# How does time dilation really work?

1. Jun 1, 2009

### Negatratoron

I have a problem with time dilation... You have all heard the story where there are two identical twins and one goes on the space ship and flies around at nearly the speed of light, comes back, and is still young while everyone on Earth, including the twin who stayed there, are old. But... What if you were the twin on the spaceship? You would see the universe moving around you at near the speed of light and time passing slower for it, and you would think that you grew old while everyone else stayed young, aye?

If the twin on the earth sees the twin on the space ship as moving and himself as staying still then time dilation applies to the one on the space ship and they would see the twin on the space ship come back and say "Ooh, you look so young!" But if you were the twin on the space ship, the earth and everything would be moving relative to you, time dilation would apply to the twin on the earth instead of you, and you too would be like "Ooh, you look so young!" So depending on the frame of reference that you use for your calculations, a different person grows old... What am i not getting about this?

2. Jun 1, 2009

### mgb_phys

The twin that was on the spaceship turned around and came back so they accelerated - so special relativity doesn't apply.

eit - no faq but wiki has quite a good overage of this http://en.wikipedia.org/wiki/Twin_paradox

3. Jun 1, 2009

### sylas

Special relativity DOES apply. What does not apply is the simple case for a single frame of reference.

Special relativity is perfectly able to handle accelerated motions, as complex as you like. What special doesn't handle is gravity... and gravity is not involved here, only acceleration. In fact, general relativity is obtained by a kind of equivalence of gravity with the effects of acceleration that can be obtained using special relativity.

Cheers -- sylas

PS. Wikipedia links to what is IMHO a better explanation at the Usenet physics FAQ. Here's a discussion of special relativity and acceleration in the same FAQ.

Last edited: Jun 1, 2009
4. Jun 1, 2009

### Negatratoron

Okay, that helps some. I read That one from the Usenet physics faq, but I still have a problem with that analysis. I saw a similar argument to the one on that page in a physics textbook, and that's what I'm going off of, so the numbers will be different but the argument works the same way.

O is the Earth, ( and ) are light pulses, and carats are the ship traveling. For convenience when calculating elapsed time, flashes are emitted every 6 minutes (instead of the 7 from the website) and the ship is traveling fast enough to double or halve the frequency depending on which direction it's going. It travels out for an hour and then back for an hour, according to its own clock. Please pardon the ASCII art as I draw this out:
Code (Text):

O sees flashes every 12 minutes as the carat departs:
O   (   (   (   (   (   (   ( >

O still sees the departing flashes every 12 minutes, return flashes piling up, invisible to it as of yet:
O   (   ( ( ( ( ( ( ( <

O finally sees returning flashes every 3 minutes and the carat is already partway back:
O ( ( ( ( ( <

The carat emits 20 flashes total at 6-minute intervals, totaling 120 minutes = 2 hours.

The O sees 10 12-minute flashes and 10 3-minute flashes by the doppler effect, totaling 150 minutes = 2.5 hours

Or you can look at this if the O is emitting the pulses of light instead:
Code (Text):

O is sending flashes every six minutes; carat sees them every 12 minutes as it departs
O  )  )  )  )  >

Return trip: carat moves ahead to meet flashes coming from the O as they travel and sees them at 3-minute intervals
O  )  )  )  <

When the carat is at its turnaround point, it has been out for one hour according to its clock; it sees 5 flashes of 12 minutes each. While the carat returns to O, it needs to account for that other hour and it takes 20 flashes of 3 minutes each to make that work.

So we have 25 flashes total: 2 hours for the carat is 2.5 hours for the O.

But everything that I just said can be easily reversed. Just swap the symbols so that carats are the earth and O represents the ship. Now you have become the twin on the ship, the fixed reference frame.

5. Jun 1, 2009

### sylas

There are some other rather drastic differences. The frame for the twin on the ship is not a single inertial reference frame, but two different inertial frames at least (instantaneous turn around) or else it is an accelerating reference frame, in which strange things happen, like remote objects moving backwards in time.

But keep it simple. Image an instantaneous turn around, using some space warp of some kind that turns the ship through 180 degrees at a fixed instant.

