# Need help understanding the twins

1. Nov 14, 2009

### Malorie

I am having some trouble undestanding why speed would cause time dilation.

Here's why:
Twin A travels at near the speed of light away from twin B for one year from in twin A's frame of reference. When he returns to twin B, he has aged two years but twin B has aged significantly more. Right so far?

What is the difference if it's twin B that does the travelling? Why would twin A now be the one to age faster? From twin A's frame of reference, nothing is any different, other than who experiences the changes in velocity to get up to speed.

This would imply to me that it's not the speed that dilates time, but the changes in velocity used to get up to speed. This would be consistant with with what we know about gravity and time dilation and the fact that gravity and mass are one in the same thing.

Am I missing something here?

Do we see time dilation between the equator and the poles, acounting for any gravitational or centrifugal differences?

Last edited: Nov 14, 2009
2. Nov 14, 2009

### Janus

Staff Emeritus
There are three factors that have to be considered when dealing with the Twin paradox: Time dilation, length contraction and the Relativity of simultaneity.

As far as A in concerned, he can consider B as the one moving, and from his measurement it is B that undergoes time dilation. But also, the distance between B and the turnaround point undergoes length contraction.

So for example, if the relative velocity of A and B is 0.866 c, and the distance to the point where A travels to is .866 ly as measured by B, then according to B, it takes 2 years for A to complete the trip, and A ages 1 year due to time dilation.

By A's measurement however, the same distance measured as 0.866 ly by B is only 0.433 ly due to length contraction. Thus according to A, a relative motion of 0.866c results in only 1 year passing before A and B rejoin.

Relativity of simultaneity explains why even though A measures B as aging more slowly on the outbound and return trips, he determines that B has aged more when they meet up again. In essence it means that when A turns around to head back to B, he changes inertial frames which causes him to determine that B has "jumped forward" in age between the times that they were heading away from each other and when they are heading towards each other.

In the example I gave this means that while they are receding from each other, according to A, B will age 3 mo, and the same will be true when they are approaching each other. So when A accelerated to go from heading away to heading towards B, B ages 1 1/2 years.

If you haven't familiarized yourself with the Relativity of Simultaneity yet, I suggest that you do so.

You can use the equivalent of gravitational time dilation in this problem, but you do have to be careful. Gravitational time dilation is not due to a difference in the gravitational force, but a difference in gravitational potential.

So for instance in your question about clocks running at different speeds at the pole and equator, the answer is no. While the gravitational force differs between these two points, the surface of the Earth is at an equal gravitational potential at all points, which results in no time dilation.

So for the Twin paradox consider this:

We add a third "twin". He travels at the same speed as A, using exactly the same acceleration at all points of the trip. However, after he reaches the point where A turns around, he continues on. He doesn't turn around until he reaches a point twice the distance from B. When he returns he will have aged 2 years while 4 years have passed for B. In addition, A will have aged 3 years. (1 yr during his trip and 2 years waiting with B waiting for the other twin to return.

So even though A and the third twin experienced exactly the same accelerations, they end up aging differently.

3. Nov 14, 2009

### Malorie

I think you missed my point. Or I may have missed yours. :)

With the twins, who's to say which twin should age? Without any outside point of reference and barring changes in velocity, the observation from either twin's point of view is the same in either case. Why would either twin age differently because of percieved speed which could only be measured from the other's point of view and would be exactly the same wheather A travelled away from B or B travelled away from A.

The only difference between each case (ie. A travels from and to B, or B travels from and to A) is the changes in velocity.

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4. Nov 14, 2009

### DrGreg

There is one significant difference between A and B. B turns round. A does not. When B turns round he feels a "G-force" of acceleration, and A does not, which proves that it is B who turned round, not A. So the situation is not symmetrical.

If neither turned round and just kept moving apart forever, there is no absolute answer to which of the two is older. And if, instead of B turning round, A decided to chase after B and catch up with him, then it would be A who ended up younger than B.

