Negative interference destroys photons?

[Felix]

Let's say you have two coherent laser beams.

Now you arrange them in a way that there is total negative interference.

The light would disappear. Like two soundwaves extinguishing each other.

But where does the photon go?

This is brutal oversimplification, but I do it for clarity:

There were two photons before. One for beam 1 and one for beam 2.

Now we mix the beams for negative interference. The photons disappear.

Doesn't this break the law of energy conservation?

[Proverb]

Though we hear that a light beam can be considered "wave-like," the quandary is that it is also considered "particle-like" when you observe it in a certain context.

I am not versed in the theory of quantum-physics but I think that, though you might be able to construct a beam of negative orientation to another beam, the way they interact would be within the realm of particles.

Though, to possibly construct your example, it might be possible to arrange to beam sources in such a way that the processes creating the beams would cancel each other out. However, this is not a process of the attributes of light.

I am merely postulating here on my current knowledge of quantum theory which I am sure is incomplete.

[Felix]

..., the way they interact would be within the realm of particles.

You mean that the light behaves particle-like?

How, if there is no light?

[source]

Photons are energy. Therefore, I'm thinking in the lines of energies canceling out when two light beams interfere destructively. However, I'd rather first revise some interference equations before submitting this as my final answer.

[Proverb]

[...]How, if there is no light?[...]

So you have observed this? I thought this was a hypothetical construct.

[Felix]

I talked to physics students about it and one way to create such an experiment would be to have two coherent lasers one horizontally aimed (right to left), the other one vertically aimed (top to bottom) with a semipermeable mirror at 45° at the point where the beams cross. Both beams now have to extinguish each other and they said that there is no outcoming light beam and that the energy would heat up the mirror. But they could not explain why and referred me to someone else whom I have yet to meet.

[jrs]

Let's say you have two coherent laser beams.  Now you arrange them in a way that there is total negative interference.  The light would disappear.

What you are suggesting is impossible. There will always be regions of constructive interference as well as regions of destructive interference.

...  one way to create such an experiment would be to have two coherent lasers one horizontally aimed (right to left), the other one vertically aimed (top to bottom) with a semipermeable mirror at 45° at the point where the beams cross.

Assume that the lasers were phase-locked so that no light emerged to the right of the half-silvered mirror. Then a more intense beam would emerge downward from the mirror. If we ignore losses in the air and the mirror, the total power in the out-going beams is always equal to the total power in the in-coming beams.

[Felix]

So you say thay it is impossible to actually have two lightbeams completely negatively interfering. Do you say that, if you could, the energy would disappear, but because it doesn't happen, it's a non-issue? Or do you dismiss the hypothesis altogether? And if so, why?

[Proverb]

You have to understand that, on a basic level concerning the interaction of simple waves, energy does not 'disappear' when waves cancel out. So, even if there was a way to arrange this quantum cancellation it wouldn't be a matter of lost energy.

Waves cancel when they are of equal energy and wavelenght, and opposite in phase. It's like a tied tug-of-war with two people puling in opposite direction and in the same intervals of time. The result is no motion.

From the previous posts I was unsure if you were aware of this principle.

[Felix]

You have to understand that, on a basic level concerning the interaction of simple waves, energy does not 'disappear' when waves cancel out. So, even if there was a way to arrange this quantum cancellation it wouldn't be a matter of lost energy.

From the previous posts I was unsure if you were aware of this principle.

Where does it go? The movement is cancelled but the energy of the movement is still there? Where?

I always believed that the energy (previously contained in a field) is changed into kinetic energy showing in the movement of a body. If this body doesn't move, then there is no energy there. Otherwise it would be possible to derive energy from a static body.

Waves cancel when they are of equal energy and wavelenght, and opposite in phase. It's like a tied tug-of-war with  two people puling in opposite direction and in the same intervals of time. The result is no motion.

... and no saving of energy.

[jrs]

... lasers one horizontally aimed (right to left), ...

... no light emerged to the right of the half-silvered mirror. ...

Sorry. I should have said "emerged to the LEFT".

So you say thay it is impossible to actually have two lightbeams completely negatively interfering.

Yes. Total destructive interference everywhere is impossible. See my explanation below.

Do you say that, if you could, the energy would disappear, but because it doesn't happen, it's a non-issue? Or do you dismiss the hypothesis altogether? And if so, why?

Asking what would happen, if an impossible hypothetical situation occurs, is like asking "If A is not A, would red be green?" or "If a rhinoceros spontaneously transformed itself into a watermelon, would that violate the conservation of energy?". It is a meaningless and unanswerable question.

