Okay, here’s the set up of the classic Einstein ToR problem that many of you are probably familiar with:
You: standing on a platform with a pocket watch, keeping time.
Train: coming in at some high rate of speed, say 90% of the speed of light and there is a clock on the flatbed of the car and you see it is moving slower than your pocket watch.
So far so good. As expected.
Here is the twist:
The flat car of the train has two firecracker on board. One on the front of the car and one on the back of the car.
Train: they are detonated at the same time and the train passengers hears essentially a single bang of both firecrackers going off together.
You: hear them go off one after the other but not only that, you hear the one on the back before you hear the one on the front.
This was the problem and expected experience as described by a physicist on a “Closer to Truth” physics channel I recently watched. I assume it was correctly described.
Can someone explain to me using short sentences and shorter words for the above described behavior? For the life of me I can’t understand why this would be the case.
Don’t have time to watch the video at the moment, but I’ll guess that the firecrackers are set to go off when (from the train’s point of view) the center of the train is passing you. From your point of view, the back of the train is approaching you and the front is going away from you - so you hear the back cracker first.
You might want to look at the Wikipedia article, which has a lengthy explanation and some diagrams.
I’d also like to clarify/rephrase some of your original question:
“they are detonated at the same time” – “Same time” isn’t meaningful without a reference frame. You mean, I think, they are simultaneous in the reference frame of the train.
“and the train passengers” – One passenger please. If multiple passengers are spread out over a long distance in the train, they will not experience the same thing.
“hears” – Should be “sees”. You want to use light, not sound, because the speed of light is the same for all observers, unlike the speed of sound. With sound you’ll get into irrelevant complications like the relative speed of the air with respect to each observer.
Wouldn’t make any difference in timing if they were equidistant. The only difference would be the Doppler effect.
I think this is the key. Suppose you and the train were both stationary at the same time and place and synchronized your clocks, and the firecrackers were timed to go off at exactly midnight. When the flatcar went by at midnight, you would see its slower clock considerably earlier than midnight. By the time midnight arrived in the train’s reference frame, it would be long past you and so the firecracker at the rear would be the first one you heard.
Okay, I watched the video again and at the 2 minute mark Kip Thorne notes that he’s “measuring the event” of the firecrackers going off. I misstated the problem in the sense that he was measuring the sound. Although, as I understand it now, it would also work for sound waves. Thing is, I thought I understood the experiment with the classic light light traveling to the back and front of the moving train car. The firecracker somehow broke my understanding. Which I guess means I didn’t have as good an understanding of this concept as I thought.
Yeah, he’s saying that in the reference frame of the firecrackers, they are going off at the same time. But it’s a very simple description and to really get into it we need a definition of what “the same time” means, even for to events with the same velocity. In this very simple version that definition is sort of supplied by there being a “you” who is holding the firecrackers and setting them off.
This subjects the scenario to the same rules as the more familiar one where there is a light switch in the middle of a train car and lights at either end. If you are in a reference frame where the train car is moving, the signal moving in the same direction as the train car will take longer to reach the light than the signal moving in the opposite direction of travel, so the lights will not turn on at the same time, the back one will turn on first. The light from the rear one will then take longer to reach the, in your reference frame, moving central target, and both light sources will illuminate the center at the same time in both reference frames.
Same applies to the nerve signals in your arms and the light from the fire-crackers. For an observer considering you to be moving, the rear cracker is going off later.
Sound would confuse this, as it does have a preferred reference frame in the one where the medium it’s moving through is stationary.