Twin Paradox

Ok, to understand where I’m coming from here, I’ve been thinking about this for years. I’ve heard a lot of other people’s explanations, read some web sites, and even a cliff’s notes on physics (I wasn’t about to buy a whole book when I can’t believe any of it.) So why do I ask here? Someone, somewhere has to understand my objections to current explanations of the twin paradox, and I believe that person is in the best position to make me understand it.

Either I’m wrong and there is no paradox, or it’s the rest of the world that is wrong and there is a paradox that for some reason most everyone isn’t capable of seeing. Normally, when it’s just you against the rest of the world, it’s a good idea to think that maybe the rest of the world understands something that you don’t. But I’ve never been able to do that. Supposedly, somewhere, science is being done in which this paradox would arise all the time, and supposedly it works out just fine, and if that’s the case then one must suppose that there really is no paradox, but look where I’m coming from:

When I was taking any science class in high school, we would do some experiments now and then. Although the school had the necissary chemicals for chemistry, and some things that could roll and fall for physics, we didn’t have anything that could preciesly measure mass, time, all we could accurately measure was distance and temperature. So, needless to say, all the experients came out wrong, for everyone, not just me. However, I was the only one who turned in work that blatently came to the wrong conclusions. (For instance, we once had some piece of metal, and we were supposed to identify it by calcuating it’s specific heat, the answer I came up with wasn’t a metal.) All the other students simply figured out by other means what the metal was, and then fudged with their numbers until they came to the correct answer. I never understood why. Coming to the wrong answer says nothing about wether or not you know how to do science. It just says that you don’t know how to keep track of signifigant digits, which was ultimately the problem. If I had said that the scale was accurate to one gram, which I strongly suspected since it was a flimsy piece of trash, it would have been obvious that my answer was useless, however the teacher said they were accurate to something like 0.01 grams, so that’s what everyone used.

Now some of those kids probably went on to college and became scientists, whereas I dropped out a year later and went on to deliver pizza, so simply put, I don’t have enough faith in what people say, regardless of how much smarter than me they theroetically are, to believe anything they say that I can’t understand myself. So my only hope is that someone can explain this in a way that makes sense to me, and I can stop getting so worked up over this that I want to beat someone in the head with a baseball bat. (I’m otherwise a very peaceful person.)

So, as if anyone doesn’t know what the question is, I’ll restate it again: Two twins, bob and tom, live on earth. On one day, bob takes off at a high rate of speed, then later comes back. When he does come back, one of the twins is now older than the other, but which one?

Some sort of relativity says that when an object is moving, it’s clocks run slower than something that is not moving. The problem, of course, is that from each perspective, it is the other that is moving, and each perspective’s time cannot be moving slower than the other’s, as that would be a silly idea.

Every explanation I’ve read on this cannot resolve the problem without taking into account that one of the observers had to change inertial frames at some point, as I would expect, since that is the only difference, and thus the only means by which any explanation could be offered. However, it’s irrelevant since the time dialation is based on speed, and has nothing to do with inertial frame change or acceleration. In particular, I read one explanation that said that the paradox was resolved when you consider that bob occupies two different inertial frames, thus there are three frames involved. However this doesn’t resolve anything, it still doesn’t explain how you know that bob’s two frames are slower than tom’s one frame. I could just as easily say that bob’s two frames remain constant, and it’s tom’s one frame that runs slow. So we’re right back where we started, just now we have a third inertial frame tossed into the problem.

An explanation that does not take into account a change of inertial frame seems like an impossibility, but that’s exactly the point of the paradox, that’s where the paradox comes from. The paradox is that the idea of one frame’s time being slower than another’s based upon the speed between the two doesn’t make sense since there’s no means to determine which frame gets the slower time, and if they both get it, then there really isn’t any change.

Now why the twin story was ever created I’m not sure, I think the above paragraph sums up the paradox much better than the twin story, but just in case a twin story is necessary to figuring this out, how’s about we create a new twin story, since everyone keeps getting hung up on the change of inertial frame in the current one, and quite often I don’t think they even realize that they are taking it into consideration. I call this new twin story “the ‘my brain is going numb trying to sort out why I can’t understand something everyone else thinks is obvious and at the same time no one else can understand something I think is obvious’ paradox.” An appropriate name, I think.

