# Just how large is a photon?

1. Dec 9, 2009

### Neo_Anderson

A high-energy photon needs a smaller aperture to get down to its limit of resolution. Conversely, a radio wave needs an enormous aperture if it is to go through it (an RF waveguide, eg, is like 3"x7").
So what exactly is the size of the photon? Since they're created in atoms, I'd think they're about the size of an atom, maybe smaller. Interesting, since an atom can generate an RF wave that can't even fit in something smaller than a waveguide, whereas another atom can generate a photon that has no problem entering a 600 nm aperture...
A ridiculous question, I know, but valid nonetheless.

2. Dec 9, 2009

### hamster143

How large is a wave on the pond?

3. Dec 9, 2009

### ansgar

Photons are pointparticles in QM, they have no spatial extension, just as electrons, quarks and force carrier bosons.

4. Dec 9, 2009

5. Dec 9, 2009

mass = 0...

6. Dec 9, 2009

Energy != 0.

7. Dec 9, 2009

8. Dec 9, 2009

### dmtr

How comes? Schwarzschild radius is a real radius in the real space.

9. Dec 9, 2009

### ansgar

Can you explain to me what the Schwarzschild radius is? The earth has a radius differnt than it's density distribution radius (which is what we commonly call "size")

10. Dec 9, 2009

### dmtr

For an electron it is a lot smaller compared to the Plank's length. Still, it is better, compared to the point!

11. Dec 9, 2009

### dmtr

The original question was "what exactly is the size of the photon", it can be reformulated - "in how small volume can you 'squeeze' the photon", well, to do that you only need to throw it in the black hole. The resulting volume wouldn't be zero.

Last edited: Dec 9, 2009
12. Dec 9, 2009

### ansgar

I know what it is, but you didn't seem to know it so I asked you to explain it.

One can also use the "Classical electron radius" (http://en.wikipedia.org/wiki/Classical_electron_radius) if one just wants a number, but the figure of interest is the radius for the matter distribution, not "Schwarzschild radius" etc.. and the radius asked for should be understood as the matter radius...

13. Dec 9, 2009

### dmtr

AFAIK Schwarzschild radius sets a fundamental limit of how much mass/energy (information) you can pack in space. And it do set the lower limit on the size of the photon and electron.

14. Dec 9, 2009

### ansgar

Can you say what the smallest size of a photon then, which has zero mass...

15. Dec 9, 2009

### Dmitry67

In QM, it is a point particle.
All speculations about the plank length, Schwarzschild radius etc require the Quantum Gravity theory which is not ready yet.

16. Dec 9, 2009

### ansgar

that was supposed to be my next move! :D

17. Dec 9, 2009

### dmtr

$$R_{s} = \frac{2Gh\nu}{c^{4}}$$

And just for the fun of it:
$$A = 4\pi{R_{s}}^{2}$$,

$$S = \frac{c^{3}A}{4 \hbar G} bits$$

18. Dec 9, 2009

### ansgar

derivation?...

19. Dec 9, 2009

### dmtr

Well, you are right of course. But I see nothing wrong in throwing an electron or a photon into a black hole and considering 'how small can it get there'.

20. Dec 9, 2009

### dmtr

$$E = mc^{2} = h\nu$$

$$R_{s} = \frac{2Gm}{c^{2}}$$

$$R_{s} = \frac{2Gh\nu}{c^{4}}$$

21. Dec 9, 2009

### hamster143

That is incorrect.

If someone asks "what is the size of dmtr", we don't start looking for the answer by squeezing dmtr with a hydraulic press.

The natural size of dmtr is the size of the smallest hole through which we can shoot him without significantly distorting the form of his wave packet. It is probably between 1 and 2.5 meters - many orders of magnitude greater than Schwartzschild radius of dmtr.

Similarly, the natural size of a photon with wavelength $\lambda$ is approximately $\lambda$.

Last edited: Dec 9, 2009
22. Dec 9, 2009

### dmtr

My protest was to the notion of 'point particles' and the associated infinities. As to the size, I think it is very natural to measure sizes in bits. For example, imagine a photon with a wavelength comparable with the radius of the universe. All you can tell about that photon, is whether it is present, or not. Nothing else. That would be exactly one bit. So very naturally the size of that photon would be one bit. ;)

Last edited: Dec 9, 2009
23. Dec 9, 2009

### Staff: Mentor

24. Dec 9, 2009

### ansgar

Does not apply to a photon...

25. Dec 9, 2009

### hamster143

Well, let's just agree that the protest was worse than the notion.

The other problem I have with Schwarzschild radius is that it's just a severely overhyped number. There's nothing magical about Schwarzschild radius. If you're falling into a black hole, you don't "hit the surface", so to speak, at $\frac{2Gm}{c^{2}}$. You may not even notice that anything has happened. The black hole itself is pointlike (or, rather, has the diameter on the order of Planck length).