Thought Experiment regarding Time

[dfaullin]

Consider this scenario involving twins.

The twins, A and B, are some unspecified distance apart and are placed inside a container. They are told that one of them will be traveling to the other at a given fixed speed, but things will be done so that neither twin will know which one did the traveling.

When the twins are next to one another, a sensor will go off. The twins are instructed, once the sensor goes off, to write down how long it took the other twin to reach them and to calculate the distance between them based on this information (before seeing each other).

WLOG, let's suppose Twin B actually did the traveling. Then Twin B will record the time it took Twin A to reach him as being less than what Twin A will have measured for Twin B to reach him. Based on this, and given the fact that the speed was fixed and known to both twins, Twin B will calculate that Twin A was not as far away (as Twin A would calculate for Twin B).

Is this an already known thought experiment? I am interpreting the results of this experiment as follows:

The time being measured by each twin actually applies to the other twin, not just themselves. In Twin B's frame, it literally took Twin A less time to arrive. Another way to word it would be that, in Twin A's frame, Twin B had longer to make the trip since Twin A will have measured a longer time period for Twin B.

I would appreciate any thoughts anyone has on this.

~Dylan

 

[ghwellsjr]

If both twins start out at rest with respect to each other, then one of them will have to accelerate and they will feel that acceleration, won't they? It's like they are in two elevator cars many floors apart and either the lower one will go up to the higher one or the higher one will go down to the lower one but as you well know, when an elevator starts moving and when it stops moving, you can tell, even though you don't have any other information to tell you that you are the one that is moving.

So what's with the secrecy? Why not just say you have two stop watches that are separated in space traveling towards each other and at some moment in time you start both stop watches and when they reach each other you stop them? Well this is an exactly symmetrical problem so obviously, there cannot be an answer as to which one has less time on it, correct? Isn't that what you're trying to point out in your scenario?

The point of this is that there is no single answer to the issue of starting both stop watches at the same time if they are already moving with respect to each other which is the only way you can remove the distinction of which one is actually moving. Time will be ticking away at different rates for them depending on the Frame of Reference that you choose to look at the problem with. And that FoR defines what "starting at the same time" means.

 

[dfaullin]

Is there no way to trick them so that they don't know which one is moving toward the other? For example, have one being spun around in a circle to simulate the same motion that the other is feeling due to acceleration? Or would this introduce too much SR complication? I would only want to do that if the effect on the situation would be minimal enough to ignore.

I was just trying to create a scenario in which one could argue that the time kept applies to the other twin. For example, Twin B would say that Twin A took X amount of time to arrive at Twin B, based on Twin B's timepiece. Twin A would say that it took Y amount of time for Twin B to arrive at Twin A, based on Twin A's timepiece.

Why the secrecy? I think with the secrecy, the twins will apply their measurements to the other twin and not themselves. Twin B will not say "Hey, I look younger therefore this clock measured my time." Twin B will think "It took this long (according to my clock) for Twin A to get here; hence Twin A was traveling for this long." Same for Twin A's point of view. His clock will be thought of as keeping track of how long it took Twin B to arrive.

In the conventional story, Twin B's clock measures Twin B's passage of time and same for Twin A. In this way, they will be thinking that their clocks have kept track of how long the other one was gone.

Maybe my situation is more elaborate than it needs to be to get this effect. Maybe you can think of it this way even in the traditional twin paradox.

Thanks for your thoughts on the situation! If you have any more, I'd like to hear them.

 

[Tea Jay]

Time would be slower for the faster twin, or clock, and, the one who's watch had the least elapsed time was living slower/traveling faster.

When they launch a GPS satellite with an onboard atomic clock, they set it to run fast on Earth before launch...because they know it will run slower in orbit, and they know by how much.

IE: The cesium vibrations that are the clock's "ticks" are faster on Earth than in orbit...so the computer that translates the "ticks" into time is set to essentially count the clicks as representing a bit more time on Earth than they really do...so it runs a bit fast here.

That way, the clocks in orbit keep time in synchronization with Earth based clocks, even though the cesium is vibrating more slowly in space.So, it seems to be straight forward that the stop watch with less elapsed time, regardless of the details of the scenario...would be the one that was traveling faster.I'm new at this, so if I'm missing the point, etc...please, be gentle.

:D

 

[dfaullin]

I'm new too! I have met a few not-so-nice physicists in my life and so I was very nervous to post here. But so far, I have not been chewed out or made to feel that I do not belong here. I appreciate your response.

I agree with you that the twin who finds their clock is the slower clock will realize that they must have been the one traveling. Hence all the secrecy in my thought experiment. Before they are aware of each others' measurements/calculations, they would not know which one traveled and which one was stationary. So they would have to assume that they were the one stationary and that their twin was the one that traveled to them and that what they read on their clock would be how long the other twin spent traveling to them. The clock is for their frame, but they would project that time on their twin. They would say their twin spent that time either waiting or traveling.