Two twins, bob and tom, were born into seperate inertial frames (don’t ask how). They remain in these seperate inertial frames forever. Now, accordingly, since they are moving at a speed relative to eachother, there must be a time dialation between them, however, with nothing around to use as a refrence (there’s nothing else in their universe, again, don’t ask) each thinks it is the other who is moving away, and thus they can’t resolve who’s clock should be running slower. So who’s clock is running slower, bob’s or tom’s?

(BTW, if anyone says that both of their clocks are running slow, and thus they both see the same time, I’m going to go buy a baseball bat. Remember, it’s the relative speed of one frame as seen from the other frame, and it’s that speed that determines the time dialation, and that dialation is one frame’s time relative to the other’s, thus there must be a difference. You can’t just pick your own third frame in the middle and declare the dialation relative to that.)

Unfortunately, I can psychically see in the future that I’ll be given an explanation that involves them looking at eachother’s clocks over the distance, and through some sort of nonsense involving the speed of light and the doppler effect (not that the speed of light or the doppler effect are nonsense, it’s just he explenation I’ll be given will be nonsense) the explanation will be that you can’t see the dialation until one of them goes back to the other so they can compare clocks at a close distance and similar speeds and thus there’s no paradox, so before you say this, let me append to the end of this new twin story something I don’t think should have to be there:

For some mysterious reason, after some great time, bob and tom cease to move away from eachother, and both are accelerated equally until each is moving towards eachother. Later, they are accelerated again, once again equally, so that they end up right next to eachother with no movement relative to eachother. Now they compare clocks. Who’s clock is behind?

Unfortunatly, once again, I can psychically see being told that when it all starts out, one twin has his clock slowed, and when they reverse direction, it’s the other twin’s clock that is slowed, and thus they end up the same in the end. So if you’re thinking this, let me ask one more question: How do you decide who’s clock slowed first?

And having hit preview, I see that this will be the longest text I’ve ever seen in this message board, so let me thank everyone who made it all the way to the bottom for wasting 15 minutes of your life just for me. Thanks everyone.

Where you are running into difficult is the propostion that time dialtion has nothing to do with inertial frames, it does. In special realtivity accelarion is absolute. The Twins paardox is not a true paradox it’s results are self-consistent. As soon as you start bringing in accelration you break the symmetry that leads to the apparent paradox.

Perhaps some additional reading here might help explain it.

My physics education ended some time ago, but I believe the crucial observation for the Twin Paradox is that the relative speeds do not remain constant.

Sorry this post is so short … relatively speaking.

Me too, he chimed. As soon as I hit this line:

I went booiinnnggg.

You have to accelerate to get to time dilation speeds, and decelerate again afterward. So acceleration has everything to do with it.

It’s really quite simple and straightforward, and my understanding has nothing to do with acceleration.

When you are travelling near the speed of light, you distort. The speed adds mass, reduces volume, and slows time. From your perspective, everything looks and feels normal. That is because the actual space and time you occupy have been altered by your speed.

Take a spaceship on a circular journey 3 light years around, ending back at earth, at .99c. It will take you slightly more than 3 years. You will have aged 3 years.

When you get back, however, several hundred years will have passed on earth. This is because your time, which you altered by your velocity, moved at a different speed.

The main reason that c is a universal speed limit is that your mass will increase to infinite, or undefined. (You end up dividing by zero.)

This effect was experimentally verified using atomic clocks and jet airliners. It’s not a paradox at all. It’s an aspect of reality that speed can change it. (reality)

It’s really quite simple and straightforward, and my understanding has nothing to do with acceleration.

When you are travelling near the speed of light, you distort. The speed adds mass, reduces volume, and slows time. From your perspective, everything looks and feels normal. That is because the actual space and time you occupy have been altered by your speed.

Take a spaceship on a circular journey 3 light years around, ending back at earth, at .99c. It will take you slightly more than 3 years. You will have aged 3 years.

When you get back, however, several hundred years will have passed on earth. This is because your time, which you altered by your velocity, moved at a different speed.

The main reason that c is a universal speed limit is that your mass will increase to infinite, or undefined. (You end up dividing by zero.)

This effect was experimentally verified using atomic clocks and jet airliners. It’s not a paradox at all. It’s an aspect of reality that speed can change it. (reality)

Corrections welcomed.

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Ok, so… If bob and tom start in the same place, and accelerate equally in opposite directions so that they’re moving away from eachother, then some time later accelerate equally the other way so they’re going towards eachother, and then some time after that accelerate equally to come to be in the same inertial frame again, which one is older? There was a speed difference between them, and so there was time dialation, right?

