# Can photons be attracted to one another?

by sts107a
Tags: attracted, photons
 P: 7 I just had a quick question; I’m an armature so please excuse my ignorance. But can photons be attracted to one another? And if so how? Thanks for all your help :)
 Sci Advisor HW Helper P: 11,915 What do you mean "attracted",as in they are beautiful and may fall in love one with another...? Daniel.
 P: 7 Attracted as in say assort of magnetic attraction.
 Sci Advisor HW Helper P: 11,915 Can photons be attracted to one another? Sure,electric is outta discussion.Well,free photons DO NOT INTERRACT.Actually photons interact through other particles (their interaction is mediated by other particles),but that is what physicists call SCATTERING... Daniel.
 P: 7 Ok try this if two frequencies were transmitted from two different transmitters, if they get close enough would they attract one another? In that same case would to photons be attracted to one another
 Sci Advisor HW Helper P: 11,915 No,classically,the two waves would simply INTERFERE...As for photons,things are more complicated and cannot be put in laymen terms...Definitely not "attraction". Daniel.
 P: 297 I am presuming you mean "is there any gravitational attraction between photons?" Since photons are quantum objects and there is no quantum theory of gravitation then this cannot be answered with today's physics. However you can ask "do two light beams attract one another." The answer to this is that parallel beams do not but anti-parallel beams do.
 P: 388 asking if photons can attract one another is like asking whether the electromagnetic force can attract itself.
 Emeritus Sci Advisor PF Gold P: 5,532 I've never worked this out, so forgive me if it sounds dumb, but can't photons attract in GR? I mean, both have energy density and therefore affect the spacetime around them.
P: 297
 Quote by Tom Mattson I've never worked this out, so forgive me if it sounds dumb, but can't photons attract in GR? I mean, both have energy density and therefore affect the spacetime around them.
That is the context in which I answered above. I forgot to say "according to GR". Photons do not exist in GR but lights beams or light rays do.
 P: 7 Ok but here is what I was thinking. Now I know this is pretty much out of the realm of possibility at this point, but if two photons with the same frequency (I know that one can’t be the other but if it could) couldn’t their same frequencies attracted one another being that it is electromagnetic? And could someone please give me the equation for a photon? I’m having a hard time finding it. Thanks for all your replies
HW Helper
P: 11,915
 Quote by Tom Mattson I've never worked this out, so forgive me if it sounds dumb, but can't photons attract in GR? I mean, both have energy density and therefore affect the spacetime around them.
There are no photons in GR,the only theories which account for a decent photon descriptio are the ones in the SM:QED & EW.In both theories,photons do not interact.They scatter one on another via particle +antiparticle fields.

GR is a very classical theory.Einstein-Maxwell and Kaluza-Klein are both classical models.

Daniel.
HW Helper
P: 11,915
 Quote by sts107a but if two photons with the same frequency couldn’t their same frequencies attracted one another being that it is electromagnetic? And could someone please give me the equation for a photon? I’m having a hard time finding it. Thanks for all your replies
Frequency are numbers.Physical quantities measured in $Hz$.How can they ATRACT...?

Daniel.
 Sci Advisor P: 1,135 While the educational answer should be a clear "No they don't interact" there are the ever so small effects. The standard ones: 1) GR: everything which has energy "attracts" anything which has energy. 2) QED: higher energies or smaller scales cause more interaction with virtual particles. But I can also imagine the following effect: Light moving through a dielectricum causes currents at a 90 degrees phase shift with respect to the electric field. Parallel currents do attract each other even if it's at a ratio of (v/c)2 where v is generally very small. This might even be extended to the dielectricum of the vacuum if it's interpreted as vacuum polarization which is in general attributed to virtual particles. The amount of current is then expressed by the usual dD/dt from Maxwell. The dD/dt would cause the effect to be more significant at higher frequencies: light, x-ray, gamma photons..... I could imagine that such an effect could lead to the compactification of wave packets in the direction transversal to the propagation, or at least to less spreading. Regards, Hans.
 Sci Advisor HW Helper P: 11,915 Let's keep the discussion within the theoretical framework which accounts for photons:equilibrium statistical mechanics in second quantization and QED. I think reference towards classical theories (such as GR & CED) is of no relevance. And EW will not bring anything new in photon/quantized QED description... Daniel.
P: 4,006
 Quote by Tom Mattson I've never worked this out, so forgive me if it sounds dumb, but can't photons attract in GR? I mean, both have energy density and therefore affect the spacetime around them.
I was under the same impression, though i am not sure. However if we have a particle (we don't need to call it a photon) that has an associated energy-density of some kind (it does not matter whether this energy comes from restmass or dynamical mass generation-processes like in the photon-case), then space time must be curved right ???

In the end it is the stress energy tensor that curves space time not just the rest-mass...This notion is adopted by QFT where the perturbations (you know, the "current" in QFT-language) of a spin 2 field is expressed by this stress-energy tensor T.

This field needs to be spin 2 (the gravitons) because otherwise it cannot couple to the stress energy tensor which is a symmetric tensor with two indices and has therefore 5 degrees of freedom.

So TOM, i think you are quite right on this one

marlon
P: 1,047
 Quote by Tom Mattson I've never worked this out, so forgive me if it sounds dumb, but can't photons attract in GR? I mean, both have energy density and therefore affect the spacetime around them.
I am afraid the question is more complicated. After reading a comment in this thread, I searched about this subject and found this: http://arxiv.org/gr-qc/9811052. There it is shown that two parallel light beams do neither attact nor repel, since their gravitoelectric field cancels their gravitomagnetic field. (If you want to avoid the whole calculations go directly to chapter 4). In case of antiparallel light beams there is indeed an attraction.

This concerning light beams. Now, it seams to me that the question about single photons might be more subtle. They are always moving at speed c, and their gravitational field should also propagate at that speed. Consider for example two parallel photons. Will one photon feel the gravitational field of the other one? In case of photons moving towards each other, they probably will. I wonder how to figure out the bending of spacetime produced by a photon.
P: 4,006
 Quote by hellfire I wonder how to figure out the bending of spacetime produced by a photon.
Well, we need to know the actual formula for the stress energy tensor in the specific case of a photon. If it is zero, then there is no curvature of spacetime.

According to me we need to know how this energy tensor looks like in the case of a photon. Does anyone know this ???

marlon

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