Interference puzzle - Where does the energy go?

[sophiecentaur]

The point is that their CAN be an even number of photons overlapping such that EVERY part of them is anti

Using photons to discuss a wave problem is likely to get you nowhere. Inequality of multiple waves will always be way more than Quantum levels.

 

[Charles Link]

Ah, so that's how you upload a picture. Thanks to everyone who jumped to my aid. Now I can have my avatar back. And here's the picture.

View attachment 223327

@Derek P The cartoon is good, but the interference that occurs when two coherent beams are incident on a beamsplitter, as represented by the picture, is really quite fascinating.

 

[Derek P]

How does any of that bring true satisfaction. The point is that their CAN be an even number of photons overlapping such that EVERY part of them is anti and so they would seeeem to cancel out... No beam splitting no phase shifting... Sooo? What's the answer to that!?

The question was not about photons, let alone mulitiple photon systems. I explicitly stated it was about EM waves.

I'm not averse to generalising the question, but you'll just have to spell out the scenario and use baby-talk maths. Perhaps starting with exactly how you prepare the two-photon state and how you arrange for total destructive interference. A picture would be fine.

 

[Four-D-Topology]

A laser beam is split into two identical beams which impinge on a half-silvered surface from opposite sides. The reflected wave is out of phase with the transmitted wave. There is destructive interference on both outputs. Where does the energy go?

See my avatar - I can't upload my own picture, not sure if it's possible without a URL. Yes it was triggered by reading about the HOM effect, but as far as I can see it should be true for classical waves - even radio or sound waves.

Normally when someone asks this question of an interference experiment I am the first to say "wherever there's destructive interference somewhere there's constructive interference somewhere else" and waffle on about normalisation and conservation. But I can't see how it would work in this case. If there were random phase jitter it would "all average out" too, but this doesn't occur with a split laser beam.

And I am assuming that the surface is symmetrical with inversion at both reflections. That's why I specified "half-silvered" which in principle could be a thin, self-supporting, film. Or an array of fence posts if you want to use sound. I'd even settle for non-inversion all round and get twice the energy out as I put in, but that probably has a flaw somewhere too.

I dare say the answer is obvious - when it's pointed out. So if you want to me - please do. I will consider it a favour.

I have also puzzled about this many times. As you say above, "wherever there's destructive interference somewhere there's constructive interference somewhere else", but I've never understood how the energy is 'diverted' into those constructive areas from the destructive ones.
I mean, a light ray (and the energy it contains) travels along a straight line so how is the energy from the destructive areas shoved aside (forwards, backwards, left, right, up or down) to an adjacent constructive area??
If these were solid particles instead of photons (or waves) I could see them 'bouncing' off to the sides, but clearly that is not happening, so what is 'effecting' the transfer of energy away from its straight line path??

 

[Charles Link]

For the dielectric beamsplitter (with one face AR(anti-reflection coated), it is the $\pi$ phase change on the external reflection that makes this interference possible, so that two beams incident on the single interface becomes an asymmetric problem. The classical wave equations are then sufficient to determine the outcome, using the Fresnel coefficients.

 

[Four-D-Topology]

For the dielectric beamsplitter (with one face AR(anti-reflection coated), it is the $\pi$ phase change on the external reflection that makes this interference possible, so that two beams incident on the single interface becomes an asymmetric problem. The classical wave equations are then sufficient to determine the outcome, using the Fresnel coefficients.

Sorry to say that this explanation is 'greek' to me.

 

[Charles Link]

Sorry to say that this explanation is 'greek' to me.

See https://www.physicsforums.com/insights/fabry-perot-michelson-interferometry-fundamental-approach/ It turns out, (as I found out later), the formalism in this Insights article for the two beams incident on a single interface was actually previously formulated by Schwinger in matrix form. I was unaware of his results, which I think are in the Born and Wolf Optics text, when I authored this article.

