EM drive - predictive analysis

[cristian]

I want to emphasize a few points related to this issue. I will assume that the thrust experimentally observed, as related to the EM drive, is a real phenomenon, and I will try to explain it. I will mention the following interconnected effects, the dynamical Casimir effect, Unruh radiation of accelerated mirrors, and the Schwinger effect.

First, the dynamical Casimir effect. There is an interesting reference here:

http://www.physik.uni-leipzig.de/~bordag/Talks/talks_on_QFEXT07/Ruoso.pdf

Basically, semiconductors under illumination can change their dielectric properties from completely transparent to completely reflective for selected wavelengths. A train of laser pulses will produce a frequency variable mirror and this will result in a dynamical Casimir effect.

Other similar experiments have been performed, with positive results.

https://www.technologyreview.com/s/424111/first-observation-of-the-dynamical-casimir-effect/

The problem with only photons being involved in the generation of thrust (related to the EM drive) is that the conversion of the battery energy (energy source in the experiment) into kinetic energy of the spacecraft is an inefficient process. Almost all the energy goes into photon energy. This inefficiency follows since the ratio of momentum to energy for the photon is 1/c.

You can find the proper reference about this here:

https://arxiv.org/pdf/physics/0303108v1.pdf

So we have a problem. The thrust observed in EM drive experiments is several orders of magnitude higher that what should be possible, if only photons (and the dynamical Casimir effect) are involved in the generation of this thrust. What is the solution then? Neutrinos cannot be seriously considered, because of their very small probability of interaction with matter and transfer the momentum. The only option left is electron-positron pairs.

Related to the Schwinger effect, a very interesting reference can be found here:

http://dunne.physics.uconn.edu/dunne-schwinger/

Professor Dunne discusses possible mechanisms through which virtual electron-positron dipole pairs can gain energy from an external field. If the field is sufficiently strong, these virtual particles can gain the threshold pair creation energy 2mc^2, and become real particles. The problem here is that the electric field required is very large, so unless the electromagnetic near field (around the mirror), and interference effects are considered, the energy level required is orders of magnitude higher than in the EM drive experiments.

We can also assume that the Coulomb fields of the nuclei of the atoms in the mirror might be involved in the process (but this would require gamma photons). This means that the presence of the nucleus facilitates the splitting of the virtual electron-positron pair, while the nucleus carries some of the momentum of the virtual electron away.

Conclusions. The energy - time uncertainty relations and the relativistic energy - momentum relation will help us estimate the energy range in which electron-positron pair creation becomes a possibility, and the magnitude of the transferred momentum. The Coulomb fields of the nuclei of the atoms in the mirror might be involved in the process. The dynamical Casimir effect and the Schwinger effect are probably the key to the problem. The momentum transfer is mediated not only by photons, but by virtual electron-positron pairs, which become real due to the effects mentioned above. Multiply layered mirrors, special cavity geometries, interference effects, near fields, specially designed metamaterials, might need to be considered, because the energy level in EM drive experiments is too low (in order to make the electron - positron pair creation relevant).

Predicted experimental result. If the thrust is real in EM drive experiments, positrons should be detected behind the system (in the opposite direction of thrust, if the dynamical Casimir effect and the Schwinger effect are involved). In this case, the momentum transfer is mediated by the electrons. If positrons are indeed detected in these experiments (or even electrons), then at least we are on the right track. In order to detect the positrons, the whole system must be isolated in a vacuum, and the presence of positrons should be simultaneous with the presence of thrust. There are two questions to be considered here:

Could the Schwinger effect come into play at lower energies?
Have any experiments been conducted, in order to detect the presence of positrons?

Any useful comments will be appreciated. Note that no new physics is required in this model, and all the laws of conservation (energy and momentum) are valid.

