Does light accelerate to its speed or is it instant?

[Magnus Warhol]

Someone actually asked me an interesting question. Does light accelerate to its top speed or is its acceleration at 0 and is always at the top speed. Please assume we are in a vacuum, and you slam two protons together to release light, does that light start of at max speed or does it accelerate to top speed? Is there such a thing as Planck Acceleration?

 

[Zmunkz]

Photons always move at Speed c in a vacuum... there is no acceleration. Newton's law doesn't do well solving for a if m=0

a=F/m

 

[Simon Bridge]

I'll second that - photons are created traveling at c.

 

[al onestone]

First of all, the quantized EM field is not constituent of individual systems, photons, although we do measure them as such they do not exist as such prior to our measurement in the interim.

To picture a photon you have to understand the field excitation process that results in a quantized version of it, and when you understand this (which I don't completely) then apparently you can envision how it is always at light speed.

 

[Sonderval]

To be honest, AFAIK there is no clear definition of a "photon" anyway, nor of its "speed". Is it any state of the photon field with number operator eigenvalue 1?
Is it an excitation with a definite wavelength?
If you have a wavepacket, where and how exactly would you measure its group velocity?

 

[Bill_K]

AFAIK there is no clear definition of a "photon" anyway, nor of its "speed".

Resolve the electromagnetic field into normal modes. A photon represents the first excited state of one of those normal modes. The normal modes aren't unique, you're free to choose to use any set you like. Mosttimes we use the plane waves, which possesses a well-defined wave vector k, and they clearly travel at speed c.

Another common choice is the set of angular momentum states wrt a particular origin. Nuclear gamma decay is usually expressed as the emission of a photon which is E1, M2, etc according to its L and J values. These states don't have a unique wave vector, they are linear superpositions of such.

In any case photons in free space obey the wave equation and have speed c in that sense.

 

[Simon Bridge]

What Bill_K said. We need to have a clear definition of what "photon" means if we are to be able to say we have detected them.

Thus, what a photon is and how fast it goes can be established experimentally.
For instance, you can measure the speed of a particle in a pulse by timing between two detection events at different places.
What I think you mean is that we don't time a particular photon so what we get at the finish-line detector are different photons from the start-line photons.
We have to find the speed indirectly. Would that be correct?

 

[Sonderval]

@Bill_K
If this is your definition of a photon, first of all a single photon is not normalisable in space and the speed would be the phase velocity, not the group velocity.
This does not fit the original question, I think, because there it is assumed that the photon is created somewhere in space (implying that it is a wave packet).