It's only arrogance if you're wrong. If you are correct, it's knowledge. If you're wrong, it's arrogance. Sadly, many employers do not understand this little bit of wisdom. [Jane Q. Public, 2012-10-25]

Jane, are you sure you want to use that criterion? Let's reminisce...

How do they know they were the same neutrinos they launched out? [Dr Max]

... they know the beginning ratio and ending ratio of the different types. If they are not the same, then some must have flipped (or rotated, or whatever language the neutrino guys use these days). [global_diffusion]

Not necessarily. They could be different neutrinos, caused by atoms in the way absorbing some neutrinos and emitting others. I am not sure but I suspect that is what GP [DrMax] was getting at. Rather than evidence of neutrinos actually changing from one type to another, it seems just as likely (more likely?) that intervening matter performed a conversion. Just as, say, a crystal or a gas can "change" a laser's color by absorbing photons and then emitting others of a different frequency, maybe matter is absorbing these neutrinos and emitting others with different properties. [Jane Q. Public, 2011-06-17]

Nonlinear crystals can change a laser's color by absorbing photons and then emitting others of a different frequency because photons are mediators of the electromagnetic force, so they interact with comparatively large (~10^(-10) m) electron clouds. But neutrinos only interact via gravity (irrelevant here) and the weak force which has a comparable range of ~10^(-18) m. Since the cross section determines how likely interactions are, neutrinos are roughly ten thousand trillion times less likely to interact with matter than photons. This is just an approximation, but experiments yield similarly tiny cross sections.

If neutrinos have to interact with intervening matter before hitting the detector, an extra interaction is involved. That's why Chris Burke pointed out that detecting neutrino flavor change due to an interaction with intervening matter would depend on the square of the interaction probability. Detection in the conventional flavor oscillation theory just depends on the interaction probability because it only involves a single interaction, so it's trillions of times more likely to explain the observed electron neutrino events.

In fact, that T2K paper acknowledged a much bigger source of noise on page 8: the muon neutrino beam was slightly contaminated by electron neutrinos. This contamination doesn't invalidate their results because it only explains ~1.5 out of 6 observed electron neutrino events.

Anyway, the processes that change a laser's color are given names like "second-harmonic generation" (where a crystal combines two photons into one, commonly used in green laser pointers) and "parametric down-conversion" (where a crystal splits one photon in two, commonly used as a source of entangled photons). To the best of my knowledge, these nonlinear processes only work in crystals, not in gases.

I haven't studied second-harmonic generation in depth, but five years ago I reviewed a quantum teleportation experiment that used a beta-barium borate (BBO) crystal to generate entangled photons via parametric down-conversion. Look at figure 1 on page 6 of the PDF or slide 12 of the powerpoint animation. Notice that the down-converted photons leaving the BBO crystal aren't collinear with the original UV pump laser beam.

That's because the down-converted photons are emitted in two cones which don't generally align with the pump photon, as shown in this diagram. Careful phase matching of the BBO crystal is required for the down-converted photons to leave in the same direction of the pump photon. For example, here's an experiment using collinear parametric down-conversion. Notice that they had to buy a BBO crystal that was likely periodically poled, then arrange it at exactly the right angle with respect to the pump beam in order to produce collinear down-converted photons. This is highly unlikely to happen naturally, as you suggest is happening with neutrinos.

Also, the total number of photons in the universe isn't conserved. That's why parametric down-conversion can turn one photon into two photons. But the total number of leptons is usually conserved, and the total number of baryons minus leptons is even more likely to be conserved. So the neutrino analogue of parametric down-conversion would increase the total number of leptons by +1 unless it also creates an antilepton (or destroys an existing lepton). Alternatively, it could create a baryon (or destroy an existing antibaryon, which seems unlikely) to keep B-L constant instead. Both possibilities seem to either violate conservation of energy or imply neutrino-induced radiation.

