Twin 1 goes on a rocket flys to pluto at .99c

[um0123]

I have questions:

1) twin 1 goes on a rocket flys to pluto at .99c and comes back to Earth (all uniform motion, somehow). When he gets back he sees twin 2 is older. But since twin 2 was moving away from him at .99c why doesn't twin 2 see him as older?

2) Why does something gain mass as it approaches c? Appearently when you hit c you have infinite mass, and therefore need infinite energy to continue, so you can't hit c, but why do you even gain mass? i know you use the energy-mass equivalence to find out how much energy is turned to mass, but why can't it just get faster?

I had more but i lost my train of thought, so more to come!

 

[HallsofIvy]

I have questions:

1) twin 1 goes on a rocket flys to pluto at .99c and comes back to Earth (all uniform motion, somehow). When he gets back he sees twin 2 is older. But since twin 2 was moving away from him at .99c why doesn't twin 2 see him as older?

There is no answer to a question about an impossible situation. You cannot go away and then come back with uniform motion. The twin who flys to pluto and then comes back must undergo acceleration the other twin does not. That is what creates the asymmetry.

2) Why does velocity turn into mass when you approach c? why can't you just get faster? i know you use the energy-mass equivalence to find out how much energy is turned to mass, but why can't it just get faster?

Did you look at the thread titled "mass due to velocity"? Velocity does NOT "turn into mass". What is true is that the mass of an object, as observed from frames with different relative velocities will depend on the relative velocity. That is NOT a matter of "velocity turning into mass".

I had more but i lost my train of thought, so more to come!

 

[um0123]

There is no answer to a question about an impossible situation. You cannot go away and then come back with uniform motion. The twin who flys to pluto and then comes back must undergo acceleration the other twin does not. That is what creates the asymmetry.

Okay, that's beside the point though, the fact of the matter is we can't possibly go near the speed of light, but we still make theories as to what would happen. You can't just dismiss a question like that by saying its simply not poissible, when all of relativity is based on what is not possible (moving at the speed of light).

Did you look at the thread titled "mass due to velocity"? Velocity does NOT "turn into mass". What is true is that the mass of an object, as observed from frames with different relative velocities will depend on the relative velocity. That is NOT a matter of "velocity turning into mass".

Okay, that doesn't answer my question though, I asked why something gains mass as it approaches the speed of light. Which i know is true, but i don't know why. Unless you want to not asnwer that and dismiss it as "not possible" like you did for my first question.

 

[Tac-Tics]

Okay, that's beside the point though, the fact of the matter is we can't possibly go near the speed of light, but we still make theories as to what would happen. You can't just dismiss a question like that by saying its simply not poissible, when all of relativity is based on what is not possible (moving at the speed of light).

That's not what Halls said. In fact, we can go as near the speed of light as we want. We just can't get to it. Hell, he even highlighted the critical part. A round trip flight will never be uniform. You go one way, then you have to reverse your direction of motion and go the other.

Furthermore, relativity is not at all based on something impossible. Something impossible doesn't happen. Relativity has proven itself time and time again to be exactly what happens in the universe.

Unless you want to not asnwer that and dismiss it as "not possible" like you did for my first question.

Please do not be rude on the forums. You're not going to get better answers by criticizing others who reply to you.

 

[um0123]

Okay, sorry. But i got a little ticked off when he wouldn't even consider my question valid. So ill rephrase it, twin 1 gets on a ship and takes off when he reaches .99c he stays there until he gets to a planet - let's say 10 light years away. He slows down and turns around and gets back up to .99c and comes back. Let's just assume his acceleration was fast enough that 90% of the trip was uniform. He gets to Earth and sees his twin is older. But to him Earth was traveling away from him at .99c so why doesn't he see his twin as older?

 

[Mentz114]

Okay, sorry. But i got a little ticked off when he wouldn't even consider my question valid. So ill rephrase it, twin 1 gets on a ship and takes off when he reaches .99c he stays there until he gets to a planet - let's say 10 light years away. He slows down and turns around and gets back up to .99c and comes back. Let's just assume his acceleration was fast enough that 90% of the trip was uniform. He gets to Earth and sees his twin is older. But to him Earth was traveling away from him at .99c so why doesn't he see his twin as older?

