Einstein's Thought Experiment on Simultaneity | Newbie Q&A

[paulie2018]

Hello

I am investigating a thought experiment conducted by Einstein in which he imagines a man on a train platform (it is being explained on a documentary I am watching). Two lightning bolts equidistant from him strike at either side. He sees these bolts of lighting strike at the same time.

A woman on a train traveling at the speed of light observes this event. She is traveling toward one lightning bolt and away from other and therefore observes the bolt of lightning she is traveling toward first, followed by the one she is traveling away from.

The documentary I am watching goes on to state that there is no such thing as simultaneity and that we can derive equations and our whole understanding of the Universe from this and that Newton was incorrect in his assumptions.

My question is, just because these events are perceived by the human eye at different speeds due to proximity and speed light, why does that mean they are actually occurring at different times?

If i conduct a similar thought experiment by replacing the lighting bolts with two people hammering a nail into a piece of wood at exactly the same moment, do the nails get hammered in at different times for the woman on the train or is it just her perception of it?

In my mind the nails always get hammered in at the same time, but they are just perceived in different ways depending on your vector.

If they do get hammered in at different times, does that mean therefore that matter does not exist as actual matter and that it is just made up of light.

Apologies, English is not my native language.

 

[Orodruin]

My question is, just because these events are perceived by the human eye at different speeds due to proximity and speed light, why does that mean they are actually occurring at different times?

The entire point is that the perception of the events have nothing to do with it. Based on where the events occurred and when the observer sees them, you can compute the time they must have occurred at taking the travel time of light into account. Assuming that the speed of light is the same for all observers, you then invariably arrive at the conclusion that the events really must occur at different times for the train observer if they occur at the same time for the ground observer.

If i conduct a similar thought experiment by replacing the lighting bolts with two people hammering a nail into a piece of wood at exactly the same moment, do the nails get hammered in at different times for the woman on the train or is it just her perception of it?

Again, they physically occur at different times according to the train systems definition of time. Perception has nothing to do with it.

If they do get hammered in at different times, does that mean therefore that matter does not exist as actual matter and that it is just made up of light.

No. It is unclear to me why you would come to that conclusion.

 

[Nugatory]

My question is, just because these events are perceived by the human eye at different speeds due to proximity and speed light, why does that mean they are actually occurring at different times?

This isn't just about how the the lightning strikes are perceived, it's about what really happens.
Suppose I fire a gun at a clock two kilometers away. The bullet moves at 1000 meters per second and the clock stops when it is smashed by the bullet. If the stopped clock reads noon, what time was the bullet fired? It had to have been fired at two seconds before noon, because it took the bullet two seconds to reach the clock and it reached the clock at noon.

It's the same thing with things that we see. If we see something happen, it's because light from that event has reached our eyes. We know it didn't happen at the exact moment that the light reached us because it took some time for the light to move from the event to us. Instead we look at the time when the light reaches us, subtract the light travel time, and that's when it happened.

The point of the train thought experiment is that when we use this sensible way of determining when things really happened, and allow for the fact that the speed of light is $c$ for all observers, different observers moving relative to one another will find that things that happen at the same time in different places according to one may happen at different times according to the other.

If i conduct a similar thought experience by replacing the lighting bolts with two people hammering a nail into a piece of wood at exactly the same moment, do the nails get hammered in at different times for the woman on the train

"Exactlybthe same moment" according to the guy on the tracks, you mean? Yes, as long as the nails are being hammered at different places. The logic is the same: the nail is hammered; it takes time $t$ for the light leaving the hammering event to reach the woman; if the the light reaches someone at time $T$ then the hammering event must have happened at time $T-t$; when both the man on the tracks and the woman on the train do this analysis they get different results for whether the events happened at the same time.

Do not fall in the trap of arguing that the man on the tracks is right because the train is "really" moving and the tracks aren't so we should trust the analysis done by the man on the tracks instead of the woman on the train. The Earth is moving around the sun at many kilometers a second, the sun is orbiting the center of galaxy, the galaxy is drifting through intergalactic space - the Earth is moving too, so there's no reason to say that the track analysis is more or less right than the train analysis.

