
What is a photon? (2017) - memexy
http://blog.sigfpe.com/2017/08/what-is-photon.html
======
supernova87a
The blog post was interesting, but I wouldn't say it explained "what is a
photon", it explained more, why do photons have energies and propagation
properties that they do. The first 2/3 of it I was wondering, why go through
all this intro about springs...

Although, there is one thing that I have always searched for an explanation of
-- why the speed of light is invariant with reference frame.

The idea that space is filled with springs might help me with that. If
light/photons are the passage of a wave from spring to spring, then the speed
of that propagation is always at the "spring speed" however you measure it, or
however fast you are going. You can only ever receive the microscopic spring
transmission speed of the photon at the place you receive it. (Although it
brings up the complicated followup of, how are you traveling through the
"springs", etc, I guess).

But I'm sure I'm wrong about that too -- if anything QM has taught me is that
my attempts at physical intuitions are usually wrong about QM.

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anonymousiam
WiFi could also interfere with other frequencies if a non-linear device is
nearby. See:
[https://en.wikipedia.org/wiki/Intermodulation#Passive_interm...](https://en.wikipedia.org/wiki/Intermodulation#Passive_intermodulation_\(PIM\))
The article does not consider this, but it works with light as well as RF.

------
cycomanic
I'm surprised that nobody pointed out yet, that harmonic oscillators have
discrete energy states as well.

I think that's why the explanation is somewhat makes things more confusing.
The fundamentally different thing about quantum mechanics is that even waves
in free-space have discrete energy states.

I think the video by 3blue1brown posted by someone else is a much better
explanation.

------
gfody
another great explanation here
[https://www.youtube.com/watch?v=MzRCDLre1b4](https://www.youtube.com/watch?v=MzRCDLre1b4)
also from 2017

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mikhailfranco
sigfpe is too simplistic and conflates a few different aspects of atomic
spectra, photons and EM fields.

The sci.physics reference for this is Baez & Weiss:

[http://math.ucr.edu/home/baez/photon/schmoton.htm](http://math.ucr.edu/home/baez/photon/schmoton.htm)

If you have read that, you know the number of photons is just another quantum
number, with aspects of uncertainty, superposition and entanglement, so this
will not be a surprise:

[https://phys.org/news/2019-08-photon-number-quantum-
superpos...](https://phys.org/news/2019-08-photon-number-quantum-
superposition.html)

------
MaXtreeM
For others who like to learn from video, here is lenghtier explanation of
quantum fields, discrete energies, plane waves, etc. from Sean Carroll:
[https://www.youtube.com/watch?v=Dy1LNk_B6IE](https://www.youtube.com/watch?v=Dy1LNk_B6IE)

------
maxk42
What I really want to know is: Can someone describe what "heat" is to me?

------
mike1101
How does this explain the duel split experiment?

~~~
jabl
It doesn't directly address it.

But they key is right there in the beginning; photons are NOT small billiard
balls moving along ballistic trajectories.

"Wave-particle duality" doesn't mean that you can think of flicking a light
switch as alternatively an electromagnetic field propagating from the light
bulb, or that the light bulb shoots out a stream of tiny billiard balls.

No, there's only the electromagnetic field. However, if you squint closely
enough you see that the energy levels of the field are quantized (aka
photons).

Now, back to the double slit experiment. So a wave propagates from the source,
through the slits, interferes constructively or destructively, and then hits
the detector screen. However, due to the quantum nature of, well, everything,
the "hits the detector" interaction is quantized. The field "deposits" quantas
of energy (photons) to the screen in a localized interaction (say, a photon
causes an electron in the screen to jump to a higher energy level). If the
detection apparatus is sensitive enough you'll see that single interaction as
a dot on the screen, rather than a faint interference pattern (which you'll
eventually start to see if you repeat the experiment long enough).

So: Lets forget about the "wave-particle duality" already. There's only
fields. Fields which interact in a quantized fashion.

------
carrolldunham
The author left off at precisely the point I was hoping they would get across:
How the wave that extends everywhere in space, obviously doesn't. I mean, I
know you can make a localised 'packet' or whatever with an infinite sum of
sine waves, but then wouldn't you have to talk about infinite photons moving
every time 'one photon' hits a detector?

~~~
krastanov
It is a neat trick actually. If you superimpose a few of these waves with
frequencies that are fairly close, then you will see how they cancel out in
the distance, while they reinforce each other in the center. This is called a
"wave packet". 3blue1brown was somewhat useful, somewhat tangential video on
the topic
[https://www.youtube.com/watch?v=MBnnXbOM5S4](https://www.youtube.com/watch?v=MBnnXbOM5S4)

The more rigorous way to say "superimpose a few of these waves", is to say
that there is some uncertainty in the frequency. This uncertainty in the
frequency lets you have more certainty about the position (the wave packet is
centered somewhere, instead of being completely distributed the way an
infinite plane wave is)

------
GolDDranks
This is a nice article, but it feels like it leaves a half of the puzzle to
the table. We know by everyday experience that photons _do_ have some time-
and place-varying properties: my WiFi has a perfect strength here, but
absolutely zero at my friend's house 5 kms away. The photons emitted by my LED
lamp are not a static field: I can switch it off by pressing a button so it's
time-varying.

