About interference, momentum and thrust....

[cala]

[Mentors' note - this post has been edited to remove some discussion of the EM-drive. See https://www.physicsforums.com/threads/nasas-em-drive.884753/ for our current policy with regard to em-drive discussions]

Hello.
Imagine a closed box with reflecting walls. Inside you have two antennas emiting electromagnetic waves of certain wavelength. Both antennas are separated 1/4 of the wavelength (or some N wavelengths + 1/4) and one antenna is 90º phase-shifted (1/4 wavelength delayed) with respect to the other.

I attach a picture of the superposition we will get inside the box. We will get one side of destructive interference, one region between the antennas where a standing wave develops, and another side of constructive interference. You can see that the wall on the left is on the destructive interference region, so it almost doesn't receive any photons, but the wall on the right will receive a wave created by constructive interference:

I also attach a top-view animation of the box and the different regions and waves that will develop. You can see there'll be more photons impacting the right wall:

So my question is: if we have more photons impacting one wall than the other, why shouldn't the box start moving to that direction?

 

[andrewkirk]

The coloured diagram, which is of a wave in a 1D medium (eg a wave in a stretched wire) does not take account of the reduction in amplitude in proportion to the inverse square of the distance, that occurs with EM waves. Because it assumes no reduction, one of the antennas is always an exact offset and the other is an exact duplication of amplitude. That is incorrect.

I suspect that when the 3D nature of the waves is taken into account the difference in photon flux between two opposite walls will disappear.

 

[Dale]

So my question is: if we have more photons impacting one wall than the other, why shouldn't the box start moving to that direction?

If you have asymmetric external radiation (either emitted or absorbed) then you will have a net force.

 

[Nugatory]

So my question is: if we have more photons impacting one wall than the other, why shouldn't the box start moving to that direction?

You've left out the reaction forces on the antennas as they emit radiation.

 

[Cutter Ketch]

Having nothing to add I still can't help jumping in and seconding what Dale said. I can believe that the photons are pushing harder on the right wall of the box. However, I can't believe that without also believing that the antennae are being pushed to the left. You can't have it both ways. If the antennae aren't attached to the box, then this could push the box to the right, but that doesn't violate any conservation laws. If the antennae are inside and attached to the box then there is no net force. If the antennae are inside and NOT attached to the box, then the box will move to the right up until the moment the antennae fly into the left wall!

 

[cala]

Hello.

The antennas are attached to the box.

The signals will be not exactly added or cancelled, but the effect will still take place (there will be an imbalance).

I thought also about possible reaction forces on the antennas, but the antennas are firing equally to all directions, so I think there should be no reaction, but can someone explain how the reaction forces on the antennas would develop if that's the case?

 

[andrewkirk]

I thought also about possible reaction forces on the antennas, but the antennas are firing equally to all directions,

I suspect that is not the case. What the antennas are sending out symmetrically in all directions is waves, not photons. If it is photons and not waves that transfer momentum, then that symmetric emission of waves need not correspond to a symmetric emission of photons. If more photons are hitting the front of the box than the rear then it seems to make sense that more were emitted in a frontwards than in a rearwards direction, so that the net momentum transfer at the antennas from emission will oppose the net momentum transfer at the walls from impact.

Of course, this is all just words. To make a concrete claim about impulse one has to write equations, and to contest that claim one has to critique the equations. I haven't seen any equations suggesting the creation of a net nonzero impulse on the box from photons, so at this stage there's no concrete claim to critique.

 

[cala]

Yes, I thought about that difference between waves and photons. But if the antennas are able to know were the photons will be impacting (in order to "counterbalance" the momentum exchanges that will happen at the right wall), then you're saying we could know where a photon will arrive since emitted, and that is something that is not allowed on quantum mechanics (that's where the probability wave comes from).

Imagine you have a photon source surrounded by a metallic sphere. When a photon leaves the source it's a probability wave until it hits the ball, because by definition you can not know where the photon will hit until it's detected.

If you could measure the momentum at the source as some kind of force in opposite direction to the direction where the photon will land, then quantum mechanics wouldn't need the probability wave function concept.

So if there's a reaction on the antennas, then I don't understand why quantum mechanics needs the wave-particle duality to explain photons.

 

[cala]

I made another animation separating the antennas, to show the different regions better.
You can see that the interference pattern changes a bit, and that the imbalance on both sides tends to disappear as the distance between the antennas gets bigger (the constructive and destructive interference regions begin to distribute more evenly on the available space).