5. Nov 14, 2009

### tiny-tim

Welcome to PF!

Hi Malorie! Welcome to PF!

Two brief points:

i] Why are you using the word "inertia"??

("inertia" is usually another name for "mass")

One twin experiences acceleration, not inertia, to get up to speed.

ii] yes, gravity and acceleration are more-or-less the same thing …

and if one twin experienced changes in gravity while the other didn't (both remaining stationary), then the different gravity would cause a "time dilation."

What you're saying is;
If we analyse it the usual way, then the steady velocity causes the time dilation, while the three periods of acceleration (which can be as short as we like) contribute nothing

But if we analyse it substituting gravity for acceleration, and invoke the equivalence principle, then the gravity (which is standing in for the accelerations) causes the time dilation.​

No, between the affected twin's three changes in gravity (which can be as short as we like) there are two periods of steady gravity at a different strength to that of the unaffected twin.

And these two periods of steady gravity (which is standing in for steady velocity) contribute most of the time dilation … this is exactly equivalent to the effect of steady velocity in the original case.

6. Nov 14, 2009

### Malorie

I guess the confusion then is my use of the word inertia, I was mistakingly using it to describe changes in velocity. Fixed my previous posts. :)

Which would be why I said that the only difference between the two cases was that one of them experiences inertia. You could just exchange the words 'changes in velocity' or 'acceleration/deceleration' for the word 'inertia' in my post. Outside of that, the velocity itself is irrelevant as the pair could possibly be travelling through space at an unknown velocity at the outset of the experiment.

My whole point is that I don't believe it is the velocity that causes the time dilation, but the changes in velocity that do.

This is the only logical conclusion that can be drawn from this paradox.

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7. Nov 14, 2009

### DrGreg

Here's an analogy. Consider a triangle PQR. Why is PQ + QR greater than PR?

(a) because PQ and QR are not parallel to PR
(b) because the route P-Q-R is not straight and the route P-R is straight

In this analogy (a) is equivalent to there being a velocity between A and B. (b) is equivalent to B turning round.

8. Nov 14, 2009

### JesseM

Also, if you're dealing with paths on a 2D plane, you can add a cartesian coordinate system with x and y axes and then the "slope" of a path at any point (dy/dx) will be pretty closely analogous to the notion of velocity (dx/dt) in an inertial coordinate system in spacetime--if you have multiple paths between the same pair of points, then whichever path has a constant slope will be the the one with the shortest distance, analogous to how in spacetime, if you have different worldlines between the same pair of events (in the twin paradox, the event of the twins departing from one another and the event of them reuniting), then whichever path has a constant velocity will have the greatest proper time.

You can actually use the slope to find the rate that the length of the path is increasing with each incremental increase of the x-coordinate, and integrate over x to find the total length of the path, in a way that's analogous to how you can use the velocity to find the rate a clock ticks with each incremental increase of the t-coordinate, and integrate over t to find the total time elapsed on a given worldline. I expanded on this in post #64 of this thread:

9. Nov 14, 2009

### D H

Staff Emeritus
One way to look at the twin paradox is to determine what each twin sees.

Assume acceleration is essentially infinite (e.g., some future scientist has found a way to instantaneously transfer momentum to/from some parallel universe). With this technology, the space twin can instantly start moving toward some remote star at a large fraction of the speed of light. For instance, suppose the space twin moves at 112/113 the speed of light and that the star is 12.656 light years away in the frame of the Earth twin.

Suppose the twins remain in constant communication and that each twin regularly broadcasts time as measured in their own rest frames. During the outbound journey, each twin will see the other twin's clock running slow. Fifteen seconds will pass between each tick of the clock in the received signal due to the relativistic doppler effect.

This symmetric relation would continue if the traveling twin was the Energizer Bunny twin (she just kept on going and going and going). That is not what happens. The traveling twin turns around. A symmetric condition exists shortly before she returns to Earth: Each twin will see the other twin's clock as running 15 times *faster* than their own clock.

