Some conceptual questions on SR

[Reshma]

I need to clear some conceptual doubts in the Special theory of relativity. So could anyone explain them in context to the following questions:

1. The speed of light in glass is 2.0 x 10⁸m/s. Does it violate the second postulate of SR in any way?

2. A uniformly moving train passes by a long platform. Consider the events 'engine crossing the beginning of the platform' and 'engine crossing the end of the platform'. Which frame (the train frame or the platform frame) is the proper frame for the pair of events?

3. An object may be regarded to be at rest or in motion depending on the frame of reference chosen to view the object. Because of length contraction at relativistic speeds the same rod may have two different lengths depending on the state of the observer. Am I right?

4. Mass of a particle depends on its speed. Does the attraction of the Earth on the particle also depend on the particle's speed?

 

[russ_watters]

1. The speed of light in glass is 2.0 x 10⁸m/s. Does it violate the second postulate of SR in any way?

No. That is an apparent speed caused by interaction with the glass. Photons themselves only move at C.

2. A uniformly moving train passes by a long platform. Consider the events 'engine crossing the beginning of the platform' and 'engine crossing the end of the platform'. Which frame (the train frame or the platform frame) is the proper frame for the pair of events?

There is no such thing as a "proper frame". Either will work depending on what you are trying to accomplish in the analysis.

3. An object may be regarded to be at rest or in motion depending on the frame of reference chosen to view the object. Because of length contraction at relativistic speeds the same rod may have two different lengths depending on the state of the observer. Am I right?

Yes.

4. Mass of a particle depends on its speed. Does the attraction of the Earth on the particle also depend on the particle's speed?

Not sure...

 

[gurkhawarhorse]

I need to clear some conceptual doubts in the Special theory of relativity. So could anyone explain them in context to the following questions:

1. The speed of light in glass is 2.0 x 10⁸m/s. Does it violate the second postulate of SR in any way?

u know what, i heard that electrons travel faster than light in impure water if it is made conductive(as 100% pure water is non-conductive at least i think so ).

 

[Doc Al]

Just to add to Russ's comments.

2. A uniformly moving train passes by a long platform. Consider the events 'engine crossing the beginning of the platform' and 'engine crossing the end of the platform'. Which frame (the train frame or the platform frame) is the proper frame for the pair of events?

In the train frame, the two events happen at the same location. Thus the train frame will measure the proper time between those events. (If that was what you were getting at.)

4. Mass of a particle depends on its speed. Does the attraction of the Earth on the particle also depend on the particle's speed?

See this thread: https://www.physicsforums.com/showthread.php?t=84366

 

[HallsofIvy]

3. An object may be regarded to be at rest or in motion depending on the frame of reference chosen to view the object. Because of length contraction at relativistic speeds the same rod may have two different lengths depending on the state of the observer. Am I right?

Russ Watters answered this "yes", but I am going to pick a nit. I would be inclined to say "No, that is not right. The same rod may have an infinite number of different lengths since an observer may have an infinite number of different speeds with respect to the rod."

 

[pervect]

I need to clear some conceptual doubts in the Special theory of relativity. So could anyone explain them in context to the following questions:

1. The speed of light in glass is 2.0 x 10⁸m/s. Does it violate the second postulate of SR in any way?

No. Why would you think it would?

2. A uniformly moving train passes by a long platform. Consider the events 'engine crossing the beginning of the platform' and 'engine crossing the end of the platform'. Which frame (the train frame or the platform frame) is the proper frame for the pair of events?

I don't understand the question. Relativity has technical notions of "proper time" and "proper distance", and even "proper acceleration", but there isn't any technical notion of "proper frame". You can do your calculations in any frame you like, then convert the results to any other frame via the Lorentz transform. Any frame is as good as any other. This is the principle of Lorentz covariance.

I could define proper time and/or proper distance if that's your real question, but I don't want to get off on a tanget if it isn't.

3. An object may be regarded to be at rest or in motion depending on the frame of reference chosen to view the object. Because of length contraction at relativistic speeds the same rod may have two different lengths depending on the state of the observer. Am I right?

Right, length is an observer dependent quantity. The Lorentz interval of the rod is a (the!) quantity which is the same for all observes - the length of the rod is not the same for all observers.

4. Mass of a particle depends on its speed. Does the attraction of the Earth on the particle also depend on the particle's speed?

