# Object with *multiple* velocities nearing the speed of light-effect?

1. Sep 22, 2013

### JacobQuestion

Object with *multiple* velocities nearing the speed of light--effect?

Hello!

I've had this question for sometime and I'd love if someone could shed some light on it for me.

Here's the situation:

Lets say that you were able to make an object reach velocities (and maintain) nearing the speed of light from point A to point B while also having the object rotate at a velocity nearing the speed of light simultaneously. Thus, the object would have BOTH a velocity moving from point A to point B nearing the speed of light as well as a 'spinning velocity' nearing the speed of light. What effect would this have on the mass of the object as well as the effect of time? How would 2 near light speed velocities affect the object?

Lets go a step further: say the object was a spacecraft of some sort that was able to hold passengers. In this case, if you had the craft moving from point A to point B at nearing the speed of light and then you were able to design a rotating mechanism on the outside of the craft that would rotate at nearing the speeds on light (the point here being to keep the actual craft from spinning itself but to have the changes of time and mass affect the area inside the rotation (i.e., the craft and the inhabitants of the craft)), what would the effects be for the passengers and the craft in relation to the space outside? And finally, if you had both velocities (the point A to point B velocity and the 'spinning velocity') at only half the speed of light, would the effect on time and mass on the craft and the passengers be equivalent to 1 velocity that was nearing the speed of light?

Thank you everyone! I really look forward to hearing some educated feedback.

Kind regards,
J

2. Sep 23, 2013

### Simon Bridge

Welcome to PF;
If you have a disk spinning so that points on the edge have tangential velocity 0.8c, wrt its center of mass, and that disk is also moving wrt some inertial observer at speed 0.8c, then, classically, one edge of the disk must be instantaneously stationary while the other is 1.6c.

This is what you are thinking about right?

In relativity there is no absolute speed ... you have to say who is doing the observing ad specifically what they are looking at. So your questions are a little general.

All inertial observers are stationary in their own reference frames. There is no experiment you can do to tell who is moving. You travelling at high speed does nothing to your mass, or your watch. It's everyone else who's different. What relativity does is tell you how your watch compares with someone elses.

Note: the idea of "relativistic mass" is no longer in common use. "Mass" and "rest mass" now mean the same thing. Effects attributed to relativistic mas increases are more usefully associated with kinetic energy... though there are still some who hang on to the concept ;)

The rotating disk represents a special problem in relativity - an observer on the edge of the disk is not an inertial observer. Further reading:
http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html
... basically, "rigid" is not a good approximation for how things behave.

However - a passenger on the rim of the rotating section of the spacecraft would not experience any additional effects due to the craft's linear motion. No part of the spacecraft may exceed the speed of light in any reference frame - which can mean that some observers may see it warp or twist depending on the details of the relative motion.

3. Sep 23, 2013

### A.T.

Here are some visualizations of rotating wheels at relativistic speeds. However, they not only include relativistic effects like length contraction, but also the visual effects from finite signal speed like Terrell rotation.

4. Sep 23, 2013

### yuiop

The effect on time is easy to answer. Each point on the rotating object will have its own total velocity which is the vector addition of the velocity components for that point. Once we know that total velocity we know the time dilation for that point. The total velocity is always less than the speed of light from any observers viewpoint. To see how velocities add in Special Relativity see: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

Lets take the example given by Simon where the disc is rotating around an axis at right angles to the line connecting A to B like a rolling wheel on a road. The rocket is travelling at 0.8c and according to the rocket observers the rim velocity of the wheel is also 0.8c. Naively you might expect there to be a point on the rim that has a velocity of 1.6c but this is not the case. Using the equations given in the link the total velocity of that point on the rim is (0.8 + 0.8)/(1 + 0.8*0.8) = 0.976c.

Now take the slightly more complicated case where the disc is rotating around the line connecting A to B (Call this the x axis). In this case the velocity vector of a point on the rim is at right angles to the velocity vector of the rocket. (For this example lets say the instantaneous velocity of a point on the rim is 0.9c in y direction, as measured by observers on the rocket and the rocket is travelling at 0.8c relative to observers that remain at A). The transformed y component of the point on the rim, according to the observer at A is $W_y = 0.9 *\sqrt{ 1- 0.8^2}/(1+0.8*0.9) = 0.313953488c$ The total resultant velocity of the point on the rim relative to A, is obtained using Pythagoras theorem and is $\sqrt{W_y^2+W_x^2} = \sqrt{0.314^2 + 0.8^2} = 0.8594c$.

Note that the rim velocity of the disc according to A is lot slower than the rim velocity according to the rocket observers. The disc velocity remains constant according to the rocket observers even when the rocket is accelerating and appears to slow down according to the external non accelerating observers. This is because to the external observers the relativistic inertial mass of the disc appears to be increasing and to conserve angular momentum the rotation rate has to slow down.

Note that when describing the disc mass in the context of its angular momentum I mentioned relativistic "inertial" mass. The concept of relativistic mass is sometimes useful when considering conservation of momentum for example in elastic collisions, but its use is largely discouraged these days because the rest mass (as measured by observers co-moving with object) and gravitational mass certainly do not change. There is no danger of the rocket collapsing into a black hole no matter how fast it goes or how fast it rotates.

I also notice that you ask how the passengers are affected by the rotating disc if the passenger compartment is not rotating. the answer is that the rotating disc will have almost zero effect. For bodies that are not large gravitational bodies, the time dilation of one part does not affect other parts. For example the time dilation of a clock on the rim of the disc will be greater than the time dilation in the passenger compartment, because the rim clock is travelling faster than the passenger compartment, relative to A. If the disc is removed, there will be no change in time dilation of the passenger compartment, all else being equal.

Last edited: Sep 23, 2013