If they do get hammered in at different times, does that mean therefore that matter does not exist as actual matter and that it is just made up of light.

No, it means that time doesn't work the way you've always thought it did.

 

[paulie2018]

Thank you for your replies.

If then, we had two people who stood on the platform side by side. They would each be holding an electronic device which had a button on. When the buttons are pressed by both people simultaneously the devices emit a green light. If they are not pressed exactly simultaneously they emit a red light.

Taking the example before, if with respect to the two people they pressed at the same time and the buttons emitted a green light, would the woman on the train see a red light or green light emitted from the devices?

I am confused because I read some articles about time slowing down and also the observer effect with regard to the double slit experiment.

 

[Orodruin]

When the buttons are pressed by both people simultaneously the devices emit a green light. If they are not pressed exactly simultaneously they emit a red light.

Your problem here is that you have not defined in which frame the buttons need to be pressed simultaneously. The actual physical setup depends on this and the entire takeaway from the relativity of simultaneity should be that it is not sufficient to say "if these things happens simultaneously then A, if not then B". To have a well defined setup, you also need to specify in which frame the things need to happen simultaneously.

 

[paulie2018]

My frame of reference would be the platform on which the two men are standing (the earth) who are operating the buttons. My second frame would be the train.

Could we say that with respect to frame 1 the answer is green and with respect to frame 2 it is red? Is that what you mean?

 

[Dale]

If then, we had two people who stood on the platform side by side. They would each be holding an electronic device which had a button on. When the buttons are pressed by both people simultaneously the devices emit a green light. If they are not pressed exactly simultaneously they emit a red light

There are a few subtleties you have to consider in a scenario like this.

First, you say they are standing side by side. If they are so close together that they are considered to be at the same location then all frames will agree on their simultaneity. In other words, it is only with respect to spatially separated events that simultaneity is relative. If they are colocated then all frames will agree if they are simultaneous or not.

Second, no signal can travel faster than c. So your detector simply physically cannot detect spatially separated simultaneous events. There must be some signal that reaches the device at c or slower. It is imperative to include that in the description of any device that purports to measure simultaneity.

Last, if you work in detail the outcome of any measurement, then all frames will agree. Some frames may attribute the outcome of the measurement to different causes, but they will all agree on the actual outcome. In this case, all frames will agree if the red light or the green light is illuminated, regardless of their disagreements about simultaneity.

 

[Ibix]

My frame of reference would be the platform on which the two men are standing who are operating the buttons. My second frame would be the train.

Could we say that with respect to frame 1 the answer is green and with respect to frame 2 it is red? Is that what you mean?

No. If the two people are next to each other (in the same plane perpendicular to the velocity of the train, strictly), there is no disagreement about simultaneity. It's only if events are not at the same location that one can disagree about simultaneity.

 

[Nugatory]

Could we say that with respect to frame 1 the answer is green and with respect to frame 2 it is red? Is that what you mean?

The color of the light that comes out of the device will be the same for everybody. Whether it is red or green depends on the details of your setup, including the all-important point that @Orodruin just made - when you say that the buttons are pushed at the same time, which frame do you mean?

You also have to allow for the time it takes for the signal to get from the button to the device. If you analyze the problem i the track frame, and the buttons are pushed simultaneously in the track frame, you will conclude that the signals take the same amount of time to get from each button to the device; the buttons were pushed at the same time so both signals reach the device at the same time and the device emits a green light. If you analyze the problem from the train frame, you will find that the two buttons were not pushed at the same time, but the signals in the two wires also have different travels times so they end up both reaching the device at the same time - again, green light.

(This thought experiment is somewhat harder to analyze because the signals in a wire do not travel at the speed of light.).

 

[paulie2018]

If you analyze the problem from the train frame, you will find that the two buttons were not pushed at the same time, but the signals in the two wires also have different travels times so they end up both reaching the device at the same time - again, green light.