[cristian]

In most experiments related to the dynamical Casimir effect  (Ruoso or Wilson), varying the electrical properties of the mirror is mathematically equivalent to physically moving the mirror through space. This means that for relativistic speeds of the mirror, the relativistic Doppler effect  might come into play, thus the frequency of an incoming photon will be elevated 3 or 4 orders of magnitude (as seen from the mirror ). That means that the conversion of the virtual electron - positron pairs into real electrons and positrons in the Coulomb field of the  nuclei of the atoms in the mirror,  becomes possible. For non relativistic speeds of the real electron  (which transfers the momentum to the nucleus),  the coefficient mentioned above  (momentum over energy ) is 2/v , where v is the velocity of the electron.  If we compare this with the same coefficient for the photon  (which is 1/c), we see that the efficiency of  converting the battery energy (energy needed in the experiment ) into momentum transfer could be improved 4 or 5 orders of magnitude.  This is what has been experimentally observed in EM drive experiments. This is a strong indication that the electron - positron pairs are involved in the process.

[aero]

Ran across this yesterday and I wonder - can anyone explain why this works on astronomical scales, but doesn't seem to work at human scales? "The dipole repeller"

http://www.nature.com/articles/s41550-016-0036#f2

Steve

[cristian]

Your question does not stay on the topic that I proposed,  but it's interesting and I will try to answer it. You can look at the discovery of the Dipole Repeller as a large scale Alcubierre drive, but this loose analogy is not perfect 

The Alcubierre drive stretches spacetime in a wave, causing the fabric of space ahead of a spacecraft to contract and the space behind to expand. The ship rides the wave to accelerate to high speeds.  Alcubierre first specifies a metric, and then finds the energy-momentum tensor associated with it, based on Einstein field equations. The solution can violate certain energy conditions,  and require negative energy or exotic matter.

Related to the Dipole Repeller,  in addition to being pulled towards  the known Shapley Concentration,  our galaxy is also being pushed away from the newly discovered Dipole Repeller.

This is a technology that might or might not become feasible in the far future. On the other hand,  the phenomena discussed in my post can lead to interstellar travel 'today'. In fact 'yesterday', some time ago the Chinese already tested the EM drive in space,  and they say that it works. If I am correct about what makes it work  (as I explained in my post ),  then it can be greatly improved.

One of the reasons why  there are major difficulties with building an Alcubierre drive at smaller scales is that it it not easy to collect a lot of negative energy in a small region of space.  Different story for astronomical scales.

Going back to my post,  I am a mathematician,  not a physicist.  I don't have a problem with the mathematical framework of QM, SR, or even GR, but the mathematics of QFT (the Schwinger effect ) is complex,  it would take me a few months  (at least ) to study it,  and I am not going to take that fight (posting here is fun, but I am not going into hard work with no motivation ).  I leave that for experts,  but I think that my intuition is correct. 

[cristian]

The detection of the positrons  (mentioned in my post ) might be impossible,  due to the rapid annihilation between the positron and an electron of an atom in the mirror.  The gamma photons created in the annihilation process will lead to the replication of the electron - positron pair production in the Coulomb field of the nucleus of another atom in the mirror (as long as the relativistic Doppler effect will elevate the frequency, so the  energy of the photon stays above the threshold value necessary for pair production), and so on. The electron will still transfer momentum to the nucleus, in each case, and the rest of the arguments remain valid.

[cristian]

When the mirror moves at 25% of the speed of light  (as in Wilson 's experiment ) in the direction of the incoming photon,  an observer on the mirror sees the frequency of the photon increased by only  about 30%. The observed frequency is elevated orders of magnitude only when the mirror moves at speeds very close to the speed of light. Still, this is sufficient to make the reasoning in my post valid. Also note that I am not talking about a 'quantum vacuum virtual plasma', a concept dismissed by well established physicists (I would just call it QED vacuum). I am talking about  a chain of events related to known phenomena of electron - positron annihilation,  and pair creation in the Coulomb field of nuclei of atoms in the mirror,  and the mediator of the momentum transfer is the electron.

I welcome any constructive comments,  pro and specially against my train of thought,  that would lead to progress in this matter. Note that in my model no laws of physics are broken  (the laws of conservation of energy and momentum are valid as always ).  Too much nonsense has been written about the EM drive  (and related designs, unfortunately including Shawyer's original explanation ), so that even if you get close to a forum of repected physicists, once you mention the EM drive you are classified as a dilettante. It's a pity, because I think that there is something interesting here, and many experiments proved that point.