The article acknowledges place only in this short sentence in the end:

> This means that adding a quantum to a system has an effect that extends
> across the entire system. That makes it problematic to talk about the
> location of a photon.

But then leaves the experience gap between the model and our everyday
experience totally without discussion.

~~~
GolDDranks
Btw. I have an impression that time- and place-local behaviour can be modelled
as a collection of photons that destructively interfere "elsewhere" than where
we tend to actually see light. Fourier transform seems to play a big role
here.

~~~
krastanov
Your statement is not very rigorous, but the intuition it provides is spot on.
It is pretty much exactly this intuition I convey the first time I teach such
topics.

------
remote_phone
One question I have:

One thing I remember is that as something approaches the speed of light, its
mass increases. This is why we can never achieve the speed of light because as
we approach the speed of light, our mass increases which requires more energy
to accelerate.

If that’s the case, the how can photons have a mass? Wouldn’t something
traveling at the speed of light need to have infinite mass, regardless of how
light it started off with?

~~~
krastanov
There is rest mass, which is the mass of an entity when it does not move. And
there is relativistic mass, which is the rest mass plus the mass due to all of
the kinetic energy of the entity. Photons have zero rest mass, but depending
on the energy they carry, they have different relativistic masses.

By the way, only entities with zero rest mass can move at the speed of light.
Actually, in relativity it is mathematically inconsistent for something with
zero rest mass to exist unless it is moving at the speed of light.

~~~
remote_phone
Very excellent answer, thank you for this! I will do more reading in this
direction!

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pdonis
The article leaves out a crucial item. When it says:

"The normal modes are plane waves traveling at the speed of light in a
particular directions with a given frequency."

This is not quite correct. A correct statement would be that plane waves are
_one possible choice_ of "normal modes" for the quantum electromagnetic field.
But not the only possible choice. (In more technical language, they are one
possible choice of basis for the Hilbert space of states of the quantum
electromagnetic field, but not the only possible choice.)

In fact, the plane wave states (whose technical name is "Fock states") are
often not very useful, because they are very hard to produce experimentally
and pretty much never occur naturally. The states that are closest to
naturally occurring states and which are easy to produce experimentally (for
example in a laser) are coherent states. But coherent states are nothing like
plane waves.

~~~
krastanov
I am pretty sure you are confounding the basis of functions (harmonics) that
one can use to describe an EM field, with the basis of a Hilbert space used to
quantize them. You can have a mode (e.g. a plane wave) and the field of that
particular mode can be quantized and you get to pick whether to use Fock
states or coherent states or any other basis. In other words, "plane wave"
refers to a particular mode of the field and Fock/coherent states refer to the
quantum state of that particular mode. Two different plane waves are two
completely different modes, e.g. two completely different Hilbert spaces,
__not __basis vectors of a given Hilbert space.

~~~
knzhou
Nah, GP is right, if he's talking about how you can decompose states into
superpositions of coherent states of the whole _field_. These are different
from coherent states of individual modes.

Specifically, a coherent state of a field is a state which is an eigenvector
of the positive-frequency part of the field operator, when that operator is
evaluated at any position.

~~~
krastanov
See the sibling comment and my answer. A plane wave can very well be a plane
wave "containing" one photon or containing multiple photons or containing a
coherent state. There is a big difference between saying "I can use different
sets of creation operators to form a basis for the field operator" (what I
think you are saying) and the confounded statement mixing up basis of a
Hilbert space with basis of integrable functions of the OP.

------
Zamicol
What is the amplitude of a single photon's wave?

Yes, it's well taught that wavelength is related to frequency. Higher
frequency is higher energy energy and lower frequency is lower energy, but
it's the frequency of what? Unlike ocean waves, photons do not have a spacial
amplitude. A photon does however have a spacial wavelength. This distinction
between photonic wavelength and amplitude I've never heard explicitly
addressed.

My understanding is that a photon's amplitude is the likelihood of interaction
at a specific point in space. High amplitude is likely interaction, low
amplitude is low likelihood of interaction. This means at a photon's
peaks/crests it has high interaction and at its troughs the photon has low
interaction likelihood. These likelihoods are repeated every wavelength, a
length measurable in physical space.

This is some of the reason why an antenna for a given frequency range needs to
be a specific size. Too small and there's a good chance of missing a signal. A
proper sized antenna, related to wavelength, guarantees high interaction
somewhere along the length of the antenna.

When speaking of many photons, amplitude (like AM radio) is simply flux, how
many photons at a particular frequency exist during a given unit of time.
That's not related to the amplitude of a single photon and not what I'm
talking about here.

~~~
pdonis
_> My understanding is that a photon's amplitude is the likelihood of
interaction at a specific point in space._

Not really, because there isn't really a well-defined wave function for a
photon in the position representation (which is the one that has the
interpretation "the likelihood of detection at a specific point in space").

