How does the Famous Twin Paradox work?

Question

I'm talking about the one on

http://www.mathparadise.com/?p=82

Answer 1

The Twin paradox is NOT really about time dilation. Yes, the Earth twin observes that the clocks on board the spacecraft run slow, because moving clocks run slow. But it is NOT correct to say that "an object nears the velocity of light (186,000 miles per second), time slows down." There is no absolute rest frame to measure this speed from. There is nothing special that the rocket has during the trip that Earth doesn't have. In other words, it's just as legitimate to say that it is the rocket that is at rest during the trip and the Earth that moves. As observed by the pilot twin, his clocks run normally and it is the *Earth's* that are slow.

The reason that the pilot returns younger than his Earthbound twin is NOT time dilation (which each twin observes happening to the other). It is relativity of simultaneity. Observers in relative motion to each other disagree on which events are simultaneous. When the pilot twin turns around, he changes reference frames, and thus changes his observation of which time on Earth is simultaneous with his own. When he first gets there, the clocks on Earth simultaneous with his own read a small value: the time the trip has taken on his own clock, corrected *downwards* because of time dilation. The next moment, after he has turned around, he is in a brand new reference frame and disagrees with his previous observation: the clocks on Earth simultaneous with his own (as observed by him) now read many, many years ahead. Thus his brother is very old when he returns.

Answer 2

This best explains the twin paradox so pay attention. But if you don't understand this just use the force(google). this was proven; an airplane was traveling really fast with an accurate clock on board. there was another clock on earth. but when the plane was done traveling they compared the clocks and the one on earth(i think) was milliseconds slower then the one on the airplane i can't confirm this but you can look it up yourself on you guessed it....... google

http://www.youtube.com/watch?v=V7vpw4AH8...

Answer 3

The time dilation effect of high constant velocity travel does not depend upon the direction of separation between the fast traveller and sedate home dweller. Einstein's theory of Special Relativity relates the two identical clock times in the equation: -

t(home) = t(traveller)/sqrt(1-(v/c)^2)

Where 'c' is the speed of light and 'v' the travellers close to light speed velocity. This equation does not have a direction of travel component and so the total time dilation effect depends upon the high and constant velocity v' and the elapsed time as measured by the traveller's, 't(traveller)', slower running clock.

Thus, if two identical twins were separated for one day as measured by the clock of the space travelling one - who travelled at 99.9999999% of the speed of light (this of course is not possible because the velocity is unattainable and furthermore the traveller would have to accelerate gently to this velocity and thus take a lot of time to achieve it!). Then the identical clock of the home staying twin would elapse an enormous 22360.7 (rounded) days or just over 61 years!

If, however, the travelling twin spent a lot of time accelerating or decelerating then his clock would run faster than the stay at home twin's. Again, the second relativistic effect is not direction of travel dependent! Thus, time dilation effects, due to near luminal constant velocity travel, have to balanced against the time reasonably required to achieve the high velocity and the faster clock rate due to accelerating and or decelerating.

Answer 4

the twin that stays on Earth will be older because when as an object nears the velocity of light (186,000 miles per second), time slows down.

This is discussed in Einstein's Theory of Relativity. Time is relative to the velocity at which an object moves. So two weeks as experienced by the twin in the space ship may only seem like a couple of days.

Answer 5

Much can be said about this, and much has been!

I like to say that what Einstein figured out is that when something is traveling at any speed "relative" to you, it is in a different universe. You get from your universe to this other universe by "accelerating" and in order to get back you must accelerate in the opposite direction.

Consider yourself driving down the freeway at 60 mph. You are in a different universe than the world outside your car. You can't get to that other universe without slowing down. Hopefully you slow down gently.

The faster you go, the more different your universe becomes than the one you left behind.

Surprisingly, everything in your car (or rocket or...) seems normal. Einstein investigated this by asking: What if I assume that everything in these "accelerated" universes is "exactly" the same? In particular he focused on the speed of light as being constant.

With that very simple assumption he showed that not everything could be the same unless time changed its pace. The world outside your universe appears to be going slower because it is in motion with respect to you (and I won't do the math here).

The Paradox is: why should the car (or rocket or...) traveler be younger when to the car traveler, time looked slower for those standing still and for those standing still, the car traveler's time seemed slower?

The answer is that the acceleration only happened to the traveler.

So be careful with your accelerations or you may never grow old!