[meberbs]

Any useful comments will be appreciated. Note that no new physics is required in this model, and all the laws of conservation (energy and momentum) are valid.

You should check your math again. If particles are being created, that is a lot of energy, and would make the result even worse performance than a photon rocket.

Saying no new physics means the emDrive does not produce useful force.

[cristian]

Thank you meberbs  for your comments. At the lower range,  a gamma photon can be  involved in the photoelectric effect. At higher energies, we have Compton scattering.  Around the threshold value of 2mc^2, the energy of the gamma photon is converted into an electron - positron pair. At much higher energies, we have photodisintegration and photofission.  We work around the threshold energy 2mc^2,  where m is the rest mass of the electron.An electron - positron pair is created. The electron is attracted by the Coulomb field of the nucleus, thus transferring momentum to the nucleus. The positron is repelled by the Coulomb field of the nucleus, and annihilates with the electron of another atom. Two gamma photons are produced,  at exactly the threshold energy. Now the  relativistic Doppler effect comes into play, and the frequency of the gamma photon is increased.  The Doppler shift must at least double the frequency of the  photon. Now, both  gamma photons have sufficient energy to participate in electron - positron pair creation in the Coulomb field of other nuclei,  and the process repeats. With each pair creation,  momentum is transferred to the nucleus. We have here some sort of chain reaction. The essential ingredient here is the relativistic Doppler shift, which makes it all possible. The process of momentum transfer with the electron as the mediator is much more efficient than the case when only photons are involved in momentum transfer.  What has been observed in the case of the EM drive  (in the microwave range energies ) is probably just a residual effect. The effect can probably be vastly amplified if we work in the right energy range.  If an X ray laser is considered, after the mirror has been put in motion  (using Wilson 's method,  for example ),  I suspect that interesting phenomena will come into play. Math checks out.

[meberbs]

So your claim is that the relativistic Doppler effect violates conservation of energy and momentum?

This is untrue, so I again suggest double checking your math. (There was almost no math in what you just posted.)

[cristian]

No, at no point do I claim anything like that.  People who attack the laws of conservation of energy and momentum are cranks. At every stage of the process,  energy and momentum are conserved. If you want some mathematics,  have a look here:

http://physics.stackexchange.com/questions /50106/pair-production-mathematically

There is a lot more mathematics involved in what I described,  and it all checks out. So much more that there is not enough space here for that.  Experts can retrace the steps of what I described. Photon drives are inefficient,  due to the very small coefficient,  momentum over energy,  for the photon, which is 1/c. The mechanism that I describe can transfer momentum to the mirror orders of magnitude more efficiently, and I emphasize,  the laws of conservation of energy and momentum are never violated .

[meberbs]

Energy and momentum conservation show that photons thrust is the best you can do if you start with pure energy. Generating particles to emit as reaction mass consumes energy and reduces the thrust per input power. I can just look at the initial and final conditions of your claimed setup and tell that you are violating energy or momentum conservation.

This means you are making a mistake in the middle somewhere. There is plenty of room for you to post your math here, and then someone (me if I have time) can help you find your mistake.

[cristian]

The ratio momentum over energy for a non relativistic electron is 2/v , where v is the velocity of the electron. This is orders of magnitude higher than 1/c, in the photon case. The chain reaction involving pair creation and annihilation,  facilitated by the relativistic Doppler shift, where momentum is trasferred by the electron for each pair creation step,  more than compensates for the energy required for the creation of the electron - positron pair. Your assumption that having the photon as the mediator of momentum transfer is the best you can do, is incorrect. Have you ever had a look at QFT mathematics? There are tomes of dense mathematics,  just to understand the basics, and this is what we are talking about. Any attempt to dive into that on these posts would be a joke.