 

[Four-D-Topology]

See https://www.physicsforums.com/insights/fabry-perot-michelson-interferometry-fundamental-approach/ It turns out, (as I found out later), the formalism in this Insights article for the two beams incident on a single interface was actually previously formulated by Schwinger in matrix form. I was unaware of his results, which I think are in the Born and Wolf Optics text, when I authored this article.

I read through the link you provided, however, it is over my head and does not give me a common sense understanding of how the energy is 'shifted' from one location to another in the interference pattern.
I fear that you will have to try to talk 'down' to me.

 

[Charles Link]

I read through the link you provided, however, it is over my head and does not give me a common sense understanding of how the energy is 'shifted' from one location to another in the interference pattern.
I fear that you will have to try to talk 'down' to me.

It is a similar type of result that occurs in a two-slit interference pattern. The energy is conserved, and the equations for the electric fields follow linear principles, because Maxwell's equations are linear. However, because the energy is proportional to the second power of the electric field, the properties of the system involving the energy do not need to obey linear principles such as superposition. The result is a redistribution of the energy from that which would occur with simple superposition of the energy (intensity) patterns.

 

[Four-D-Topology]

It is a similar type of result that occurs in a two-slit interference pattern. The energy is conserved, and the equations for the electric fields follow linear principles, because Maxwell's equations are linear. However, because the energy is proportional to the second power of the electric field, the properties of the system involving the energy do not need to obey linear principles such as superposition. The result is a redistribution of the energy from that which would occur with simple superposition of the energy (intensity) patterns.

Yes, but, how is the 'redistribution' accomplished??
Without the overlapping of the different waves the energy of each would occupy a specific place at a specific time. But, with the overlap the energy of each no longer occupies that space at that time and is instead at a 'nearby' location with no indication of any 'path' that it took to arrive there nor the amount of time it took 'traveling' there.
Certainly, if the energy is physically being moved from the 'destructive' location to an adjacent 'constructive' one it takes time to travel the added distance and would arrive 'later' than the other energy which went into making the rest of the 'constructive' area. Yet I have never heard of any reference to any 'distortion' in the shape of the constructive area to account for it.
My imagination wants to believe it is transmitted through some of those 'curled up' dimensions I've heard we are supposed to have.

 

[jtbell]

Yes, but, how is the 'redistribution' accomplished??
Without the overlapping of the different waves the energy of each would occupy a specific place at a specific time. But, with the overlap the energy of each no longer occupies that space at that time and is instead at a 'nearby' location with no indication of any 'path' that it took to arrive there nor the amount of time it took 'traveling' there.

Imagine that you are performing a single-slit diffraction experiment. The energy carried by the light arrives on your "viewing screen" according to the amplitudes of the electric and magnetic fields in the light wave, producing a single-slit diffraction intensity pattern.

At some point in time, t₀, you open a second slit near the original slit. Electromagnetic waves spread out from the second slit at speed c, and "add to" the waves from the first slit (the technical term is "superposition"). After a period of time equal to L/c, where L is the distance from the slits to the viewing screen, the new two-slit pattern appears on the screen.

The energy that arrives on the screen before time t₀ + L/c is distributed according to the single-slit pattern. The energy that arrives on the screen after time t₀ + L/c is distributed according to the two-slit pattern. No "chunk" of energy "moves" from one place on the screen to another. Each "chunk" moves from the slit(s) to the screen according to the pattern established by the number of slits that are open when the "chunk" is emitted.

 

[Four-D-Topology]

Imagine that you are performing a single-slit diffraction experiment. The energy carried by the light arrives on your "viewing screen" according to the amplitudes of the electric and magnetic fields in the light wave, producing a single-slit diffraction intensity pattern.

At some point in time, t₀, you open a second slit near the original slit. Electromagnetic waves spread out from the second slit at speed c, and "add to" the waves from the first slit (the technical term is "superposition"). After a period of time equal to L/c, where L is the distance from the slits to the viewing screen, the new two-slit pattern appears on the screen.

The energy that arrives on the screen before time t₀ + L/c is distributed according to the single-slit pattern. The energy that arrives on the screen after time t₀ + L/c is distributed according to the two-slit pattern. No "chunk" of energy "moves" from one place on the screen to another. Each "chunk" moves from the slit(s) to the screen according to the pattern established by the number of slits that are open when the "chunk" is emitted.

