# What does the Uncertainty Principle say about the location of photons?

#### JJRittenhouse

Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?

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#### Upisoft

Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
We know precise speed(in vacuum), not velocity. And yes we cannot know exactly where the photon is.

#### jostpuur

Uncertainty principle deals with position and momentum, not with position and velocity. Quantum mechanical particles have probability distribution for momentum, and its variance is the relevant quantity for uncertainty principle.

The position of photon is more mysterious than the mere uncertainty principle might suggest, however.

#### JJRittenhouse

The position of photon is more mysterious than the mere uncertainty principle might suggest, however.
explain?

#### JJRittenhouse

We know precise speed(in vacuum), not velocity. And yes we cannot know exactly where the photon is.
Isn't the speed still the same in another medium, just interrupted by electron interaction?

#### Upisoft

Isn't the speed still the same in another medium, just interrupted by electron interaction?
AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.

#### JJRittenhouse

AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.
Well then I guess Feynman was mistaken.

#### Fredrik

Staff Emeritus
Gold Member
The uncertainty relation is derived from the commutation relation for the position and momentum operators (see this post), but there is no position operator for photons. There are mathematical theorems that tell us that it's impossible to define one.

#### Tac-Tics

There is actually no guarantee that light moves at the speed of light. It's more LIKELY to do so, but it's not a rule.

If you measure the position of a photon with 100% precision, suddenly, you have no idea which direction it's moving. Think of a lightbulb. A single photon coming out of a light bulb might be sent in any random direction. Thus, you don't know its momentum.

On the other hand, try to measure the momentum. Paint the light bulb black except for one tiny hole at the top. For every photon that comes out, you can be pretty sure about what direction it's going. But if you make the hole small enough (and thus, the direction certain enough), the light ends up diffracting! It spreads out all over the place, and the result is you have no idea where it will end up when you measure it!

#### Upisoft

Well then I guess Feynman was mistaken.
What did Feynman think about that?
Anyway it is impossible to express transparency as absorption/re-emission, because there will be discrete spectrum of the possible state transitions of the electrons. And we clearly have continuous spectrum.

#### JJRittenhouse

What did Feynman think about that?
Anyway it is impossible to express transparency as absorption/re-emission, because there will be discrete spectrum of the possible state transitions of the electrons. And we clearly have continuous spectrum.
doesn't matter, my question is about the position of photons as they travel.

#### JJRittenhouse

The uncertainty relation is derived from the commutation relation for the position and momentum operators (see this post), but there is no position operator for photons. There are mathematical theorems that tell us that it's impossible to define one.

So can it be said photons aren't anywhere until they are absorbed?

#### diazona

Homework Helper
There is actually no guarantee that light moves at the speed of light. It's more LIKELY to do so, but it's not a rule.
I'm not so sure about that. Can you provide a reference?

#### Fredrik

Staff Emeritus
Gold Member
So can it be said photons aren't anywhere until they are absorbed?
That can be said about massive particles too. To be honest I don't fully understand what the result that there's no position operator for massless particles really means.

I'm not so sure about that. Can you provide a reference?
If the term "photon" is defined by QED, then they are massless by definition, and the claim that they might have mass doesn't make sense. You can however consider the quantum theory of a massive spin-1 field in Minkowski spacetime, and use it to make predictions about results of experiments. There's one such theory for each value of the mass (and of course for each choice of interactions). Experiments that test those predictions to see which values of the mass gives us the best predictions can be thought of as measurements of the mass of the photon, if the term "photon" is now defined by that class of theories, instead of specifically by QED. I think I've read somewhere that if the mass is small enough, the results are predictions are practically indistinguishable from the predictions of QED. (No, I don't know where). So measurements that tell us that the predictions of QED are "at least this accurate" also give us an upper bound on "photon" mass.

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#### zonde

Gold Member
So can it be said photons aren't anywhere until they are absorbed?
No, this can not be said.
For example, if you connect your source and detector with optical fiber then considering travel time of photon it can be said that it is in fiber before detection.
However if you consider wavefunction then it can be more tricky. As operators acts on wavefunction considerations about problems with some operator should be related to wavefunction not particles.

#### zonde

Gold Member
Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
No, photon direction is uncertain after position measurement.
Before position measurement photon trajectory can be described classically.

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#### etamorphmagus

What is the reason for lower light speed in medium? They suddenly gain mass or something?