So the antennas should be as close as possible (but keeping the wavelength ratios and delays to work properly).

 

[sophiecentaur]

The effect of radiation pressure is a very well established (classical) bit of theory and it has been detected with a (proper) radiometer. I don't understand how there seems to be doubt about it applying when a 'certain' arrangement is involved. If momentum is conserved and photons leave in one direction then is there any point in trying to show that there will be no overall force on the 'craft'?

So the antennas should be as close as possible

I would have thought the reverse would be the case. A large aperture would produce a more directional beam, which would waste less energy.

 

[cala]

The point is that I think the radiation pressure on the antennas will manifest equally all around them (they emit waves in all directions, so any possible forces at emission will express as pressure or tension around the whole antenna, so no displacement), yet the patterns the propagating waves will create at each atom position on the walls dictate the probability of energy being transferred to the atoms on that specific positions.

So each point in space will see two waves propagating, but the energy available for absortion at each point will depend on the pattern both waves create there (and matter presence at that point).

What I mean is that the electromagnetic waves are created simmetrically around the antennas, yet the probability of energy absortion at the walls is asymmetric.

 

[Nugatory]

I thought also about possible reaction forces on the antennas, but the antennas are firing equally to all directions, so I think there should be no reaction, but can someone explain how the reaction forces on the antennas would develop if that's the case?

The reaction force on an antenna or other emitter of electromagnetic radiation depends on the interaction between the antenna and the electromagnetic field around it. You've set things up so that the electromagnetic fields are different on different sides of the two antennas, so the forces on the two sides of the antennas are also different. (One way to see this is to calculate the momentum flux through vertical surfaces on each side of and arbitrarily close to the two antennae).

I think that you may be misleading yourself by thinking in terms of "Firing equally in all directions". That phrase tempts us to think that the antennas are shooting out photons like little bullets, transferring momentum equally in all directions and making it very hard to see where the net reaction force comes from. However, this image of electromagnetic radiation as photons being fired off in various directions is seriously misleading - photons are not what you're thinking when you hear the term "particle of light" and they don't move through space from source to target like little bullets. A better way of visualizing it is that the photons go where the fluctuations of the electromagnetic field are greatest; thus no photons are emitted in the leftwards direction at all, so there is nothing to balance the reaction force from the photons being emitted to the right.
(Note: This "better way" is a math-free waving of the hands suitable only for a B level thread. In an I-level thread, we'd be telling you to analyze this setup using classical electrodynamics and Maxwell's equations - no photons required because there are no significant quantum effects involved).

 

[sophiecentaur]

If you think of the ship as one large antenna, which only fires on one direction, you have the answer in one.

 

[cala]

I get that in order to object the generation of an asymmetric energy distribution that could provide momentum mainly to one side of the box, we need a balancing force somewhere, and that place seems to be the antennas.

But if I were talking just about the antenna system alone (with no enclosing box), would you then tell that the antennas would displace to the left just by the effects of the radiation pressure of their own fields?

If the antennas somehow create a counterbalancing force using just the fields they generate, then we could remove the box altogether and just have the antennas displacing to the left by the fields they create on each other!

I mean that I don't know which mechanism would make the antennas know that there's a metallic box picking up the energy they emit. The antennas don't care if there's a box around to absorb the energy or not, so they should behave the same way with or without the box around. So if the antennas are somehow counteracting the photon imbalance and momentum transfer present on the right wall, then they would displace to the left when left alone.

So either way, we end up with a system that is able to displace on its own!

 

[sophiecentaur]

The antennas don't care if there's a box around to absorb the energy or not, so they should behave the same way with or without the box around.

It's the whole system that you need to be considering. The 'box' is no different from a parabolic reflector, in principle (part of a directive array) - except in the actual efficiency of the propulsion unit.
It is not true to say that the antennae would not 'know about' the box. The box can easily have an effect. If there is significant energy reflected by the walls, it will interact with the metal of the antennae and change its input impedance. If the walls are perfect absorbers, no energy would be reflected back to the antenna.

 

[Cutter Ketch]

If the antennas somehow create a counterbalancing force using just the fields they generate, then we could remove the box altogether and just have the antennas displacing to the left by the fields they create on each other!

Yes, exactly, and there is nothing wrong with that. That is just like a rocket. You fire something off to the right and as a reaction get pushed to the left. The center of mass, well ok, make that the net momentum of the system doesn't change.