So if we removed the wire component and our device could light instantly once the button is pressed it would be red and therefore frame 1 and frame 2 would not agree?

 

[Orodruin]

So if we removed the wire component and our device could light instantly once the button is pressed it would be red and therefore frame 1 and frame 2 would not agree?

No. You are still missing the main point that whatever setup you make the physical result cannot depend on the frame.

 

[Nugatory]

So if we removed the wire component and our device could light instantly once the button is pressed it would be red and therefore frame 1 and frame 2 would not agree?

It is logically impossible to build such a device, because "device could light instantly once the button is pushed" requires that the signal travel instantly from the button to the device, meaning that the travel time is zero, meaning that its speed would be infinite. There is simply no logically consistent way of analyzing your setup without considering the necessarily non-zero time it takes for the signals to get from their respective buttons to the device.

Thus, in asking your question you are already assuming a contradiction: you are trying to reason as if something that doesn't exist does exist. When you start with inconsistent premises, you will end up with inconsistent conclusions. In this case, your assumption of instantaneous signal propagation leads you to conclude that we have a device that emits light that is both red and green; this impossible result is just telling you that something is wrong with your initial premise (can't assume instantaneous propagation) or your analysis of the situation (incorrectly neglecting the signal travel time).

 

[Dale]

So if we removed the wire component and our device could light instantly once the button is pressed it would be red and therefore frame 1 and frame 2 would not agree?

If you removed the wire component then the device wouldn’t work at all. You could replace the wire with some other physical signal, but then we are back to the same situation as with the wire.

 

[Sorcerer]

So if we removed the wire component and our device could light instantly once the button is pressed it would be red and therefore frame 1 and frame 2 would not agree?

What does "could light instantly" mean? You mean light up instantly? That still makes no sense, because wires or no, it still takes a finite time for the signal to move from one point to another- even from your finger press of a button to the activation of the switch. Light moves at c, and it's the fastest possible speed. Your set up requires an infinite speed in order for one person to see red and another green. That is impossible.Think about it:
(1) There is a finite speed (the speed of light) that every inertial observer agrees upon, regardless of how fast they or the source of light are moving.
(2) Because of this, it is not possible for every observer to agree upon measurements of time (or distance, for that matter).
(3) If every observer cannot agree upon time, how can every observer agree about simultaneity? Simultaneity depends upon time.
This is a very difficult subject to grasp, but I think we should spend a lot of time thinking about what simultaneous means, and what happens when it is impossible for signals to travel at an infinite speed. Simultaneity depends on agreement of time, does it not? If there is a universal finite speed that is independent of the speed of its source (like light is), then by logical necessity, time cannot be universal for every inertial observer. This is a huge oversimplification, but think about it: we use time and distance to measure speed. If the speed of light from rest is the same as the speed of light from a flashlight in a moving spaceship, and speed is a function of time and distance, and the moving object is covering more distance, in order for the speed of light to be measured the same, the measurement of time must be different. Since time is therefore not universal, how can simultaneity be universal?I'm pretty sure the logic is usually worked out a little differently (relativity of simultaneity is used to argue that time and distance are relative as well), but this always made sense to me. If there is a finite speed everyone agrees on, then everyone cannot agree upon time, and as a result, everyone cannot agree upon whether or not two events were simultaneous.

 

[David Lewis]

A woman on a train traveling at the speed of light observes this event.

The speed of the train is irrelevant, but it's less than the speed of light.

The documentary I am watching goes on to state that there is no such thing as simultaneity

Simultaneity is not a bona fide feature of the universe as we had (pre-Relativity) tacitly assumed.

If then, we had two people who stood on the platform side by side. They would each be holding an electronic device which had a button on. When the buttons are pressed by both people simultaneously the devices emit a green light. If they are not pressed exactly simultaneously they emit a red light. ...if they pressed at the same time and the buttons emitted a green light, would the woman on the train see a red light or green light emitted from the devices?

To her, they pressed the buttons at different times, and the device emitted a green light.