#### Fredrik

Staff Emeritus
Gold Member
No, this can not be said.
Hm, the negation of "isn't anywhere", is "is somewhere", right? So to answer "no" to the question asked, is to answer "yes" to the question of whether the photon "is somewhere" before detection. I would interpret that as having a specific well-defined position, not as being spread out over a smaller region, like the insides of an optical fiber. That's why my answer is "yes".

Of course, it can also be interpreted the way you did, which is why "no" is also a valid answer.

#### DrChinese

Gold Member
doesn't matter, my question is about the position of photons as they travel.
The controlling rule is in fact the Uncertainty Principle. So answering your question with anything else ends up stretching the language in a fashion which leads to either contradiction or confusion. (Which is why Fredrik is correct.)

It is probably easiest to say that when a photon has a known velocity (momentum actually), it's position is essentially undefined.

#### DrChinese

Gold Member
Light gets absorbed and emitted over and over ...
Just to amplify on this: it is not absorbed and re-emitted in the classical sense. There are probabilities that activity occurs. I.e. various paths or histories. The probabilities (paths) then sum (integrate) in a way that has the overall result averaging to a value lower than c.

#### etamorphmagus

Light gets absorbed and emitted over and over (and over and over). You can think of it like a busy man walking to work from the train station. If a pan-handler asks him for money, it'll slow him down, even though when he's walking, he's always walking as quickly as he can without appearing to be in a hurry :)
Well:
Originally Posted by JJRittenhouse
Isn't the speed still the same in another medium, just interrupted by electron interaction?
AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.
What happens with visible light then? it can't have a different explanation.

Edit: Understood Dr.Chinese

#### DrChinese

Gold Member
AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material.
This is not accurate, and I probably should have commented earlier. The excitation energy of electrons does not determine whether a material is transparent or not. It is more closely related to field effects of the atomic structure. I.e. the arrangement and type of atoms/molecules. They create a virtual field and this leads to the effects of color we see.

ZapperZ has commented on this in the Physics FAQ in much better words than I could provide:

This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower than it is in vacuum. This FAQ will strictly deal with that scenario only and will not address light transport in anomolous medium, atomic vapor, metals, etc., and will only consider light within the visible range.

The process of describing light transport via the quantum mechanical description isn't trivial. The use of photons to explain such process involves the understanding of not just the properties of photons, but also the quantum mechanical properties of the material itself (something one learns in Solid State Physics). So this explanation will attempt to only provide a very general and rough idea of the process.

A common explanation that has been provided is that a photon moving through the material still moves at the speed of c, but when it encounters the atom of the material, it is absorbed by the atom via an atomic transition. After a very slight delay, a photon is then re-emitted. This explanation is incorrect and inconsistent with empirical observations. If this is what actually occurs, then the absorption spectrum will be discrete because atoms have only discrete energy states. Yet, in glass for example, we see almost the whole visible spectrum being transmitted with no discrete disruption in the measured speed. In fact, the index of refraction (which reflects the speed of light through that medium) varies continuously, rather than abruptly, with the frequency of light.

Secondly, if that assertion is true, then the index of refraction would ONLY depend on the type of atom in the material, and nothing else, since the atom is responsible for the absorption of the photon. Again, if this is true, then we see a problem when we apply this to carbon, let's say. The index of refraction of graphite and diamond are different from each other. Yet, both are made up of carbon atoms. In fact, if we look at graphite alone, the index of refraction is different along different crystal directions. Obviously, materials with identical atoms can have different index of refraction. So it points to the evidence that it may have nothing to do with an "atomic transition".

When atoms and molecules form a solid, they start to lose most of their individual identity and form a "collective behavior" with other atoms. It is as the result of this collective behavior that one obtains a metal, insulator, semiconductor, etc. Almost all of the properties of solids that we are familiar with are the results of the collective properties of the solid as a whole, not the properties of the individual atoms. The same applies to how a photon moves through a solid.

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

Moral of the story: the properties of a solid that we are familiar with have more to do with the "collective" behavior of a large number of atoms interacting with each other. In most cases, these do not reflect the properties of the individual, isolated atoms.

#### JJRittenhouse

The controlling rule is in fact the Uncertainty Principle. So answering your question with anything else ends up stretching the language in a fashion which leads to either contradiction or confusion. (Which is why Fredrik is correct.)

It is probably easiest to say that when a photon has a known velocity (momentum actually), it's position is essentially undefined.
we were getting bogged down in the mechanics of the speed of light through a medium, I was just drawing that to a close where it could be asked in a different topic.

Thanks for the help, though guys.

"What does the Uncertainty Principle say about the location of photons?"

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