# B Accuracy in speed of photon - uncertainty?

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1. Jul 16, 2016

### chester20080

Hi there!
I wanted to ask you, we know that light, photons have a certain fixed speed generally. Wouldn't this imply, considering Heisenberg's uncertainty principle, that the uncertainty for the speed (momentum) of the photons, should be infinite? But we know for sure, for example, that photons exist somewhere (in my fist,inside a building, all over earth,universe etc haha!..)
Isn't there a contradiction? How can we know exactly (in general) the speed of the particles and at the same time have an idea of where they are located?

2. Jul 16, 2016

### Staff: Mentor

The speed of the photon is c to a very high degree of accuracy.

Position is not an observable for a photon so the Heisenberg uncertainty relations does not apply.

Why you would believe its infinite has me beat.

Thanks
Bill

Last edited: Jul 17, 2016
3. Jul 17, 2016

### chester20080

The uncertainty says that the more we know about momentum (speed) the less we know about position, right? So if we know exactly the speed of the photon then according to the above we should know nothing about its position thus infinite uncertainty about the position. Isn't this right? Can't we apply this principle here ? Why not? What is wrong about that?
And a side question is : can we know for certain the exact speed or even the position if we don't care for the other characteristic? Or always should there be an amount of uncertainty, even if we study only the one property of the two?

Last edited: Jul 17, 2016
4. Jul 17, 2016

### weirdoguy

You've got the answer for that question:

5. Jul 17, 2016

### chester20080

But why can't they be localized? Of course not exactly. For instance, is it wrong to localize them inside my apartment? I don't technically localize them but I have an idea of their position. I don't need to measure them to localize them. Since I can see a thing in my apartment I know for sure (with infinite certainty) that for that moment, there are photons in there!
Since you say that the principle doesn't apply as it is for photons, what applies for them in a similar way?
We don't need to apply the equations. We need to consider the general idea behind the theory, and behind the theory of uncertainty, there are probabilitites and their result, measurement. What are they? They are information. And information is what WE know it is. What our mind regards as reality. Anthropic principle. And the info I collect is that I know for sure the speed and at the same time I have an idea, only a mere idea of the location, without getting into observations and such things. But according to the theory behind uncertainty, not the equations, I shouldn't have an idea. There should be no information about it, whatsoever.

After all, the uncertainty principle is in no way dependent on measurement techniques or observations, it is an inherent property of nature. And its general idea, in some form is valid always for particles,nevertheless.

6. Jul 17, 2016

### Staff: Mentor

Actually, you don't know that - and a good thing too, because it's not what's happening, at least not the way that you're thinking about photons.

You can see things in your apartment because there is weak electromagnetic radiation in your apartment, and this radiation is interacting with the light-sensitive cells in the retina of your eyes. When you do a quantum mechanical treatment of electromagnetic radiation (this is the subject of quantum electrodynamics, called QED for short) you'll find that it delivers its energy in discrete lumps at a single point in space, and when that happens we say "a photon was detected there". Thus, there is no meaningful way of assigning any position to a photon except as the point where electromagnetic radiation interacts with matter in some way. Now, we can say that the photon that materializes at the light-sensitive cell in your eye has been localized to the general vicinity of that cell.... But there is a corresponding uncertainty as to its momentum so the uncertainty principle is still respected. The fact that disturbances in the electromagnetic field propagate at the speed of light is irrelevant to the analysis.

If you can get hold of Feynman's book "QED: The strange theory of light and matter", it provides a decent layman-friendly view of how QED describes the behavior of photons and especially how we calculate the probability that a photon will be found at a given point in space if we put something there for it to interact with.

7. Jul 17, 2016

### chester20080

But since there is indeed EM radiation, photons must be there right? Radiation is consisted of photons.
I don't assign any position to a photon. I only say that at least one photon, which speed I do know, must be in there, therefore I have an idea about its location. I don't need to measure it or detect it, no. It's impossible not to be there. In the extreme case, we can consider virtual photons.

Why the momentum is unknown to some extent? We know its speed exactly (considering space as medium).

8. Jul 17, 2016

### phinds

No, radiation consists of quantum objects which when considered as radiation have the characteristics of waves. If the wave/quantum object interacts with something material THEN a photon (which is just a particle-like characteristic of the quantum object) comes into existence.

9. Jul 17, 2016

### weirdoguy

10. Jul 17, 2016

### Staff: Mentor

Nonetheless, it is not there unless and until you measure or detect it.

When you hear that a photon is a particle of light, it's very tempting to form a mental picture in which photons are to light as water molecules are to water, in which light is made of photons the same way that water is made of water molecules. It doesn't help any that in ordinary English usage, the word "particle" means a small object that has a definite position - a grain of sand can be here, or there, or somewhere else, but it's always somewhere. It's an unfortunate historical accident that the same word is used to describe things like photons, which aren't small objects that have to be somewhere - they are quantized excitations of the electromagnetic field.

I'll repeat my recommendation for Feynman's book - it's a good starting point. There are also the links in the first two posts of this thread; they'll give you a feel for just how much you aren't getting from the popularizations.

11. Jul 17, 2016

### chester20080

I see.. I will read it soon. So if we do make the measurement, we will localize it. The uncertainty about its momentum how will be? Since we know its speed exactly then we'll know momentum and position. The speed can't change while we are making the observation. What is wrong?

12. Jul 17, 2016

### Staff: Mentor

We do not know its momentum exactly. All photons move at $c$ (to the extent that is meaningful to speak of them moving at all), but that doesn't tell us anything about their momentum, which is given by $p=E/c$ where $E$ is its energy.

13. Jul 17, 2016

### DrChinese

In addition to the excellent comments above: a photon has as an observable its frequency. Frequency is proportional to its energy E and therefore its momentum, and is inversely proportional to its wavelength. So for a photon, the uncertainty in momentum is more or less analogous to uncertainty in frequency - rather than uncertainty in velocity as you might otherwise expect.

High frequency photons have high energy and a short wavelength, and high momentum.

Just saw that Nugatory mentioned this while I was posting...

14. Jul 17, 2016

### chester20080

You're of course right, I falsely correlated uncertainty to speed not to frequency and energy, for momentum... Thank you all for your answers!

15. Jul 17, 2016

### Staff: Mentor

That's a deep question requiring an advanced answer that a beginner would not understand:
http://www.mat.univie.ac.at/~neum/physfaq/topics/position.html

For now simply accept the position operator cant be defined for a photon hence the usual wave-function interpretation does not follow, nor do the usual Heisenberg uncertainty relations.

But it can be accommodated if we don't interpret the wave-function in the usual way:
https://arxiv.org/ftp/quant-ph/papers/0604/0604169.pdf

Thanks
Bill