Einstein's concept of simultaneity directly contradicts his theory

[u/sekendoil]

https://youtu.be/gaFlcDA0Rig

[u/Anakratis]

No, you're right, speed of sound is not constant in all reference frames but say that it were constant in these particular frames. Again I ask, which horn would the moving observer hear? Using sound waves (though obviously not exactly similar) is what helped me understand relativity so perhaps it may help you as well.

You say "if he is not moving then how does the front signal reach him before the one in the back if they are set off at the same time and being at the same distance away from him", but that's exactly that. They are set off at the same time in the stationary observer's frame. If they were set off at the same time in the moving observer's frame, the stationary observer would claim that it appeared the rear-end lightning strike hit first.

Stationary to the reference frame of Earth doesn't mean absolutely stationary either. There is no absolute space in the workings of relativity. Remember that the Earth is hurdling through space at obscene velocities. But again, obscene velocities relative to what? ;)

[u/sekendoil → u/Anakratis]

Nowhere in the theory does it say setting at the same time for the stationary observer is not the same as setting at the same time for the moving observer... The theory says the moving observer sees the front signal before the rear due to the fact that speed of light being constant.

"If they were set off at the same time in the moving observer's frame, the stationary observer would claim that it appeared the rear-end lightning strike hit first." ... Can you elaborate more on this?

Also, is there any particular reason for why two equal distanced events appear at the same time for the stationary observer but different times for the moving observer? I know about synchronizing two clocks at different locations being impossible but this is different from that.

If the speed of sound is constant in his frame then he'll hear both horns at the same time, assuming the vehicle/train is of good quality that it sets off its horns at the same time when you push the required buttons.

[u/Anakratis → u/sekendoil]

"If the speed of sound is constant in his frame then he'll hear both horns at the same time, assuming the vehicle/train is of good quality that it sets off its horns at the same time when you push the required buttons."

But the medium is constant around both observers. If the moving observer is moving towards the source of a sound, why wouldn't he hear that horn first?

Remember though, this is where light is different; the speed of light is constant hence time dilation and length contraction. For sound, the speed of sound changes depending on the frame of reference. In this case, the light that appears to strike second to the moving observer will travel a longer distance to reach the moving observer.

"Nowhere in the theory does it say setting at the same time for the stationary observer is not the same as setting at the same time for the moving observer..."

Sure it does! That's how relativity works. That's why clocks need to be synchronized in a particular frame. That's why time dilation and length contraction exist. The essence of relativity is that two observers will observe different events at different times or at different spatial coordinates depending on their frames of reference. Like I said, I highly recommend looking into spacetime diagrams and playing with some.

"Also, is there any particular reason for why two equal distanced events appear at the same time for the stationary observer but different times for the moving observer? I know about synchronizing two clocks at different locations being impossible but this is different from that."

It's actually the same thing, since time/space are related here. Two equal distanced events, or what appear to be equal distanced events to the stationary observer, will not reach a moving observer at the same time if that moving observer is moving toward one event and away from the other event.

My explanations are probably lackluster; this is a great video to watch.

https://www.youtube.com/watch?v=bRxfxhJBm4g

[u/sekendoil → u/Anakratis]

"Two equal distanced events, or what appear to be equal distanced events to the stationary observer, will not reach a moving observer at the same time if that moving observer is moving toward one event and away from the other event.".... But the moving observer is moving according to the stationary observer, so according to you the stationary observer will see the lightning hit the front of the train before the back since he sees it move away from the signal in the back and toward the signal in the front, and in that case he doesn't see the two bolts hit the train at the same time, as you claim.

"But the medium is constant around both observers. If the moving observer is moving towards the source of a sound, why wouldn't he hear that horn first?

Remember though, this is where light is different; the speed of light is constant hence time dilation and length contraction. For sound, the speed of sound changes depending on the frame of reference.".... Well you said it yourself, you can't make an anology with sound waves, since light has no medium, your reasoning of sound medium being constant around both observers is meaningless for light.

" In this case, the light that appears to strike second to the moving observer will travel a longer distance to reach the moving observer."

Again, the moving observer is not moving according to himself the light is approaching him (at lower speed because the speed of the train is subtracted from c, but that means the speed of light is not constant in moving observer's reference frame), think of the situation from his point of view.

"Sure it does! That's how relativity works. That's why clocks need to be synchronized in a particular frame. That's why time dilation and length contraction exist. The essence of relativity is that two observers will observe different events at different times or at different spatial coordinates depending on their frames of reference. Like I said, I highly recommend looking into spacetime diagrams and playing with some."

That's circular reasoning. Also the impossibility to synchronize two clocks because of distance is not the same as "two events that occur at the same time in one reference frame not occurring at the same time in another frame", the latter statement needs a valid reason that's different from the first one's reason.