## Monday, March 26, 2007

### Can anything move faster than the speed of light?

The answer is no, but there are some subtle concepts here. Relativity says that, in a vacuum, nothing can locally move faster than the speed at which zero-mass particles move. Light is composed of zero-mass particles called photons, hence this limit on the local speed of motion is typically expressed in terms of the speed of light. However, any particle of zero-mass should move at the same speed in a vacuum: if neutrinos are of zero mass, then they move at the same speed as the speed of light.

If there isn't a vacuum, then things can move faster than the speed of light, even on a local basis. For example, Cerenkov radiation, the blue-tinged light emitted by the water in nuclear reactors, is the shock-wave of radiation produced by a charged particle moving through an insulator at a speed greater than the speed of light in that insulator.

On a non-local basis, the time taken to travel between two spatial locations is dependent upon the geometry of the path taken between those two locations. If one creates or chooses the appropriate path, one can complete the journey before photons of light taking a different path. This is demonstrated by Miguel Alcubierre's model for a warp-drive. The basic idea of the warp drive is that it creates a bubble of compressed space which the space-ship travels within. The space-ship reaches its destination very rapidly because it travels a very short distance, not because it locally violates the speed of light.

Things can also change faster than the speed of light. For example, a pair of galaxies can recede from each other faster than the speed of light, under the expansion of the universe. The recession velocity v of a pair of galaxies separated by a distance d is given by

v = H d,

where H is the Hubble constant. Hence, any galaxies separated by a distance greater than c/H (where c is the speed of light), will recede at a rate greater than the speed of light. The recession velocity of the galaxies is due to the expansion of space between the galaxies, not due to the motion of the galaxies through space. There is no limit at all on the rate of change of spatial distance.

Unknown said...

OK, this is where I get confused. If photons have zero mass, why is their trajectory curved around massive objects? There should be no gravitational attraction at all.

Here's another question I've had about relativity for a long time. It has to do with the time dilation effect for objects moving very fast. An astronaut in a spaceship going some fraction of the speed of light will age more slowly than an astronaut on Earth. But their motions are relative to each other, not absolute, correct? The astronaut on Earth is travelling just as fast relative to the astronaut in the spaceship as that astronaut is traveling relative to the one on Earth. So why is the astronaut on the spaceship aging slower?

Gordon McCabe said...

Zero-mass objects follow curves in space-time called geodesics, and a massive object changes the geometry around it, including the geodesics. Geodesics are the generalisations to curved geometries of straight lines in Euclidean geometry.

In the case of the so-called 'twin paradox', the situation isn't symmetrical. One astronaut (twin) is in free-fall, following a geodesic of space-time, whilst the other one is jetting back and forth, following non-geodesic curves, and expending less personal time.

Unknown said...

So time dilation has nothing to do with speed, but with motion relative to a geodesic? That's not how it is popularly described.

Please indulge my ignorance a little longer, because I still don't grasp it yet. I was under the understanding that free-fall was the equivalent of zero gravity, or zero acceleration. So a person standing on the Earth's surface, since he is experiencing an acceleration of 1g, and therefore is not in free fall. However a person in space in orbit around Earth, or in an unpowered trajectory toward some destination, no matter how fast he is going relative to the Earth, is in a zero-g environment, and therefore in free fall. Is this not correct?

And how does one measure one's movement relative to a geodesic of space-time, if not by acceleration?

Gordon McCabe said...

You're on the right path, Duck, (if you'll excuse the pun). A geodesic is a curve of zero acceleration. Acceleratory motion means non-geodesical motion. The astronaut jetting back and forth to Alpha Centauri has to engage in heavy acceleration and deceleration at both ends of his journey, and it is this which causes the discrepancy in personal time, relative to the other astronaut, who is, say, in a free fall orbit around the Earth. It's not speed which makes the difference, but acceleration.