question about reference frames & time dilation

[Farsight]

Magic? Magic? Aw forget it.

[insane_alien]

Farsight, you made the claim, not us. what was it you said once, 'if you can't explain it then you don't understand it'? i think it was something like that.

[Tom Mattson]

Whenever Einstein's theory of relativity is explained, it always starts out with the premise that the laws of physics are the same no matter what frame of reference you observe them in. How does this idea lead to the dilation of time?

 

Those are the two postulates of special relativity. I'm not sure who "they" are that are omitting the second postulate; it appears in all the treatments of SR that I recall reading.

 

In all the full treatments' date=' I'm sure. To name one person, there's Richard Wolfson of Middlebury College who, in an introductory lecture on Relativity, says that all the bizaar and non-intuitive phenomena that SR predicts follows just from the fact that the laws of physics are the same in all inertial frames. He mentions nothing of the constant speed of light.

[/quote']

 

There's a discussion of this issue in Gravitation and Spacetime by Ohanian and Ruffini when they talk about the covariance of physical laws. They argue that SR can be reduced to a single postulate if we are more economical about our definitions. Einstein's relativity postulate says, in modern parlance, that the laws of physics are covariant. That is, they have the same mathematical form in every inertial frame. This says nothing about the fundamental constants that appear in the equation. For instance you could have something that looks like [math]y=kx[/math], and if it's covariant then all that's guaranteed under a coordinate transformation is that you will get [math]y^{\prime}=k^{\prime}x^{\prime}[/math]. So the relativity postulate guarantees that Maxwell's equations have the same form in every inertial frame. It's the speed of light postulate that fixes c.

 

Ohanian and Ruffini say that if both the form and the fundamental constants (not just c, but also h, e, etc...) of an equation are preserved under Lorentz transformations then we can define that equation as Lorentz invariant, which says more than Lorentz covariance.

 

Thus they reduce the postulates of SR from 2 to 1: The laws of physics are Lorentz invariant.

[swansont]

There's a discussion of this issue in Gravitation and Spacetime by Ohanian and Rufini when they talk about the covariance of physical laws. They argue that SR can be reduced to a single postulate if we are more economical about our definitions. Einstein's relativity postulate says, in modern parlance, that the laws of physics are covariant. That is, they have the same mathematical form in every inertial frame. This says nothing about the fundamental constants that appear in the equation. For instance you could have something that looks like [math]y=kx[/math], and if it's covariant then all that's guaranteed under a coordinate transformation is that you will get [math]y^{\prime}=k^{\prime}x^{\prime}[/math]. So the relativity postulate guarantees that Maxwell's equations have the same form in every inertial frame. It's the speed of light postulate that fixes c.

 

Ohanian and Rufini say that if both the form and the fundamental constants (not just c, but also h, e, etc...) of an equation are preserved under Lorentz transformations then we can define that equation as Lorentz invariant, which says more than Lorentz covariance.

 

Thus they reduce the postulates of SR from 2 to 1: The laws of physics are Lorentz invariant.

 

So the information presented (if done properly) depends on whether you are getting an historical treatment, where you will get the two postulates, or a more modern view, where you get the statement about Lorentz invariance. It seems to me the former is better for introductory circumstances.