# Interference defies thermodynamical laws, and creates energy!

Quite the contrary - gravity between the particles is pulling them together in a direction perpendicular to their propagation, so that's the direction in which they'd have to slow down. You're right that the average velocity in directions other than the beam propagation direction is zero:

$$\langle p \rangle=0$$

But kinetic energy doesn't go as velocity. It goes as velocity squared, and the uncertainty principle guarantees that this will be nonzero in all directions:

$$\langle p^2 \rangle>0$$

Total energy, or the expectation value of the Hamiltonian, is the sum of this kinetic energy and the gravitational potential energy:

$$\langle H \rangle=\frac{1}{m}\langle p^2 \rangle+\langle V_g \rangle$$

To see whether energy is conserved, you have to compare $$\langle H \rangle$$ between your initial state and your final state. The final state has a larger potential term, but the velocity spread is narrower, so the kinetic energy term is smaller.

OK, I see what you mean, the kinetic energy on average is always non-zero, but the average velocity is zero. There is no other explanation unless you are willing to assign the velocity and momentum a non-zero average value. You can say "the particles have no average velocity but they travel towards the fringes on average". Since this is your explanation then I would ask you to break the mathematics down to something which evaluates areas that are smaller than the uncertainty so you can see each part of the distribution changing by itself. But this is not possible in QM.

Although your explanation in terms of the hamiltonian does suffice as an explanation. Your opinion seems to be that the transverse directional motion of the particles is averaged to zero, but still each particle moves, and that the combined movement creates the fringing that is observed. And then it is natural to assume that the "slowing" of the particles is the energy loss that makes up for the energy gain in average gravitational potential. I would say that this is an eloborate explanation that is worth testing, because most physicists do not have the interpretation that would allow for "movement of the particles" prior to measurement.

The point is that in general, objects are at lower gravitational potentials when their mass is grouped together within a tighter area, because it takes more energy to separate all of their atoms.

Yes, but if we look at the whole interference pattern then we see that after the fringes are lumped together, they would attract one another. This would then cause them to come together and mix again and again until equilibrium was reached, which is the state of the non-interference pattern.

As I mentioned earlier, you started with a coherent source, which means that the "excess" order is accounted for - there is no change in entropy merely by forming fringing, since the waves were in-phase to begin with.

This point is not relevant, but your wrong anyway. The initial state is a single particle state on one path. In order to get interference you must split the state which expands the basis to multiple paths. This is a decrease in order. Then you recombine the state to a single path, which means the increase of disorder is now erased. Somehow along with this we get an increase in the order in the position distribution, and apparently its because of the wave nature of the source. The detection probability will dictate this, and it is evaluated with the split state of increased disorder.

Captain Bork,

On the other hand, I don't think two separate particle beams can interfere to produce fringing anyhow- to get coherence and interference you need the two beams to actually consist of single particles being allowed to simultaneously take two paths, so that you have actual wave interference rather than beam-beam scattering.

Two separate particle beams cannot produce interference, or at least no one has ever shown this. With massive particles one requires a single source for interference.

Fednis48 sais it this way,

For what it's worth, you could get interference between two particle beams if they were somehow "mode-locked" so that the particles they produced were indistinguishable. I have no idea how you'd do that with anything other than a laser, but it's possible in principle

Actually, it might be proven one day that you cannot do this in principle with massive particles, only photons.

This point is not relevant, but your wrong anyway. The initial state is a single particle state on one path. In order to get interference you must split the state which expands the basis to multiple paths. This is a decrease in order. Then you recombine the state to a single path, which means the increase of disorder is now erased. Somehow along with this we get an increase in the order in the position distribution, and apparently its because of the wave nature of the source. The detection probability will dictate this, and it is evaluated with the split state of increased disorder.

I'm not able to get there from here. I'm stuck at the beginning, in which the source had to be coherent in the first place, as I understand your assumptions. I feel like we are on a different page, but it may be that I've misunderstood this. I haven't even gotten to the actual physics. What's hindering me is that fringing is a measure of coherence, so to assume you have any fringing is to assume that the source is coherent in the first place, since you've assume it produces fringing at all -- that is, the regular stripes of a fringe pattern, not just the accumulation of random phases. As I understood you, you are sending your source straight through a double slit. How else do you get interference bands if the source is not coherent to begin with? That's where I'm not plugged in here.

If I've derailed my thinking, maybe you or any one else here can help get me back on track. Thanks.

Just forget about order and coherence. Of course the source must be coherent. And the recombination is what producs the fringing. The problem I have is that the fringing represents a change in the spatial distribution, which apparently takes place without any energy loss.

OK, I see what you mean, the kinetic energy on average is always non-zero, but the average velocity is zero. There is no other explanation unless you are willing to assign the velocity and momentum a non-zero average value. You can say "the particles have no average velocity but they travel towards the fringes on average". Since this is your explanation then I would ask you to break the mathematics down to something which evaluates areas that are smaller than the uncertainty so you can see each part of the distribution changing by itself. But this is not possible in QM.

Although your explanation in terms of the hamiltonian does suffice as an explanation. Your opinion seems to be that the transverse directional motion of the particles is averaged to zero, but still each particle moves, and that the combined movement creates the fringing that is observed. And then it is natural to assume that the "slowing" of the particles is the energy loss that makes up for the energy gain in average gravitational potential. I would say that this is an eloborate explanation that is worth testing, because most physicists do not have the interpretation that would allow for "movement of the particles" prior to measurement.
I was thinking of addressing the changing spatial distribution by using the electrodynamical uncertainty relation $$\Delta Q\Delta \Phi \geq \frac{h}{4\pi}$$

Just forget about order and coherence. Of course the source must be coherent. And the recombination is what producs the fringing. The problem I have is that the fringing represents a change in the spatial distribution, which apparently takes place without any energy loss.

The only change in spatial distribution was the deformations of the wavefront as is passed through the slits. There was loss, not gain, in that step. The rest of what happened was the projection of the bent wavefronts onto the screen, which is also lossy. I thought you were rejecting the order of the fringe pattern, which is why I reminded you that it stems from the coherence of the source. Here, the fact that the phases are shifted as you pan across the screen, is just a consequence of all of the different path lengths resulting from projecting the curved wavefronts onto a flat surface.

Aqueous ID,

...the wavefront as is passed through the slits...the projection of the bent wavefronts onto the screen...it stems from the coherence of the source...projecting the curved wavefronts...

Wow, I wonder if you're biased to the wave interpretation of quantum mechanics?

Try thinking about this experiment in the context of particles.

...electrodynamical uncertainty relation $$\Delta Q\Delta \Phi \geq \frac{h}{4\pi}$$

What is the "electrodynamical uncertainty relation". I've never heard of this before. What is Q and what is phi? Is this from QED?, because I'm not too familiar with it. I wikipediaed the phrase EUR and came up with nothing. Google gave me a paper on arxiv by Ghaboussi that has the uncertainties as position and guage potential for Q and phi. This strikes me as odd, because there is already a position momentum relation, so there can't be a relevant position-guage potential relation also. Not to mention the fact that the Schrodinger eqn. is guage invariant (so you can assign any guage you want as long as it is scalar).

The paper explains the quantum hall effect. How does this new uncertainty relation apply to interference.