There's a formula in relativity that let's you calculate something called 'proper-time', which is the time that will be ticked away on a clock traveling through space-time. Suppose two people start at the same place ( at rest wrt to each other ) and synchronise their clocks, then go on separate journeys. The formula tells us what each clock would show when they get back together. There is no symmetry involved. If their journeys just happen to have the same proper-time, they will be the same age, even though they might have visited different places.

 

[Tac-Tics]

Keep in mind there are two flavors of time dilations in relativity. The first kind, I think they are called Lorentz dilations, apply only as long as the observers are in relative motion to each other. When the two objects return to the same frame of reference, their clocks tick at the same rate still.

The second kind, gravitational time dilation, is a consequence of lingering in a gravitational field. This is the effect that you see when you find your twin is now older than you. One very rough way of thinking about this is that it costs you "time" when you are pulled on by a gravitational field.

I should add, in general relativity, one of the founding principles is that acceleration is indistinguishable from gravity. So even in an accelerating spaceship in the middle of empty space, you still feel gravity.

 

[diazona]

Okay, sorry. But i got a little ticked off when he wouldn't even consider my question valid. So ill rephrase it, twin 1 gets on a ship and takes off when he reaches .99c he stays there until he gets to a planet - let's say 10 light years away. He slows down and turns around and gets back up to .99c and comes back. Let's just assume his acceleration was fast enough that 90% of the trip was uniform. He gets to Earth and sees his twin is older. But to him Earth was traveling away from him at .99c so why doesn't he see his twin as older?

He (twin 1) actually doesn't see his twin as older while he's flying away from Earth. Once he slows down and stops, though, he would see his twin (2) as being older, if it weren't for the fact that there's a 10-year time delay (because light takes 10 years to travel from Earth to the remote planet, of course).

The fact that 90% of the trip was uniform doesn't really make much difference, actually. It's more important that the traveling twin did accelerate at all, than how long he spent doing it.

 

[bucher]

Another reason why the traveling twin aged slower was because he went out and back into his other twin's reference frame. It was the traveling twin that underwent the accelerations to travel (he would feel the accelerations in his ship). The other twin stayed put and didn't accelerate anywhere with respect to his surroundings.

 

[diazona]

Keep in mind there are two flavors of time dilations in relativity. The first kind, I think they are called Lorentz dilations, apply only as long as the observers are in relative motion to each other. When the two objects return to the same frame of reference, their clocks tick at the same rate still.

The second kind, gravitational time dilation, is a consequence of lingering in a gravitational field. This is the effect that you see when you find your twin is now older than you.

uh... no?

There is no gravity in the twin paradox and thus no gravitational time dilation. We're talking about the time dilation from Lorentz transformations only.

It is true that when two objects return to the same frame of reference, their clocks return to ticking at the same rate, but that doesn't mean that the time dilation they experienced while one was moving was somehow imaginary. It has very real effects.

 

[um0123]

thanks for all the replies, but i understand that when twin 1 re enters twin 2's frame he is begins to age at the same rate. I am still confused, though, why twin 2 doesn't age even though to twin 1 Earth is the one moving at .99c.

Is it because twin 1's sorounding are moving relative to him, but twin 2's soroundings are staying put relative to him?

 

[Al68]

There is no gravity in the twin paradox and thus no gravitational time dilation.

Strictly speaking, time dilation in a gravitational field is just a specific example of "gravitational time dilation", which is an effect in any accelerated reference frame whether real gravity is present or not. For example, a clock at the rim of a spinning disk compared to a clock at the center, or clocks at the front and rear of an accelerating spacecraft .

If you wanted to consider the reference frame of the ship's twin during the turnaround, it would be an accelerated frame, and subject to gravitational time dilation effects. The twins paradox can be "resolved" using this reference frame, with the same result as the standard resolutions.

 

[bucher]

Look at it this way, which twin is feeling the acceleration (like what you would feel in an accelerating car)? The twin that is noticing the acceleration is the one who will age slower due to time dilation.

