Special Relativity - clocks on two trains

[PeterDonis]

There is no quote box:

Call it whatever you want: the box that contains "Relativity of simultaneity" and the following few sentences is clearly not just being directly posted, it's in a special box that sets it apart. Stop quibbling and answer my question.

 

[Mike_bb]

Call it whatever you want: the box that contains "Relativity of simultaneity" and the following few sentences is clearly not just being directly posted, it's in a special box that sets it apart. Stop quibbling and answer my question.

You asked me "what's problem?". I have no problem and I wrote that I solved my problem (see above).

 

[PeterDonis]

I wrote that I solved my problem

I'm not sure you have. See below for my comments.

I solved my problem (big thanks to Dale). But if you want to know:
1. Frame F - left train (at rest). Frame F' - right train(moving).

This doesn't make sense. The sort of description that would make sense (and which I think you might intend, but it's not what you said) would be:

Frame F is the frame in which the left train is at rest and the right train is moving (to the right).

Frame F' is the frame in which the right train is at rest and the left train is moving (to the left).

Event1: reading the left clock Δt when distance between left and right clock is Δx

Clocks don't read $\Delta t$. They read $t$. The clock reading is a time, not a difference in time.

Event2: reading the right clock Δt′ when distance between left and right clock is Δx

Distance in which frame? It looks like you are reading a time in Frame F' and a distance in Frame F. That doesn't work.

 

[Mike_bb]

This doesn't make sense. The sort of description that would make sense (and which I think you might intend, but it's not what you said) would be:

Frame F is the frame in which the left train is at rest and the right train is moving (to the right).

Frame F' is the frame in which the right train is at rest and the left train is moving (to the left).

Each frame is associated with one clock.

 

[PeterDonis]

Each frame is associated with one clock.

"Associated" is vague: what does it mean? Both clocks have coordinates in both frames. Saying that a clock is at rest in a frame, as I did, is precise.

 

[Mike_bb]

"Associated" is vague: what does it mean? Both clocks have coordinates in both frames. Saying that a clock is at rest in a frame, as I did, is precise.

My previous comment is wrong. Each frame is associated with 2 clocks (in our example).

 

[PeterDonis]

My previous comment is wrong. Each frame is associated with 2 clocks (in our example).

This isn't any better. What does "associated" even mean?

A frame describes a region of spacetime (in the example under discussion, all of spacetime, as with any inertial frame in SR). Different frames are just using different coordinates to describe the same spacetime. Of course that includes whatever objects, clocks or anything else, we want to include in our scenario, but it's not limited to them.

 

[Mike_bb]

Frame F is the frame in which the left train is at rest and the right train is moving (to the right).

Frame F' is the frame in which the right train is at rest and the left train is moving (to the left).

Frame F is the rest frame but frame F' is moving frame.

 

[Dale]

@Mike_bb a general strategy is to pick one frame, and describe everything in complete detail in that frame. Then transform to another frame and calculate any quantities of interest in that other frame.

 

[PeterDonis]

Frame F is the rest frame but frame F' is moving frame.

This makes no sense. A frame can't be "at rest" or "moving" in any absolute sense. You need to specify what is at rest and moving relative to each frame.

 

[Mike_bb]

This makes no sense. A frame can't be "at rest" or "moving" in any absolute sense. You need to specify what is at rest and moving relative to each frame.

Frame F is "at rest" relative to frame F'. Frame F' is moving relative to frame F.

 

[A.T.]

Frame F is "at rest" relative to frame F'. Frame F' is moving relative to frame F.

 

[Mike_bb]

Ok. It's impossible to say which of frames is at rest relative to another. This is principle of relativity.

 

[Mike_bb]

The state of rest depends entirely on your choice. If two inertial reference frames (IRFs) are moving relative to each other at a constant velocity (for example, a train platform and a passing train), you can:
• Define the platform as being at rest, in which case the train is in motion.
• Define the train as being at rest, in which case the platform (and the entire Earth) are moving in the opposite direction.

