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What characteristic of photons causes them to travel with constant speed in all frames of reference? Till the topics I have studied, we always assume this but never got any ideas what can be in the nature of photons (the quanta of electromagnetic field) that causes this. Maybe something is not clear to me. Please explain.

Qmechanic
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cleanplay
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    Related: http://physics.stackexchange.com/q/3541/ – Michael Sep 06 '13 at 12:42
  • related: http://physics.stackexchange.com/questions/76492/special-relativity-and-massless-particles –  Sep 07 '13 at 00:16
  • @MichaelBrown & Ben Crowell : all the answers are based on the assumption which relativity makes. My question is whether we know of a deeper reason in the nature or characteristic of massless particles that their speed is frame-independent. What could be the fundamental reason in mass being used as something which makes speed frame-dependent ? – cleanplay Sep 15 '13 at 17:23
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    Here is a modern attitude: Special relativity is one of the only options you can write down for a mathematically consistent theory. Once you have the discrete list of options you can simply compare them to nature one by one and rule them all out except for SR (and de Sitter relativity, as it happens). Either there is a universal speed or there isn't. The fact that there is a universal speed is an experimental fact which is established now with great confidence. – Michael Sep 16 '13 at 00:53
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    Once you have the kinematical group established ($R^4 \rtimes O(3,1)$ for SR or $O(4,1)$ for de Sitter) it is a straightforward exercise to compute the addition of velocities and verify the constancy of the universal speed in every frame. Then, in SR, you define the mass to be the invariant of the kinematical group $m^2 \equiv E^2 - p^2$ and from that you find that massless particles move at the universal speed. For massive particles on the other hand, you can always find a boost which brings their velocity to anything else $<c$. – Michael Sep 16 '13 at 00:55

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The reason can be found in the masslessness of photons. What this means is that the rest mass of the photon vanishes. This can be seen by analyzing the framework of special relativity, which is based on the observation that light is moving at the same velocity in all frames of reference.

The relativistic energy-momentum relation of a general particle is given by

$$E =\sqrt{(pc)^2+(m_0c^2)^2}, $$

where $p$ is three-dimensional momentum, $m_0$ is rest mass and $c$ is the speed of light.

So how can we see that for a particle moving at the speed of light, $m_0$ has to be zero?

A particle moving through Minkowski space can be classified in terms of its momentum vector. It can be either timelike (velocity smaller than c), lightlike (also called "null", velocity equal to c) or spacelike (velocity larger than c). For reference, see the diagram below (source: Wikipedia).

enter image description here

The condition for a vector to be lightlike is that the square of its norm has to vanish. The momentum-four vector in special relativity is given by

$$\textbf{P}=(\frac{E}{c},p_x,p_y,p_z)$$,

with

$$\textbf{P}^2=-\frac{E^2}{c^2}+p^2, $$

where $p$ is the norm of the spatial components, where I have assumed the Minkowski signature to be $(-,+,+,+)$. If this expression is equal to zero, we arrive at the relation

$$-E^2/c^2+p^2=0,$$

or

$$E=pc.$$

When we compare this to the relativistic energy-momentum relation I have written down above, we see that the two expressions are consistent if the ress mass $m_0$ vanishes. This should give some insight on how the two concepts of masslessness and moving at the speed of light in all reference frames are related.

Frederic Brünner
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  • yes, but in special relativity we assume that light is moving at the same velocity in all frames of reference. I meant to ask whether we know of any deeper reason for this nature or is it just from observation ? The constant speed limit c may be valid for all massless particles but why does this happen that changing the frame of reference for massless particles does not change their speed. – cleanplay Sep 12 '13 at 08:59
  • It is a postulate of special relativity that light travels at the same velocity in all frames of reference, one which is consistent with experiment. – Frederic Brünner Oct 07 '13 at 09:32
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They travel at the speed of light because they have zero mass.

Enucatl
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  • Please read my comment in response to Frederic's answer above. – cleanplay Sep 15 '13 at 17:19
  • Ah, that's a quite different question though. Then @Michael Brown was closest to this. You can read the details in this paper http://arxiv.org/abs/math-ph/0602018 but it's quite advanced.

    It boils down to this: if you enforce the symmetry principles of empty space, you end up with a limit speed that is the same in any reference frame. If you want electromagnetism to be consistent, that speed must also be the speed of light.

     – Enucatl Sep 16 '13 at 07:28
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I am postulating that they may be driven forward or repelled by the fabric of space and not by the initial velocity imparted to them when they are created i cant back it up with any data as yet but it may explain why they don't slow down over long distances and encountering masses

terry1234
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