Light's Instantaneous Wordline: Is Time Really Zero?

[OS Richert]

The proper time of a photon which always has a lightlike wordline is zero, correct? Does this mean from the perspective of light (which doesn't have any conscience to have a perspective) that it travels instantaneously in zero time. So while we see light from Alpha Centari and can watch it travel for four years to get to earth, it thinks it traveled from Alpha Centari to Earth instantaneously?

 

[mathman]

Yes. Also this approach is the easiest way to understand the twin paradox. One twin goes to Alpha Centauri at almost the speed of light and to him it takes a very short time. After stopping to catch his breath, he returns to Earth at the same speed, so to him the round trip took a very short time. On the other hand, his twin on eath has aged around 9 years,

 

[MeJennifer]

One twin goes to Alpha Centauri at almost the speed of light and to him it takes a very short time.

Not only does it take him a short time but the distance to Alpha Centauri is much shorter for him than for an observer on Earth.

 

[pervect]

The proper time of a photon which always has a lightlike wordline is zero, correct? Does this mean from the perspective of light (which doesn't have any conscience to have a perspective) that it travels instantaneously in zero time. So while we see light from Alpha Centari and can watch it travel for four years to get to earth, it thinks it traveled from Alpha Centari to Earth instantaneously?

Actually it is mathematically inconsistent to say that a photon has a perspective in terms of time and space. The problem isn't so much with "proper time" for the photon which goes to zero, but with any idea of assigning a frame or distance to the photon.

What one can safely say is that the limit as one approaches light speed, the time it takes to get to Alpha Centuari from Earth approaches zero. A seemingly minor, but potentially important, distinction.

The closest thing to giving a photon a perspective is to adopt a system of null coordinates, which are neither timelike nor spacelike, but null.

For instance, if x and t are cartesian coordinates, U= x-t and V = x+t are null coordinates. U gives a constant number for the worldline of a photon moving in one direction, V gives a constant number for the worldline of a photon moving in another direction.

 

[MeJennifer]

For those interested in null coordinates, mathpages has an interesting http://www.mathpages.com/rr/s1-09/1-09.htm" on it.

Note that the anonymous author expresses a remarkable level of lucidity on the subject which not everybody might appreciate.