Interference defies thermodynamical laws, and creates energy!

[al onestone]

In a simple spatial interference effect we start out with a source of particles (lets say very heavy molecules) that are emitted in a spontaneous manner with a position distribution that is determined by the state description in position representation. This also indicates the momentum/energy of the system.

The system is then "split up" into multiple possible paths (lest say with a double slit aperture) which will still have a state description that is a single particle pure state accept it has an expanded path basis. (note: pure states apparently have zero entropy)

The system is then prepared to be recombined which would have the multiple paths converge to a single spatial outcome.

At the point of recombination/overlap the position of the system is measured (with a screen) and when it is measured there is the presence of fringes in the detection probability. There is interference.

My claim is that the system has went from a state of spontaneous emission to an ordered state of fringes. If we had measured the system after emission then we would measure a position distribution that is determined by the uncertainties, a virtual "blob", a gaussian. But the interference measurement has an ordered position distribution, and an increase in order is a decrease in entropy.

Although, many would argue that the state is always pure, therefore no change in entropy. And if there was a decrease in entropy there would be an increase in energy, so where is the increase in energy?

The increase in energy is like this, consider the interference effect and its preparation to be the only things in the universe. By going from the state of emission, where the position distribution is a blob, to a state of interference, where the position distribution is ordered in fringes, we have an increased state of total gravitational potential of the system. We all know that a state of "lumped up" mass is a state of greater total gravitational potential energy as long as its being compared to a state of more evenly distributed mass evaluated over the same volume (in our case the system is spread over the total uncertainty in position which does not change). Therefore the state of interference fringes is a state of increased gravitational potential energy. Ergo, interference creates energy! (even though it is an extremely small amount of energy)

Consider the case of charged particle interference effects, the energy created is not gravitational potential energy but it is electromagnetic potential energy.

 

[CptBork]

My claim is that the system has went from a state of spontaneous emission to an ordered state of fringes. If we had measured the system after emission then we would measure a position distribution that is determined by the uncertainties, a virtual "blob", a gaussian. But the interference measurement has an ordered position distribution, and an increase in order is a decrease in entropy.

That doesn't work, because a particle state whose position is well-localized will have a wide spread of possible momenta, thus the entropy would actually be very high. The widespread uncertainty in momentum is the whole reason narrow slits produce such wide interference patterns in the first place.

 

[al onestone]

Captain Bork,

That doesn't work, because a particle state whose position is well-localized will have a wide spread of possible momenta, thus the entropy would actually be very high. The widespread uncertainty in momentum is the whole reason narrow slits produce such wide interference patterns in the first place.

OK, then imagine using a beamsplitter instead of a double slit. Combine the two outputs at a small angle where the beams overlap on a screen. They still have the exact same uncertainty in position (beam cross section) and within that uncertainty you will find fringes. So there is an increased order of the system in its position distribution.

In fact forget the whole question related to entropy. Just think about the difference in position distribution (fringes versus a blob). Doesn't this difference account for a difference in the energy of the system when we evaluate the gravitational potential of the accumulating particles? When the particles "bunch up" in fringes they have a different state of total gravitational potential.

 

[al onestone]

Anyone interested in further reading on this thought experiment, I invite you to read the webpage I have created for it as linked here:

http://violationprotocol.webs.com/redistribution-protocol

 

[Fednis48]

In a simple spatial interference effect we start out with a source of particles (lets say very heavy molecules) that are emitted in a spontaneous manner with a position distribution that is determined by the state description in position representation. This also indicates the momentum/energy of the system.

The system is then "split up" into multiple possible paths (lest say with a double slit aperture) which will still have a state description that is a single particle pure state accept it has an expanded path basis. (note: pure states apparently have zero entropy)

The system is then prepared to be recombined which would have the multiple paths converge to a single spatial outcome.

At the point of recombination/overlap the position of the system is measured (with a screen) and when it is measured there is the presence of fringes in the detection probability. There is interference.

My claim is that the system has went from a state of spontaneous emission to an ordered state of fringes. If we had measured the system after emission then we would measure a position distribution that is determined by the uncertainties, a virtual "blob", a gaussian. But the interference measurement has an ordered position distribution, and an increase in order is a decrease in entropy.

Although, many would argue that the state is always pure, therefore no change in entropy. And if there was a decrease in entropy there would be an increase in energy, so where is the increase in energy?

The increase in energy is like this, consider the interference effect and its preparation to be the only things in the universe. By going from the state of emission, where the position distribution is a blob, to a state of interference, where the position distribution is ordered in fringes, we have an increased state of total gravitational potential of the system. We all know that a state of "lumped up" mass is a state of greater total gravitational potential energy as long as its being compared to a state of more evenly distributed mass evaluated over the same volume (in our case the system is spread over the total uncertainty in position which does not change). Therefore the state of interference fringes is a state of increased gravitational potential energy. Ergo, interference creates energy! (even though it is an extremely small amount of energy)

Consider the case of charged particle interference effects, the energy created is not gravitational potential energy but it is electromagnetic potential energy.