 

[cala]

Yes, after reviewing my own answer I saw that the antenna system cold be working like a normal engine, but with a photon exhaust.
So in a sense it's like a lantern left in space, but with a complicated and inneficient way of letting the photons scape (or appear) on one direction.

I thought that reflecting waves with mirrors was fundamentally different to making fields interfere themselves, but it seems the antennas work like mirrors (at least in this case).

As the antennas seem to be the problem, is there any way we could get the antennas out of the interference area of the fields?

 

[Nugatory]

But if I were talking just about the antenna system alone (with no enclosing box), would you then tell that the antennas would displace to the left just by the effects of the radiation pressure of their own fields?

Yes. You've built a (somewhat complicated and hard to analyze) photon rocket: https://en.wikipedia.org/wiki/Photon_rocket

 

[Nugatory]

As the antennas seem to be the problem, is there any way we could get the antennas out of the interference area of the fields?

No. That would require an electromagnetic field that doesn't conserve momentum and energy and there is no such thing.

 

[andrewkirk]

But if the antennas are able to know were the photons will be impacting (in order to "counterbalance" the momentum exchanges that will happen at the right wall), then you're saying we could know where a photon will arrive since emitted, and that is something that is not allowed on quantum mechanics (that's where the probability wave comes from).

On what do you base that 'is not allowed' claim? It doesn't sound right to me, although it's not clear to me exactly what it is that you are saying is not allowed. Can you write an equation to make the claim clear and then prove it?

Apparent retrospectivity (note the emphasis on 'apparent') is easy to achieve in QM - eg delayed choice quantum erasers. In this case the waves generate probability functions that result in certain photon impacts against certain walls. Each photon impact implies a photon emission from one of the antennas in a certain direction. We don't know which antenna but that doesn't matter because, whichever one it was, the momentum transfer to the box, via the antenna and its supporting arm, upon emission, would be the same.

So if there's a reaction on the antennas, then I don't understand why quantum mechanics needs the wave-particle duality to explain photons.

The waves specify the probability distributions for momentum transfers from impacts. The photon impacts, and their corresponding emissions, are realisations of that distribution.

I have to reiterate though that without equations this discussion is really just a vague hand-wave.

 

[Nugatory]

I thought that reflecting waves with mirrors was fundamentally different to making fields interfere themselves,

This is something of a digression in this post, but you will be interested to know that reflecting waves with mirrors is an example of fields interfering with themselves. It turns out that the interference is destructive everywhere except along one path, and that's the reflected beam.

If you want to learn more about how this works, get hold of Feynman's book "QED: The strange theory of light and matter". It's written at the right level for this thread.

 

[sophiecentaur]

I have to reiterate though that without equations this discussion is really just a vague hand-wave.

I sort of agree but this is such well established Physics that it hardly needs any special calculations to justify the principle of EM waves having momentum and producing 'light pressure'. It's a topic that goes back way before QM.

 

[cala]

As the antennas seem to be the problem, is there any way we could get the antennas out of the interference area of the fields?

I remade the animation in order to show a setup that keeps the antennas (or whatever method we use to create the waves or photons) outside the interference area. Now it looks more like the double slit experiment (where the interference area doesn't affect the emitter), but with two sources sending waves at the frequencies and distances we need to create the asymmetric distribution of the field.

It's as if we could change the position of the spot on the double slit experiment to left or right just by changing the delay between the two emitters:

Now, where would the reaction forces develop in this case?

 

[sophiecentaur]

Now, where would the reaction forces develop in this case?

Using standard antenna theory can give you the radiation pattern (directivity) for virtually any arrangement (including drive antennae and other components). That will tell you the directions in which most of the radiation is directed - which gives you the Momentum transferred. I find those ripple tank animations tend to be very confusing.

 

[sophiecentaur]

It's as if we could change the position of the spot on the double slit experiment to left or right just by changing the delay between the two emitters:

Absolutely. That's the first lesson in two source interference.

 

[Dale]

So why shouldn't the device move, if the right wall is receiving more photon interactions?

The right wall is receiving more momentum flux. Momentum is conserved, so where is the momentum flux coming from?