Yes, but when I trace a line from the single slit to a location that corresponds to where destructive interference would be displayed on the double slit image, I have to wonder how the energy which was traveling on that straight line actually ended up in hitting the image in a neighboring constructive interference location.

To look at it from another perspective, what if you stuck a 'pin' at a location where it was determined that there was complete destructive interference occurring. Would this 'pin' block any energy from passing on to other locations further away from the slits?? We had already determined that there was no energy present at that location so there should have been nothing to block.
I've never heard of such an experiment being tried, have you?

 

[jtbell]

I have to wonder how the energy which was traveling on that straight line actually ended up in hitting the image in a neighboring constructive interference location.

The energy that was traveling from the single slit to the screen when you opened the second slit, continues to travel according to the single-slit pattern, and arrives on the screen according to the single-slit pattern. Only the energy that left the slits after the second slit opened, arrives according to the two-slit pattern. Or maybe I've misunderstood your confusion?

 

[Four-D-Topology]

The energy that was traveling from the single slit to the screen when you opened the second slit, continues to travel according to the single-slit pattern, and arrives on the screen according to the single-slit pattern. Only the energy that left the slits after the second slit opened, arrives according to the two-slit pattern. Or maybe I've misunderstood your confusion?

Sorry, I wasn't clear enough in my description when I referred to tracing a line from 'the' single slit I should have said from 'a' single slit in the double slit example.
The energy that follows that line passes through regions in the interference pattern of both constructive and destructive interference with lines of energy from the other slit. However, when it is passing through a position of destructive interference we cannot detect it, but it is seen to be present in the adjoining position of constructive interference.
Since the position of constructive interference in not on the line being traced from the slit how did its energy get to that position from the position where it was in destructive interference??
It seems as if the actual path of energy flow during interference traces a 'wiggling' line from one constructive interference position to the next avoiding the positions of destructive interference. Is this a plausible explanation/description of what is taking place??

Thank you for sticking with me in this inquiry.

 

[sophiecentaur]

I mean, a light ray (and the energy it contains) travels along a straight line so how is the energy from the destructive areas shoved aside (forwards, backwards, left, right, up or down) to an adjacent constructive area??

does not give me a common sense understanding of how the energy is 'shifted' from one location to another in the interference pattern.

Yes, but, how is the 'redistribution' accomplished??

These three quotes all show that you are looking for some sort of Force or almost tangible effect which redirects energy. But Interference only requires Geometry to explain it. If two waves are coherent (same frequency and with very long wave trains) then they will produce a resultant wave. The amplitude and phase of the resultant will depend on the amplitudes and phases of the two waves. By this stage in the thread, I feel confident that you will have looked at the classic images of two slit interference. (?) The relative phases of the two waves in the two slit experiment will depend on the difference in the lengths of the two paths at any point on the 'screen'. The path difference is a function of the geometry and sometimes the waves add in phase and sometimes out of phase (and all phases in between). There is nothing 'pushing' energy from one place to another; the interference just results in energy turning up at different levels in different places. None of the energy that emerges from the two slits is lost and no extra energy comes from anywhere. It all 'has to go somewhere' as it cannot just disappear.
People try to invent arrangements in which two beams manage to cancel each other out in all directions but there is no geometrical arrangement that will allow it if two sources are not EXACTLY in the same place.
Several people have tried to give you a variety of slants on this argument but I think you are sticking too hard to your personal view of the nature of waves. You should perhaps take a step backwards and revisit the basics of waves first. I think there is actually no explanation that uses your particular model of waves.

My imagination wants to believe it is transmitted through some of those 'curled up' dimensions I've heard we are supposed to have.

Do not trust your imagination here. Extra dimensions are not needed. What is needed is for you to take on board the basics of accepted wave theory and not to look for some magic trap door to give you an answer. I guess that you do not want to get into the Maths of this but you may need to because Maths describes these things so much better than waving hands and simple pictures.

