Resnick's Introduction to Special Relativity

[Angelos]

Hi,
I'm learning special relativity with the book Introduction to Special Relativity by R. Resnick, but unfortunately he doesn't provide answers to the questions (not problems). So I would like to aks you if you could correct some of my answers.

Homework Statement

1. Can a particle move through a medium at a speed greater than the speed of light?
7. Discuss the following comment, which applies to most of the figures: "The figure itself belongs to some particular reference frame, that is, the picture represents measurements made in some particular frame." Can we look omnipotently at moving frames, wave fronts, and the like, with-out realizing first what frame we are in?
10. Does the Lorentz-Fitzgerald contraction hypothesis contradict the classical notion of rigid body?

The Attempt at a Solution

1. I don't see any reason why it couldn't. The speed limit is the speed of light in vacuum and so theoreticaly some particle can travel faster than the speed of light in that medium. (I'm definitely not sure if it is possible practically...?)
7. I don't really understand what "omnipotently" means (English is not my native language) and generally I don't really understand the question. I would say we firstly have to measure the speed relative to the moving frame and thus realize what frame we are in (relatively to the moving frame). So the answer is we can't.
10. I think it does. Simply because the length of an object is dependant upon its velocity. That is in cotradiction with the notion of a rigid body.Thank you very much for your help.

 

[lzkelley]

1) for the most part you're right; the speed limit for a medium is the speed of light in that medium (which is determined by the index of refraction). I would say that the answer is no, "a particle can NOT move through a medium at a speed greater than the speed of light" - because i would assume they are referring to the speed of light - in the medium!
But your understanding of the situation is correct, and that's what matters. Look up cherenkov radiation for situations when this occurs (very important for astrophysics!).

7) Omnipotent = all-powerful, its usually the term used to describe a god in religions; all powerful, all knowing, unbeatable .. etc etc. So they don't mean it literally in this problem.
Your answer is correct. They are essentially asking whether or not an observer needs to consider their relative reference frame... and of course they do.

10) you got it.

 

[Moetasim]

I am happy to assist with your understanding of special relativity.

1. In special relativity, the speed of light is considered to be the maximum speed that any object can travel. This is a fundamental principle and cannot be exceeded, regardless of the medium the object is traveling through. Therefore, no particle can move through a medium at a speed greater than the speed of light.

7. The comment is pointing out that each figure in the book represents measurements made in a specific reference frame. This means that the measurements and observations in the figure are only valid in that particular reference frame. We cannot simply look at a figure and know what frame it represents, we need to know the frame first in order to interpret the measurements correctly.

10. The Lorentz-Fitzgerald contraction hypothesis does not contradict the classical notion of a rigid body. In classical mechanics, a rigid body is defined as an object that does not change its shape or size when subjected to external forces. In special relativity, the length of an object is affected by its velocity, but this does not mean that the object is not rigid. The concept of a rigid body still holds in special relativity, but it is described differently due to the effects of relativity.