# B Photon in a box?

1. Jun 28, 2016

### jonatron5

Ok im no physicist, by any means but a thoughy struck me the otherday.

If i where to build a box with a volume of 1 cubic plank length , and the inside of which was a perfect mirror, and i contained within it a photon or multiple photons, how would this affect the speed of light?

I beleive i asked a similar question severeal years ago, and the trick to it was that photons being massless are theoretically infintessimally small. But would changing the volume of the box to a cubic plank length have any affect? Or is it the same situation?

I appologise if this question seems primitive, im imagining a photon to be a particle like a pingpong ball, and I cant quite wrap my head around a particle not being able to be physically constrained

My understanding is that a plank length is the smallest length of matter that can be understood with our models.

2. Jun 28, 2016

### Staff: Mentor

An initial note: thoughts that strike you in this way are unlikely to be fruitful. If you want to learn about physics, you have to spend some time learning about physics--not pop physics, but actual physics. Your questions indicate that what you know of physics is probably from pop science sources, not actual textbooks or papers. Questions that arise in this way are extremely likely to be ill-formed; they can't be answered because they are based on faulty assumptions. Yours fall into this category; see below.

Made of what? Do you understand how small a Planck length is? It is about 20 orders of magnitude smaller than the size of an atomic nucleus.

Why would it affect the speed of light at all? (Assuming "speed" even had a meaning on this scale; see below.)

Why do you think this? Bear in mind that "photons" are not little point particles moving at the speed of light. The actual physics is a good deal more complicated than that.

That's not a good model to use when trying to imagine a photon. See above.

There are speculations somewhat along these lines, but that's all they are: speculations.

Why do you think photons can't be physically constrained?

3. Jun 29, 2016

### Staff: Mentor

4. Jun 29, 2016

### newjerseyrunner

Your idea that a photon can be made to bounce around a box is problematic (ignore the Plank length for now.) Even if you could make it somehow be reflected perfectly by some unknown physics, the fact is that you can't place a photon in a box. Photons' positions are represented as a wave function of possible positions. So there is a distinct possibility that if you place a photon in a box, it'll teleport it's way out of it as if the walls weren't even there.

The plank length has nothing to do with matter, it's a limit to quantum mechanics. In fact, you can't have a box that's a plank length wide and have a photon or any quantum mechanic entity inside of it. In order for a photo to move through it, you'd have to be able to say it's on one side of the box or another, which is nonsensical at that scale.

5. Jun 29, 2016

### pixel

Unless you are an Einstein thinking about chasing a light beam at the speed of light.

6. Jun 29, 2016

### Staff: Mentor

Einstein would not have introduced his thoughts with the words "I'm no physicist." His thoughts were fruitful precisely because he was a physicist--he had invested years in developing a thorough understanding of the best current physical theories of his time, and so he could see exactly where their limits were and push them.

7. Jun 29, 2016

### jonatron5

Neutronium? If we constructed a box out of neutrons I know its a very hypothetical situation.

Sadly i wish i could study real physics. Cant really afford to take a nonmajor class right now.

I also have only had basic highschool physics very newtonian, so i have a verrrrrrrrrrry hard time picturing quantum mechanics, or particle physics

I read about the double slit experiment and entanglement and my brain just breaks

8. Jun 29, 2016

### jonatron5

Maby build it out of quarks

9. Jun 29, 2016

### pixel

Do physicists not have a sense of humor? Also, Einstein was 16 at the time he had this thought, so not a physicist then.

10. Jun 29, 2016

### Staff: Mentor

Once again, do you realize how small a Planck length is? Do you understand that it is 20 orders of magnitude smaller than the size of an atomic nucleus--which is also the approximate size of an individual neutron in neutronium, and at least within an order of magnitude or so of the effective size of the quarks inside nucleons?

You don't have to take a class in it in school to study it. There are plenty of good online resources.

11. Jun 29, 2016

### Staff: Mentor

He was a physicist in the sense I was using the term: he had already invested time and effort in understanding the best current physical theories of his time. In particular, he already understood Maxwell's Equations well enough to see that they did not have a solution describing a motionless standing wave in space; they only had solutions describing waves moving at $c$. So he was a physicist in the sense that mattered--his thoughts were fruitful because he had built the necessary background knowledge for them to be fruitful.

Bear in mind that this thread was not started by you or me. We are trying to help the OP understand why his thoughts are highly unlikely to be fruitful at this stage of his knowledge. The comparison with Einstein is helpful only if we highlight the critical differences between the OP's case and Einstein's case.