[meberbs]

The ratio momentum over energy for a non relativistic electron is 2/v , where v is the velocity of the electron. This is orders of magnitude higher than 1/c, in the photon case. The chain reaction involving pair creation and annihilation,  facilitated by the relativistic Doppler shift, where momentum is trasferred by the electron for each pair creation step,  more than compensates for the energy required for the creation of the electron - positron pair. Your assumption that having the photon as the mediator of momentum transfer is the best you can do, is incorrect. Have you ever had a look at QFT mathematics? There are tomes of dense mathematics,  just to understand the basics, and this is what we are talking about. Any attempt to dive into that on these posts would be a joke.

If total energy and momentum at the end is not equal to total energy and momentum at the start, then energy and momentum are not conserved.

You are claiming that by some magic, you don't have to pay the E=m*c^2 cost for creating the electron. This violates energy conservation. If you included the energy to create mass, you would realize that 2/v is not the right answer. Try to explain where the energy that went into creating the electron came from (what is missing energy in the final state) this may help you see the issue.

Nothing you have described involves QFT math, at most it involves special relativity. Maybe in your head you have imagined some quantum way that quantum allows energy conservation to break, but it doesn't.

[as58]

The ratio momentum over energy for a non relativistic electron is 2/v , where v is the velocity of the electron. This is orders of magnitude higher than 1/c, in the photon case. The chain reaction involving pair creation and annihilation,  facilitated by the relativistic Doppler shift, where momentum is trasferred by the electron for each pair creation step,  more than compensates for the energy required for the creation of the electron - positron pair. Your assumption that having the photon as the mediator of momentum transfer is the best you can do, is incorrect. Have you ever had a look at QFT mathematics? There are tomes of dense mathematics,  just to understand the basics, and this is what we are talking about. Any attempt to dive into that on these posts would be a joke.

So where does the momentum go? What does the engine emit?

[sanman]

cristian,
So this Schwinger effect relates to gamma-gamma photon interaction, right? (ie. the high energies you mentioned)

Is it possible to achieve this with Squeezed Light? I realize Squeezed Light is just manipulating the overall distribution of the photon within the bounds of Heisenberg Uncertainty, but if a sufficiently high peak amplitude (dB) is achieved, then can't this result in a similar kind of interaction via the peak values?

If Squeezed Light can be produced at little/no energy cost via non-linear optical crystals, then couldn't it lower the burden on your power supply?

[cristian]

Answer for meberbs.

Thank you for your comments. Looks like I have to put my thinking cap on. First, and answer for meberbs. I attached a file (pairproduction.pdf), where everything related to this is nicely explained. We consider just a single event, pair production. Pair production cannot happen in empty space (the simultaneous validity of the laws of conservation of energy and momentum forbid it). We need a third body, we need the nucleus with its Coulomb field. In order to satisfy the conservation laws, the system that we study is the gamma photon + the nucleus (before pair creation), and the system electron-positron + nucleus (after pair creation). The law of conservation of energy says that the total Energy of the system before pair production is equal to the total energy of the system after pair production. Similar for the momentum. Everything is explained in the attached file (in relativistic notation). We agree up to this point, nothing funny up to this point. Momentum is transferred to the nucleus, with little energy transfer.

Where we disagree is related to whether momentum transfer with the electron as the mediator is more efficient than a photonic drive, where momentum is transferred directly, with the photon as the mediator.

For a single event, you are correct meberbs, the momentum transferred to the nucleus is smaller than the initial momentum of the photon.

Now we get into the hairy part, the chain reaction. We are on a reference frame tied to the mirror, in particular, to the nucleus. The electron - positron pair is created. The electron transfers momentum to the nucleus. The positron is repelled by the Coulomb field of the nucleus, and annihilates with the electron of another atom. Two gamma photons are created (at or slightly above the total threshold energy 2mc^2 , where m is the rest mass of the electron ). At about 60% of light speed, due to the relativistic Doppler effect, an observer on the mirror will see the frequency of the incoming gamma photon doubled (when moving straight towards the photon, all the possible geometrical configurations have to be considered, this is just a special case ). That means that each of the two gamma photons that were released after annihilation, now can trigger pair creation events in the Coulomb fields of the nuclei of other atoms (this is exponential increase!!!). The process repeats, and at each step, momentum is transferred to the nuclei of the atoms of the mirror. This is the chain reaction facilitated by the relativistic Doppler shift.

