The Twins' Paradox

Robby · #1 23-05-2005, 07:14 PM

I'm starting a seperate thread for this.... This has puzzled me for awhile now, so anyone got any ideas??

I've always been confused by the "twins paradox". One twin leaves earth travelling at close to the speed of light. He returns some years in the future and due to relativity the twin the remained on earth has aged alot more than the travelling twin.

I can understand half of it, based on the clock explanation...
If we travel away from a clock at close to the speed of light, the time on the clock will appear to run slower. This is fine. This must mean that when you head back towards the clock, the clock will appear to run faster. Therefore when you return to the clock the same amout of time will have elapsed for both the traveller and the clock.
This seems to contradict the "twins paradox". Sure when the traveller is travelling away from home, time for the traveller is slower (relative to earth), but on return time is faster. Surely these would cancel each other out and the twins should have aged by the same amount.

I'm probably missing something here??
Cheers

[1ponders] (Paul) · #2 23-05-2005, 07:25 PM

Robby, it doesn't matter which direction you are going, away or towards someone. Its your relative speed that's important. For someone at rest (relative) viewing someone travelling, the traveller time will appear to be slowing, regardless of direction. It has little to do with the speed persay, but more to do with the increase in mass and therefore local gravity field and its effects on space time. The faster you go the heavier you weigh the more effect you have on spacetime through gravitational distortion, sort of. It can be seen in the effect of gravity round a black hole. If you viewed someone falling into a black hole, they would appear to slow down and it would take foreever to cross the event horizon. For the person falling the crossing would seem normal. There have been experiments done with very accurate clocks, one on earth and one in space the the one on earth ran slower due to the greater influence of gravity.

If anyone is seriously interested in this stuff then I can highly recommend a book called "The New Physics" a collection of works by leading modern astrophysicists and mathematians like Steven Hawkings on quantum gravity, black holes, big bang, nature of the universe... yadda yadda, and all sorts of aesoteric "stuff". If you can ignore most of the maths (I did) its an interesting read.

mojo (Terry) · #3 23-05-2005, 08:28 PM

Quote:

Originally posted by [1ponders]
There have been experiments done with very accurate clocks, one on earth and one in space the the one on earth ran slower due to the greater influence of gravity.

clocks on GPS satellites run fast.

acropolite (Phil) · #4 23-05-2005, 08:50 PM

Paul's right about GPS clocks. There are adjustments made to account for the fact that time at the surface is affected by gravity more so than in space.

Dennis · #5 25-05-2005, 06:26 AM

Hi

Hmm, my physics is a bit rusty but I seem to recall that relativistic time dilution (slowing of clocks) only occurs during the acceleration phase of leaving the Earth, the deceleration phase prior to the turn round, the re-acceleration phase to come back to Earth and the deceleration phase when arriving back on the Earth. Whilst traveling at uniform motion in between these phases, with no acceleration and no relativistic effects due to e.g. large mass bodies nearby, time on the Earth and time on the spaceship would "tick" by at the same rate?

Cheers

Dennis

acropolite (Phil) · #6 25-05-2005, 07:56 AM

The GPS time difference is well documented, I read about it in an article in one of the electronics Journals some years ago. Check out this link.
http://egtphysics.net/GPS/RelGPS.htm

[1ponders] (Paul) · #7 25-05-2005, 09:06 AM

That's right Dennis. No accelleration, mass returns to normal, space time curvature returns to normal around the mass. For *significant* effects both accelleration and decelleration need to be at relativistic rates.

Robby · #8 25-05-2005, 09:20 AM

Thanks for the feedback guys.
I know what you are getting at, and you buggers are all too clever for me. I know what you are saying, but I just can't seem to get my head around it...!! I guess this is the point at where you have to let the Math's speak for themselves....
Sun's out, so that must mean time to return to imaging.. Oh arn, moons up to. Ok Jupiter it is.
Cheers
Rob

slice of heaven · #9 25-05-2005, 10:10 AM

I think you got it in reverse Dennis.
The main point of Robbys question is that its a paradox.
So its logical not to understand it. Its a contradiction.

If we simplify it and dont try to prove it wrong or right it goes like this.....
Time is relative to your reference frame(where you are,your movement etc).The guy on earth maintains his reference frame and time ticks away normally for him while his twin goes for the joyride. The twin travels at near lightspeed so he has a different frame of reference and time slows down (only compared to the guy on earth, not to the twin).It doesnt matter which direction he goes as long as he maintains that frame of reference time will pass slower. When the twin arrives back on Earth less time has passed for him than the guy on Earth.

Time passes at different rates depending on where you are and your motion. Thats why clocks run differently on Earth compared to other locations off the planet. The gps clocks was a good example.

Dennis · #10 25-05-2005, 09:50 PM

Hi Slice

Not sure what you mean by "got it in reverse”?

