B Time Dilation Theory Flaw: How Can They Be Different Ages?

[Chris S]

The theory regarding two persons experiencing different amounts of time dilation due to the two persons being influenced by different amounts of gravity states that while one person stays on Earth under its gravity and another person travels through space under less influence of gravity (less time dilation), the space traveler will be older when the persons meet, and both people will have experienced the same, typical rate of time passing; however, how can they both perceive themselves experiencing the same, typical rate of time passing (aging at the same rate) but be different ages when they meet?

 

[PeroK]

however, how can they both perceive themselves experiencing the same, typical rate of time passing (aging at the same rate) but be different ages when they meet?

That's what it means to say that time is not universal or absolute. There is no "master" clock that they can both use.

 

[russ_watters]

...how can they both perceive themselves experiencing the same, typical rate of time passing (aging at the same rate) but be different ages when they meet?

It's like being in a boat on a river vs a pond. If you just look down at the water around you, there's no way to tell if you are moving or not. Only by watching the shore can you tell. Time dilation is rather like that: you only notice it by watching someone else's clock and comparing it with yours.

 

[Nugatory]

The theory regarding two persons experiencing different amounts of time dilation...

Strictly speaking, that's not a theory, it's an observed experimental fact. The theory is what explains this fact.

But with that said... A less complicated version of what you're describing is the "Twin Paradox"; Google will find you many good explanations and we have many threads about it already. Also there's a good starting point here: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

(And an aside - "time dilation" is most often used to describe the way that a moving clock runs slow when compared with one at rest. It's not the same thing as what you're describing: two people separate, then discover when they meet up again that different amounts of time have passed for them).

 

[Ibix]

The theory regarding two persons experiencing different amounts of time dilation due to the two persons being influenced by different amounts of gravity states that while one person stays on Earth under its gravity and another person travels through space under less influence of gravity (less time dilation), the space traveler will be older when the persons meet, and both people will have experienced the same, typical rate of time passing; however, how can they both perceive themselves experiencing the same, typical rate of time passing (aging at the same rate) but be different ages when they meet?

There are two different effects here. One is that, even in the absence of gravity, someone traveling "out and back" will end up younger than someone who remains floating the whole time. The other is that someone higher up in a gravitational field will age faster than someone lower down.

As Nugatory points out, this isn't theory. The Hafele-Keating and Pound-Rebka experiments are the classic demonstrations. The theory that explains them is that the time you experience turns out to be a measure of the "length" of your path through spacetime ("worldline"). Just like paths through space, different routes from A to B can have different lengths - so you experience different elapsed times.

Your own clock will always look normal because it follows the same path through spacetime as your brain, so it ticks at the same rate as your thought processes. Other people may say your clock is ticking slow (or fast), but they will also realize you are running slow (or fast) by the same amount so will be unsurprised that you see nothing unusual in your clock.

 

[Janus]

The theory regarding two persons experiencing different amounts of time dilation due to the two persons being influenced by different amounts of gravity states that while one person stays on Earth under its gravity and another person travels through space under less influence of gravity (less time dilation), the space traveler will be older when the persons meet, and both people will have experienced the same, typical rate of time passing; however, how can they both perceive themselves experiencing the same, typical rate of time passing (aging at the same rate) but be different ages when they meet?

First off: It isn't a difference in gravity that would result in the difference in age upon reuniting. It is a difference in gravitational potential. While the first involves how much gravity each person would feel at his location, the second involves how much energy would be needed to move one person form his location to the other. Thus if you imagine a gravity field that does not weaken with altitude and put two clocks at two different heights in it, the upper clock will run faster than the lower clock.

Secondly when we say that each person experiences the same rate of time, that just means that neither person could tell that there was anything "amiss" with the way time flowed for him. His clock, biological processes, etc all will appear to be normal. However, if he were to compare his clock to the other person's clock, he would note a difference. The higher person would note the other person's clock was ticking slower than his own and that he was aging at a slower rate, etc. While the lower person would note that the higher person's clock was ticking faster and that the other person was aging faster.
After some interval, if we bring the two people back together, they will both agree that one of them aged more since they were separated. Though they may argue as to the reason. The lower person will claim it is because the higher person's time ran fast, while the higher person will say it is because the lower person's time ran slow. There is no one absolutely correct answer to this.

This disagreement of how the end results came about becomes even more apparent when dealing with the situation where one person flies off at a high speed, stops, turns around and comes back. Upon meeting up again they will both agree the the person who left and returned will have aged less.
However, according to the stay at home person, this will be because the traveler aged slower than he did during the two legs of the trip, while the traveler will say that it was the homebody that aged more slowly during the legs of the trip, but aged very rapidly when the traveler was making his turnaround at the far end of his trip.
Again, both versions the sequence of events are equally valid, and neither can lay claim to be the right answer.

This manner of treating time takes some getting used to. We tend to think of time as being a much more universal standard, and accepting that it is more in the line of being a "in the eyes of the beholder" thing can be hard to swallow.

 

[cordless03]

It's like being in a boat on a river vs a pond. If you just look down at the water around you, there's no way to tell if you are moving or not. Only by watching the shore can you tell. Time dilation is rather like that: you only notice it by watching someone else's clock and comparing it with yours.

Very good analogy!