No, twins travelling close to the speed of light, but in opposite directions, would still be exactly the same age. Take Ellis Dee’s experiment and say one traveller goes clockwise, the other counterclockwise. It makes no difference.

The rest of the universe will still have aged hundreds of years, though. Dig?

Who on earth is still calling the Twins Problem a paradox? The only paradox that exists is the one created by people who ignore the IRF requirement. The fact that you get a paradox when you ignore the requirement ought to be a clue that, duh, it really is a requirement!

Don’t get hung up on acceleration. The answer to your question is that they are the same age as each other. But when they both get back home, a few centuries will have already passed for everybody else.

Assuming, of course, that in each stage of your experiment, they were moving at the same speed, relative to the speed of light.

Hmmm…I could be wrong about the answer to your question. Let me try a different tact.

Take my example again. Bob and Tom both take a 3 light year journey that begins and ends at earth. But Tom goes “clockwise”, while Bob goes “counterclockwise”. They both will experience the same distortion when compared to the inhabitants of earth.

What this all boils down to is that it is indeed possible to make a trip to the nearest star in a single lifetime. If you travel at .99c, you’ll get to Alpha Centauri in about 4 years, and the return trip will take another 4. So you’ll be 8 years older. But it will have taken you 500 years to complete the trip, even though it only felt like 8.

There’s a time-traveling loophole built into the scenario, but I can’t seem to remember it properly. (Unless it is just that you could travel 500 years into the future.)

hehheh, jpeg beat me to it. I should preview more. :slight_smile:

That’s not quite it.

In your new example, the two travellers are moving with perfect symmetry — I assume you intend that the accelerations are identical, merely in opposite directions — and therefore neither of the twins will have aged relative to the other one.

Some points to keep in mind when considering the Twin Paradox:
[li]We’re given that one twin remains in an inertial frame the whole time, and the other twin undergoes accelerated motion. This is what makes their situations asymmetrical, and why the time doesn’t pass equally for each of them.[/li]
(The at-rest twin is normally said to be “on Earth”, which is not really an inertial frame either, but is close enough for the thought experiment.)

[li]Although velocity is always a relative physical quantity, and the universe has no preferred frame in which to measure it, acceleration is in fact absolute. Meaning, even if you shut yourself in a windowless spaceship in the middle of nowhere, any accleration you undergo is well defined and physically unambiguous, regardless of the motion of other objects.[/li]
[li]Special Relativity — in particular the Lorentz transformations — will give you the space contraction and time dilation between observers moving at constant velocity with respect to each other, as long as neither of them are accelerating. Both frames must be inertial. Adding acceleraton violates this prerequisite.[/li]
However, I believe it’s possible to reveal the Twin “Paradox” by applying the Lorentz transformations with some additional mathematical trickery, but I’m afraid I’ve forgotten how that’s done. In any case, it’s supposed to be more obvious if you apply General Relativity instead, because this model takes accelerations (and gravity) into account from the beginning.

I’ll take a crack at a simple explanation of the Twins Problem:

In addition to the IRF requirement, there are two more things you have to understand about relativistic effects as you approach the speed of light, c:

  1. The closer you get to c, the more exaggerated the effects become.
  2. You can’t simply add 2 velocities or effects seen by 2 different observers. Example: If Person-A is speeding away from an IRF Observer at 0.75c, and sees Person-B ahead of him and rushing away at 0.75c, that does not mean that the IRF Observer sees Person-B speeding away at 1.5c. The observer will see that Person-B is moving closer to c than Person-A, and that Person-B will be subjected to much more time dialation than Person-A.

Twins Problem:

Case 1: If you select an Inertial Reference Frame (IRF) in which the Brother Tom-who-stays-on-Earth is stationary, it’s clear that when Bob speeds away and then returns to Earth, that Bob has been subjected to more time dialation than Tom and that Bob’s clock will be slow.

Case 2: Select an IRF that matches Bob’s outward trajectory. During the first half of Bob’s trip, when Bob is outbound from Earth, he is appears to be stationary, and it’s Tom-on-Earth who appears to be rushing away and being subjected to time dialation. HOWEVER, when Bob turns around and rushes back to Tom-on-Earth, Bob is moving away from the IRF observer much faster than Tom-on-Earth. Bob has to be moving faster in order to reach Tom-on-Earth. So during the second half of Bob’s trip, Bob is being subjected to much more time dialation that Tom-on-Earth. If you actually do the math, Bob’s total time dialation effect turns out to be more than Tom-on-Earth’s. Why? Because the time dialation effect is much more exaggerated the closer you get to c, and no matter what IRF you use, Bob will spend more time closer to c than Tom-on-Earth does.

