On the idea of time in physics-relativity

The deeper question was whether the light signal could reach the front of the train at a time that would be earlier than the time the winning number would be drawn. As eram correctly noted, it would not be possible. This has to do with the past and future light cones which you were musing about earlier.

 

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true you can't beat the light cone.

 

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I don't think the diagram here still shows gauge invariance. The flashes of light ( yellow and red lines) do not intersect the black lines ( frame of the train ) to intersect at the same times. If they where gauge invariant, then you should be able to draw a vertical line from the intersection of the flashes of light to the black lines of the frame on the train. It is starting to make me think that if you did apply the Lorentz transformations to the diagrams correctly, that the Lorentz Transformations are not gauge invariant. I think an accurate description of photons would have to be gauge invariant. So then Lorentz transformations would not be an accurate description of the properties of light and their arrival times.

It would be like saying the Earth itself, is the train. You can shine a light in a room on Earth and then say that the beams arrive at the same time from opposite ends of the room. But, if you say the Earth is the train in the TE, then the flashes don't arrive at the same time. So then what happens in rooms on Earth, is not the same thing that happens in Einsteins train.

 

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That's so deep.

No, wait - that's so rubbish. Not deep, rubbish.

Glad we got that sorted out. Move along now, nothing to see here.

 

Layman, this has nothing to do with gauge invariance. This scenario does not involve any field applying any force to any thing, which I'm led to believe is required to make gauge theory relevant.
I'm quite sure the Lorentz transformation has been applied correctly. You can check for yourself by doing a little maths, or by looking at other sources (You'll notice that I got the axis convention wrong in my diagrams - the usual convention is to have time on the vertical axis and distance on the horizontal)

In the rest frame of the train, flashes that start in the middle arrive at the ends at the same time (the blue lines):

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The red and yellow flashes don't start at the same time, so they don't finish at the same time.

Looking at the train frame diagram on its own, is there anything in this diagram that is unusual?

 

What happens in Einstein's train also happens in rooms on Earth all the time. Imagine you are looking out the corner windows of your hotel room on a rainly night. First you see a lightning bolt strike to the east, approximately 1000 meters away from you. A short time later, you see a different lightning bolt strike to the west, approximately 1000 meters away from you. The light from the strikes reaches your eyes at different times because the lighting bolts occur at different times. Simple!

You keep making the mistake of assuming that the lighting bolts must have occurred simultaneously according to the train frame, but the whole point of the TE is that the strikes must not have occurred simultaneously according to the train frame.

 

Yes, the blue lines. I think you just drew those in. This has everything to do with gauge invariance. The photon is the force carrier of the electromagnetic force. The photon is supposed to be gauge invariant so that it agrees with scientific experiments in quantum physics.

In order for the diagram to show that it is gauge invariant, the intersection of the yellow line going upwards would have to intersect the top black line so that the red line going downwards would then intersect the bottom black line so that these two points would pass a vertical line test. They would reach opposite sides of the train from being sent from opposite sides of the train so that they arrive at the opposite side at the same time. Then the same should be true for pointing the beams in any direction on the train relative to the observer on the train.

 

What is unusual about the blue lines in the train reference frame?

Since the red and yellow flashes start at different times, why would the train observer expect them to finish at the same time?

 

They are gauge invariant, I thought that would be something beyond your grasp.

That's right, the starting times are also not gauge invariant. So then they shouldn't arrive at the same time, but if they where gauge invariant then they would arrive in a difference of time equal to the difference of times that they where sent.

 

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What exactly does the train observer notice about the flashes designated by the blue lines that is unusual?
The flashes start with the train observer, hit the ends of the train at the same time, and come back to the train observer at the same time.
How is that unusual?

 

He wouldn't notice anything unusual. It is unusual that you say the mathmatics of gauge invarience is too complex, but then somehow you have applied mathmatics to a diagram that then has gauge invarience.

 

Excellent.
So is there any problem with the train frame diagram? If so, what is that problem, exactly?
Please don't just say "it's not gauge invariant", because I don't know what you're thinking when you say that.

 

I don't think both frames would agree that the photon was at the same location simultaneously even if an event was simultaneous when their clocks read different times.

So, what equations did you use for the blue lines?

 

I'm terribly confused. Since when does the term "gauge invariance" pop up in relativity?

 

Is this a problem in the train frame diagram?
For which flash?
At what time?

Is there a problem with the blue lines?

x' = ct' (0<t'<12.5)
x' = -ct' (0<t'<12.5)

x' = -ct' + 25 (12.5<t'<25)
x' = ct' - 25 (12.5<t'<25)

Since Layman. I don't know what he thinks it means.

 

I don't think it is anything about one thing in particular, but the connection or relation between the two frames, the blue lines in relation to the yellow and red lines.

No I was just surprised that there wasn't a problem with them, in Minkowski diagrams distance is supposed to be the speed of light times time. Then they are said to be accurate when used this way. I think it explains why they work out the way they are supposed to, it becomes gauge invarient, at least locally, idk if it would be globaly. I am thinking about trying to derive some Layman Transformations as opposed to Lorentz Transformations, to see if I find out if there is any difference.

Do you know of any sources that derive the Lorentz Transformations? I wonder if they assume that light measurements are measurements, that are measurements of things other than measuring the speed of light. Or do they come from the measurements of the objects velocity?

 

I don't think it is mentioned in relativity really, and I think that is the problem or the source of all the confusion.

 

Neither does he. :shrug:

 

I have been trying to explain it the best I can the way it is explained in layman terms. What part about it did you not understand? Or that has gotten you confused?

 

Layman, you're constructing your own meaning for a term that already has a well established meaning that you don't understand.

Don't do that. It's counterproductive to communication.

Good, so we've established that there's no problem in the train observer's frame, and no problem in the platform observer's frame.
All experiments carried out by each observer happen as expected, with light always moving at c.

Now:
The blue flashes are like the Michelson-Morley experiment.
The yellow and red flashes are Einstein's thought experiment.
Can you see that there is no conflict between the two?