 

[Four-D-Topology]

sophiecentaur[/B]]results in energy turning up at different levels in different places

sophiecentaur[/B]]It all 'has to go somewhere'

It is statements like these that make me think of energy 'moving' to end up in places they otherwise would not have occupied.

sophiecentaur[/B]]I think there is actually no explanation that uses your particular model of waves.

This is actually the crux of my problem, the fact that the models I have been presented with in every explanation I have ever seen illustrate a circumstance that is not consistent with the mathematics result.
I am trying to get someone to come up with a different 'waving hands and simple pictures' explanation that adequately shows how the energy 'goes somewhere' to 'turn up at different places'.
I have long since accepted the models and formulas that show it does what it does. But those explanations and models end up looking like a magic trick where you show one hand holding a ball and the other empty and say 'ah, but when I bring my hands together, lo the ball is now in the other hand'. I want someone to admit the ball was passed into the other hand and didn't just 'appear' there without a process of transfer.
More than that, I also want a description of how the ball was transferred to the other hand without my being able to see it move there!
Perhaps I am asking for a level of understanding that doesn't exist yet.

 

[Charles Link]

It is statements like these that make me think of energy 'moving' to end up in places they otherwise would not have occupied.
This is actually the crux of my problem, the fact that the models I have been presented with in every explanation I have ever seen illustrate a circumstance that is not consistent with the mathematics result.
I am trying to get someone to come up with a different 'waving hands and simple pictures' explanation that adequately shows how the energy 'goes somewhere' to 'turn up at different places'.
I have long since accepted the models and formulas that show it does what it does. But those explanations and models end up looking like a magic trick where you show one hand holding a ball and the other empty and say 'ah, but when I bring my hands together, lo the ball is now in the other hand'. I want someone to admit the ball was passed into the other hand and didn't just 'appear' there without a process of transfer.
More than that, I also want a description of how the ball was transferred to the other hand without my being able to see it move there!
Perhaps I am asking for a level of understanding that doesn't exist yet.

The case of the dielectric beamsplitter with two beams incident on it is a little like magic. You can block one beam, and the energy gets split equally, and equal energy goes to the two receivers. When you have both beams on at once, you can suddenly have all of the emerging energy going to a single receiver. It is all explained completely by the mathematics though.

 

[Nugatory]

I am trying to get someone to come up with a different 'waving hands and simple pictures' explanation that adequately shows how the energy 'goes somewhere' to 'turn up at different places'.

Don't start with the energy flow. Start with the electrical and magnetic fields because it's easy to handwave (just by considering the phase shift along different paths) how the amplitude of their oscillations will be different in different places.

 

[sophiecentaur]

This is actually the crux of my problem, the fact that the models I have been presented with in every explanation I have ever seen illustrate a circumstance that is not consistent with the mathematics result.

With respect, I feel you may have been misinterpreting the results. The Maths of interference and diffraction works perfectly for X Ray crystallography, Radio Antenna Array Design, Interferometers for looking into Space or measuring minute deflections in machinery.

 

[Four-D-Topology]

With respect, I feel you may have been misinterpreting the results. The Maths of interference and diffraction works perfectly for X Ray crystallography, Radio Antenna Array Design, Interferometers for looking into Space or measuring minute deflections in machinery.

It has become clear to me that my ability to express my question in a way to get the type of answer I'm looking for is inadequate.

I will have to delay my pursuit of this question until I can find a better way to present my question.

Sorry for having wasted everyone's time with this. Thank you for showing as much patience as you have.

 

[CWatters]

I think I understand what you are asking but it's a mistake to think of balls or packets of energy. If you "slow down" the light source so you have individual photons traveling through the slits then surprisingly you still get interference patterns. It's as if individual photons somehow turn into waves, spread out and go through both slits at once, are defracted before interfering with themselves to produce both light and dark fringes.

This MIT video might be of interest. It shows that when using interferometers to set up destructive interference energy isn't destroyed its reflected back to the source...

