# Is a photon an excitation of the electromagnetic field?

• B
• entropy1

#### entropy1

Allow me to hijack this thread for a second: a photon is an excitation of the electromagnetic field, right? The photon does not exist until measured. So how can we send a photon in a particular direction, so it has a known position and momentum?

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Allow me to hijack this thread for a second: a photon is an excitation of the electromagnetic field, right?
Yes.

The photon does not exist until measured.
What makes you think that? Photons are no magicians that just pop into existence when the curtains go up. :)

danielhaish
Photons are no magicians that just pop into existence when the curtains go up. :)
A photon is a wave until measured, when it becomes a particle, right?

Demystifier
A photon is a wave until measured, when it becomes a particle, right?
No. It is actually neither. Photons are really tricky little rascals.
There's a good Insight article on this, and I will try to find it and post it here later.
But it is true that when a photon (or electron, proton etc.) is detected it is detected as a whole "unit", and in just one place (e.g. on a screen).

vanhees71
A photon is a wave until measured, when it becomes a particle, right?
There's a good Insight article on this, and I will try to find it and post it here later.
Here it is (it wasn't an article, but a FAQ post):

IS LIGHT A WAVE OR A PARTICLE?

DennisN
@DennisN Thank you.
You're welcome!

how can we send a photon in a particular direction, so it has a known position and momentum?

You can't. Position and momentum are non-commuting observables, so it's impossible for any quantum object to have definite values for both.

For photons, position is not even a well-defined observable to begin with (because the position operators that work for particles with nonzero rest mass don't work for particles with zero rest mass).

What you can do is emit a photon whose momentum is well collimated in a particular direction.

vanhees71 and entropy1
Position and momentum are non-commuting observables, so it's impossible for any quantum object to have definite values for both.
So that rather means the photon has a certain chance of being detected somewhere sometime, so that it doesn't exist as particle-like until it is detected?

so that it doesn't exist as particle-like until it is detected?
It's best to give up the idea that it "exists like a particle" altogether.

That idea is largely based on a historical misunderstanding. Early in the last century physicists observed interactions that suggested that light involved something that had a position: for example the photoelectric effect and Compton scattering both look as if something happened at the exact position of an electron. Until then, everything they had ever seen that had a position was a particle so it was natural for them to think that these interactions showed a photon "existing like a particle" - but that has turned out to be a misleading and inaccurate way of thinking about it.

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vanhees71 and entropy1
the photon has a certain chance of being detected somewhere sometime

Yes.

so that it doesn't exist as particle-like until it is detected?

No. In addition to what @Nugatory said, photon detectors typically absorb the photons, so a photon that has been detected by such a detector no longer exists at all after it is detected.

More precisely, the "detection of a photon" transfers energy from the quantum electromagnetic field to the detector.

mattt, vanhees71 and entropy1
I am always curious when it is said that "a photon is an excitation of the EM field". Do free photons exist? 'Cause I think they do. An "excitation" being something that seems to be less "long lasting" than a truly free photon that has been hanging around since shortly after the big bang.

I would say a photon is as much a quantum particle as an electron. Yes, its creation/destruction rules are a bit different than an election. But all particles have fundamental differences from other particles.

Delta2
An "excitation" being something that seems to be less "long lasting" than a truly free photon that has been hanging around since shortly after the big bang.

In the particular context of quantum field theory, "excitation" just means "state with energy greater than the ground state". I don't think it implies a (relatively) short lifetime of the state. As you say, free photon states (or at least, free to a very good approximation, as many photon states are in our universe) that can last indefinitely do exist.

A "particle" is then just an "excitation" that is (at least to a good enough approximation) an eigenstate of the appropriate particle number operator with eigenvalue ##1##. At least, that's what I would say a precise usage of the term "particle" would imply. In reality, "particle", or a term designating a particular kind of particle, is often used to refer to excitations that are not even close to being number eigenstates; for example, coherent states emitted by lasers are referred to as "photons".

DennisN, mattt, DrChinese and 1 other person
A one-photon Fock state is a specific state of the free electromagnetic field. If you take a cavity then you can define proper one-photon energy eigenstates, and these have an energy ##\hbar \omega>0##, i.e., it's a specific excited state of the free electromagnetic field in the cavity.

For free fields it's more subtle, because there the energy spectrum is continuous and the "energy eigenstates" are thus generalized states. But in any case the important points are

-the notion of "photon" makes sense for (asymptotic) free states of the electromagnetic field only

-a photon has no point-particle properties; particularly it doesn't allow for a proper position observable and thus is not localizable. Thus it's much more appropriate to think about photons as specific excited states of the free electromagnetic field rather than in terms of "point particles".

DennisN, Imager, DrChinese and 2 others