 

[Chris S]

Thanks for the replies and term corrections, but they don't explain how time can pass for persons "A" & "B" at different rates, and at the same rates, during the same time period. Perhaps the answer to my question is that there is no explanation for the inconsistency, and that's why it's called a paradox. Perhaps the answer is similar to my answer to resolve Zeno's Paradox. Zeno's Paradox states that there are an infinite number of halfway points to any destination, and given that you have to travel those infinite distances, which can't be done, you never get to your destination; but you do. It's true that there are infinite halfway points and it's true that we do reach destinations, but I resolve the inconsistency by explaining how each condition does not violate the other: Although there are an infinite number of halfway points to any destination, the halfway points are an infinite number of measurements, not an indication of infinite distance between two points. Now, each condition doesn't conflict with the other. My guess is that the Twin Paradox inconsistency may be explained in a manner so the two inconsistent aspects don't violate each other by re-characterizing or separating fact and measurement/perception. Can anyone explain how time can pass for persons "A" & "B" at different rates, and at the same rates, during the same time period in a manner so the two inconsistent aspects don't violate each other?

I just read more replies that appeared while I was creating the paragraph above, and Janus explained it: Each person does not experience/perceive time at the same rate [as the speakers on the TV space shows say.]

 

[Drakkith]

There isn't a single time period you can use here. Both observers experience a different period of time. So there is no paradox. They age differently because they have experienced a different period of time.

 

[ZapperZ]

It is not inconsistent, because there is a logical explanation for it. It is only called a "paradox" to make it sexier in the popular press.

The reason why it is not inconsistent is because one can transform to the other person's frame and be able to understand what he/she is measuring. That's the whole reason why it is called "relativity". You are used to time being of a fixed period for everyone. This is what you are used to, and you're are implicitly being prejudiced by such a view. Instead, we have numerous experimental observation to show that this view is valid for a special case.

If you wish to actually learn the mechanics of how this is derived, there are numerous sources and even videos available. Otherwise, it is foolish to title your thread by claiming that time dilation is a "flaw" when the flaw here is in your understanding.

Zz.

 

[Ibix]

they don't explain how time can pass for persons "A" & "B" at different rates, and at the same rates, during the same time period

That's not a very sensible way to think about it, which is probably why you are having troubles with our explanations.

The simplest way is exactly what I said - elapsed time is the "length" of your path through spacetime, and different paths have different lengths. As Janus points out, that's a very different way to think about time from the Newtonian "universal time" idea that we intuitively use, but it's the way the world works as far as we can see.

 

[russ_watters]

Thanks for the replies and term corrections, but they don't explain how time can pass for persons "A" & "B" at different rates, and at the same rates, during the same time period.

How it can be explained is a different and more involved question than how can it be perceived, which is what you asked in the first post. How much have you read up on the subject? Have you at least read the wikipedia articles on relativity and time dilation?

Also, the way you worded the question, ending with "during the same time period" implies you think there is one "true" time period. There isn't. Everyone Carrie's their own clock and any may be different from any other. You kind of need to accept the fact - at least tentatively - before why is true can be explained.

 

[Dale]

but they don't explain how time can pass for persons "A" & "B" at different rates, and at the same rates, during the same time period. Perhaps the answer to my question is that there is no explanation for the inconsistency, and that's why it's called a paradox.

They do explain and answer the questions, but it is not obvious that they do. The paradox is called a paradox because the answer is surprising, not because it doesn’t exist.

Consider a sheet of paper with two dots on it. Now, draw two paths connecting the dots. One path is a straight line and the other is a curve. The lengths of the two paths is different. The straight line is shorter and the curve is longer. Distance passes at the same rate along each path (one mm per mm), but since they are different paths over the paper there is just more distance on one path than on the other.

Similarly with spacetime. The two travelers went on different paths through spacetime. Those different paths had different lengths. The length of a path through spacetime is measured with a clock that travels on that path. So one clock measured more time than the other clock. A clock is like a spacetime odometer measuring the length of the spacetime path traveled. Different paths have different lengths.

 

[Chris S]

Do two clocks, each within different gravity potentials, show different times when they are re-united because one clock had more time to tick and ticked more times with the same length of time between ticks (unit of time measure increment) or are the times different when the clocks are re-united because each tick (unit of time measure increment) was a different length than the other clock (relatively stretched/condensed)?

 

[PAllen]

Do two clocks, each within different gravity potentials, show different times when they are re-united because one clock had more time to tick and ticked more times with the same length of time between ticks (unit of time measure increment) or are the times different when the clocks are re-united because each tick (unit of time measure increment) was a different length than the other clock (relatively stretched/condensed)?

The first answer is correct.

 

[Dale]

one clock had more time to tick and ticked more times with the same length of time between ticks (unit of time measure increment)

This one is the usual interpretation

Edit: @PAllen ftw!

 

[Chris S]

I think I got it, thanks to all of you: The "flaw" in my understanding was that although both people experience the same rate of time passing, they don't experience the same elapse time. Two clocks in different gravity potentials measure time passing at the same rate, and the clock that experiences a lower gravity potential relative to the another clock will experience more elapse time. The difference in relative age of the clocks [or people] will increase. There is no absolute time that the clocks are measuring or people are perceiving. No one gains time or loses time; it's all relative.

 

[phinds]

I think I got it, thanks to all of you: The "flaw" in my understanding was that although both people experience the same rate of time passing, they don't experience the same elapse time. Two clocks in different gravity potentials measure time passing at the same rate, and the clock that experiences a lower gravity potential relative to the another clock will experience more elapse time. The difference in relative age of the clocks [or people] will increase. There is no absolute time that the clocks are measuring or people are perceiving. No one gains time or loses time; it's all relative.

You got it. Good job.