This would imply that the absorbing/emitting matter emitted it in exactly the same direction, which seems unlikely. [AlecC]

That's why I used the example of the laser: the photons are emitted in exactly the same direction, however unlikely you might think that is. [Jane Q. Public]

Here you've switched to a different topic: stimulated emission, which does happen in gases, and is collinear. But why is it collinear? Photons produced via stimulated emission are identical to the original photon not only in terms of direction, but also in terms of frequency, phase, polarization, and transverse and longitudinal spatial states. In fact, they're in exactly the same quantum state. As I've explained:

Bosons and fermions are both types of indistinguishable particles in quantum mechanics. Fermions have half-integer spin, like protons, electrons, antiprotons and positrons. Bosons have integer spin, such as photons and mesons. Some implications of this distinction can be deduced using nonrelativistic quantum mechanics, such as the fact that fermions obey the Pauli exclusion principle while bosons actually attract each other into the same state (Griffiths 1st ed p179). The connection between these statistics and spin is simply assumed in nonrelativistic quantum mechanics, but it can actually be deduced using relativistic quantum field theory.

Because photons have spin 1 and are thus bosons, they attract other photons into the same state. Griffiths derives Einstein's "B coefficient" governing stimulated emission on p311 of the 1st edition; this derivation depends on the fact that photons are bosons. However, neutrinos have spin 1/2 and are thus fermions, so the Pauli exclusion principle prevents them from occupying the same quantum state as other neutrinos. Therefore, stimulated emission of individual neutrinos is impossible.

Not necessarily. They could be different neutrinos, caused by atoms in the way absorbing some neutrinos and emitting others. ... [Jane Q. Public]

It's not entirely an oversimplification to say "that won't happen" - solar neutrinos pass straight through the Earth for example. (See the Wikipedia page) [Tim C]

Do they? Or do they often collide with atoms and experience the same kind of "conversion"? As far as I know, nobody has performed any experiments to find out. The very idea that they might change from one form to another is very recent. [Jane Q. Public]

Sure, if 1957 fits your definition of "very recent".

Do they? Or do they often collide with atoms and experience the same kind of "conversion"? As far as I know, nobody has performed any experiments to find out. The very idea that they might change from one form to another is very recent. [Jane Q. Public]

I guess just over half a century is 'very recent' by some standards, but I'd say probably not by the standard of "recent enough for me to assume no experiments have been conducted." [Chris Burke]

This was the first experiment of this kind to be performed, as you well know. Those others you mention over that last century are not relevant to my comment. Tell me: when was the last other experiment performed to find this evidence about the third leg of the oscillation? What's that you say? Never? Wow. How about that. [Jane Q. Public]

You originally wrote "change from one form to another" which isn't flavor-specific and thus refers to neutrino oscillation in general. Here you seem to be asserting that "change from one form to another" means "change from muon neutrino to electron neutrino which is controlled by theta_13". Even if that's what you originally meant, you still need to redefine "Never" to mean the papers published in 1992, 2001, 2002, 2003, 2003, 2003, 2005, 2006, 2007, etc.

I think it'd be Nobel prize material if one found neutrino-stimulated neutrino emission, as that is what you're alleging. I'm not saying it's impossible, just that IIRC my undergrad physics at all, it'd be a big discovery. [tibit]

Bigger than, say, neutrinos spontaneously, and without obvious cause, changing from one form to another? I don't see why. In fact, I think it is the more likely explanation. It fits Occam's razor a hell of a lot better, because you don't have to assume some kind of spontaneous process from a cause unknown. [Jane Q. Public]

This still begs the question: they are claiming that this is a "new type" of neutrino oscillations. So what causes the oscillations? So far I have yet to see an explanation, anywhere. [Jane Q. Public]

You are saying that the cause of this oscillation is known? If so, can you enlighten us, or at least link to an explanation of this behavior? Because everything I have read about it so far says that (a) this is the first time it has been observed, and (b) the cause is unknown. [Jane Q. Public]

You tell me: what is the most likely hypothesis for why this happens? Not how... stop getting that confused. I asked why. What is the cause behind neutrino oscillation? I will patiently wait for at least one, or hopefully at least three hypotheses about the cause of these theoretical oscillations. I don't want to hear any garbage about waveforms and probability. That's a how. I asked for a why. ... Come back when you can explain to me some hypotheses for the cause of neutrinos oscillating. NOT an equation (still very much speculative, at that) purporting to describe how. [Jane Q. Public]

Dismissing wave functions and probability as "garbage" isn't a very productive approach to learning quantum physics. The cause of neutrino oscillation is that a neutrino's wave function interferes with itself, because neutrino propagation eigenstates aren't identical to the flavor eigenstates involved in neutrino detection, and propagation eigenstates with different masses have different wavelengths. As a result, flavor detection probabilities vary spatially.