 

[sophiecentaur]

t the type of answer I'm looking for

This could be a problem for you. You may well be looking for a type of answer that just doesn't apply to Physics. I have a feeling that you have not learned many of the basic ideas that Physics is built on so it is hardly surprising that, when you jump into the middle of the subject, you have not the tools to advance further. There is nothing demeaning about reading very basic Physics and it can. in fact be very satisfying to get a grasp of the nuts and bolts of the subject. You will not find any 'seriously good' Physicists who skipped past the ground work on their way to conquering frontiers of Science.

 

[sophiecentaur]

This MIT video might be of interest. It shows that when using interferometers to set up destructive interference energy isn't destroyed its reflected back to the source...

The fact that one source can affect another source in this way is not intuitive but there are many examples of waves in transmission lines that behave like waves in free space. The effect of interference on the source of the wave power can easily be ignored (at your peril!). A radio transmitter, feeding into a transmission line can interact with another transmitter (it's common to use multiple transmitter amplifiers to produce high power transmissions) in such a way that neither transmitter manages to feed any power into the antenna and all the power is dissipated in the transmitters themselves. This is a situation which needs to be avoided, of course.

 

[Cthugha]

I have also puzzled about this many times. As you say above, "wherever there's destructive interference somewhere there's constructive interference somewhere else", but I've never understood how the energy is 'diverted' into those constructive areas from the destructive ones.
I mean, a light ray (and the energy it contains) travels along a straight line so how is the energy from the destructive areas shoved aside (forwards, backwards, left, right, up or down) to an adjacent constructive area??
If these were solid particles instead of photons (or waves) I could see them 'bouncing' off to the sides, but clearly that is not happening, so what is 'effecting' the transfer of energy away from its straight line path??

It seems to me that the problem here is simply that your basic assumption is wrong. Light (or rather the energy stored inside the light field) simply does not travel along a straight line as a fundamental law. This is the exception rather than the rule, although it is a very common thing to happen.

Huygens' principle might be the kind of visual explanation that helps you. https://en.wikipedia.org/wiki/Huygens–Fresnel_principle
If you throw a stone into a pond, the water wave will not move along a line, but the wavefront will form an expanding circle. In order to have the wavefront travel along a straight line, you will also need to throw something that resembles a line into the water. On a classical level, light behaves somewhat similar. Huygens' principle (or rather the Huygens-Fresnel principle) describes this in a rather empirical manner. If you place some symmetric light emitter somewhere, it will also not emit lines of light, but will equally emit into the full solid angle. If this emitter is point-like and you have a look at the emitted wave, you will find that it somehow resembles the wave seen then throwing a stone into a pond. You get a spherical wave moving outwards from the emitter, not a straight line. Huygens principle now simply states that you get the resulting light field by assuming radially expanding light waves and adding up all of the waves at one point (considering phase). Every point reached by light is then also the source of another radially expanding wavefront. This way the whole light field can be constructed. You can easily do this yourself using a pair of compasses.

Now how can this be in line with your everyday observation of light traveling in straight lines like (to first approximation) for a flashlamp? If you place a lot of emitters along a line and apply just the construction scheme mentioned above (again, you can do this simply by drawing circles around each point emitter), the lines of the circles represent points, where the light fields are in phase. These are the wavefronts. You will find that this gives you a wavefront that is parallel to the initial line of emitters. The wavefront kind of reproduces itself. All these circular partial waves interfere such that the initial wavefront seems to move forward in a straight line. You will only see deviations from that linear propagation at the edges of the initial line, where you can actually see that the underlying expanding waves are expanding circularly as they move to the side.

Now transport of energy essentially follows the direction of phase gradients. As I told you before, for the line geometry, you will also get lines of constant phase parallel to the initial emitter line. As phase is constant along this line, you will only get phase gradients and energy transport in the direction perpendicular to this phase front line, which corresponds to straight linear propagation of energy. However, this requires the absence of other mutually coherent fields, which might interfere with your propagating light field and will drastically change the phase gradients. So for small regions in space, linear propagation is the exception rather than the rule - however the absence of other fields is a condition that is fulfilled very often.