Two naive, completely unrelated physics questions

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So, here they are:

1) Let's say you have an atom, and you shoot a photon at it. The photon hits an electron, but only has half the necessary energy to bump the electron up to the next energy level (or knock it out of the atom, as in the photoelectric effect). The question is this: if another photon, also with half the necessary energy, hits that same electron a bit afterward, will the electron go up to the next energy level? If so, where is the "bookkeeping" of the energy done, if at all; i.e., where is the information that the electron already has half the energy stored? If not, is this a violation of the conservation of energy?

2) This is the standard objection to time travel with relativity. If you run at close to the speed of light, from the perspective of someone watching you, your clock will run slower than his. As a result, when you stop running, less time will have passed for you than for the outside world, so you will have traveled into the future. However, looking at your own perspective, the world is running by you at close to the speed of light, and the clocks in the outside world appear to run slower. So if you stop running, more time will have passed for you than the outside world, and you will have traveled to the past (but not to before you've left). I've heard the usual explanation for this, which is that the acceleration that takes place when you stop or turn around causes the symmetry to break. But couldn't you just attribute the acceleration to a gravitational field (which would slow time down further)? How, precisely, does the breakage of symmetry (or whatever other explanation you happen to use) work?

Last edited by physicsnut42 on 29 Apr 2013, 4:22 pm, edited 1 time in total.

with number one, I can be a bit of service. It depends on how much time has passed since the initial proton has hit the electron, If soon enough, it could be bumped up to the next energy level. If left to long, the energy will dissipate into surrounding space, and thus not enough will remain for the second proton to be enough to bump the electron up. The energy is never spent or gone, it just moves into surrounding space.

I assume here that when you said "proton", you meant "photon" (I've made the same mistake several times myself!)

Anyway, if the energy "dissipates", what exactly does this mean? When the heat energy from a hot oven "dissipates", the hot, fast-moving molecules from the oven knock into the slower molecules of the surrounding air, speeding them up. The heat thus flows into the surrounding air. But how can energy "dissipate" on such a small scale? Where does the energy go, and could one in principle extract at least some of it? Wait a minute--maybe the photon just bounces right off the electron, instead of getting absorbed! Gee, I hadn't thought of that...

This thread reminds me of the time when Sheldon Cooper accidentally broke some plates while working at the Cheesecake Factory and the resultant pieces on the floor suddenly triggered a solution to a physics problem he'd been losing sleep over. Then again, I could be wrong.

Why would small scale make it impossible? It just would make it difficult to measure. In theory, one could redirect that energy for use elsewhere, but most likely it would dissipate as either heat or, perhaps, light energy. Think of the dissipation as a kind of osmosis, the energy spreads out until it is even within the room. Even if that energy was harnessed, the process in doing so might spend more energy than it captures. An interesting idea, though.

What I mean by this is that if we're talking about individual atoms, there are no other particles to be knocked around. Light energy might make sense, but my point is that there's nowhere for the energy to go. A perfect vacuum (assuming one could exist, which by Heisenberg's uncertainty principle, it cannot) would automatically have a net energy of zero. Perhaps the extra energy gets transmuted into virtual particles, but then they would no longer be virtual. That the photon simply bounces off the electron if it doesn't have enough energy might make the most sense, as I stated earlier. Why I didn't see this solution before I made this thread, I do not know.

First, acceleration. On a treadmill, you can not expect to have acceleration if you plan to stay on the treadmill for very long. So, the example you give is not actually possible. More specifically, the treadmill is exerting an acceleration in one direction and you are exerting an equal acceleration in the other direction thus cancelling each other out. If we remove the treadmill and have you simply accelerating you will move farther away. The symmetry is still held because the time it takes for information to travel from you to the observer still has to be accounted for. As long as the information is slower than the speed of light, we are not actually able to observe the time difference because of the symmetry. There will only be a measurable time difference if you can break the speed of light.

Let's replace acceleration with a gravitational field. Again, it requires an impossible situation. You and the observer have to experience drastically different gravitational pulls. In reality, if we are in the same room we are experiencing the same gravity. The only method we currently have to create different gravities is large distances. Specifically, large enough distances where the speed of light becomes a factor again. Again, when you account again for the time it takes information to travel from me to you, the discrepancy in the time observed will be negated.

Theoretically, yes we can travel through different times by use of acceleration or gravity manipulation but it's almost meaningless because the time difference only exists as long as we have no connection to the origin. You personally would experience no time shift, you would only experience a time shift in comparison to your origin. As long as you maintain contact with the origin to make the comparison you negate all the work put into the time travel. Or you can break the speed of light. We haven't figured out how to do that yet.

Lets be realistic here. In reality, no atom simply stands alone. In your fantasy land of one single atom, that might be an issue, but that would never happen nor could it even be simulated.

The relativistic effects apply to inertial reference frames, that is reference frames that move with respect to each other at constant velocity. In the treadmill example, the reference frame of the person on the treadmill is not actually moving at all with respect to an observer not on the treadmill because the person on the treadmill stays at the same spot and is therefore actually at rest. So there is no time dilation or anything else. The velocity of the person running on the treadmill is canceled by the velocity of the conveyer belt of the treadmill in the opposite direction.

For the first question, I think it may be simply not possible for a electron to absorb only half the energy "to bump" to another level. As it work by quanta, it's all or nothing. Which may explain why the light is only absorbed or emitted at certain frequency when it work with the excitation of electrons.

I guess you could, after all in general relativity gravitational fields got some effect on time.

Electron can absorb only multiples of it ground state energy. If a photon is too feeble to kick an electron up one or more quantum levels it will bounce of and be deflected. This is a special case of the Compton Effect.. It is the only way that energy can be conserved.

ruveyn

Thanks, that makes sense.

And to all those who pointed out the flaw in the treadmill example: I agree wholeheartedly. I actually fixed that in the original post. I was too stupid to realize that mistake earlier (maybe because I was reading a book about the Flash's time-travelling treadmill, or something).

The chances for a photon to be deflected by an atom that does not have the relevant energy interval between orbitals are very small. The much more likely result is to go through unaffected, which means that the atom is transparent to such photons. Now what makes usual materials not transparent, and more precisely dark (absorbing photons), is they have complicated molecular structures and interactions between molecules, which offer a sort of continuous multitude of energy levels, unlike the kind of short list of orbitals that occur for simple isolated atoms. Moreover photons do not need to be absorbed by some "first layer" but can go to some depth until they are absorbed.
On the other hand a very similar scenario to the question here is the cause of fluorescence: a high energy photon bumps an electron up 2 levels, then it comes down in 2 steps while emitting a photon in each step. The reverse process is usually less likely for thermodynamical reasons (roughly, a system of 2 photons has more entropy than only one photon, though it may depend on the exact circumstances: maybe well-tuned lasers can make it... if we can find 2 lasers whose sum of energies per photon coincides with one interval somewhere).