Thanks for the mention of MSW Effect. The idea of coherent forward scattering is something that I mentioned myself earlier, but I was merely speculating about the possibility, without actually knowing about it. [Jane Q. Public]

... I only mentioned the possibility that coherent scattering might exist, in a completely different comment that did not directly bear on the first one. And, as it turns out, coherent scattering does exist. But the possibility that it is the actual cause of the results of this experiment are, admittedly, near nil. The point of that comment was only that coherent scattering should be possible... and it turns out that it is. [Jane Q. Public]

No, you made a vague reference to parametric down-conversion which isn't naturally collinear and seems to either violate conservation of energy or imply radiation if it could happen with neutrinos. Then you made a separate vague reference to stimulated emission which doesn't work with fermions like individual neutrinos. Saying the word "laser" isn't the same as saying that "coherent scattering should be possible" because MSW effect (i.e. coherent forward scattering) is analagous to refraction, not to a laser. Just because a laser emits coherent light doesn't mean you get to reinterpret your previous statements like those of Nostradamus.

You're trying to draw a distinction between the MSW effect in matter and neutrino flavor oscillation in vacuum that simply doesn't exist in our universe. The MSW effect is analagous to the way a prism separates white light into a rainbow, which is an example of dispersion. A prism's index of refraction is wavelength dependent, so photons with different wavelengths travel through it at different speeds.

Electron neutrinos interact with electrons in matter via W bosons, but muon and tau neutrinos don't. This is a kind of dispersion where electron (anti-)neutrinos travel slower(faster) in matter than muon or tau neutrinos because they have different effective masses. Both vacuum and MSW oscillations occur because a neutrino's flavor (detection) eigenstates are rotated with respect to its propagation eigenstates, which travel differently because they have different masses. If we lived in a universe where all neutrinos were massless, neutrino oscillation wouldn't happen in vacuum, but the MSW effect would still cause neutrinos to oscillate in stars.

But we actually live in a universe where neutrinos have very small but non-zero masses, so the same physics that explains the cause of the MSW effect (where neutrinos oscillate in stars) also explains the cause of neutrino oscillation in vacuum. For example, Boris Kayser derives functionally identical Hamiltonians for vacuum and MSW oscillations in equations 25 and 37.

I am curious ... What is the proposed mechanism by which these neutrinos oscillate? If flavor is a measurable property, then how can they "spontaneously" change? [Jane Q. Public]

... I am still left, however wondering not how neutrinos oscillate, but rather the why. What causes them to oscillate in the first place? I understand about spontaneous propagation and destruction of virtual particles, for example, and to me that needs little explanation, because it's all probability and there is no -- or very little anyway -- net gain or loss. Things aren't changing properties, on average... just form. But it seems to me that this neutrino oscillation is different. There is a macroscopically measurable difference of properties, and so I have a hard time accepting that it is merely probability "driving" the neutrino oscillations. [Jane Q. Public]

A few years ago, I mentioned that virtual particles can explain why light slows down in materials, which is related to the MSW effect. But I also said that "I couldn't spinor my way out of a paper bag" so here's a simpler analogy for understanding the cause of neutrino oscillations.

Consider the famous double-slit experiment which is performed in freshman physics classes. Photons actually go through both slits, then interfere with themselves to cause a counterintuitive oscillatory pattern on the screen. Neutrinos interfere with themselves too, which causes a similar pattern of neutrino flavor oscillations. Both patterns exist because of wave function interference, which makes the resulting detection probabilities vary spatially.

In other words, by questioning the long-established cause of neutrino flavor oscillation, you're also questioning basic quantum theory.

