The Twins Paradox

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The Twin Paradox: If one identical twin left on a rocket ship at near the speed of light and then returned to Earth, the two twins would be of different ages, with the travelling twin the younger of the pair.

OK, here is my thought: Since all motion is relative, couldn't the twin on the rocket ship just see the entire universe speed away at nearly the speed of light and then return, making the twin still on Earth the younger of the pair?

Clearly, I am missing something...

Could someone (i.e. Darkthrone) explain to me why I am wrong?

 

No - the difference between the two is acceleration. The twin on the rocket ship has had to turn round, which requires a change of velocity - i.e. an acceleration. The twin paradox is an example of Special Relativity - the "Special" means it is a theory only applicable to a specific case; motion at constant velocity, without a gravitational field. Because the rocket twin has accelerated, a part of his motion is not "relative" - basically, you can tell it is him that has accelerated, not the Earth-based twin. His motion is only completely described by General Relativity - and you don't want to have to go in to that, believe me.

 

But why is the rest of the universe not accelerating away from the twin and then accelerating back? Why is it just the rocket ship that is accelerating?

Edit...Oh because of inertia...OK

 

Here's another related question: Would a trip at the speed of light be instaneous relative to the perspective of a person making the trip? Using the example above, if the twin traveled 10 light-years (at the speed of light), and then turned around and came back, 20 years of time would have passed on Earth. However, for the twin abord the spaceship, would the trip have seemed instantaneous?

 

Huh? Some of you people are far too smart for your own good (I think - I can't tell if you're making sense or talking gibberish!)

 

@AFI:
Actually, I think that's one point that Einstein never found an answer to. He had it just fine as velocity approached the speed of light, but if you were to actually reach it, what would happen is anyone's guess.

 

Hmm... That's a slightly irrelevant question, because nothing with finite rest-mass can ever travel at the speed of light. Only particles of zero rest mass can ever attain the speed of light, and their journeys do take a finite amount of time. Assuming a journey at 0.999...c (where c = the speed of light in a vacuum), then sure, the difference in their ages might be huge, but no one's ever going to have an instantaneous journey. That would imply infinite velocity, and that ain't possible.

 

OK Magpie, let me restate the question. If the trip was conducted at 0.9999 the speed of light, would the length of trip from the perspective of the person taking the trip be considerably shorter?

 

Time for the Stars, Robert Heinlein, 1956

Time is relative and dependant on the difference between the speed of the individual and the speed of light. As the rocket increases speed the difference becomes smaller and time, as it effects the rocket ship and it's passengers, slows down (i.e., the occupants age slower, act slower, etc.). According to theory, time would stop for the occupants if the rocket acheived the speed of light (and they would also attain infinite mass).

Of course, this could be all bunk. It's just a mathematical possibility derived from the Theory of Relativity.

 

T2Bruno, it certainly sounds like bunk to me. How can flying in rocket really fast make you 'act slower' (or 'more slowly')? Sounds like a contradiction.

 

Heh. It's a mathematical prediction which has been experimentally tested.

Take muons, for example. These are unstable particles, which are produced in the upper atmosphere by cosmic rays. One can compute the lifetime of muons (how long it takes them to decay); it comes out to about 10^{-6} seconds (I think) -one milionth of a second. Now, even if they move with the speed of light (3x10^8 m/s) they should be able to travel no more than about 100 meters before they decay, and therefore we should not see any at ground level.

However, because of the time dilatation effect, muons live for about two hours in our reference frame (they really go with 0.9999 of the speed of light). So we can see them at ground level. So time dilatation is real and it can be a big effect. Now, the problem is getting so close to the speed of light in the first place ,

 

@ HB

It all comes back to the fact that light travels at a constant speed for every object. How it all comes back...well, I have no idea. But if an object flying away from you at .9999 c emitted a photon, you would still measure that photon travelling past you at c, not .0001 c.

 

T2Bruno is right - time dilation does occur as you approach the speed of light. Where confusion occurs (and where I misunderstood AtFI's question ) is that although the interval between any two events is greater in the rocket as measured from a "stationary" perspective, as far as everyone on the rocket is concerned, nothing unusual is happening. Time is appearing to pass normally - in fact, as far as they're concerned, it's the people on Earth who have abnormal timekeeping. That's because relativity - as it's name implies - removes all absolute notions of time and space, and everyone will measure different lengths of a second and a metre at different velocities.

 

Questions:
1) What is a "muon"? (sounds like some sort of Japanese anime monster)
2) How come SP is suddenly full of masters of quantum physics?

 

we haven't even broached quantum yet -- only particle physics and relativity.

I have a copy of Cohen-Tannoudji in my bookshelf when we start on quantum....

Oh, yeah -- I recommend the Heinlein book. It's a bit outdated, but an interesting read.

 

Harbourboy:
1) a muon is sort of a 'brother' to the electron that is, is identical in every way to the electron, except is about 200 times heavier (and it does not live very long). It has been discovered around the fifties, I think, so this is not exactly "the bleeding edge" in particle physics

2) there are 'masters' on about every topic on these boards, so why not quantum physics ? really now, I thought this stuff is taught in undergrad physics these days (granted, not many people bother with those courses).

 

OK...here goes...

So lets say a rocket ship is speeding away from Earth at .999 c and the dashboard "seatbelt" light is on. Now the pilot (me) is going to measure that stream of photons passing by at c, however, as the photons stream out the back window, an observer (my ex-girlfriend) on Earth would also record them speeding by at c. Since, from the perspective of my ex-girlfriend, I am speeding away at .999 c, for me to measure that stream at the same speed (i.e. not 1.999 c), my sense of time must be a lot slower.

Here is my issue (among many others not related to physics): That would make my velocity versus my sense of time inversely proportional on a one to one scale. However, I know this not to be true; time dilation can only be noticed nearing the speed of light. According to my scenario, I should measure time at half the rate of my ex-girlfriend when I am moving at half the speed of light. But that is not true.

So I am missing something...

Sigh.

Edit...

Wait up...if my sense of time slowed down, wouldn't I measure that stream of photons moving even faster? Oh, this is maddening!

 

The time dilation equation is:

(t')^2 = t^2 / (1 - [ v/c ]^2)

Or at least that's the best I can do in UBB / ASCII.

t is the time interval from your perspective. t' is from you girlfriend's. And x^2 is just another way of writing x squared. v is your velocity.

 

Now that is the first thing anyone has said in this thread that has made any sense!

Why does perception of the photon have to be constant to all observers? That seems like a nonsense to me. Why does it only apply to photons and not to trains or bumblebees?

 

LNT, it's an exponential function.

edit: The Magpie beat me to it -- I tried to put the equation on, but deleted it (good job).