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Although the second law of thermodynamics makes the laws of physics non-reversable at the macroscopic level, it is actually a statistical phenomenon based on certain assumptions about the initial conditions of the Universe.

At the level of elementary particles, physics is reversable. More precisely, the equations of motion are invarient under TCP: Time-reversal plus Charge-conjugation (replacing each particle by its anti-particle) plus a spatial-inversion (Parity).

Consequently, information can neither be created nor destroyed. It cannot be destroyed because that operation could not be undone uniquely by reversing time. It cannot be created, because the reversal of that would be destruction of information.

In quantum mechanics, this is manifested by the Unitarity of the time-evolution of a system under the Schrodinger equation. That is, the length of the state-vector (psi, the wave function) of a system does not change with time; and the inner product of two state-vectors both evolving according to the same equation also does not change with time.

In classical mechanics, this is manifested by the theorem that the "volume" of a region in phase space does not change as the system evolves.

Now, look at your example: Your laser beams are initially seperate and thus their inner-product (when viewed as two seperate state-vectors) is zero. So it must remain zero. Thus balancing the regions of destructive interference (which make a negative contribution to the inner-product) there must be regions of constructive interference (which make a positive contribution).

Electro-magnetism satisfies the superposition principle (just as Schrodinger's equation does). So adding the two beams together to create one state-vector does not change this result.

[source]

Where does it go? The movement is cancelled but the energy of the movement is still there? Where?

It's called "potential energy." Like with the example of gravity - there is a gravitational force that is pulling you towards the center of the Earth, and there is the force of the ground which stops you from falling. So, you have potential energy and there is even a formula to calculate it. So, if the ground miraculously disappears beneath you, your potential energy will turn into kinetic energy and you will fall in the direction of the force of gravity.

[Felix]

It's called "potential energy."

Wait a minute. If two men pull a rope on two opposing sides (and the rope isn't elastic), how does this add to the 'potential energy' of the rope? The forces compensate and nothing happens. Therefore, no energy.

Edited September 18, 2005 by Felix

[Felix]

Asking what would happen, if an impossible hypothetical situation occurs, is like asking "If A is not A, would red be green?" or "If a rhinoceros spontaneously transformed itself into a watermelon, would that violate the conservation of energy?". It is a meaningless and unanswerable question.

Yes. That's what I wanted to say.

At the level of elementary particles, ...

In quantum mechanics, ...

In classical mechanics, ...

Hmmm, guess I need to read more physics books. I only understand part of your answer.

Thanks a lot anyway. Now I know that a satisfiable answer exists.

[jrs]

In my last message (Post #11), I said that electromagnetism satisfies the superposition principle. This is just a fancy way of saying that the differential equations are linear and homogeneous. That is, you can multiply a solution by a constant and the result is still a solution. And you can add two solutions together and the result is still a solution.

Also I should have mentioned that electromagnetic waves under-go a phase shift when they are reflected by a mirror. This is vital to understanding your example.

I think that Proverb and source are mistaken. The energy density of the electromagnetic field depends only on the total magnitude of fields at that point. In the MKSA system of units, it is:

(E*D + H*B)/2

This is true whether you are talking about moving waves or a static field or some combination.

If two men pull a rope on two opposing sides (and the rope isn't elastic), how does this add to the 'potential energy' of the rope? The forces compensate and nothing happens. Therefore, no energy.

This is entirely different from the case of electromagnetic waves which we were discussing. Any real rope will stretch at least a little bit when pulled. The work done by pulling and stretching will be converted (in part) into potential energy of the rope (if it continues to resist being stretched further).

Hmmm, guess I need to read more physics books. I only understand part of your answer. Thanks a lot anyway. Now I know that a satisfiable answer exists.

You do not KNOW anything until you check it out for yourself. Do not just take my word for it. For all you KNOW, I could just be some kook who is good at spouting plausible bull-shit.

[Felix]

In my last message (Post #11), I said that electromagnetism satisfies the superposition principle. This is just a fancy way of saying that the differential equations are linear and homogeneous. That is, you can multiply a solution by a constant and the result is still a solution. And you can add two solutions together and the result is still a solution.

I knew that. But thanks for explaining.

Also I should have mentioned that electromagnetic waves under-go a phase shift when they are reflected by a mirror. This is vital to understanding your example.

This is something I didn't know. Thanks again.

I don't BELIEVE anything. I said I need to read more books on that before I can be sure.

But before proof of the opposite, I assume that people are basically good. You could have screwed me here, but I will check it. I will learn the reasons behind your statement and evaluate them myself. Hey, it's MY problem. I want to understand it.

Never put another one's head above your own.