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

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All I did was help you with some equations.

 

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The direction doesn't really matter when finding length contraction. This is because the horizontal distance the light travels from both frames are the same. It is just that one is seen to travel at an angle when the other does not, but the total distance perpendicular to the direction of motion is the same if you don't consider the greater distance made by it seen traveling at an angle. So, since I started with d for distance from the equation v = d/t, and it being the real distance as measured by their measuring rods;

\( d' = c t' \) The distance the beam is seen to travel

\( d' = c t sqrt {1 - {v^{2}/c^{2}}} \) Substitute the time dilation equation in for t'

\( d' = d sqrt {1 - {v^{2}/c^{2}}} \) Substitute c t for d, since d = c t

I have seen a derivation a while back of the lerentz transformation a while back, (should have wrote it down), but it was worked with a different method, but I think it is possible from a right triangle, they do this by finding the relation of vectors from an orgin but I have derived this equation from just a right triangle. The time dilation equation that Lorentz and Einstein agreed upon as being correct was basically the one I gave.

 

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Well Tach does have a point here. With time dilation you're comparing the rate of one ("moving") clock with the time standard of an entire reference frame. So I really think it can be a bit misleading to say things like "time slows for moving observers" or talk about the "(relative) rate of time passage" as if there were a single such relation. This is especially an issue if what you're saying is going to be read by someone who doesn't already have a good grounding in relativity (the infamous "twin paradox" stems from this confusion for example).

Of course, Tach understands this and I would have assumed you did too.

 

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Too late, you already helped me, so when (not if) the wonderful world of physics presents me with a check for a bazillion dollars for saving the universe, you will be justly compensated, I promise.

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The same intro class that you need to take.

 

Looking back how this discussion got started:

I don't agree with the way you're formulating things (in particular I don't think it's really helpful to think of relativity in terms of "everything depends on c"), but I think you're touching on something that is already known.

Stated more concisely, the two postulates you quoted are asserting that there is a velocity dependent symmetry of the laws of physics that leaves the speed of light invariant. What I get the impression you're touching on is that this "definition" doesn't uniquely characterise the Lorentz group. The obvious counter-example is that rescaling all the space and time coordinates by a given factor, i.e.

\( \begin{eqnarray} t &\mapsto & \lambda t \\ x &\mapsto & \lambda x \,, \end{eqnarray} \)​

also leaves the speed of light invariant, so combining a Lorentz transformation with any global rescaling of this type will also give you a transformation that preserves c (see e.g. the Voigt transformation, which is just the Lorentz transformation divided by \(\gamma\)).

So if you define special relativity as the (meta) theory stating that all the laws of physics are Lorentz invariant, then, strictly speaking, relativity by that definition does not uniquely predict the standard length contraction and time dilation formulae. You also need to use that rescaling is not a symmetry of physics.

 

What if all of the laws of physics was not Lorentz invariant? Then wouldn't you be able to tell if you where traveling at a constant speed faster or slower than some other constant speed? In other words, wouldn't there have to be an absolute frame in order for all the laws of physics to not be Lorentz invariant? The laws of physics would have to be the same for all constant speeds, so then I think I would then be able to know that the laws of physics are Lorentz invariant for all uniform motion. Otherwise we would be able to distinguish from one frame or another, and then it would give tell, tell signs of an absolute frame, like this object is actually traveling faster than this other object and then they all wouldn't be able to assume they are at rest.

 

To apply Lorentz you have to know a velocity already don't you? They can't all be a rest!

 

According to Einsteins postulates of relativity, they all can. Laws of physics not being Lorentz invariant would go against this postulate. The problem is that you can only say that your speed is relative to something else. There is no way to know if that something else is actually at rest or just traveling at a constant speed. So then anything traveling at a constant speed can say that it is at rest and that something else is traveling at a velocity relative to it.

It is a concept from Galilean Relativity, Einstein followed with this in the Special Theory saying that it also claims that any object can say that it is at rest while traveling at a constant speed. He didn't introduce an absolute frame that says, oh this object is really going faster because its laws of physics changed. This gives rise to the twin paradox. Both twins are equally valid in saying they are at rest at the start of the situation that creates this paradox.

 

So whoever thinks they are at rest, thinks the other is in motion. So they aren't "all at rest". But neither can be deterministic about it, i.e. if they were in communication they might always disagree who is at rest, in fact they could be both moving but they can't be both at rest.

 

I'm not following the problem with rescaling; is there something obvious I'm overlooking? Also, to be clear, I've changed my position from "everything depends on c" to something like "everything depends on the invariance of the rate of proper time passage". I'm suggesting that SR's first postulate is perhaps equivalent to this, and the second postulate is a consequence of it (and therefore redundant).

After some digging...from here:

 

I already pointed this out to you, see post 163.

 

So you did, thanks. Przyk's posts generally lack the overtly derogatory comments that make me want to skip over the rest of what he's writing.

 

What's funny about this is that you're saying I'm wrong while also pointing out that others have already successfully done what I'm suggesting.

 

You don't even understand the errors that you make. It also takes u a loong time to learn how to correct your statements (the distance between your incorrect post 162 and your corrected post 231 is .... 5 days). You are a very sloow learner.

 

My stance did not change between post 162 and 231, what are you talking about? I was speaking freely in post 162 but made my conclusions at that point. I'm philosophizing about physics and SR and it appears that I'm on the right track if Rinder and Pauli came to the same conclusions, none of which is attributable to your "help".

 

Like I said, you don't even understand your errors.

You are also lying: in post 162 you were talking about adding postulates ...to wit:

...whereas I explained to you that this is not only incorrect but also that there are formulations of SR that rely on one postulate only. Then, there is also the nonsense of "everything that depends on c" that you dropped over the 5 days between 1/31 and 2/5 (between posts 162 and 321). Your problem is that there is a huge chasm between what you pretend to know and what you really know. as long as you continue along the path "this is what I was saying all along", you will never learn. You really need to take the SR 101.

 

No, in post 162 I suggested that the invariance of the rate of proper time needs to be postulated for SR to be complete...THEN I realized that SR's first postulate is possibly equivalent to this; IOW, a constant proper time rate would exhibit consistent inertial physics. I then concluded that the 2nd SR postulate isn't needed at all. Re-read the post, it's there for all to see.

 

You are lying again (or maybe you don't understand what you have been posting, I'll give you the benefit of the doubt). Here is your exact post 162:

How many errors can you count ? (hint: they are all redlined, for your benefit). Post 163 corrects your misconceptions.

 

Christ, I've explained it. It was a developing post (meaning, stream-of-consciousness; my demand for an additional postulate was dropped which is obvious from the quoted text) which came to the conclusion that SR Postulate #1 and the constant rate of proper time passage are equivalent; I also concluded that #1 is sufficient for SR without the need for SR Postulate #2.

Highlighting everything in red just because you didn't read it in your textbook or because you don't understand it doesn't make it wrong.