 

[PeterDonis]

Frame F is "at rest" relative to frame F'. Frame F' is moving relative to frame F.

These two statements contradict each other.

 

[PeterDonis]

The state of rest depends entirely on your choice. If two inertial reference frames (IRFs) are moving relative to each other at a constant velocity (for example, a train platform and a passing train), you can:
• Define the platform as being at rest, in which case the train is in motion.
• Define the train as being at rest, in which case the platform (and the entire Earth) are moving in the opposite direction.

As far as being able to arbitrarily pick one frame and call it the "rest frame", sure, this is fine. But it contradicts other things you have been saying. Please make up your mind and stop going all over the place. If you want to say that Frame F is the "rest frame" and Frame F' is the "moving frame", as a matter of arbitrary choice, that's fine, but then you need to stop saying other things that contradict it.

And then we can move on to the actual physics, which doesn't care about any of this.

 

[PeterDonis]

Ok. It's impossible to say which of frames is at rest relative to another. This is principle of relativity.

No, it's not. The principle of relativity says that the laws of physics are the same in all frames. Not only does it not say that it is impossible to say which frame is at rest relative to another, that's not even true. If you have specified your scenario properly, you can always tell which frames are or are not at rest relative to which other frames. If you can't do that, it means there's a problem with how you specified the scenario.

 

[Mike_bb]

If you have specified your scenario properly, you can always tell which frames are or are not at rest relative to which other frames.

Non-inertial frame solve this problem, but I've never heard how to differ which inertial frame move relative to another.

 

[PeterDonis]

Non-inertial frame solve this problem

I have no idea what you mean. Using a non-inertial frame doesn't magically guarantee that you've specified your scenario correctly.

I've never heard how to differ which inertial frame move relative to another.

Have you studied basic SR?

If an object at rest in Frame X is also at rest in Frame X', then the frames are not moving relative to each other.

If an object at rest in Frame X is moving in Frame X', then the frames are moving relative to each other.

 

[Doc Al]

Non-inertial frame solve this problem, but I've never heard how to differ which inertial frame move relative to another.

Huh? In your setup, there are three "things": Train 1, Train 2, and the Platform. All move relative to each other. You may choose whichever one you like to be "at rest" for doing a calculation.

 

[Mike_bb]

We can conduct experiments in the trains. Fictitious forces will emerge in moving non-inertial frame.

 

[Doc Al]

We can conduct experiments in the trains. Fictitious forces will emerge in moving non-inertial frame.

Why are you bringing up non-inertial frames? How is that relevant here?

 

[Mike_bb]

Huh? In your setup, there are three "things": Train 1, Train 2, and the Platform. All move relative to each other. You may choose whichever one you like to be "at rest" for doing a calculation.

I've mentioned it above. See comment #74.

 

[Mike_bb]

If an object at rest in Frame X is also at rest in Frame X', then the frames are not moving relative to each other.

We have big stone at rest in Frame X and moving train (Frame X'). These frames are moving relative to each other.
Could you provide example?

 

[PeterDonis]

We can conduct experiments in the trains. Fictitious forces will emerge in moving non-inertial frame.

Fictitious forces will appear in a non-inertial frame whether you call it "moving" or not. You don't seem to grasp that "moving" and "at rest" are just labels--they tell you nothing about the actual physics.

 

[PeterDonis]

We have big stone at rest in Frame X and moving train (Frame X'). These frames are moving relative to each other.

Yes.

Could you provide example?

Didn't you just do that yourself? The stone is at rest in Frame X but moving in frame X'. The train is moving in Frame X but at rest in Frame X'.

 

[PeterDonis]

I solved my problem

What is the solution?

 

[Mike_bb]

What is the solution?

Dale explained what's wrong in my calculations. His explanation is the best solution.

 

[PeterDonis]

Dale explained what's wrong in my calculations.

@Dale made a number of posts pointing out things that were wrong in your posts. Which one are you referring to?

 

[Mike_bb]

@Dale made a number of posts pointing out things that were wrong in your posts. Which one are you referring to?

See comment #44.