Timeline for Calculations in the Relativity of Simultaneity Train Thought Experiment
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2017 at 15:18 | comment | added | safesphere | When the lightnings strike, they emit light that eventually reaches the observer. While there is no "proper time between the lightnings", because they are at different places, consider the events of their light reaching the observer. He can measure the time period between the flashes he sees by his watch as his proper time between the events of the light flashes coming to him. This is not the "proper time between the lightnings", but it is the proper time between the flashes he sees, because the events of him seeing the flashes happen at his location and are local to him. | |
| Sep 24, 2017 at 15:07 | comment | added | safesphere | Consider you are at the station and I am in the moving train. You see my time moving slower by gamma=2. I measure the period between my heartbeats by my watch as 1 second. It is my proper time tau=1 sec. You see me moving twice slower. By your wristwatch the period between my heartbeats is 2 seconds. This is the coordinate time, my time in your coordinates t=2 sec. So you know my t, but you want to know my tau. The formula gives you tau=t/gamma or tau=2/2=1 sec. (TBC) | |
| Sep 24, 2017 at 9:54 | comment | added | Quantum Dot | So, when I try to find $\tau$ for some observer in the formula, I am really just trying to find the time elapsed by that observer in their own frame of reference? That's all? I don't need to think of events and such? Also, in the formula, what precisely is $t$? For example in this thought experiment, what is Observer 1's $t$ really referring to? Is it the time they record between the lightning striking and reaching Observer 2, from their own wristwatch? Or is it the time they observe Observer 2's wristwatch to elapse for these events? I'm assuming it is the former. | |
| Sep 24, 2017 at 7:46 | comment | added | safesphere | Yes, the ticking of Observer 2's wristwatch is local only for this observer. The lightnings are not local for any of the observers and neither lightning is local to the other lightning, because they are spatially separated. It's all really very simple once it lines up properly in your mind. Special relativity is easy to understand, but hard to believe. | |
| Sep 24, 2017 at 7:12 | comment | added | Quantum Dot | Okay, so for clarification: In this thought experiment, is it correct to say that the "local events" are just the ticking of Observer 2's wristwatch? So really we are just trying to see how much Observer 2's wristwatch has elapsed from Observer 1's frame, just with the lightning strike reaching him defining the time interval we care about? | |
| Sep 24, 2017 at 6:37 | comment | added | safesphere | The proper time is the time between two local events measured by the local clock. For example, you can use your wristwatch to measure the time between your two heartbeats. If at this moment I see you from a moving train, by my clock the time between your two heartbeats would be different and not proper. However, as @CRDrost pointed out, I can calculate your proper time to know what you measure. As repeated once and again, there is no such thing as "the proper time" between two events that happen at different locations. No such thing as "the proper time" between the lightnings in your case. | |
| Sep 24, 2017 at 6:23 | comment | added | Quantum Dot | So does this mean that the proper time for events and observers is "different?" Or that, for an observer, the "events" are simply recording the ticking of his own clock? Also, @CR Drost, what would be the "proper time" between events in this thought experiment, if it is even applicable to talk about it? | |
| Sep 24, 2017 at 6:14 | comment | added | safesphere | That was the point of my answer, there is no such thing as "the proper time" between two spatially separated events. The proper time is by definition local. You can say, "the time between two events as measured by the observer". So he is in his frame uses his proper clock to measure the time interval between two events the way he sees them. This would not be "the proper time between the events", because a different observer in his own proper frame would measure (using his proper clock) a different time interval between the same two events. | |
| Sep 24, 2017 at 6:08 | comment | added | CR Drost | The proper time between two events is measured by an observer who sees both events happen at the same place. Every inertial observer's measurements of events at their own position is a measurement of a proper time in their own reference frame. Any other observer can derive the proper time as $\sqrt{c^2 t^2 - d^2}$ where $t$ is the time they measure and $d$ is the distance between the positions that they saw the events happen at. | |
| Sep 24, 2017 at 6:05 | comment | added | Quantum Dot | So then when is it appropriate to talk about the "proper time between events" as opposed to just the proper time of an observer? I see this distinction being made but do not see the direct relationship between them or why one is done over the other, etc. | |
| Sep 24, 2017 at 5:44 | comment | added | safesphere | It doesn't matter which observer, because each of them is stationary in his own frame. The Observer 1 sees the time of the Observer 2 dilated relative to the proper time of the Observer 1. At the same time, the Observer 2 sees the time of the Observer 1 dilated relative to the proper time of the Observer 2. In other words, if you move fast away from me, I see your time moving slower than mine while you see my time moving slower than yours. | |
| Sep 24, 2017 at 5:36 | comment | added | Quantum Dot | "We are measuring the dilation of time of the moving observer relative to the proper time of the stationary observer. " Why are you able to call the time of the stationary observer the "proper time?" Do you mean Observer 1 or 2 in my question? | |
| Sep 24, 2017 at 5:33 | history | answered | safesphere | CC BY-SA 3.0 |