FTL train + FTL communication thought experiment

[Ibix]

So what about speaking of TODAY, rather than back then?

You can deduce the Lorentz and Galilean transforms from the principle of relativity and assumptions of homogeneity and isotropy. Assuming you trust those three assumptions, any experiment that distinguishes Lorentz from Galileo is enough. I'd want something a bit more comprehensive to convince myself that I can trust the three assumptions, though.

 

[Sorcerer]

You can deduce the Lorentz and Galilean transforms from the principle of relativity and assumptions of homogeneity and isotropy. Assuming you trust those three assumptions, any experiment that distinguishes Lorentz from Galileo is enough. I'd want something a bit more comprehensive to convince myself that I can trust the three assumptions, though.

Well, correct me if I'm wrong, but, speaking merely of the Michelson-Morley experiment, wouldn't you need TWO experiments to distinguish between Lorentz and Galileo?

(1) An experiment that shows that the speed of light is independent of its source (Michelson-Morley).
(2) If (1) is true, an experiment that shows that the speed of light is finite (because if light moves at an infinite speed than all observers will agree upon it, since ∞ + x = ∞).The reason I think (2) is important is because if you allow c to approach infinity in the Lorentz factor, it becomes equal to 1. Which would reduce the Lorentz transformation to the Galileo transformation, wouldn't it?Am I incorrect in this reasoning here? Thanks for the reply btw.

 

[Nugatory]

Would knowing that the speed of light is finite, and then finding all the repeated negative results of the Michelson-Morley experiment be enough to deduce the Lorentz transformation?

Not quite... To tie off the all the loose ends, you also need homogeneity and isotropy to get around the impossibility of measuring the one-way speed of light.

 

[Sorcerer]

Not quite... To tie off the all the loose ends, you also need homogeneity and isotropy to get around the impossibility of measuring the one-way speed of light.

So add those assumptions in there, we'd then have enough, right?

 

[Mister T]

I did not really get the wedge analogy , couldn't "picture it" in my mind.

This figure shows two wedges.

The upper surface of each wedge forms an angle $\theta$ with the horizontal. Another way of describing the tilt of that upper surface is with the slope. Imagine increasing the value of the angle $\theta$ so that the upper surface becomes more steep. When $\theta$ is zero the slope is zero, but as the angle increases so does the slope. As $\theta$ approaches 90° the upper surface approaches vertical and the slope increases beyond all bounds. The slope is given by $\tan \theta$.

This next figure shows those two wedges stacked, one on top of the other.

Now the upper surface forms an angle $2\theta$ with the horizontal, but the slope is not $2 \tan \theta$.

 

[Sorcerer]

This figure shows two wedges.
View attachment 224383
The upper surface of each wedge forms an angle $\theta$ with the horizontal. Another way of describing the tilt of that upper surface is with the slope. Imagine increasing the value of the angle $\theta$ so that the upper surface becomes more steep. When $\theta$ is zero the slope is zero, but as the angle increases so does the slope. As $\theta$ approaches 90° the upper surface approaches vertical and the slope increases beyond all bounds. The slope is given by $\tan \theta$.

This next figure shows those two wedges stacked, one on top of the other.
View attachment 224384
Now the upper surface forms an angle $2\theta$ with the horizontal, but the slope is not $2 \tan \theta$.

I suck at trig, but in summary then, the slope should be $tan{\ 2 \theta}$ , right?

And when $\theta → 0$ , $tan{\ 2 \theta} → 2 \theta$ , but when $\theta$ gets larger, the two diverge from one another?

 

[girts]

pardon me if this comes off as ignorant but @Sorcerer, with respect to the questions you asked here about the M-M experiment etc, haven't we already found the speed of light to be finite and precise with experiments and also that it is independent from it's source with experiments, or is there something I'm missing here ?

 

[Ibix]

There is a mountain of evidence that SR is correct. Sorceror is thinking of minimum requirements to convince a student of this today.

 

[Sorcerer]

pardon me if this comes off as ignorant but @Sorcerer, with respect to the questions you asked here about the M-M experiment etc, haven't we already found the speed of light to be finite and precise with experiments and also that it is independent from it's source with experiments, or is there something I'm missing here ?

What Ibix said here is mainly my concern:

There is a mountain of evidence that SR is correct. Sorceror is thinking of minimum requirements to convince a student of this today.

Although there is a bit more to it than that. I am certainly interested in convincing students, but I'm also interested in the "lower division level" minimal amount simply theoretically speaking. Aside from assumptions about space and time not depending on location or direction, what are the minimum requirements? From what I can tell, it's that the Lorentz transformation is the correct transformation law and the speed of light is finite. (note: in this viewpoint, I am taking the Galileo transformation as a special case of the Lorentz transformation: when the speed of light is infinite)

So yeah, mostly I'm interested in convincing students and your stereotypical person who thinks that "the establishment" is missing out on some simple and obvious intuitive truth that invalidates the foundations of all of modern physics.EDITED TO ADD: The best part is that if someone is willing to spend a little bit of money, there are kits available to duplicate the M-M experiment. As for the motion of the Earth through space, a necessary requirement for this to matter, there is a bunch of evidence for that (it's a bit obvious). I'm taking that part for granted here. The people who think the Earth doesn't orbit the sun or move through space/rotate are the type who believe the Earth is flat and that the universe was created during the Neolithic period, so they are a lost cause anyway.

But as for determining if the speed of light is finite or infinite, I'm not sure what kind of experiment is available to a lay person (I'm sure there is a way, I just haven't researched it).

And lastly, in terms of an infinite one way speed and 2c return speed, I'm not sure how you could differentiate that from just the assumption that the speed of light moves at c both ways. I'm also not sure that it matters, because you'd still end up with the Lorentz transformation in that case, if I understand it correctly (since the two way speed would still end up being c).

 

[girts]

thanks for all the input,
as for what you said , well one thing would be to configure the two laser pulses one hitting a sensor located near the laser and the other hitting a sensor only after reflected from a mirror further away, clearly the second longer traveling laser pulse would arrive later. I am sure there is a name for this method I'm just not sure what.
another interesting video I actually knew sometime ago is about simply filming a light pulse with a very very high speed camera, then slowing down those pictures shows an interesting thing where one can really see the light moving along instead of just shinning everywhere at once a we see with our naked eyes.
here is the video.
one thing that came to mind is that since in conductors changes in E field travel at c in vacuum, maybe one day we will have a camera so fast that we could literally catch light at "standstill" with every frame equal to every smallest change in the traveling light pulse, even though I guess such an apparatus wouldn't tell us anything new that we don't already know.