 

[sophiecentaur]

@cala Those 'simulations' are what the standard analysis of two source interference will give you . I am not sure what your "pulsations" represent apart from the variation in time of the wave amplitude. Normally, this would not be included in the pattern plots as it just makes viewing difficult. Normally the radial scale would represent the RMS value of the wave amplitude in any particular direction. Those pictures are far more useful than the ripple tank - type pictures you started with.
I still don't understand why you are giving all this more relevance than the results of 'radiation pressure' calculations which have been made for at least a hundred years. Classical theory is very approachable if the Maths is OK for you. (Which I think it is, because your 'simulations' will have used it.)
Under real conditions, the Diffraction Pattern of the whole Rocket / engine would be more appropriate for finding the distribution of momentum flux from the system. That is what will really count, compared with what is happening inside the cavity / 'combustion chamber'. It will govern the direction of the thrust of the engine. What goes on inside will not just depend on those patterns but on the impedance that the transmitter will 'see', looking into the antenna drive points. In the near field (inside the cavity), there will be standing waves, not only from the original sources but from their Images, in the cavity walls. Doing the whole analysis could be very difficult.

 

[cala]

The right wall is receiving more momentum flux. Momentum is conserved, so where is the momentum flux coming from?

Dale, I think momentum is conserved even in this experiment. I'm not saying that there's more momentum on the walls than on the sources, I'm saying that momentum is transferred to the fields in a symmetric way on the sources, then it's collected in a spatially asymmetric distribution on the walls. But there's the same amount of momentum being transferred from sources to fields and from the field superposition to the walls.

I think the central question here is what happens to photons or energy on destructive interference. As it's usually said, energy is not really "destroyed", but found "elsewhere". So just by timing alone we can distribute energy on one side of the sphere or the other. Just changing the rythmic generation of the fields on the sources we can make one side of the sphere receive more energy or momentum than the other. You change the spatial shape of the energy field just by timing alone.

I think we should understand how the interference mechanism is able to spatially re-distribute energy or momentum just by field superposition. How does the 3th Newton Law holds when you are merging two spatially symmetric energy fields into one spatially asymmetric energy field when you are not using any mechanical means to get the final distribution?

 

[Dale]

Dale, I think momentum is conserved even in this experiment. I'm not saying that there's more momentum on the walls than on the sources, I'm saying that momentum is transferred to the fields in a symmetric way on the sources, then it's collected in a spatially asymmetric distribution on the walls.

This is not how momentum works. Momentum is a conserved vector quantity meaning both the amount and the direction are conserved.

If no momentum escapes the system then on average the asymmetry on the walls must be balanced by an equal and opposite asymmetry on the sources. A conserved vector cannot magically change direction and still be conserved.

So just by timing alone we can distribute energy on one side of the sphere or the other. Just changing the rythmic generation of the fields on the sources we can make one side of the sphere receive more energy or momentum than the other. You change the spatial shape of the energy field just by timing alone.

Sure, and doing so also necessarily makes the forces on the sources asymmetric.

I think we should understand how the interference mechanism is able to spatially re-distribute energy or momentum just by field superposition.

We do understand this. It is a standard part of all EM textbooks. You can find online good EM textbooks from Duke, MIT, and U Texas that all address this topic.

 

[cala]

If the sources are not inside the interference region, and the field from one source is not affecting the other (think of two light cones getting merged far from the sources), why would the forces on the sources have to be asymmetric? You are getting the asymmetry from specific timing of symmetric fields, not from material interactions between the different fields and sources.

I understand you are saying that in order to get a spatially asymmetric field, the original forces have to be asymmetric, but I'm just trying to show one case where you can create an asymmetric field starting from two symmetric ones.

Can you explain what would make the forces asymmetric in the sources if the fields are interfering on another region far from them?

 

[Dale]

Can you explain what would make the forces asymmetric in the sources if the fields are interfering on another region far from them?

The whole point of finding conservation laws is that the details are totally irrelevant. From the basic laws governing the system we know that momentum is conserved, regardless of the specific details.

If you don't have momentum leaving the system then both the magnitude and the direction of the momentum of the system is constant. That implies that, on average, any net force on one part of the system is balanced by an equal and opposite net force on another part of the system.

Do you understand that?

 

[sophiecentaur]

The whole point of finding conservation laws is that the details are totally irrelevant

I think that cala is just not recognising this.

If the sources are not inside the interference region,

For two coherent sources there is no "interference region". The interference is there over all space. If what you claim were true then directional antennae would not work over large distances (inter-galactic, even). By concentrating on the near field situation around your two sources, you are not grasping the whole problem and your conclusions are not valid. Actually, the same thing would apply if you consider tennis balls being fired from a serving machine. If you operate it in a box with just one hole in it, that hole will provide drive from the balls that happen to get out (possibly after bouncing around inside for some time).