And that’s the whole point of the concept of relativity: different observers of the same event will measure somewhat different results, relative to their different positions and/or velocities, but science should be able reconcile these differences and show that all observations are logically consistent. e.i. At the end of the Twins Problem, the essential result is that Tom-on-Earth is older than Bob, no matter which IRF you use.

Peajay does raise an interesting point, though;

in an imaginary universe with no stars or other masses in it, except Bob and Tom …
one stationary and one already travelling at (say) 0.8c with respect to the other one
no acceleration involved (the universe was created that way)

how do we tell which one is moving at near light speed?

the one which is moving fast should have a much slower rate of time passing than the stationary one…

but as there is no absolute frame of reference both experience rates of time which are slowed with respect to the other!


of course this universe is entirely imaginary, so I expect it has no relation to the real world…

still, makes you think.

If we toss in the requirement that all things start in the same inertial frame, how about this story:

Say we have again a lone universe, except for three objects, A, B, and C. All start in the same inertal refrence frame. Object B and C accelerate to move together in the same direction away from object A. Now say that C departs from B’s inertial frame (while B continues on) and accelerates until it’s once again in the same inertial frame as A (although it’ll be pretty far from A at this point). So now B is moving at the same speed from A and C, and A and C are in the same inertial frame. Since A and C are now in the same inertial frame, they should be able to use telescopes to see eachother’s clocks and see that each is running at the same time as theirs, correct? Here’s the question: When BC left, since they accelerated, their time slowed down, right? Now since all inertial frames are equal, when C leaves B, C’s time is slowed down relative to B’s since it’s the one doing the accelerating. So how does C’s time being slowed twice put it at the same ‘time speed’ as A, which it must be at since it’s now in the same inertial frame?

You do see why I’m confused, right? I can come up with a lot more if anyone thinks it’ll help…

I just thought of this, which I think might explain the regular twin paradox, but I don’t think it does much for the one I just wrote. Anyway:

Maybe it isn’t the speed that causes the time dialation, but rather it is the acceleration. However, it’s not the fact that you are currently accelerating that does it, but rather it is the changing of inertial frames (a.k.a. accelerating) changing some sort of ‘time speed factor’ for yourself, and when you’re done accelerating, you still have that same modified ‘time speed factor’. Thus the Lorentz formula uses speed not because speed is the deciding factor, but because when you take an acceleration (m/s^2) and multiply it by the time you accelerated (s) you end up with an amount of acceleration, which is expressed in m/s, which is, well, speed.

This I might be able to believe, mostly because it doesn’t immediatly sound implausable, although it doesn’t sound completely correct either, such as how do you decide if a paricular acceleration will increase or decrease the ‘time speed factor’ . I’ll have to play with it for a while and see how it works out since I don’t think it’s impossible that it will. In the meantime I’ll just let someone tell me if thinking along that line puts me on the right track or not, and if not, then I guess we’re still at the paradox at the top of this reply.

If you’re having trouble understanding it via special relativity think about it this way. Time runs slower in a gravitational field, and in fact, for a faraway stationary observer time comes to a stop at the event horizon of a black hole.

The twin who turns around is perfectly free to consider himself at rest and that it’s actually the rest of the universe that’s accelerating. From this viewpoint he finds himself in massive gravitational well and his clock therefore runs slow with respect to the Earth based clocks.

It looks to me like A and C will show time passing at the same rate, but their clock don’t have to match. It is acceleration that causes clock wackiness…

In your 2nd post here you say that “there was time dialation”… which would be true if there was a 3rd party at rest someplace. As far as I can tell (and I may be corrected here), each person experiences similar magnitudes of acceleration, and thus their timepieces should still be synchronized.

Look…Here’s the true question…If a lawyer and an accountant were both drowning in a pond, and you could only save one…what would you do? Read the newspaper or go shopping?

If B anc C accelerate away from A, and C later returns to the same IRF as A, C has to decelerate (negative acceleration) to do this. Its clock was running slower during the acceleration, but when it again is in the same IRF as A, Cs clock is running at the same speed but shows an earlier time.

Wait a second here. If the twins take a 3 light year journey the IFR is earth and their trip takes three years. They come back a few minutes older, I am three years older, big deal.