The twin on the ship sees redshifted pulses on the way out, and blueshifted pulses on the way back. It sees these for equal amount of time.

The twin at home sees redshifted pulses for a much longer period... the time for the trip PLUS the time it takes light to get from the turn around point back to Earth.

Here's a diagram I have used in other threads, representing a trip at 60% light speed to star six light years distant. It takes 10 Earth-years for the trip, and 10 back again, during which time the ship experiences 16 years.

Note that there is a drastic discontinuity in the "frame" of the travelling twin, in which Earth is suddenly moved 9 light years away and 9 light years back in time. This is simply the result of a new perspective when they turn around. The angle subtended by Earth in the sky would also suddenly reduce by a factor of 4 when the remote twin turns around, because in the new perspective the light is coming from a point four times further away.

The twin at home sees no such discontinuity.

Cheers -- sylas

6. Jun 2, 2009

### Negatratoron

Ahh, now we're getting somewhere. Thank you sire for helping.. I don't mean to be frustrating, but i'm still sorta confused.. Let's take this into a void with absolutely nothing in it but two ships. One fires its thrusters and moves away, and then comes back, and the ship that does not fire its thrusters explodes a bomb like in those figures. You could say that the stationary ship is the dark green line and that the ship that fired its thrusters is the purple and brown lines... But from the perspective of the people on the ship with the thrusters, the ship without the thrusters went away from it, and then sharply started coming back towards it. You could just decide that the ship with the thrusters drops a bomb such that the light will reach the one without the thrusters as soon as it changes directions and starts making the return trip, and make that your fixed reference frame.

As i wrote that, i think i figured something out too, that would differentiate the ships. The ship that fires its thrusters feels its own inertia as it moves. Maybe that acceleration, even if instantaneous, somehow.... But the reason I think that shouldn't matter is that because this universe is made entirely of a void and two ships, you on the thruster ship might as well just say "Our ship didn't move at all. We are the reference frame. That other one had the instantaneous acceleration." I don't know any formulas whatsoever that apply to this, and acceleration was mentioned in an earlier post here, but... All I can say is that inertia could be used to differentiate the two ships. I'm not sure exactly why or how it would impact time dilation, though, if at all.

7. Jun 2, 2009

### yogi

There are many ways of working out the twins puzzle that give the same correct answer - you can send signals back and forth, count pulses and take into account the Doppler shift going out and coming back - you can use the fact that the slope of the lines of simultaneity change when the twin turns around, or you may prefer to approach the problem as Einstein did in his 1918 article and use a pseudo G field to explain why the home twin's clock apparently jumps ahead etc. For me, most of the methods always left me wondering "why did it work?" So it seems easier to break the problem into two parts, then apply the idea of the invariance of the spacetime interval to each half of the trip - so on the outward leg, there are two spacetime points - the starting point and the destination point - the traveling twin's clock willl have accumulated less time when he goes from the start to the turn around point on the outward leg - to get the final result, double the result for the one way trip.

There is at least one other poster and myself that keep trying to get this across (AI68)

8. Jun 2, 2009

### sylas

Yes. This is one of many ways in which the two ships are different., even from their own perspective.

It's not the acceleration that matters, but the change of velocity. If you hard a warp drive that somehow reverses your direction without acceleration, it would still be the same. Imagine two space ships passing by one another, and Captain Kirk using a teleporter to jump from one to the other as they are passing. No acceleration; but a change in reference frame.

There has to be more in the universe than the two ships, if they can see each other. There needs to be light. There needs to be a reaction mass if you are using thrusters. Here are two more differences for you.

Angular size

The ship that reverses direction sees the other ship suddenly become much smaller in the sky, as if the light is coming from much further away. That is because the the light IS coming from much further away, in the new frame of reference.

The ship that remains inertial sees no change in the angular size of the other remote ship when the other one reverses direction.

One shift, two shift, red shift, blue shift

If one ship moves away from the other at 60% light speed, moves for eight years by their own clock, then reverses direction and returns at 60% light speed, then they see the other ship redshifted for 8 years, and blue shifted for eight years. The factor of the shift is two. (Frequency is halved, then doubled).

The ship that remains inertial sees the other ship red shifted for 16 years, and then blue shifted for 4 years.

