left out of the analogy with rotation.

 

Lorentz boosts (likewise for Translations, Rotations and Poincaré transforms) is about the relation between coordinates of the same object in two different inertial coordinate systems. \(X'^{\nu} = \Lambda_{\mu}^{\nu} X^{\mu}\)
Penrose-Terrell effects are about the coordinates of the image of the object on a retina, film or CCD device in a camera, based on the geometric effect of light at different distances needing different amounts of time to reach the imaging surface. Similar geometric effects cause classical Doppler shifts and explain why relativistic Doppler shifts are not just explained by time dilation. In astronomy, some objects apparently move with a angular speed so high that at their distance they seem to be somewhat superluminal, but this too is a geometric effect when most of their movement is along the line of sight. \(|v| = \frac{ \left| \Delta \vec{x} \right| }{\left| \Delta t \right|}\)
The two classes of effect (change of coordinate system, geometric effects in a single coordinate system) do not fundamentally interact and are easily separated in experimental design or compensated for in analysis.

 

I'd like to clarify a point to be sure I am not mistaken. While the Lorentz boosts are certainly not Euclidean, aren’t the results of transformed coordinates Euclidean? In other words where x, y, z, are transformed to x’, y’, z’ aren’t both coordinates Euclidean from their own frames perspective while the transformation is not?

Maxila

 

I think that if the time coordinate is held constant, then the spatial coordinates form a Euclidian space.

Space (in a uniform gravitational field) is Euclidian, Spacetime is not.

(But take with salt - I'm no expert)

 

Relative position invariance should subsume absolute position invariance because it would cover moving frames, yes?

I believe that proper time invariance implies a symmetry; the measured value of c determines whether is is Lorentz or Galilean. Newtonian mechanics + electromagnetism is actually a contradiction (i.e. is not proper time invariant) because electromagnetism ultimately is a measurement of a finite value of c.

I'm asking the reverse question: can we derive the entire group of symmetries under consideration from what we are calling proper time invariance?

 

Let's try something really simple. Questions:

1. Define "relative position".
2. Define "relative position invariance". (przyk already asked you this)
3. Define "absolute position".
4. Define "absolute position invariance". (przyk already asked you this)
5. "Moving frames" with respect to what?
6. "Moving frames" as opposed to "non-moving frames"?
7. Define "proper time invariant".
8. What does it mean that "Newtonian mechanics + electromagnetism is actually a contradiction (i.e. is not proper time invariant)"
9. Did you read about the above terms somewhere or did you make them up all by yourself again?

 

I think you can if you assume space-time is a real (3+1)-dimensional manifold and that the finite form of the relativistic invariant interval holds (which is path-invariant and shows the curvature of the manifold is zero). Then again, you might derive the double-cover unless you add an axiom that a rotation of 360 degrees leaves everything the same (which is not the case in physics).

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

 

You haven't answered my question. How are you defining "absolute" position invariance? How are you defining "relative" position invariance? What exactly is the distinction between the two?

I don't know about your own definitions, but translation symmetry in physics technically means that for any evolving system that is a solution to the laws of physics (whatever they might be), a translation of that solution is also a valid solution.

You still haven't answered my question: how do my toy example and Newtonian mechanics + electromagnetism violate your principle of proper time invariance? The latter does not satisfy the relativity principle. The former also doesn't for most velocity-dependent clock rates (with the exception of the Galilean (constant) and relativistic clock rates).

By the way if you just want a symmetry - any symmetry - then you are effectively already asserting one (the defining property of a symmetry in general is that it is a transformation that leaves something invariant). But the relativity principle doesn't refer to just any symmetry. It refers to a specific type of symmetry with respect to a velocity-dependent transformation.

Following on from what I said above, you are getting ahead of yourself here. The Galilean and Lorentz transformations aren't the only allowed symmetries in physics. The sort of result you cited earlier refers to something much narrower than that: the Galilean and Lorentz groups are the only symmetry groups that include velocity-dependent transformations, include only linear transformations, include the rotation group, exclude scaling symmetry, and are compatible with causality (meaning they keep past and future distinct at least to some extent; this rules out 4D rotations). The string of assumptions needed to "derive" the Galilean and Lorentz transformations usually goes something like that.

How so? It doesn't help that you still haven't defined what you mean by "proper time invariant" very clearly.

I don't see what this is supposed to mean. Electromagnetism implies that electromagnetic radiation propagates at a finite speed predicted by the theory, in coordinate systems in which Maxwell's equations take their canonical form, and little more than that. Electromagnetism alone implies nothing about processes that aren't purely electromagnetic in nature. Electromagnetism as a theory can coexist just fine with Newtonian gravity for example; you just don't have a relativity principle in that case, although you still have space and time translation as a more restricted symmetry.

Based on the counter-examples I gave you, which satisfy your principle of proper time invariance just fine as far as I can tell, obviously the answer is no (and I don't see why you are calling this the "reverse question" because that is exactly the question I was addressing).

If you mean something different by "proper time invariance" than what I've understood from your posts then you're going to have to be much more specific about what that's supposed to mean. Obviously it's impossible to derive anything from an idea that's too vague and imprecisely defined for anyone to be able to actually do anything with it.

The counterexamples I gave you are intended to give you the opportunity to define more carefully what you're talking about, by the way. Seriously, use them for that purpose. Give an example of an observable prediction they might make that violates this principle of time invariance of yours and explain why it violates that principle as you understand it. That will rule out things you're not talking about and will help narrow down what you are talking about.

 

RJBeery, when are you going to answer the questions relating to your claims?

 

I'll probably respond today but it won't be to anything you've posted. I'm not here to share my ideas with Tach, I'm here to better my understanding of the world and explore ideas. I frankly don't care about your understanding. And I'm not ignoring this thread, I'm digesting the following paragraph from Przyk:

 

It is not what I posted, it is the fringe stuff YOU are posting. Please explain your claims, they are so off the wall, they require that you explain how you came about them. The terms you use cannot be found in any mainstream media, so please explain them or retract them.

 

One more question added to the list:

10. What gives you the idea that "all available methods for measuring the speed of light are themselves dependent on the speed of light"? This is an idea that Farsight also advocates, what gives you the idea that it is true?

 

The questions were posted by you, and I'm generally not going to address them. You had an aneurysm about my "proper time invariant" phrase, but look at this wiki paragraph on Poincare Groups:

You seem to be smart enough to understand what I mean, but it's clear that you're just on this forum to pick fights.

 

Why are you running away? You make fringe claims, post crank stuff, you should try to explain them. Please do so, or retract them.
Here is the list:

1. Define "relative position".
2. Define "relative position invariance". (przyk already asked you this)
3. Define "absolute position".
4. Define "absolute position invariance". (przyk already asked you this)
5. "Moving frames" with respect to what?
6. "Moving frames" as opposed to "non-moving frames"?
7. Define "proper time invariant".
8. What does it mean that "Newtonian mechanics + electromagnetism is actually a contradiction (i.e. is not proper time invariant)"
9. Did you read about the above terms somewhere or did you make them up all by yourself again?
10. What gives you the idea that "all available methods for measuring the speed of light are themselves dependent on the speed of light"? This is an idea that Farsight also advocates, what gives you the idea that it is true?