Time Dilation Paradox: Exploring What Prevents it From Happening

[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.