Think of it this way, twin 1's ship is accelerating through the universe. The universe is not accelerating around the ship. Depending on who is noticing the affects of acceleration, that twin will age slower.

For an example, if twin 1's ship turned on its boosters, he would feel himself accelerate. Twin 2 would not feel any of these affects. Since twin 1 is noticing the accelerating affects, it is he who is changing his velocity and so it is he who will age slower. If twin 1's ship was able to accelerate the universe around it, then twin 2 would feel the affects and not twin 1. Since twin 2 is feeling the affects now, he would be changing his velocity and so would age slower with respect to twin 1.

It is not just what is happening relative to something else. You must also incorporate who is experiencing the acceleration.

 

[um0123]

It is not just what is happening relative to something else. You must also incorporate who is experiencing the acceleration.

Oh, i didn't know that! now it makes sense. Thanks for the response.

 

[Mentz114]

What if both twins had accelerations, but different ones. How would you calculate the elapsed time on their clocks ( that is, how much they aged ) ?

Proper time is the answer.

 

[bucher]

Well yes proper time is the answer. But I think that the question was more on who experiences the time dilation and why.So um0123, with question #1 out of the way, do you understand the answer for #2?

 

[Al68]

2) Why does something gain mass as it approaches c? Appearently when you hit c you have infinite mass, and therefore need infinite energy to continue, so you can't hit c, but why do you even gain mass?

Because as the velocity of an object approaches c, it takes more energy to accelerate it faster, as you point out, and mass by definition is a measure of an objects resistance to acceleration.

 

[um0123]

Well yes proper time is the answer. But I think that the question was more on who experiences the time dilation and why.


So um0123, with question #1 out of the way, do you understand the answer for #2?

Thanks, ill do more research on proper time! Unfortunately, no, i do not know the answer for 2. What i understand is that energy and mass are not separate things, but can be interchangeable. And when you approach c you gain more mass, until when you hit c, your mass is infinite. Thats why only things without mass, like light, and the graviton (btw, has that particle been confirmed?) can travel at light speed.

The book i was reading said that you can't add more velocity so instead you add mass. But i don't understand this.

 

[ZikZak]

Because as the velocity of an object approaches c, it takes more energy to accelerate it faster, as you point out, and mass by definition is a measure of an objects resistance to acceleration.

Except for the fact that the "relativistic mass" one usually refers to is NOT in fact what you get when you measure the body's resistance to coordinate acceleration, unless the acceleration is exactly perpendicular to the motion, which it absolutely isn't in elementary treatments a la "as the body moves faster it becomes harder to accelerate." This is one reason that the concept of relativistic mass is deprecated: it is NOT in fact the measured coordinate inertia of the body. The relativistic mass concept is confusing because it encourages misconceptions such as this and a semi-Newtonian shallow understanding of Relativity.

Better to get rid of the outdated and incorrect concept altogether once and for all. Mass is rest mass. It does not increase with speed. Energy increases with speed. And if the body becomes harder to accelerate in a coordinate sense, then it's because of the geometry of a spacetime with an invariant speed.

 

[MonkeyHouse]

The fact that 90% of the trip was uniform doesn't really make much difference, actually. It's more important that the traveling twin did accelerate at all, than how long he spent doing it.

I thought that velocity changes the passage of time. Why is acceleration important

 

[haushofer]

The explanation I like the most is the fact that acceleration brings you away from a geodesic, and because a geodesic MAXIMIZES the propertime (due to the minus sign in the metric), an accelerated observer will experience less proper time than an observer who stays on a geodesic.

So in the case of the twins, the accelerating twin moves away from a geodesic, experiences less proper time and will be younger when the two meet again at another event.

You could draw this in a space-time diagram: the twin which stays behind moves on a vertical line in the spacetime diagram (if the Earth is considered to be inertial for the sake of argument) between events A and B, and the accelerating twin moves on a curved line between A and B. This line appears to be longer than the straight line of the left-behind twin. If the metric would be Euclidean, this curved line would correspond to the longest distance. But we work with the Minkowski metric, and "distance" here is proper time. So the curved line actually represents the shortest proper time.