Problems with the chain reaction.

1. The direction of travel of each of the two gamma photons after each annihilation step is important, because the frequency increase as seen from the mirror depends on the particular geometrical configuration.

2. Energy and momentum conservation, before and after the chain reaction terminates. I don't know the answer to this one, you are correct meberbs , there is a problem here. I will think about this one. I hope you will too.

3. Is the chain reaction even possible, to start with?

4. I assume that the mirror is physically moving at 60% of light speed. The experiments described in my post (Ruoso or Wilson), do not qualify.

5. If this chain reaction is impossible, why is that the case? Can you prove that this chain reaction is not possible?

By the way, QFT (in particular QED) is need, in order to calculate the probability of these types of events, in order to see which are the dominating ones. There is no going around that, and the calculations are not pretty. This is actually the heart of the problem. Speculating based on the mathematics of relativity, and intuition, is not enough.


Answer for as58

The "engine" does not emit anything. For each pair production event, momentum is transferred to the mirror, due to the laws of conservation of energy and momentum. The problem is trying to prove that the total momentum transferred makes this "engine" more efficient that a straight photon drive. I tried it with my chain reaction model (described above), but surely I am missing something.

Answer for sanman

I don't know the answer to this one. We are still struggling with pair production (as you can see). I mentioned the Schwinger effect as an interesting venue of research related to all this, but as you can see from these discussions, we cannot handle even much simpler events.




 

[aero]

Pair production - Seems to me that there is plenty of energy in the cavity. Production of one pair needs 1.022 MeV. Multiply by 1.60218 E-19 J/ev = 1.60218 E-13 J/Mev so energy required to produce a pair is 1.637E-13 J/pair. That is not very much considering that the frustum is driven by as much as kJ/second. The problem of course is frequency of the photons. That is, the energy of a single photon needed for pair production. Without getting around that we still have a problem.

But, once there are electrons and positrons inside the cavity, I'm led to believe that they will be accelerated along the energy gradient within the cavity as accel = grad * 2/3 * diameter of electron or positron. Here this is like a = grad * dx and the 2/3 comes from applying dx to a sphere instead of a cylinder of the diameter of the electron/positron.

Just some thoughts.

[MikeAtkinson]

If you draw a box around your device and its power supply, are any particles or fields crossing the boundary? If so what?

Some other ideas about how the EM drive works, have the box the size of the universe (because they act on the whole universe). These need not break conservation of mass/energy or momentum as the increase of the EM drive is balanced by reductions elsewhere in the universe.

[sanman]

Answer for sanman

I don't know the answer to this one. We are still struggling with pair production (as you can see). I mentioned the Schwinger effect as an interesting venue of research related to all this, but as you can see from these discussions, we cannot handle even much simpler events.

cristian,
regarding your thoughts on Dynamical Casimir Effect - isn't it really the small-end of the frustum that you'd mainly focus on to observe Dynamical Casimir Effect? If an EMdrive were moving in a linear relativistic velocity, it would be the trailing small-end that would be expected to accumulate those pair-escaped particles, right?

But because the frustum is asymmetrically tapering, those pairs may not be able to produce in the first place, since the space is too narrow to support their wavelength. So your Static Casimir Effect would suppress the Dynamical Casimir Effect, would it not?

And maybe that's even what helps to allow the internal "bump-dip" inside the frustum cavity to facilitate motion in the first place (the "Warp-in-a-Bottle"), even for regular slow non-relativistic velocity frames.

[cristian]

I think that aero  solved all our problems gentlemen (with his last remark above ), but maybe not exactly the way he described it .  We could consider positron channeling in crystals..  So we have an experimental setup where after the pair production event,  the electron transfers some momentum to the nucleus,  and the positron will channel through the crystal,  thus increasing its momentum. No pair production  - annihilation chain reaction, all laws of conservation of energy and momentum are valid, and it explains the enhanced momentum transfer.  Bingo. I think that we are on the right track here.