Can two photons cancel each other?

[QuasarBoy543298]

in classic electromagnetism, two plane waves with the same frequency and -1 phase difference can cancel each other.
due to conservation of energy, I assume that photons (that so far we have treated as sort of EM energy chunk traveling through space) can't truly cancel each other.
then, what really happens if 2 identical (up to -1 phase) photons travel next to each other.
if photons can be treated as some sort of EM wave mode, or even if we can just associate a phase to a photon, what stops them from canceling each other?

 

[Dale]

if 2 identical (up to -1 phase) photons

What exactly do you mean by identical photons up to -1 phase? How would you make two such photons?

 

[weirdoguy]

And in what sense they "travel next to each other"? I think it's a little bit problematic, since there is no position operator for photons

 

[QuasarBoy543298]

but there are localized photons

And in what sense they "travel next to each other"? I think it's a little bit problematic, since there is no position operator for photons

but we can have localized modes, no? After all sometimes we talk about photons coming and doing something (like in the photoelectric effect for example... )

 

[Vanadium 50]

What kind of QM is this?

The question assumes the photons are simultaneously in an eigenstate of position, momentum/energy, number and phase. Nope.

And didn't we go over all this in this thread?

 

[Dale]

After all sometimes we talk about photons coming and doing something (like in the photoelectric effect for example... )

The interaction with the device is localized to the device. The interaction is not the photon.

 

[PeterDonis]

due to conservation of energy, I assume that photons (that so far we have treated as sort of EM energy chunk traveling through space) can't truly cancel each other.

The same argument would apply to two classical EM waves: each one carries energy, so they can't cancel each other.

I think you need to rethink your understanding of classical EM as well as quantum EM.

 

[DaveE]

in classic electromagnetism, two plane waves with the same frequency and -1 phase difference can cancel each other.

No, I don't think so. In classical EM homework problems you may see this, but not in the real world. How would you make two waves that have destructive interference EVERYWHERE. How is that different than nothing? How do you "make" nothing?

BTW, you left out direction and amplitude. Plane waves have those too.

Also, while we all know what you mean, "-1 phase difference" is a confusing way to describe this. In simple waves we have f(t) = A⋅sin(ωt + Φ). The phase is Φ, with values of [0,2π) radians (some like [0, 360) degrees). The amplitude is A. You could represent the "out of phase" condition with Φ₁ = 0 and Φ₂ = π, or with A₁ = A and A₂ = -1⋅A. But mixing the words phase and giving amplitude values isn't the best way to communicate this concept.

 

[Dale]

How would you make two waves that have destructive interference EVERYWHERE.

To expand on this, the only way to make them cancel everywhere is to produce the two waves at the same source, say an antenna.

You can indeed feed a single antenna with two amplifiers that are out of phase. Then there is no current in the antenna and no wave is produced or equivalently two completely interfering waves are produced.

So where did the energy go? Into the other amplifier. Generally this is not good for an amplifier.

 

[Strilanc]

in classic electromagnetism, two plane waves with the same frequency and -1 phase difference can cancel each other.
due to conservation of energy, I assume that photons (that so far we have treated as sort of EM energy chunk traveling through space) can't truly cancel each other.
then, what really happens if 2 identical (up to -1 phase) photons travel next to each other.
if photons can be treated as some sort of EM wave mode, or even if we can just associate a phase to a photon, what stops them from canceling each other?

Individual photons don't have a phase in the way you're thinking. Instead, in a two photon system, each possible way of arranging the two photons has a phase (an amplitude to be more specific). If you line two photons up on top of each other, there's amplitude in the state "two photons here" and no amplitude anywhere else.

You'd need an "anti photon" in order to cancel the photon out instead of just stacking on top of it. Although, even if such a thing existed, the cancelling out would have to be more of a transformation into some other form since otherwise energy wouldn't be conserved or (even worse) reversibility would be lost.

 

[Demystifier]

in classic electromagnetism, two plane waves with the same frequency and -1 phase difference can cancel each other.
due to conservation of energy, I assume that photons (that so far we have treated as sort of EM energy chunk traveling through space) can't truly cancel each other.
then, what really happens if 2 identical (up to -1 phase) photons travel next to each other.
if photons can be treated as some sort of EM wave mode, or even if we can just associate a phase to a photon, what stops them from canceling each other?

See https://www.physicsforums.com/threa...conservation-of-momentum.880286/#post-6420786

 

[vanhees71]

A two-photon state is a two-photon state and not the vacuum, i.e., if you superimpose two-photon states you cannot get the vacuum. One should keep in mind that photons are (asymptotic) free Fock states of the em. field.

What of course is possible is the inverse process to pair annihilation, i.e., $\gamma+\gamma \rightarrow \mathrm{e}^+ + \mathrm{e}^-$.