# The speed of light and Heisenburg

1. Oct 20, 2005

### CJames

I have a question to ask. I am pursuing a career in theoretical physics, most likely LQG and/or cosmology, but thus far my mathematical knowledge spans only newtonian physics. My question is in relation to the Heisenburgh uncertainty principle. Now I know that there are several factors other than position and velocity, but I of course have only read the popular texts and so I only understand the uncertainty principle in this context. That is, the more precise a position you want, the more energy you must invest and thus the more the velocity has been changed. And so on. I guess my two questions are this:

1. How is it possible for us to know that photons always travel at c? Why doesn't this violate the uncertainty principle?

2. How many properties of quanta are effected by the uncertainty principle and why? For example, spin does not change, correct? Niether should charge. (I am unfamilair with quantum numbers so try to be specific. How many properties do quanta have?)

I guess that is more than two questions but they have bee bothering me.

2. Oct 20, 2005

### Staff: Mentor

To what does the Heisenberg Uncertainty Principle apply? It doesn't apply to everthing.

http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html#c1

We have not observed any photons that do not travel at the speed of light.

The proper question is "How many properties or attributes are quantized. Charge is quantized. Particles are quantized, e.g. as far as we know, all electrons have the same rest mass, all protons have the same rest mass, and so on for various types of particles.

Photons are quantized, but there seems to be a continuous spectrum, although photons generally originate with a specific energy related to atomic or nuclear structure.

Last edited: Oct 20, 2005
3. Oct 20, 2005

### Pengwuino

Why would it? The scales of the heisenberg uncertainty principle relates to things at a rather small scale while the value of c is tremendous.

4. Oct 20, 2005

### Gokul43201

Staff Emeritus
That makes no sense to me.

There certainly is an uncertainty relation for light (photons). Only, with a photon, you change its momentum by changing its frequency (or wavelength). For a photon, p = E/c = hf/c, so the uncertainty in measuring the position of photons is related to the uncertainty in knowing their frequency.

Last edited: Oct 20, 2005
5. Oct 20, 2005

### Pengwuino

haha yah i know... i was hopen people would realize what the implications were.

I figured that his idea was that if you weren't certain about a photon's position, how could you determine its velocity using a dx/dt kinda experiment. Well if you're not absolutely sure what the change in the positions are (which results from you not being certain where the photon actually is in the final and initial position), you can't be sure what the speed of the photon is. What I was saying is that since the speed of light is sooooooo fast, miniscule deviations based on the uncertainty principle won't have any effect until you get to such a large # of digits.

Guess I was kinda stretching it as far as what I thought he was thinking.

6. Oct 20, 2005

### NateTG

We don't.
James Maxwell Clark worked out a theory that related electricity and magnetism to light which suggests that the speed of light is a 'fundemental'. I'm not a specialist, but I believe that the classical notions of electro-magnetism break down at small scales so it would not surprise me if 'the speed of light' were also different at those scales.
Initially, the prediction that the speed of light was a constant seemed quite incredulus to people, and extensive experimentation did take place to verify that, if it changed, it only changed very little.

7. Oct 20, 2005

### ComputerGeek

all the experiments that have slowed light down or sped light up do not show that we have observed light traveling at different speeds?

8. Oct 20, 2005

### ZapperZ

Staff Emeritus
Be very careful here. You need to know that they measured the group velocity (or the speed of the pulse shape) in these experiments, and you need to know what a "group velocity" is. Even in the "fast light" experiments, no part of the pulse travelled faster than c (re: the NEC experiment).

Zz.

9. Oct 25, 2005

### CJames

Sorry for taking so long to respond. I used to visit this site a lot but now I don't have that kind of free time.

Anyway, is this what you are saying: That it is momentum and position I should be thinking about, not velocity and position. That does seem to make more sense as it is more general. Here is the touchy-feely explanation I am getting. Let me know if I am on track.

For a photon of large wavelength you can more precisely measure its momentum because your error in relation to the size of the wavelength will be small, but your measurement of its position will be less precise because its position could be anywhere within one wavelength. Conversely, for a photon of high frequency your measurement of wavelength will be less precise because your error will be larger in comparison to the size of the wave, but your measurement of position will be more precise because you know it is somewhere within that small wavelength.

Is this accurate or am I confusing myself?

10. Oct 25, 2005

### CJames

Does this mean that the uncertainty principle only applies to values expressable as units of (m^2*kg)/(s), that is, distance squared times mass over time? Or does it mean that it literally only applies to delta (x*p) and delta (E*t)? I realize that is a stupid question. Oh well.

EDIT: Thanks for the link by the way, it is very usefull.