# Special Relativity and direction of travel

• hrob64
In summary: Lorentz transformation , and that converts any description of motion in (x,y,z,t) coordinates to a description in different (possibly instantaneous) (x'.y',z',t') coordinates.
hrob64
As I have read, a clock in a spaceship approaching the speed of light will appear to slow down in time from the point of view of an outside stationary observer. Does the direction of travel of the spaceship relative to the observer have an effect? If it is traveling towards the observer it seems to me like it should speed up in time, and slow down when moving away? Furthermore, what would the time dilation be to the observer if the spaceship was moving in a circle around the observer? Thanks

The standard way of talking about this is that time dilation is measured by comparing clocks while the ship is next to the observer, and then comparing later when it's next to the observer again. By this definition, the time dilation is given by the factor $\gamma=1/\sqrt{1-v^2/c^2}$, which is independent of the direction of the velocity v.

If you do it instead by measuring the frequency of a radio wave sent from the spaceship to the observer, then you get the relativistic Doppler shift http://en.wikipedia.org/wiki/Relativistic_Doppler_effect , which does depend on the direction of motion.

-Ben

welcome to pf!

hi hrob64! welcome to pf!
hrob64 said:
As I have read, a clock in a spaceship approaching the speed of light will appear to slow down in time from the point of view of an outside stationary observer. Does the direction of travel of the spaceship relative to the observer have an effect? If it is traveling towards the observer it seems to me like it should speed up in time, and slow down when moving away?

ah, you're confusing how it appears to how we measure it

yes, if the speed of the clock is v = c times tanh(x),

then looking through a telescope, the clock's rate will be multiplied by ex (ie faster) if the clock is approaching the observer, and by e-x (ie slower) if the clock is going away from the observer,

but the observer knows that he is always looking at the past, and when he accounts for that, he finds the clock (in both cases) is going slower by 1/cosh(x), = √(1 - v2/c2)
Furthermore, what would the time dilation be to the observer if the spaceship was moving in a circle around the observer?

the same, √(1 - v2/c2)

hrob64 said:
... Furthermore, what would the time dilation be to the observer if the spaceship was moving in a circle around the observer? Thanks

That would involve General Relativity. Special relativity only treats straight motion at constant velocity.

danR said:
That would involve General Relativity. Special relativity only treats straight motion at constant velocity.

As long as we are dealing with a manifold with the property of global flatness then circular motion doesn't require GR. The same lorentz factor would apply and I think you would just have to evaluate it at each point of the circular path.

WannabeNewton said:
As long as we are dealing with a manifold with the property of global flatness then circular motion doesn't require GR. The same lorentz factor would apply and I think you would just have to evaluate it at each point of the circular path.

I see. And that would be homologous with looking out at a circle of infinite diameter?

danR said:
Special relativity only treats straight motion at constant velocity.

no, special relativity is about the Lorentz transformation , and that converts any description of motion in (x,y,z,t) coordinates to a description in different (possibly instantaneous) (x'.y',z',t') coordinates

as WannabeNewton says …
WannabeNewton said:
The same lorentz factor would apply and … you would just have to evaluate it at each point of the circular path.
danR said:
And that would be homologous with looking out at a circle of infinite diameter?

uhh? do you mean a straight line?

## 1. How does Special Relativity affect the direction of travel?

Special Relativity states that the laws of physics are the same for all observers in uniform motion. This means that the direction of travel does not affect the laws of physics or the outcome of experiments conducted by observers in that frame of reference.

## 2. Does the direction of travel affect the speed of light?

No, according to Special Relativity, the speed of light is constant and independent of the direction of travel. This is one of the fundamental principles of the theory.

## 3. How does Special Relativity explain time dilation in different directions of travel?

Special Relativity explains time dilation as a result of the relative motion between two observers. When one observer is moving at a high velocity compared to the other, time will appear to pass slower for the moving observer. This effect is independent of the direction of travel.

## 4. Can Special Relativity explain the concept of length contraction in different directions of travel?

Yes, according to Special Relativity, objects appear shorter in the direction of motion compared to their rest length. This is known as length contraction and is a consequence of the theory.

## 5. Does Special Relativity only apply to objects moving in a straight line?

No, Special Relativity applies to all objects in uniform motion, regardless of whether they are moving in a straight line or a curved path. As long as the motion is constant and not accelerating, the laws of physics remain the same for all observers.

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