 _> When speaking of many photons, amplitude (like AM radio) is simply flux,
how many photons at a particular frequency exist during a given unit of time._

There isn't a well-defined answer to this question, because a state like this
(which is a coherent state) is not an eigenstate of the photon number
operator. (Also, energy flux is really amplitude squared.)

A good, if somewhat lengthy, discussion of the "photon" concept can be found
here:

[http://math.ucr.edu/home/baez/photon/schmoton.htm](http://math.ucr.edu/home/baez/photon/schmoton.htm)

------
gigama
"I'd like to have an argument please."

[1] [https://genius.com/Monty-python-argument-
lyrics](https://genius.com/Monty-python-argument-lyrics)

------
jiggawatts
Unfortunately, like all such descriptions, this one misses the mark also.

I've _never_ heard a good explanation for what a photon "is", or any particle
for that matter. That's because physicists don't know either.

No, seriously. Ask a randomly selected set of physicists about any core
concept in Quantum Mechanics and you'll discover that their answers diverge
wildly. Ref:
[https://arxiv.org/abs/1301.1069](https://arxiv.org/abs/1301.1069)

Basic things like: "Are the _photons_ quantised or is it just the _photon
interaction with atomic orbitals_ that's quantised?" I've personally asked
this question and had working physicists confidently state that either the
former or latter is true, and the other is false.

(PS: Compare this to biologists, chemists, or engineers. They all 100% agree
on all core concepts. So do astronomers, and physicists studying classical
mechanics and relativity. It's only quantum mechanics that's so fragmented.)

Ask any working QM researcher to clearly show how "a single photon" interacts
with an electron in an orbital and they will without a doubt draw you a
cartoon diagram. Never in the history of theoretical physics has anyone, ever,
anywhere made a numerical visualisation of this. This is because both the QM
mental model and the mathematical theory applies only to ensembles in
potential wells.

This is a _very narrow_ scope of applicability that was explicitly called out
in the QM papers back in the early 1900s, but is now glossed over. People
assume that what applies to a special case is the hard rule that applies to
all things. It doesn't. There are no photons in free space. There are no
little hard particles of light. You can't have a point with a wavelength. You
can't have a single pure frequency with a finite duration. This is all
gibberish, it's just a simplification to make the maths tractable when done
with pencil and paper for special cases! The output of this simplified model
is a 0-dimensional scalar. It can't do output much else, such a simulation of
a full 3D interaction of any type.

Trying to work backwards from such an oversimplified model in order to explain
the deep nature of reality is futile. This is like pointing at the bandwidth
measurement in Windows Task Manager and saying "we can understand how the
Internet works by watching this number go up and down".

~~~
Ono-Sendai
_> Ask any working QM researcher to clearly show how "a single photon"
interacts with an electron in an orbital and they will without a doubt draw
you a cartoon diagram. Never in the history of theoretical physics has anyone,
ever, anywhere made a numerical visualisation of this._

I personally have made a simulation of this. It would be called a semi-
classical approximation, in that it's a simulation of a Schrodinger equation-
described electron in a hydrogen (Coulomb) potential interacting with a
classical EM wave. However I suspect that's how nature works anyway.

~~~
eigenspace
> However I suspect that's how nature works anyway.

Uh, could you clarify what you mean here? Are you saying you don't beleive
that the electromagnetic field is quantized?

~~~
Ono-Sendai
Yeah pretty much. (I say this not from a position of profound knowledge or
anything like that, just that I'm not familiar with a good argument for why it
is, not that I have looked into it in great detail. My knowledge of QFT is
very basic)

~~~
eigenspace
Ah, fair enough. I was worried you might be professing some sort of expertise
while claiming that.

I can assure you that whatever may be true of the electromagnetic field, it is
_not_ classical. We know that to about the same degree of certainty that we
know that atoms aren't classical.

It's just that when considering atoms in an electromagnetic field, there are
often situations where you can ignore the quantum mechanics of the field.

~~~
Ono-Sendai
So what would you say is the best evidence that the EM field is quantised?

~~~
eigenspace
Examples abound, but I’d say my favourite is the electron g-factor which is an
example of one of the most precise agreements between theory and experiment
ever achieved by humans and it’s calculation relies heavily on the quantum
mechanics of the electromagnetic field.

But there’s lot of other, more pedestrian examples. For example, you can (and
people have) generated entangled pairs of photons and then performed
measurements on this entangled pairs that violate the Bell inequalities,
meaning that their correlation is not classical.

~~~
eigenspace
Looking back on this, I feel I should also mention that there's not any single
piece of evidence that should be bullet-proof convincing evidence for the EM
field's quantum nature, rather it's the totality of many many many different,
independent results exploring various quantum mechanical properties of
electromagnetism (and its high energy unification with the weak nuclear
force), all of which converge on the basically undeniable fact that
electromagnetism is a quantum mechanical phenomenon.

Of course, this isn't the full story. There is physics beyond the standard
model. But whatever that physics is, it's description needs to reproduce
quantum electrodynamics in the appropriate limit.

I should also mention that it's not even mathematically consistent to have a
classical field like electromagnetism coupled to quantum matter. It's fine in
certain approximation schemes, but the breakdown and limitations of such an
approach is well documented.