12. Jun 29, 2016

### Staff: Mentor

As I said in a previous post, there are plenty of good online resources to help you increase your knowledge. But as I also pointed out, without that background knowledge, random thoughts like the ones you are having are highly unlikely to be fruitful. Your time would be better spent using the available resources to learn about physics, than trying to get something useful out of thoughts about physics that just strike you.

The questions you are asking in this thread are about a topic that is quite advanced; if you have trouble with basic quantum mechanics, you are going to have a lot more trouble even trying to follow any explanation I might try to give you about the things you are asking about in this thread. There's nothing wrong with that in itself; I started out at the same place you are now. It took me many years to get to my current level of knowledge. You have to be patient and build a foundation with the very basics first (if you can understand Newtonian physics, that's a good start), and then work up from there.

13. Jun 30, 2016

### pervect

Staff Emeritus
Unless I've made a math error, you'd have a black hole.

For a paricle in a box scenario, the wavefunction is zero at the edges of the box, assuming an ideal box. This makes the wavelength of the photon 2 planck units.

If you take $E = h c / \lambda$ and m = E/c^2, you get a mass of 68 micrograms for the (relativisitc) mass of photon with a wavelength that size. I'm not sure about spherical boxes, I think that the formula may be for a cubical box.

I haven't added in any of the pressure terms (in GR, pressure causes gravity as well as mass), but that would just make the case for a black hole even stronger. So I've only included the gravitational effects of the energy (aka relativistic mass) in the box, and left out the effects of the pressure.

Taking $2 M/c^2$ for the Schwarzschild radius, I get $1\,10^{-34}$ meters for the Schwarzschild raidus of that mass. But a plank length is only $1.616 \, 10^{-35}$ meters.

So the Schwarzscild radius is about $2 \, \pi$ times the plank length, unless I've made an error somewhere. Therefore your "box" must collapse to a black hole. This assumes that I haven't made any errors, and that the laws of physics don't change from what we know at more reasonable energy scales.

Last edited: Jun 30, 2016
14. Jun 30, 2016

### newjerseyrunner

I'd disappointed you didn't name it. Kugelblitz. Germans have some fun words.

15. Jun 30, 2016

### jonatron5

Could i bother you to possibly suggest a book or reading material for my current level of understanding?

16. Jun 30, 2016

### Mister T

What's the highest college-level math class that you've successfully completed?

In my opinion physicists have by no means understood things down to the scale of the Planck length. One of the most famous particles of matter, for example, is the electron. Currently the Standard Model, a highly successful model, treats it as a point particle, meaning it has a size of zero. But experimentally that has been confirmed down to about 10-18 meters, meaning that if it does have a nonzero size it's smaller than that.

If you want to build your knowledge of physics it's best to understand the experimental physics that underpins our knowledge. In other words, when you think of some bit of physics, also think about how it we know that bit to be valid. Validity is conditional, there are limits to the validity of all scientific knowledge because we never know what we'll find when we look beyond those limits. Experience has taught us that we will often be surprised by what's found.

17. Jun 30, 2016

### Staff: Mentor

Yes, you would (as I'll confirm below). So my earlier comments about not being able to make such a box out of anything were not really relevant.

To confirm the math, rather than crunch numbers, I'm going to derive a formula analytically for the Schwarzschild radius corresponding to the energy of a single photon confined in a box such that its wavelength is $2 L_p$, where $L_p$ is the Planck length.

First, we need the formula for a Planck length, which is:

$$L_p = \sqrt{\frac{G h}{2 \pi c^3}}$$

(where I am using $h$ instead of $\hbar$ because we will be using a formula for $E$ that uses $h$ instead of $\hbar$).

We have that the energy of the photon is $E = h c / 2 L_p$, and the Schwarzschild radius corresponding to this energy is $R = 2 G E / c^4$, so we have

$$R = \frac{2 G h c}{2 L_p c^4} = \frac{G h}{c^3 L_p} = \frac{2 \pi L_p^2}{L_p} = 2 \pi L_p$$

Just as a check, what mass is the energy above equivalent to? We have

$$m = \frac{E}{c^2} = \frac{h}{2 c L_p} = \frac{h}{2 c} \sqrt{\frac{2 \pi c^3}{G h}} = \sqrt{\frac{\pi h c}{2 G}} = \pi M_p$$

where $M_p$ is the Planck mass. This is what we expect for a black hole with Schwarzschild radius as above.

18. Jun 30, 2016

### newjerseyrunner

Don't know much about reading materials, but Youtube: five minute physics, fermilabs, pbs spacetime, scishow, and "in a nutshell".