Cheers -- sylas

9. Jun 2, 2009

### matheinste

Hello yogi.

I have seen this point raised by yourself and Al168 before but have not commented because at previous times I was not completely at ease with the so called paradox. It is perhaps strange that this simple resolution is not more widely used. An example of its being almost disregarded comes from the January issue of The American Mathematical Society journal which carries a very good 17 page exposition of various aspects of the problem. The author is Alfred Schild. In these 17 pages appears just one paragraph on page 14 relating to the “twice the one way trip” resolution. After a comment on fallacious Lorentz transformation arguments it carries on

-------- It is perhaps worth mentioning in passing that there is a simple Lorentz transformation argument which is correct------

and in the space of only 8 lines explains, very simply, how this very simple argument works .

Perhaps this method is less informative for the teaching of SR. Even so it may help those who cannor grasp, or have misgivings about some of the other resolutions.

Matheinste.

10. Jun 2, 2009

### getitright

Okay folks, take a second and feel your hearbeat. You can if you try without having a finger on your wrist. Now get in a Corvette and floor it as fast as it will go while your twin is with your girlfriend. Keep in mind you are moving away and time differential should be able to be measured.

If time travel was possible to manipulate then I would not have bought the Corvette and might have a family by now.

11. Jun 2, 2009

### mgb_phys

Sorry I was over-simplifying the answer. The reason for the apparent paradox is that you don't have an equivalent frame of reference for the two twins.

12. Jun 2, 2009

### sylas

Yes... on the same page again! That is indeed the heart of the situation.

13. Jun 2, 2009

### Negatratoron

Okay, so i think the thing that was screwing me up was a bad definition of "frame of reference"... i was thinking that a frame of reference was nothing more than a coordinate plane calibrated at every instant to set the coordinates of a specific object all to 0... Apparently it is more than that. i guess i will have to go learn some heavy duty relativity math... 'figure out what frames of reference really are and how to shift from one to another... Changing bases in linear algebra comes to mind.... AP physics next year :) will be fun. Maybe that will help.. Have a nice day anyway. Or if y'all are prepared to explain in great detail what a frame of reference is, how it works, how to convert from one to another, and all that stuff, that would be just dandy.

Or if the above paragraph on what i think was wrong with my logic doesn't actually have anything to do with what was wrong with my logic, then i'm not done here. This is fun.

14. Jun 2, 2009

### matheinste

Hello Negatratoron

The twins paradox is not the best starting point for relativity, or to answer your original question on time dilation because it is always the subject of endless discussion and unnecessary confusion.

Matheinste.

15. Jun 2, 2009

### sylas

The thing is that inertial frames are special. They are the ones within which the laws of physics are what you are used to. There are a couple of ways you could define a co-ordinate system for accelerated observer, where they were always at location "0", but in such a frame you will find various things that never show up in an inertial frame, like like particles moving much faster that light, or light that moves as slowly as you like, or event horizons, or even time running backwards for remote particles. Such frames are not particularly useful.

Lorentz transformations can map co-ordinates in one inertial frame to those in another. You can correctly calculate the age of any twin, no matter how that twin accelerates, by finding their world line in any inertial frame and then integrating proper time u, using
$$du^2 = dt^2 - dx^2$$​

You can, if you like, calculate the age of a twin piecewise, by picking a series of "events" for any given twin, and calculating the age change between events with different frames. The age change between events is the same no matter what frame you use, so this works too.

Cheers -- sylas

16. Jun 2, 2009

### mgb_phys

Probably the simplest explanation to the paradox is that the twin on the spaceship could measure the acceleration as they turned around - and so they can say that they were the 'moving' one.

17. Jun 2, 2009

### Al68

Each method has advantages and disadvantages, the reason I like the "twice the one way trip" is because realizing that a one way trip has the same fundamental result of differential aging almost makes the other resolutions superfluous. And if done correctly, it shows why the two way trip works the way it does.

And it eliminates every common objection to the other resolutions. I'll have to read the article you cite, is it online?

18. Jun 5, 2009

### matheinste

There is a website for the journal but the article is probably not avaiable for free. I would be happy to email you a copy in DJV format but I don't know if that is within the rules.

Matheinste.