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laser beams are photons with the same frequency and the same direction, but according to the wave-particle duality, photons have mass.

but if we shoot two masses and they intersect at some point they don't go through each other, they get reflected (their direction changes) and might lose some mass.

but that's not the case with laser beams, if we hold two laser beams and make them intersect at a point, they would just go through each other, neither they change direction nor they produce a new color (their masses and frequencies are the same) because mass is related to frequency from Einstein equation.

E=hf
m=E/c^2
m=hf/c^2

why does this happen?

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    $\begingroup$ "according to the wave-particle duality, photons have mass", says who? According to the wave-particle duality, photons are massless particles. $\endgroup$ – Emilio Pisanty Apr 8 '16 at 12:32
  • $\begingroup$ uhmm, photons have mass : en.m.wikipedia.org/wiki/Compton_scattering $\endgroup$ – bigworld12 Apr 8 '16 at 12:35
  • $\begingroup$ Yes, in some analyses photons can be seen as having an effective mass, which is very different. If you want to quote Wikipedia, you should start with en.wikipedia.org/wiki/Photon. $\endgroup$ – Emilio Pisanty Apr 8 '16 at 12:37
  • $\begingroup$ so why didn't this effect appear when photons intersect? $\endgroup$ – bigworld12 Apr 8 '16 at 12:37
  • $\begingroup$ photons have no rest mass, but they have effective mass proofed by Compton scattering $\endgroup$ – bigworld12 Apr 8 '16 at 12:38
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For two particles to influence each other you need some sort of interaction.

For (macroscopic) mass this is clearly Coulomb-interaction. Two atoms can not be at the same place, because their cores repell each other. If you look at smaller scales, strong and weak interaction might add their part.

Photons have no charge, no color-charge and don't interact weakly. So there is no way for them to interact directly with each other. It might be that gravitation has an effect, but one can easily assume that it is negligible. (A picture of two people standing on different sides of a soccer-field, shooting with a gun at a 90° angle to each other comes to my mind. Then assume the bullets don't hit each other but only attract each other via gravitation and calculate the effect. Might not be in any way a properly scaled example, but it should give an idea).

However if you go even deeper into particle physics, you will see, that photons indeed can interact with each other via higher order processes. See e.g. this website.
As far as i remember from last semesters particle physics lecture, photon-photon-scattering has indeed been observed, but the cross-section (basically: "how often does this happen?") is quite a few orders of magnitude to low to actually see the effect with your eyes. (Think of the two people with guns at the soccer-field again - how likely is it that their bullets actually hit each other?)

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  • $\begingroup$ their bullets will hit each other if they shoot billions and billions of bullets with the speed of light. $\endgroup$ – bigworld12 Apr 8 '16 at 12:52
  • $\begingroup$ so photons interact with each other but in special forms? $\endgroup$ – bigworld12 Apr 8 '16 at 12:53
  • $\begingroup$ Yes, thats exactly what happens: If you shoot enough photons in small enoughs space you will get some of them interacting. But not directly with each other but via other (virtual) particles involved. It's just the probability is so small, that it needs modern detectors to actually recognize it. $\endgroup$ – Anedar Apr 8 '16 at 12:56
  • $\begingroup$ Another way to say the same thing: photons need to be in enormous number in a small space to have significant probability to interact. I am not sure it has ever been accomplished on Earth. $\endgroup$ – fffred Apr 8 '16 at 12:58
  • $\begingroup$ You can also obtain effects if you have extremely large energies such as in the Schwinger limit. $\endgroup$ – Steven Stewart-Gallus Jul 4 '16 at 21:41

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