I was discussing with a few friends the idea of photons in general relativity...essentially that light is a geodesic.

 

However, it got me thinking to loop quantum gravity that would deal with a photon rather than light itself...wouldn't the photon definitionally take up space? Obviously it does, but how much space?

 

Further, isn't light energy? And as Einstein pointed out, energy has mass. So wouldn't it distort spacetime only slightly that has no real significance in everyday life?

 

But none of my texts answer these questions...and google isn't answering either. So my question is twofold: 1. What is the volume of a photon? 2. What is the density of energy for photons (or light, whichever)?

The volume isn't really well-defined, but it will behave like it's something like the cube of the wavelength. One problem is that the photons are described by probabilities and aren't well-localized, and another is that superposition applies, so two photons can occupy the same volume.

Ha! Forgot about that superposition problem...so there really is no set volume of a single photon beyond the cube of wavelength?

 

Hmm...

Ha! Forgot about that superposition problem...so there really is no set volume of a single photon beyond the cube of wavelength?

 

Hmm...

 

That's approximate, but basically yes. You can put a photon in a cavity with mirrors at the ends, a distance L apart, and the largest photon you can get in there is represented by a standing-wave with a wavelength of L/2. But you can put a large number of them in there.

Energy does not necessarily have mass.