Some asymmetry must exist to have the traveling twin age less than the Earth twin. This asymmetry is the point in time at which the received signal switches from running 15 times slower to 15 times faster. For the traveling twin, this transition point occurs at the turnaround point. From her perspective, her Earth-bound twin ages 1/15*1/2+15*1/2=113/15 times as fast as she does.

For the Earth twin, the transition from slow time to fast time occurs shortly before the traveling twin returns. The traveling twin ages at a rate of 1/15*225/226+15*1/226=15/113 his aging rate.

(1/15*x+

10. Nov 15, 2009

### Malorie

First I would like to keep earth or any other objects in the universe out of this. Using them tends to muddy up the analogy. The twins are in a region of space where the only reference they have outside their own inertial frame of reference is the other twin. If we involve other objects, then there is a tendancy to think of one twin as if they were in some sort of rest state with the rest of the universe which we know is irrelevant.

Do you mean that we are assuming that neither twin feels the affects of acceleration or deceleration due to this awsome scientist? (they ROCK!!) ;)
OK, but remember that without any acceleration/deceleration fealt, there is no way to know which twin is doing the travelling.

OK. Still assuming neither would feel the acceleration or deceleration. How do we know which twin is doing the travelling?

In order to have one age differently than the other it is certainly reasonable to assume there has to be an asymmetry. :) But again, how do we know which twin is doing the travelling without any acceleration/deceleration fealt?

I guess this is where I'm getting totally lost. Why would either twin experience anything different from the other. We have no way to know which twin is doing the travelling.

Without any acceleration/deceleration, it could be that;
Twin A moves away from twin B then stops moving in relation to twin B, Then twin B moves to rejoin twin A.

Or twin A moves away from twin B, turns around and comes back.

Or both twins move away from eachother an equal distance and come back the same distance to rejoin eachother.

Or any other of another million other possabilities.

Without the acceleration/deceleration, there is no reason to believe that there would be any time dilation whatsoever.

Again, the only logical conclusion here is that time dilation is only due to the acceleration/decelleration and has nothing to do with the velocity (speed of travel).

11. Nov 15, 2009

### D H

Staff Emeritus
Sure there is. Suppose the twins start at rest with respect to the target star. This means the star will have zero transverse velocity when viewed from the perspective of a non-rotating frame and the star's hydrogen alpha line will be at 656.281 nanometers. Note that other nearby stars might show some proper motion and their Hα line might vary a bit from 656.281 nanometers due to a non-zero radial velocity. However, this observed proper motion and radial velocity will be small compared to the speed of light.

Now the traveling twin presses the magic button. From her perspective, the target star's Hα line will blue-shift to 43.7521 nanometers, well into the ultraviolet. The Hα lines of the stars directly aft will red-shift to about 9.8442 microns, well into the infrared. The stars off to the side will show a huge proper motion. The stationary twin sees exactly what he saw before his sister pushed the button.

That is just wrong.

12. Nov 15, 2009

### Malorie

There is no target star in this scenario. As I said at the start of my last post, other items in the scenario will just confuse the subject. So the twins are in a section of the universe with no frame of reference other than the other twin.

You are implying that the twins are starting out in some sort of universal rest state by putting in a 'target star' and other stars. Then you are using that target star as proof of who is travelling.

What if the target star and everything except the other twin was matching the movements of a twin travelling away from and to the other twin? We end up with the same thing you discribed except now the star and everything else is travelling as well and the stationary twin sees the blue and red shifts. Again, I want to keep the outside celestial stuff out of the scenario to reduce the confusion.

The scenario as it was in my last post illustrates my point that there is no way to know which twin is travelling without any other reference than the other twin or the percieved acceleration/deceleration. Which follows that without knowing which twin does the travelling, there is no way to imply which twin should age faster. And that leads us logically to the fact that the velocity has nothing to do with the time dilation.

Stating that something is 'just wrong' is not an answer to anything it is just your assurtion.

