flaw in twin paradox?

Question

if earth is said to move relative to the space ship, the earth being should age less right? BUT, THIS DOES'NT HAPPEN. WHY??

Answer 1

That flaw is what makes it a paradox! A paradox is a self contradiction. If there was no such flaw, it wouldn't be a paradox, would it?

The usual answer is that you could have determined which one started moving because it experienced an acceleration. Since the Earth did not accelerate but the space ship did, it is the stationary one, not the space ship. This is true even after the space ship gets up to speed and stops accelerating to travel at constant speed, because you remember that it did accelerate.

Answer 2

Velocity is relative, acceleration is not. The twin who stays on the Earth undergoes much less acceleration than the twin who goes out and returns. It's the period of acceleration that makes the difference. Each twin knows if he's accelerating or not by the g-forces acting on him, and the traveling twin must experience a period of large g-forces during the speed-up to high velocity, the turn-around to get back, and the deceleration to match speed with the Earth.

Here's a another version of the Paradox. One twin stays on the Earth, and the other twin stays on the Earth as well. But the second twin is confined to a chamber on a platform, and a machine moves a small black hole or chunk of neutron star material nearer or further from the platform, so that the second twin experiences the same acceleration as he would have experienced on the interstellar trip. You could even fool the second twin, and not tell him he's in a simulator instead of being on an actual trip---he'd never know. (This may be how the moon landings were faked. ;-) [joke joke LOL] ) In the end, the result is the same: the second twin ages less. Yet neither twin has actually moved anywhere.

Answer 3

Twin paradox explained in a story form.

My story stars two twins, I prefer the monikers Stella and Terence. Terence sits at home on Earth. Stella flies off in a spaceship at nearly the speed of light, turns around after a while, thrusters blazing, and returns. (So Terence is the terrestrial sort; Stella sets her sights on the stars.)

When our heroes meet again, what do they find? Did time slow down for Stella, making her years younger than her home-bound brother? Or can Stella declare that the Earth did the travelling, so Terence is the younger?

Not to keep anyone in suspense, Special Relativity plumps unequivocally for the first answer: Stella ages less than Terence between the departure and the reunion.

Perhaps we can make short work of the "travelling Earth" argument. Special relativity does not declare that all frames of reference are equivalent, only so-called inertial frames. Stella's frame is not inertial while she is accelerating. And this is observationally detectable: Stella had to fire her thrusters midway through her trip; Terence did nothing of the sort.

One short paragraph, and I've polished off the Twin Paradox. Is that really all there is to it? Well, not quite. There's nothing wrong with what I've said so far, but I've left out a lot.

Answer 4

The Twin Paradox of Einstein is an interesting thought experiment involving two twins (who are nearly exactly the same age), one of whom sets out on a journey into space and back. Because of the time dilation effect of relativity, the twin who left experiences a slowing down of time and will actually be much younger than the twin that stayed behind. The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. It does, and it doesn't.

The confusion arises not because there are two equally valid inertial rest frames, but (here's the tricky part) because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, or involve General Relativity. Not so.

The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.

OK, let's see: Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.

Important question: what is the relative speed of the two Bob frames? On first glance, it would appear that one is going 3/5c in one direction and 3/5c in the other direction, so that the difference between the two frames is 6/5c! Faster than light? No, special relativity does not add speeds this way. The actual difference is only 15/17c, fast but not faster than light. Why is this important? We'll see.

Now, since special relativity lets us use either rest frame, we assume Bob is the at-home twin. Ann speeds away at 3/5c. No problem so far. But after 4 years of waiting, Bob must change his inertial frame. If we allow Ann to return, we've only restated the problem with the names switched. In the first version, Ann stayed in an inertial frame, and she must stay in an inertial frame in this version. Bob zooms off after Ann at 15/17 light speed (now we know why it was important), and of course catches up. It takes him 4 years, and he has seen 8 years since Ann left. Ann has aged 10 years. Same result. No paradox.



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Answer 5

Yes, that *is* the twin paradox. If the spaceship never turned around or experienced non-flat spacetime, then it would never be possible to compare ages directly, so no paradox arises. If the spaceship *does* turn around, there will be a strong acceleration, so the frame of the spaceship will no longer be inertial. On the other hand, the earth's frame will always be close to inertial. That asymmetry is what makes the difference.

Answer 6

The point is not that the earth is moving relative to the spaceship; it is that the spaceship is moving relative to the earth (and at a much higher velocity...).

I often struggled with this concept as well, until I read Brian Greene's "The Elegant Universe"; after I read his explanation, it was suddenly crystal clear to me, so maybe it will help you also.

The key is understanding two things:

1) Time is an actual dimension, just like the other 3 that we are familiar with, so that we now refer to space as spacetime.

2) We are always moving through spacetime at the speed of light.

No, really.

What happens is, when we are at rest relative to our surroundings in the 3 dimension we are still moving at lightspeed... but we are doing it thru the dimension of time.

Imagine for a moment that lightspeed is distributed in two columns; one marked Time, the other Space. If you & I are sitting at a coffeeshop, and I get up to get another cup while you remain sitting, that little bit of velocity (or, more accurately, acceleration) is transferred from my Time column to my Space column. This means that, relative to you, Time has so slowed a tiniest bit; I am now just the tiniest bit younger than you. (The velocity of the earth as it spins & travels around the sun is irrelevant, as we are both experiencing it at the same time...)

Now let's apply that to the twins paradox. I hop on a spaceship, and zip off to Alpha Centauri at 99.9% of lightspeed; again, all that acceleration is shifted from the Time column to the Space column. Because I am moving so fast (relative to you), I only age the 9 years that it takes me to make the round trip.

You, on the other hand, are still sitting quietly at the coffee shop, and so are moving through time much faster relative to me, so when I return I find a much, much older version of you waiting for me.

The reason we don't notice any of these discrepencies is because, on the scale of our normal, everyday activities, the differences are simply too small to detect.

But jet liners are fast enough to make a difference, at least a difference large enough to be detected by a very sensitive clock. And when "atomic" clocks became small enough to transport on a plane, that is just what they did; repeated experiments comparing time as measured by two clocks, one on a plane traveling 600mph, the other back at the university, matched Einstein's predictions precisely.

Mind you, this is not a way to cheat death; even if I stay on the spaceship and zip through the universe at 99.9% of lightspeed, I am still aging normally on the ship, and will, after 80, or 90, or 100 years, die like I normally would; this is because I am only traveling more slowly through Time relative to the rest of the universe.

If, after 50 years I reversed course, spent another 50 years returning to earth, and dropped out of lightspeed, I would find the earth gone, and the sun a brown dwarf, effectively dead; the Milky Way may even have been torn apart by it's impending collision with the Andromeda galaxy... I would be an old, old man, with nowhere to call home, adrift in a far future, alone.

Screw it; I think I'll stay here and have another cup of java. Salut!

Answer 7

It's called relativity. That means time, space and motion are all relative to the person who observes them.
So there is no problem with the twin paradox as you've described it.

Answer 8

This is because the speed of light is constant no matter to what your own velocity as an observer is.