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Four questions: (To start off, I know very little about physics it isn't even funny (I probably use a ton of wrong terms here and leave out vital information, if so I will try to edit it in as you point it out!), Anyways, I have been always curious about this scenario though so I finally figured I'd ask some people who actually know what they are talking about)

First question: Theoretically speaking, if I have a vacuum that is a closed system, it's made of walls that are 100% nonreactive and have no electromagnetic force, strong force, weak force, gravitation force, or anything, but they can still restrain things placed inside the box (without any interaction on the particles, but instead just by the laws of this system)

If I place 1 particle in the box will it stay exactly where I placed it, or will it somehow move to the center of the box thus distancing itself as far as possible away from each wall? (I've drawn a 2D demonstration) enter image description here

Now, if I place a second particle in, will they both stay where I placed them, will they divide the box in half in some way (I just gave 1 example, there are many) and then both move to the center of those halves, will they space themselves as far apart as possible (pushing themselves against the nearest corners of the box), or is there some ring of energy around particles that I don't know about that has a statistical radius and they would just distance themselves as much as the "reach" of this ring so that the rings aren't touching? enter image description here

Or will something else happen?


Second question: I'm assuming different things will happen if the particles are different things, for example if Particle A was a proton and Particle B was an electron they would just pull together? Or the electron would begin orbiting the proton (Or would they even both start orbiting each other?) (If either of these are the case what determines if the orbiting is clockwise or counter-clock-wise (Or whatever the 3D equivalent of these would be, does spin determine?)? What are some particles that would react different ways, for example 2 photons, a proton and a proton, a proton and an electron, etc. Or would it not matter?


Third and Fourth questions: What would happen in the same scenario except the walls are reactive, they are made of steel, or carbon fiber, or something strong enough to support a vacuum?

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According to the laws of quantum mechanics (you might have heard of the uncertainty principle) if you place a particle in a given position, e.g. near the corner, you are doing so by measuring its position with great precission. This means that you loose all precission about its velocity, therefore in a given instant after you placed the particle it could actually be anywhere within the box, not necessarily the center. There will be a certain probability density that it will be found in any given place of the box. If you add a second particle, then things depend of the type of particles you are dealing with (recall all particles are either fermions or bosons). If both particles are distinct (no matter if they are bosons or fermions) then they can "occupy the same point in space" without problems, the same happens if they are bosons (whether of the same type or not), but if you placed two identical fermions in the box there will be some kind of effective repulsion between them (coming from Pauli's exclusion principle), so in some sense there are some "rings" preventing the particles to get too close to each other (i.e. of having the same quantum state), this is the force that makes everyday matter seem solid.

Second question: If you place an electron and a proton, chances are they will eventually bind into a hydrogen atom, radiating a photon in the process. The rotation sense only has a meaning if you define it with respect to some axis in quantum mechanics, say the $z$ axis, in such case the angular momentum of the system is conserved, so the final angular momentum depends of the initial angular momentum of the particles before they bind (if they bind).

Pairs of particle with the same charge will not bind in the conditions of the experiment. Photons will not bind under any known circumstances, so far as I know.

Third and Fourth questions: In a real life experiment with reactive walls things will complicate, in principle there is a chance the particles can escape of the box by tunneling effect (this also depends very strongly of the energy the particles have), but most importantly it is almost certain that they will interact with the walls and eventually they will not be the only particles in the box, there will be "parts of the box" inside.

Chances are it will be very difficult to even be sure that you are observing the same particle in the conditions of the experiment, unless more constrained conditions are inforced on the particles (as a light-trap for cooling)

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Thankyou! Wow, you answered every single question ahaha +1 I do have some questions though... What's the "tunneling effect" not sure that I've ever heard of that. Also, what if the walls were made of ultra strong electromagnetic fields so that more particles could not enter the closed system, or am I delusional about what an electromagnetic field is and they are actually made of particles or require a medium? Lastly, what is "Light-trap" that you mentioned at the end? Thanks again so much! God bless! –  Albert Renshaw Oct 30 '13 at 16:07
    
Oh and is it possible for a particle to have a velocity of 0, other than energy being at absolute zero kelvin, if so can I still measure position exactly? And would it repel another particle if they were both identical fermions? –  Albert Renshaw Oct 30 '13 at 16:08
    
You are welcome. The tunneling effect is a quantum phenomenon where a particle is able to go trough barriers even if the particle does not have enough energy to do that. In your first experiment the walls were perfect so even tunneling will not work, but when they are made of an actual substance tunneling may take place. Now, using electromagnetic fields, specially strong ones, will actually not work very differently from the actual wall, again tunel effect may take place. Also, under certain circumstances electromagnetic fields may interact with the particles inside and create more particles, –  Rogelio Molina Oct 30 '13 at 22:44
    
I am afraid that even if one is able to cool down everything at zero kelvin (in principle this is not possible), thus having a particle with zero speed, Heisenberg's uncertainty principle implies that you will loose all knowledge of where the particle is. That means you cannot determine its position with any precission. (And if you were to determine its position then you would loose information about its velocity, so you wouldn't know that it is zero any longer) –  Rogelio Molina Oct 30 '13 at 22:48
    
Awesome! Thankyou very much :) –  Albert Renshaw Oct 30 '13 at 22:49

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