You're ignoring the speed of the particles. As two bodies move away from each other, they slow down to compensate for the increased gravitational potential. Even in a classical situation, you can have two objects moving away from each other over time. But you certainly wouldn't say that energy is being created because the gravitational potential is higher after they've been moving for a while as compared to immediately after their release. From a gravitational perspective, the quantum interference in your experiment is just a more elaborate way to get particles to move away from each other over time.

 

[CptBork]

OK, then imagine using a beamsplitter instead of a double slit. Combine the two outputs at a small angle where the beams overlap on a screen. They still have the exact same uncertainty in position (beam cross section) and within that uncertainty you will find fringes. So there is an increased order of the system in its position distribution.

Still doesn't work. In order to focus the two beams onto the screen, you end up giving them a horizontal momentum kick which has a high level of uncertainty to it.

In fact forget the whole question related to entropy. Just think about the difference in position distribution (fringes versus a blob). Doesn't this difference account for a difference in the energy of the system when we evaluate the gravitational potential of the accumulating particles? When the particles "bunch up" in fringes they have a different state of total gravitational potential.

It's senseless to talk about the gravity of particles in a superposition of quantum states because we don't even have a working theory of quantum gravity. Classically you've got it backwards in any case- a tightly lumped collection of mass will be at a lower gravitational potential than a system in which the same mass is more spread out, because the first case requires more mechanical energy to separate all the particles.

 

[al onestone]

Even in a classical situation, you can have two objects moving away from each other over time. But you certainly wouldn't say that energy is being created because the gravitational potential is higher after they've been moving for a while as compared to immediately after their release.

You are clearly assuming that the volume or area within which the particles exist is getting larger, which is not the case. In my thought experiment the total volume/area within which the particles are positioned will stay the same (if we dont use a double slit but rather a beamsplitter then the volume/area is the cross section of the beams which can be focussed on a screen during overlap to produce interference). It is the distribution within this uncertainty area which I consider. The distribution changes and the total volume/area remains constant. Because the particles become more lumped up, they are in a state of greater total gravitational potential energy.

 

[al onestone]

Still doesn't work. In order to focus the two beams onto the screen, you end up giving them a horizontal momentum kick which has a high level of uncertainty to it...

It's senseless to talk about the gravity of particles in a superposition of quantum states because we don't even have a working theory of quantum gravity. Classically you've got it backwards in any case- a tightly lumped collection of mass will be at a lower gravitational potential than a system in which the same mass is more spread out, because the first case requires more mechanical energy to separate all the particles.

I disagree that the focussing of the beam on the scree will cause momentum uncertainty. You dont have to actually focus it with a lens, you only need to have the overlap of the two beams on the screen. As long as the cross section of each beam stays the same, then that is the uncertainty, the cross section.

And correct me if I'm wrong but the lowest possible state of grav. potential energy for a system of a given mass spread over a given volume is definitely the state of most even distribution? Think equilibrium states, the even distribution is in equilibrium but the uneven distribution is going to create work via movement of masses. Although I'm no GR or classical gravitation expert.

 

[Aqueous Id]

My claim is that the system has went from a state of spontaneous emission to an ordered state of fringes.

When you get results that are non consistent with conventional wisdom, it's best to retrace your steps. Here you seem to have gotten from spontaneous emission to fringing by assuming that your source is coherent. Look there for the order you couldn't account for.

 

[Fednis48]

You are clearly assuming that the volume or area within which the particles exist is getting larger, which is not the case. In my thought experiment the total volume/area within which the particles are positioned will stay the same (if we dont use a double slit but rather a beamsplitter then the volume/area is the cross section of the beams which can be focussed on a screen during overlap to produce interference). It is the distribution within this uncertainty area which I consider. The distribution changes and the total volume/area remains constant. Because the particles become more lumped up, they are in a state of greater total gravitational potential energy.

Huh? I don't need to assume that the volume containing the particles is getting larger. The particles start in some configuration, and by the end of their flight they're in a different configuration with higher potential energy. To make up the difference, they slow down. That's all there is to it.

 

[CptBork]

I disagree that the focussing of the beam on the scree will cause momentum uncertainty. You dont have to actually focus it with a lens, you only need to have the overlap of the two beams on the screen. As long as the cross section of each beam stays the same, then that is the uncertainty, the cross section.

