Lorentz-Einstein transformation

[Meir Achuz]

Now to some physics. There are two points of view that clash in this thread. I see them as characteristic of Asher and (to be immodest) me.
I will give some examples: When I teach Physics 121 with calculus I derive
(1/2)at^2 by the complicated mathematical step of \int x^n=nx^{n-1}, which the class (those who have the prerequisite) understands immediately.
When I teach Physics 101 without calculus, I go through a tortuous process of "physical reasoning" with diagrams and handwaving. Even if some of the class understand this by the end, I am not sure if I do. In any event when one of the more interested students raises his hand and asks the profound question "Will this be on the test?", I answer: "Just remember (1/2)at^2. Don't worry about where it comes from." So much for the "physical" derivation. The moral for me is, if you know the mathematics, why not use it. Another example is studying an ellipse in a frame where there are xy terms in the equation. You can do all of your (rather hard) work in that frame or you can Lorentz transform (in this case rotate) to the frame without the xy terms.

Similarly, given a SR question, you can either try to derive the result as if you did not know the 4D rotation called the "Lorentz transformation", or, using the LT, you can get L=L/\gamma by just turning your head in 4-space. Being proud of not using the LT is like being proud of recognizing your friends when you stand on your head. The proper use of SR is to look at things in whatever frame they are simplest (usually the rest system).
If the object is not at rest, just look at the object at rest, and then Lorentz transform to any moving system you want.

The proper approach in physics is to try to derive specific results from general principles. Asher (Is this also true of BR?) thought this presented no challenge and was a pedestrian approach. I would be ashamed of deriving the LT from a specific result and not from the general principle of SR (really just extended Galilean invariance) that physics is the same in all Lorentz systems. Once you know the LT, why try anything else?
Now, I am out of this thread.

 

[nakurusil]

.


The proper approach in physics is to try to derive specific results from general principles. Asher (Is this also true of BR?) thought this presented no challenge and was a pedestrian approach. I would be ashamed of deriving the LT from a specific result and not from the general principle of SR (really just extended Galilean invariance) that physics is the same in all Lorentz systems. Once you know the LT, why try anything else?
Now, I am out of this thread.

You couldn't have said it any better.

 

[bernhard.rothenstein]

lorentz transformation

The proper approach in physics is to try to derive specific results from general principles. Asher (Is this also true of BR?) thought this presented no challenge and was a pedestrian approach. I would be ashamed of deriving the LT from a specific result and not from the general principle of SR (really just extended Galilean invariance) that physics is the same in all Lorentz systems. Once you know the LT, why try anything else?
Now, I am out of this thread.[/QUOTE]
Hi Meir
Please do not leave the table, the pot is still on it. Concerning Peres' paper I would mention that it was published in Russian by Usp. Fiz. He is in a very good company there being often quoted. Long time ago, in a letter I have tried to convince him that Figure 7 in his paper is not quite correct. He never answered!
Each equation Peres derives without using the LT leads directly to them. So I have shown in a Note in Am.J.Phys. that the addition law of relativistic velocities derived not only by Peres without using the LT, leads directly to the LT. The paper is quoted by physicists involved in the teaching of SR. I am not ashamed having written it. I have also shown that using the aberration of light formula we can derive the LT for the space-time coordinates of the same event generated by a light signal. If the event generated in I is E(r,theta,t=r/c) and E'(r',theta',t'=r'/c) in I' using polar space coordinates. Invariance of distances measured perpendicular to the direction of relative motion
rsintheta=r'sintheta' and the aberration of light forumula leads directly to the LT. Is there something for being ashamed. Starting to derive the LT we should put the Principle of Relativity at work. Einstein starts with his clock synchronization procedure even if does not mention it explicitly. Why not put them to guide us through a thought experiment I liked so much to discuss with my students as Peres does?
Did you ever help youngsters solving arithmetic problems? Was you ashamed solving them without using algebra they did not know? Some time the task is not very easy, but revarding.
At the end of my message I thank you for your participation at my humble thread, which started not in the spirit of sine ira et studio or imho. If something in my message is not polite enough is due only to the fact that English is not my first language. I find some of your sentences to dense.
I have started a thread "With the Lorentz transformation in hands". Would you aggree with the fact that LT properly used solves all the problems of special relativity theory?

 

[JM]

Clock rates

Not sure what you are saying here, but if you are thinking that once you correct for the travel time of the light that you will find that all clocks run at the same rate--not so.

Here's what I'm thinking. Following Einstein, the LET expresses the coordinates of a light ray as related to two coordinate systems. In order to satisfy the Light Postulat two corrections are required to the ordinary transforms, an adjustment to the time coordinate, appearing as the second term in the time equation, and a 'magnification factor', which he calls beta. After accounting for these corrections the clocks run at the same rate. A recent thread discussed the need for mechanical objects to obey the light postulate. My conclusion is that they don't, so mechanical watches would run at the same rate no matter what their speed. Then note that the light postulate requires c to be the same in both coordinates, i.e. x/t = x´/t´. Picture this as t being the time it takes for a light ray to travel a distance x. To make the comparison and get the same number for c requires that the same units be used for both x,t and x´,t´ systems.
What do you think?

 

[Doc Al]

Here's what I'm thinking. Following Einstein, the LET expresses the coordinates of a light ray as related to two coordinate systems. In order to satisfy the Light Postulat two corrections are required to the ordinary transforms, an adjustment to the time coordinate, appearing as the second term in the time equation, and a 'magnification factor', which he calls beta. After accounting for these corrections the clocks run at the same rate.

You are basically saying: If you ignore the effects of special relativity, clocks run at the same rate. Why is that of interest?

A recent thread discussed the need for mechanical objects to obey the light postulate. My conclusion is that they don't, so mechanical watches would run at the same rate no matter what their speed.

That's an incorrect conclusion. All clocks (mechanical or otherwise) exhibit the same velocity-dependent effects. If they didn't, that would be a violation of the principle of relativity.

Then note that the light postulate requires c to be the same in both coordinates, i.e. x/t = x´/t´. Picture this as t being the time it takes for a light ray to travel a distance x. To make the comparison and get the same number for c requires that the same units be used for both x,t and x´,t´ systems.

So?

 

[MeJennifer]

Actually I agree with the idea that inertial clocks do run at the same rate (assuming the clocks are accurate clocks of course). Obviously that would not be the case for the moment a clock accelerate, but most of the time that influence is assumed negligeable.

If we consider the path of two clocks between two distinct space-time events their accumulated times may however not be identical. The difference in path length in space-time determines the difference in accumulated time.