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13. Nov 15, 2009

### JesseM

You don't need any external objects to determine who moved inertially and who accelerated and changed velocities relative to all inertial reference frames. In flat SR spacetime with no gravity, whichever one moved inertially will have felt weightless throughout, while the one who accelerated will have felt G-forces during the acceleration, which could be measured with an accelerometer.

14. Nov 15, 2009

### Malorie

As DH stated
Remember the future scientists (who ROCK!)?
Without any acceleration/deceleration there is no way to tell which twin is the one travelling.

This is the whole point of my post and my confusion with the twins paradox. Without the affects of acceleration and deceleration all we are left with is realative speed and there is no way to assign that speed to either twin and therefor sensless to assume that either twin would age differently than the other. This implys that the affects of acceleration and deceleration are the only thing that cause time dilation and velocity has nothing to do with it.

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15. Nov 15, 2009

### JesseM

Even if the change in velocity is instantaneous, you can still detect that you've accelerated--for example, if you have a ball floating in a vacuum in the middle of the ship which isn't connected to the rest of the ship in any way, then when the ship instantaneously accelerates the ball will continue to move inertially, so observers on the ship will see it appear to suddenly change speed relative to themselves.

16. Nov 15, 2009

### D H

Staff Emeritus
The whole point of that supposition was to simplify the math. I could just as easily have said that science has developed some new technique that allows the traveling twin to withstand arbitrarily high accelerations.

It is important to remember that neither the ability to withstand high acceleration nor the ability to transfer momentum to another universe does not exist. In comparison, time dilation and length contraction are very real.

You appear to be intentionally misunderstanding the twin paradox.

Acceleration does not affect the rate at which a clock ticks. This is the clock hypothesis, and this hypothesis (along with other aspects of relativity) has been tested multiple times.

17. Nov 15, 2009

### Malorie

I'm not trying to argue that you could or couldn't detect the acceleration.

What I am saying is that without any way to detect acceleration, all you are left with is the relative speed. And relative speed doesn't logically cause any time dilation because you can't assign that speed to either twin if you can't tell who is doing the travelling.

DH,
So previously, you accepted my interpritaion of your scientists and now you don't?

I said;
No, you are missing my point.

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18. Nov 15, 2009

### pervect

Staff Emeritus
It does not follow logically that "relative speed can't cause time dilation", unless you make additional assumptions about time.

I can probably even guess what additional assumptions you are making, but it might be more instructive for you to work them out for yourself. Logically, what properties does time need to have so that your argument follows? You have made an intuitive leap here, you'll need to fill in the missing parts of your arguments to proceed to finding the error. (I suppose I should be diplomatic and call it a difference of thinking, but I'm feeling a bit grumpy today, so I'll be straightforwards and call it an error.).

19. Nov 15, 2009

### Malorie

Thanks for the insight on this pervect. NOT!!!

If all you are going to add is that you think I'm playing a game or something then don't.

I'm being as clear as I can think to be.

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20. Nov 15, 2009

### JesseM

But in relativity there is an objective physical truth about who really accelerated, which is why it's important that you can in fact always detect it physically. Your argument seems equivalent to "if there was no objective truth about who accelerated, all you'd be left with is relative speed"--well, there is an objective truth, and that's why there can also be an objective truth about which twin aged more?

Did you read through the analogy with the two paths on a 2D plane, with slope standing in for speed and change in slope standing in for acceleration? Do you agree there's an objective truth about which path is straight (constant slope) and which is bent (change in slope), and that the straight path between a pair of points always has a shorter distance than a bent path between the same pair of points? If I and a friend are driving down the two paths measuring our distance with our cars' odometers, I suppose you could argue "if there was no objective truth about whose slope/direction changed, then all you'd be left with would be the relative angle between the direction the two cars are moving at each instant, and since this is symmetrical there'd be no basis for saying one car's odometer would have measured a greater distance than the other when the two cars reunited". But it's a moot point, because geometrically there is an objective truth about which path is a straight line and which isn't, and it will always be the straight path which has a smaller distance.