Is the Twin Paradox Resolved by Considering the Metric of Spacetime?

[jaydnul]

when people say you can travel into the future by traveling close to the speed of light, does that mean relative to the earth? So technically, we are moving close to the speed of light relative to a distant object in the universe going that speed?

 

[phyzguy]

Traveling into the future is easy. I'm doing it right now!

 

[adjacent]

You will think you are at rest and every thing is moving

 

[uperkurk]

when people say you can travel into the future by traveling close to the speed of light, does that mean relative to the earth? So technically, we are moving close to the speed of light relative to a distant object in the universe going that speed?

To put it simply, the faster you go, the slower time goes, which in turn, causes you to age slower.

You travel at 99% the speed of light for 1 week, acording to your clocks, you have been traveling for 1 week and you will have aged 1 week but the people on Earth would have experienced 100 years go by and would have aged by 100 years.

When you stop, you think only 1 week has passed, but when you look around you, you seem to be in the future.

People often think that traveling to the future often means teleporting or skipping time, this is not true.

 

[Nugatory]

To put it simply, the faster you go, the slower time goes, which in turn, causes you to age slower.

That might be putting it a bit too simply, as this (fairly common) statement often confuses people. Better would be "While you are moving relative to someone else, he will measure time passing more slowly for you than for him".

 

[1977ub]

If you travel in circles you can slow your own aging to a crawl relative to the Earth while not traveling far away. Just stop when you pass by Earth and see a date on the calendar that looks good.

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

 

[Tosh5457]

Yes but you can't end up in the same point of space. Picking the example given by uperkuk: Imagine you leave Earth with velocity of 0.99c in relation to Earth's reference frame. After 1 week passed in Earth reference frame, people on Earth would see you aging 100 years (because you're the one moving in relation to Earth). In your reference frame, Earth is the one moving at 0.99c, so you'd have aged 1 week and see people on Earth aging 100 years. This is apparently a paradox, called twins paradox. What doesn't make it a paradox is that if you came back to Earth, the acceleration necessary for your starship to come back would compensate, and that enters in the realm of general relativity.

 

[Nugatory]

The twin paradox doesn't apply in the case where one twin is accelerating (circling) the whole time, since we can't give him an inertial frame in which to measure Earth as moving at .99c. His metric doesn't make sense, so the only one we need to consider is the Earth's.

I have to disagree - this is a well-known variant of the twin paradox.

The metric is a property of the spacetime in the vicinity of the earth, and we can use it to calculate the proper time experienced by each twin on their paths through that spacetime. There's no "his metric" or the "Earth's" metric.

 

[1977ub]

I have to disagree - this is a well-known variant of the twin paradox.

The metric is a property of the spacetime in the vicinity of the earth, and we can use it to calculate the proper time experienced by each twin on their paths through that spacetime. There's no "his metric" or the "Earth's" metric.

The usual "paradox" comes from assigning each traveler an IRF. In one person's IRF, the other person's clock is slower. Viola - a "paradox". If one person is inertial, and the other person is circling, we only assign one IRF - to the inertial observer. The other is in constant acceleration, and thus we don't dignify his measurements as being an IRF. He can make no credible claim about the unaccelerated observer's clocks appearing to run slow. The unaccelerated twin with the IRF can however find the the accelerating twin has a clock that is running slow. There is only only account of slowing deriving from measurements in only one IRF. Voila - no paradox.

Introducing the "metric of spacetime" is part of the resolution to the paradox, eh? Once you've done that, we are no longer looking at a paradox.