There's no escaping Heisenberg's uncertainty principle. The act of squeezing particles into a narrow beam confines their position and automatically results in a wide spread of momenta. Besides, when you allow the beams to hit the screen, if you're allowing for widely spaced fringes then that constitutes a state of high position uncertainty. And when a particle hits the screen and the wavefunction collapses into a small area, once again the uncertainty principle requires that a great deal of momentum uncertainty be induced in the process, i.e. you see a small dot, but the intensity can vary.

And correct me if I'm wrong but the lowest possible state of grav. potential energy for a system of a given mass spread over a given volume is definitely the state of most even distribution? Think equilibrium states, the even distribution is in equilibrium but the uneven distribution is going to create work via movement of masses. Although I'm no GR or classical gravitation expert.

The lowest potential energy state would be a black hole singularity.

 

[al onestone]

The particles start in some configuration, and by the end of their flight they're in a different configuration with higher potential energy. To make up the difference, they slow down.

If you're right about that, then that's all there is to it. But I don't think that interference causes a "slowing of the particles". And I'm assuming here that you're saying that they slow in the direction of propagation, because the average velocity in the other two directions is nil, so there could be no slowing in those directions. In effect, you're stating that there is something like a redshift that doesn't change the energy of vibration but the kinetic energy, a kinetic redshift. I think that is wrong.

 

[al onestone]

There's no escaping Heisenberg's uncertainty principle. The act of squeezing particles into a narrow beam confines their position and automatically results in a wide spread of momenta. Besides, when you allow the beams to hit the screen, if you're allowing for widely spaced fringes then that constitutes a state of high position uncertainty. And when a particle hits the screen and the wavefunction collapses into a small area, once again the uncertainty principle requires that a great deal of momentum uncertainty be induced in the process, i.e. you see a small dot, but the intensity can vary.

OK great, uncertainty is preserved. That's not what i'm thinking of here. I assume from the get go that the uncertainties will be as you've explained. No problem.

The lowest potential energy state would be a black hole singularity

OK great, but neither the emission state or the interference state is that of a black whole. Between the two, the interference state is the one of greater grav. pot. energy. It is lumped up. Where does this energy come from? Fednis48 sais there is a redshift in the velocity of the particle. I don't think so.

 

[Fednis48]

If you're right about that, then that's all there is to it. But I don't think that interference causes a "slowing of the particles". And I'm assuming here that you're saying that they slow in the direction of propagation, because the average velocity in the other two directions is nil, so there could be no slowing in those directions. In effect, you're stating that there is something like a redshift that doesn't change the energy of vibration but the kinetic energy, a kinetic redshift. I think that is wrong.

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.

 

[Layman]

OK, then imagine using a beamsplitter instead of a double slit. Combine the two outputs at a small angle where the beams overlap on a screen. They still have the exact same uncertainty in position (beam cross section) and within that uncertainty you will find fringes. So there is an increased order of the system in its position distribution.

In fact forget the whole question related to entropy. Just think about the difference in position distribution (fringes versus a blob). Doesn't this difference account for a difference in the energy of the system when we evaluate the gravitational potential of the accumulating particles? When the particles "bunch up" in fringes they have a different state of total gravitational potential.

I think you could make it even simpler. Say you tried to mathematically describe energy being reflected in a box, there is no way currently to describe this situation without getting an answer that is infinity. Brian Greene mentioned it in his latest book, and ascribed that the physics to be able to do this is wrong because you end up with an infinite answer. But the mathematics of the physics involved says that the quantum jitters would produce infinite energy in this situation. If it doesn't then it would mean that something is wrong with our current understanding of physics, either way something would be wrong here.

 

[CptBork]

OK great, uncertainty is preserved. That's not what i'm thinking of here. I assume from the get go that the uncertainties will be as you've explained. No problem.

Momentum uncertainty means there are many possible momentum eigenstates in which the particle could be found, which means higher entropy.

OK great, but neither the emission state or the interference state is that of a black whole. Between the two, the interference state is the one of greater grav. pot. energy. It is lumped up. Where does this energy come from? Fednis48 sais there is a redshift in the velocity of the particle. I don't think so.

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.

 

[Aqueous Id]

Where does this energy come from?

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.

 

[CptBork]

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.

Sorry but what does having a coherent source have to do with the entropy? I don't see how shifting the phases of the two beams would alter the number of microstates available to the system. 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.

 

[Aqueous Id]

Sorry but what does having a coherent source have to do with the entropy? I don't see how shifting the phases of the two beams would alter the number of microstates available to the system. 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.

As I understood his premise, the mere appearance of fringing represents an increase of order. But if the source is already coherent, fringing is the natural consequence. Therefore there was no change in the amount of order from the outset. That is, the phases were all ordered upon forming the coherent source in the first place.

 

[Fednis48]

Sorry but what does having a coherent source have to do with the entropy? I don't see how shifting the phases of the two beams would alter the number of microstates available to the system. 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.

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.