Mass Motion & Time: Acceleration & Momentum Impact on Measurable Time

[Christov84]

Hi Guys,

As I was wondering to the train station the other day I was thinking about gravity bends time and how momentum might also affect this.

Anyways as you guys are really cluey about this so then I ask:

If say I was in a F1 car accelerating or even going at several G's more then resting(say around a really tight corner) would this have a significant impact on time(measurable atleast )?

What i am querying is if gravity generated by acceleration is more significant then moving at a certain constant speed(i.e momentum)?

Cheers

Chris

 

[Dale]

If say I was in a F1 car accelerating or even going at several G's more then resting(say around a really tight corner) would this have a significant impact on time(measurable atleast )?

That is an interesting question. I will have to crunch the numbers, but my initial guess is that with modern atomic clocks you could indeed measure time dilation between the front and back of an accelerating F1 car.

 

[bcrowell]

The effect that DalsSpam describes equals ay/c², where a is the car's acceleration, y is the distance between the front and back of the car, and c is the speed of light. In the driver's frame, this is interpreted as a gravitational time dilation; by the equivalence principle, the acceleration has the same effect as a gravitational field.

The special-relativistic time dilation effect is v²/2c².

The ratio of the gravitational effect to the SR effect is 2ay/v². For a race car that's already up to speed, I think this is going to be less than 1, although the two effects are on the same order of magnitude.

However, there is no real reason that y has to be the length of the car. For example, if the driver is looking at distant scenery, y is the distance to the scenery, and you get a Doppler shift that is partly attributable to relativistic time dilation. Here is a nice video showing an animated simulation, in a world where c is small so that the Doppler shift is nonnegligible:

One interesting effect is that you can have an event horizon. I don't think you can see the event horizon in the animated video, because it's behind you.