The short answer is yes. A longer more detailed answer is

here

To answer the question, it's necessary to define how one compares the force on a moving object to the force on an unmoving object. This could be a long discussion in and of itself, especially if you are not familiar with relativity. I've attempted to shortcut this long discussion by using the force generated by a charge (the electric field) as a reference standard. The thought experiment is a simple way of showing that gravitational force must transform differently than electromagnetic force, given the principle of equivlalence.

More advanced treatments of the topic requrie general relativity rather than special relativity.

 

[mitchellmckain]

After making the post that refutes the value of the idea of mass increasing at relativistic velocities, I feel that I should respond to the following point to avoid confusion.

4. Mass of a particle depends on its speed. Does the attraction of the Earth on the particle also depend on the particle's speed?

Gravity couples to energy not mass. And since the energy of the particle increases according to gamma m c^2, then it is clear that the gravitational force does increase just as if the mass had increased by the factor gamma.

 

[Pengwuino]

No. Why would you think it would?

I think he forgets that its 300,000,000km/s in a vacuum

 

[Reshma]

I think he forgets that its 300,000,000km/s in a vacuum

Its 300,000,000m/s . (BTW, it is her.)

 

[Reshma]

I don't understand the question. Relativity has technical notions of "proper time" and "proper distance", and even "proper acceleration", but there isn't any technical notion of "proper frame". You can do your calculations in any frame you like, then convert the results to any other frame via the Lorentz transform. Any frame is as good as any other. This is the principle of Lorentz covariance.

I could define proper time and/or proper distance if that's your real question, but I don't want to get off on a tanget if it isn't.

I'm sorry, I would like to slightly modify my original question . Ok, these are some technical definitions of proper time & length I found in my text.

Proper time--->When two events occur at the same location in an inertial reference frame, the time interval between them, measured in that frame, is called the proper time interval or proper time. Measurements of the same time interval from any other inertial frame are always greater.

Proper length--->The length L₀ of an object measured in the rest frame of the object is its proper length or rest length. Measurements of the length from any reference frame that is in realtive motion parallel to that length are always less than the proper length.

Now what is the proper length and proper time in context to my question?

 

[Reshma]

u know what, i heard that electrons travel faster than light in impure water if it is made conductive(as 100% pure water is non-conductive at least i think so ).

Oh yes! That's how you get the Cerenkov Radiation by accelerating charged particles faster than light in a material medium. I suppose this answers my first question !

 

[Doc Al]

Now what is the proper length and proper time in context to my question?

As I mentioned in my earlier post, your two events ('engine crossing the beginning of the platform' and 'engine crossing the end of the platform') take place at the same location in the train frame. So the train frame will measure the proper time between those events. Those two events also occur at opposite ends of the platform. The platform frame will measure the distance between those events as the proper length of the platform.

Does this help?

 

[pervect]

I'm sorry, I would like to slightly modify my original question . Ok, these are some technical definitions of proper time & length I found in my text.

<snip>

Now what is the proper length and proper time in context to my question?

2. A uniformly moving train passes by a long platform. Consider the events 'engine crossing the beginning of the platform' and 'engine crossing the end of the platform'. Which frame (the train frame or the platform frame) is the proper frame for the pair of events?

Look again at the definitions you quoted.

Rather than draw ascii diagrams, let us set up a coordinate system for the platform (first), then the train.

Consider the platform frame. We will call the beginning of the platform x=0, and the end of the platform x=L. Then we have

The engine passes x=0 at some time t1, and the engine passes x=L at some time t2, where t2 is > t1.

Thus the interval between the two events is not a proper interval, because neither the position coordinate nor the time coordinate is the same.

Now consider the train frame.

We will call the coordinate of the engine x=0. Then we have

The beginning of the platform crosses x=0 at some time t1. The end of the platform crosses x=0 at some time t2. We also have t2>t1. Because x=0 for both events, the interval t2-t1 is a proper time interval.

 

[pervect]

As I mentioned in my earlier post, your two events ('engine crossing the beginning of the platform' and 'engine crossing the end of the platform') take place at the same location in the train frame. So the train frame will measure the proper time between those events.

I agree

Those two events also occur at opposite ends of the platform. The platform frame will measure the distance between those events as the proper length of the platform.

I have to disagree here, because the engine will cross the end of the platform at a different time than it crosses the beginning of the platform.

 

[Doc Al]

I have to disagree here, because the engine will cross the end of the platform at a different time than it crosses the beginning of the platform.

I see your point. It's probably a good idea to define length as the distance between points measured at the same time, even in the rest frame. (Even though, since the platform is not moving with respect to itself, the distance between those two events as measured in the platform frame will equal the proper length of the platform.)