I appreciate the information on the GPS satellites. I always wondered how they dealt with special relativity. That seems like a nice, clean easy solution. Fix the speed they will travel and account for the time dilation in the software.

If you can think of anything else, please do not hesitate to let me know!

~Dylan

 

[Markus Hanke]

I'm new too! I have met a few not-so-nice physicists in my life and so I was very nervous to post here. But so far, I have not been chewed out or made to feel that I do not belong here. I appreciate your response.

I agree with you that the twin who finds their clock is the slower clock will realize that they must have been the one traveling. Hence all the secrecy in my thought experiment. Before they are aware of each others' measurements/calculations, they would not know which one traveled and which one was stationary. So they would have to assume that they were the one stationary and that their twin was the one that traveled to them and that what they read on their clock would be how long the other twin spent traveling to them. The clock is for their frame, but they would project that time on their twin. They would say their twin spent that time either waiting or traveling.

I appreciate the information on the GPS satellites. I always wondered how they dealt with special relativity. That seems like a nice, clean easy solution. Fix the speed they will travel and account for the time dilation in the software.

If you can think of anything else, please do not hesitate to let me know!

~Dylan

So long as you start your experiment with both twins at rest, there will always be a way to tell which one moved and which one didn't because there is acceleration involved; the exact circumstances of the experiment don't matter for this. The only way to construct a scenario which makes it impossible for the twins to tell the moving one from the stationary one, would be one that allows only linear motion without acceleration, and of course provides for the absence of any external frame of reference. In such a scenario only the relative motion between the two twins can be detected by each one of them, and, due to time dilation and length contraction effects, none of them would be able to tell which one was moving. Remember though, once any kind of acceleration comes into the picture this perfect symmetry is destroyed.

 

[ghwellsjr]

Is there no way to trick them so that they don't know which one is moving toward the other? For example, have one being spun around in a circle to simulate the same motion that the other is feeling due to acceleration? Or would this introduce too much SR complication? I would only want to do that if the effect on the situation would be minimal enough to ignore.

You might be able to confuse a couple of people this way, but proper instruments could always figure out what was going on. So why not just say that you put them to sleep for a short time during the acceleration of one of them so that after they wake up, they won't know which one accelerated? Or just tell them to ignore any acceleration they feel.

I was just trying to create a scenario in which one could argue that the time kept applies to the other twin. For example, Twin B would say that Twin A took X amount of time to arrive at Twin B, based on Twin B's timepiece. Twin A would say that it took Y amount of time for Twin B to arrive at Twin A, based on Twin A's timepiece.

Why would you think that the measured time would apply to the other twin? If Twin B was the one that actually accelerated, then his measured time would be smaller and he would say that he traveled a shorter distance and he'd be right because not only was he experiencing time dilation but he would also be experiencing length contraction and the distance he was traveling would be shortened. Meanwhile, although Twin A was not moving, his calculation of the distance would be the correct one for the FoR in which both twins were at rest before one of them accelerated.

Why the secrecy? I think with the secrecy, the twins will apply their measurements to the other twin and not themselves. Twin B will not say "Hey, I look younger therefore this clock measured my time." Twin B will think "It took this long (according to my clock) for Twin A to get here; hence Twin A was traveling for this long." Same for Twin A's point of view. His clock will be thought of as keeping track of how long it took Twin B to arrive.

With or without secrecy, each twin's clock applies only to themself.

In the conventional story, Twin B's clock measures Twin B's passage of time and same for Twin A. In this way, they will be thinking that their clocks have kept track of how long the other one was gone.

Maybe my situation is more elaborate than it needs to be to get this effect. Maybe you can think of it this way even in the traditional twin paradox.

Thanks for your thoughts on the situation! If you have any more, I'd like to hear them.

No, each clock applies to each twin both in the conventional story of the Twin Paradox and in your thought experiment.

 

[Tea Jay]

Again, I think the stop watch with the shortest elapsed time is the one that traveled, and the rest doesn't matter.

As for how to obfuscate the act of travel to the twins, so they ONLY know who traveled as a result of interpreting the stop watches' times, and not due to sensing acceleration, etc...those are plot contrivances that can be filled in as mentioned above anyway you want, to render the act of travel as undetected.

Heck, you can skip even HAVING twins, and just have the luggage separated, and the watches, starting at the same time, in separate suitcases lost by the interstellar airline.

The airline claims both suit cases were at the baggage department the entire time, you claim one suit case went to the resort at Alpha Centuri and back...based upon it having a shorter elapsed time, etc.

:)

 

[Dale]

Is there no way to trick them so that they don't know which one is moving toward the other?

Sure. You can always take a well-defined scenario and remove information to the point where some specific physical value cannot be calculated, or supply false information such that a wrong physical value is calculated. That doesn't seem to say anything about the laws of physics.

In this case, if there is enough information to calculate the outcome of some physical experiment in one frame then there is enough information to calculate the outcome in the other frame, and both frames will agree on the experimental outcome.