What Prevents the Time Dilation Paradox in Intergalactic Travel?

[Drakkith]

The acceleration is necessary to understand who is actually traveling at the higher speed. Twin A takes off in a ship, and twin B doesnt. Twin A DOES know that he is traveling at X speed because he was the one that accelerated. Twin B knows that he is still stationary because he was never accelerated. Thus, both can reliably say that Twin A is the one that is actually traveling at velocity X.

If you take 2 ships, and only compare those 2 ships and their respective frames, there is no way to tell which one is actually traveling at what velocity because you have nothing to compare them against except each other. You would have to look back and see where each one came from and how much each accelerated to determine how fast each one is travelling.

Does all that sound about correct?

 

[DrGreg]

The acceleration is necessary to understand who is actually traveling at the higher speed. Twin A takes off in a ship, and twin B doesnt. Twin A DOES know that he is traveling at X speed because he was the one that accelerated. Twin B knows that he is still stationary because he was never accelerated. Thus, both can reliably say that Twin A is the one that is actually traveling at velocity X.

If you take 2 ships, and only compare those 2 ships and their respective frames, there is no way to tell which one is actually traveling at what velocity because you have nothing to compare them against except each other. You would have to look back and see where each one came from and how much each accelerated to determine how fast each one is travelling.

Does all that sound about correct?

No, because another way of looking at this is to assume that both twins were initially traveling at velocity −X and then twin A decelerated to become stationary, whilst twin B continues to move at velocity −X. That's an equally valid way to analyse the problem.

 

[Drakkith]

No, because another way of looking at this is to assume that both twins were initially traveling at velocity −X and then twin A decelerated to become stationary, whilst twin B continues to move at velocity −X. That's an equally valid way to analyse the problem.

Of course, which is why determing the initial frame is important. If you have it as earth, it's a pretty safe bet that we aren't traveling at .3c, and can say that most likely the spaceship is the one traveling at 0.3c and not us. Obviously, if this happened and it turned out that the ship was experiencing a faster rate of time, then it would be us on Earth that were traveling at 0.3c.

Hows that look?

 

[DrGreg]

Of course, which is why determing the initial frame is important. If you have it as earth, it's a pretty safe bet that we aren't traveling at .3c, and can say that most likely the spaceship is the one traveling at 0.3c and not us. Obviously, if this happened and it turned out that the ship was experiencing a faster rate of time, then it would be us on Earth that were traveling at 0.3c.

Hows that look?

No it's a fundamental principle of relativity that all velocities are relative. It's equally valid to consider the Earth stationary and a spaceship moving or to consider the spaceship stationary and the Earth moving, or to consider Alpha Centauri stationary and both Earth and the spaceship moving. That's the whole point of relativity, there's no such thing as "stationary" in any sense that everyone could agree.

 

[bobc2]

It seems like DrGreg's space-time diagram presents the situation in the most fundamental way. The world lines tell the story--the mathematical details and talk of accelerations just detracts from the fundamental simplicity of DrGreg's diagram.

 

[Drakkith]

No it's a fundamental principle of relativity that all velocities are relative. It's equally valid to consider the Earth stationary and a spaceship moving or to consider the spaceship stationary and the Earth moving, or to consider Alpha Centauri stationary and both Earth and the spaceship moving. That's the whole point of relativity, there's no such thing as "stationary" in any sense that everyone could agree.

Hrmm. Perhaps I'm misunderstanding something then. If the faster you go, the slower time goes for you, then couldn't you find a "Rest" frame by simply changing your direction and velocity compared to another object until you find the velocity and direction at which a synchronized clock runs the fastest in relation to another clock on the obejct?

Sorry if I've been incorrect in all this, I thought I knew a little of the basics.

 

[PAllen]

Hrmm. Perhaps I'm misunderstanding something then. If the faster you go, the slower time goes for you, then couldn't you find a "Rest" frame by simply changing your direction and velocity compared to another object until you find the velocity and direction at which a synchronized clock runs the fastest in relation to another clock on the obejct?

Sorry if I've been incorrect in all this, I thought I knew a little of the basics.

What gives relativity the name is that all inertial frames are equivalent, and 'at rest' has no meaning except in relation to some other object.

It is not 'the faster you go, the slower time goes for you' , it is 'the faster you go relative to some object, the slower time goes for you as observed by that object'; and also the slower *you* observe time to go on that object.

 

[bobc2]

The thing I like about DrGreg's space-time diagram is that it presents a fundamental picture from which the various Special Relativity effects can be reasoned. When beginning with space-time diagrams it might be useful to sketch the situation we see in the above left sketch where blue and red rockets are moving away from each other with respect to a "rest" refererence frame (the black coordinates, X1 and X4). Consider the rockets and the occupants to be 4-dimensional static structures (they don't actually move). But, at any instant of time, the normal 3-dimensional laws of physics are observed in a 3-D cross-section of the universe that is different for the red and blue rockets. The slanted lines indicate the two different instantaneous 3-D universes. You can see that when the blue guy is at station no. 9, his 3-D universe intersects the red rocket at station no. 8, a time much earlier than his own. And when the red guy is at station 9, his universe intersects the blue guy's rocket at blue's station no. 8, again a much ealier time than his own. A symmetric setup like this always allows you to develop the time dilation equation pretty easily just using high school algebra (my physics professor used to explain to us how the ancient Greeks could have discovered Special Relativity).

The world line (4th dimension) for observers moving at various speeds relative to some rest frame have different slants. But, the world line of a photon always bisects the angle between any observer's X1 (a normal spatial dimension) and X4 (time) axis.

Once you get the knack of the space-time diagrams you can unravel tricky problems as demonstrated so nicely by DrGreg.