The intent of my reply was to share my understanding that the slowing of a clock during the "return to home" and the "traveling away from home" journeys, occurs only during those phases of acceleration and deceleration, and not in a reference frame in uniform motion. Therefore, the canceling out effect that puzzled the original querant would not occur.

Cheers

Dennis

slice of heaven · #11 25-05-2005, 11:19 PM

Sorry Dennis my apologies
Probably didnt come out the way it shouldve. Too early in the morning probably.
I think the paradox was created to show differences between general and special relativity.
Time dilation also occurs while the twin is travelling at a faster speed than the guy on Earth. Even though the twin seems to be in a state of rest ,as is the guy on Earth, its not the same frame of reference as the guy on Earth because of the speed. If the twin had instant acceleration and instant decceleration and travelled at near lightspeed time dilation would still occur.

Dennis · #12 26-05-2005, 06:23 AM

Hi Slice

No worries - just checking if I had missed something as I am far from having a thorough understanding of relativity, especially the differences between the special and general models.

I must read further as your last sentence about time dilation at near light speed at constant speed is a new one to me - a nice read for one of those cloudy nights.

Cheers

Dennis

slice of heaven · #13 26-05-2005, 09:59 AM

Hi Dennis
In the early 1970s the Americans tested this theory using 3 clocks.1 stayed in the lab and the other 2 were sent on different planes ( around the world ? I think) in opposite directions. The clocks on the planes went slower , compared to the clock in the lab. Thats due to special relativity. All variables were calculated out of the equation ..acceleration, decceleration, Earths rotation etc.
That experiment was the only reason I had the chance to understand it .
To throw another complication in there is also length contraction as well as time dilation, so the twin also covers less distance than youd expect.

Vermin (Tom) · #14 26-05-2005, 11:11 AM

Quote:

Originally posted by Dennis
...time dilation at near light speed at constant speed is a new one to me

Where t is the time interval in the stationary frame, t1 is the time interval in the uniform motion frame, v is the relative speed, and c is the speed of light:

http://www.mrelativity.net/Equations...s/image002.gif

Lots more here:

http://www.mrelativity.net/Equations/Equations.htm

slice of heaven · #15 26-05-2005, 05:09 PM

Thanks Vermin
Now your going to have me reading up on it too. I understood the basic principle but that goes over my head. Seems everything is affected except for the size of your shoes.
Like Dennis said...A nice read for those cloudy nights.

Now we have 3, 'general' ,'special' and the new but not widely accepted 'millenium'.

Vermin (Tom) · #16 26-05-2005, 08:43 PM

I don't profess to understand the entire derivation of the equations but they are beautiful in their simplicity.

The jumble of terms after "t" is the key.

As the relative velocity "v" tends towards the speed of light "c" the whole lot tends towards 0, i.e. SQRT(c^2 - c^2) = 0

I graphed the change to get a feel for the rate of change - rather than trying to differentiate it

It starts off as a very small effect, you have to be going 30% the speed of light (90,000 km/s) before you see about a 5% change in time, length or mass (compared to the stationary reference frame). No wonder Newton did not notice it!

hector (Andrew) · #17 29-05-2005, 10:39 AM

Hi All
The effects of Relativistic speeds are not dependent on acceleration.
It is the speed that counts.
the faster to the speed of light you travel 3 things occour. Time slows down Mass increases and size decreases from a NON relativistic standpoint.
What does that mean??????
You are standing on a stationary platform in orbit about the earth and you are watching a spaceship traveling at very near the speed of light. In the window you can see a clock. That clock is ticking slower than the clock standing next to you.
At the same time your viewer devise that allows you to see into the ship is able to measure sizes of objects. you set the viewer on a 1 meter ruler that is lying conveniently next to the clock. your viewer measure the ruler to be SMALLER than 1 meter.
also at the same time your viewer devise is able to accuratly measure the mass of the ruler which you know is a standard metric kilo. the viewer tells you that the rulers mass is MORE than a kilo.
so from YOUR perspective the time on the ship is travelling slower, the mass of the ship is increasing and the size of the ship is shrinking.
an observer on the ship notices NOTHING ON THE SHIP, but if the man on th ship was to look out the window and observe you he would notice that the clock next to you the stationary observer would be ticking FASTER than the clock next to him. He would also notice that the viewer he was using would be telling him that your mass is less and that your size was expanding.
Acceleration does not come into the picture. once you are traveling at the spoeed of say 99.99999999% the speed of light relativistic effects are already taking place. they will not change till you slow down.
this is an observable effect.
In a particle accelerator certain particles have a limited lifespan. The Neutron lasts for about 11 seconds on its own before it decays into a proton and an electron and a neutrino. In a particle accelerator a neutron has been seen to last for several minutes.this is time dilation. The mass of a neutron is known and can be measured by impact. the measurement of the neutron that was travelling at 99.999999999% of light speed impacts with more mass than it should. this is mass dilation. Measuring the size of the particle is beyond science at the moment but since the first two effects of relativity have been accuratly measured, and are in complete accordance with prediction I will assume that it inly a matter of time .