Well, since it [a neutrino] isn't subject to magnetic or electrical forces, it basically has to slam into the nucleus ... it needs to get close enough to another particle - by coincidence - for the weak force to start having a decent effect on them. [OeLeWaPpErKe]

You are saying, in effect, that radioactivity is unlikely. And statistically, it is, I suppose. All I am doing is speculating. So far, I have not seen anybody (aside from a commenter here who so far has given no evidence) that there is a cause known for this "oscillation". I am simply guessing -- no more than that -- at a possible cause, rather than assume it is somehow spontaneous. [Jane Q. Public]

It's odd that you mention radioactivity, because that's a spontaneous, macroscopically measurable difference in the properties of a nucleus, and it's "driven" by mere probability. Just like neutrino flavor oscillation.

... at this time any real evidence is still waiting to show up. And I will be happy to accept that evidence, if it was responsibly gathered. Until then, I am entitled to my opinion as to what is more likely. [Jane Q. Public]

The skeptic looks for potential causes for an observation, rather than accepting that it happens spontaneously or through "mysterious" processes. If the cause is unknown, then speculation as to the possible cause is not only called for, but necessary. Further evidence will not be forthcoming until those speculations are tested. I do not claim to be as qualified to speculate on the matter as professional physicists; nevertheless, in an absence of explanation I still have a right to speculate. [Jane Q. Public]

Freedom of speech gives you the right to speculate either way, but your frequent rants about physics would be more credible if you:

1. Recognize that "absence of explanation" should read "absence of explanation that I've learned about."
2. Try to understand the conventional explanation instead of pretending it's absent.

... this looks like a definitive on-point source, from LBL by a FNAL author. Enjoy! [singlercm]

Thank you for that link. I now see how, theoretically anyway, it could be a probabilistically-determined superposition. That clears up a lot. [Jane Q. Public]

No, it really is a superposition, not just in theory but later confirmed by the experiments shown in figure 13.2 of that paper and many more. You're just manufacturing unwarranted doubt about yet another topic in physics.

I emailed the Casimir motor idea to a few scientists, saying: My gut tells me that vacuum energy can't be made to do work. But I don't see an obvious, fatal problem with the following scheme. Do you?

In response, Geoffrey Landis pointed out that there will be a latent heat at the phase transition, even for type II superconductors. He uses the same reasoning that explains why magnetic fields cause latent heat. In other words, Casimir-induced latent heat will exactly cancel the net work done by the plates, which seems to forbid this free lunch...

Maxwell's equations force E=0 inside perfect conductors, which means that vacuum fluctuations with a half-wavelength longer than the separation between the plates can't exist between the plates.

By the way: If you are going to refer to Maxwell's equations, you should use caution. Because often what are referred to as "Maxwell's Equations" are actually just Maxwell's simplifications of Heaviside's and Hamilton's quaternion equations, with introductions of arbitrary "constants" to cancel out inconveniences, much like Einstein's "cosmological constant". There is a good deal of modern evidence that Maxwell's attempt to simplify things may have been wishful thinking, and that Heaviside and Hamilton had it right all along. We rely much on Maxwell, but his conclusions are assumptions. Not only are they not proven, there is significant counter-evidence. [Jane Q. Public]

Good grief. Electric fields are zero in perfect conductors. I explain this fact to freshman physics students by asking: what would happen if we tried to place an electric field across a conductor? Electrons would move opposite the field, and positive electron holes would move with the electric field, exactly enough to cancel out the original field inside the conductor. Better conductors cancel out faster, so electric fields are zero in perfect conductors.

Mentioning that this fact can be derived from Maxwell's equations is meant to be helpful, because all physics students should be familiar with the first theory that emerged in a Lorentz-invariant form. In other words, Maxwell's equations were consistent with special relativity before relativity even existed. They're the basis of all radio equipment, and the correspondence principle checks that quantum electrodynamics (one of the most accurate theories in history) is identical to Maxwell's equations for large systems. If your reaction to hearing "Maxwell's equations" is to spray chaff about quaternions, you'll be disappointed to find that core classes based on junior-level Griffiths and graduate-level Jackson are almost exclusively about Maxwell's equations.

Quaternion notation is useful when desribing 3D rotations, but it's not used in electrodynamics because vector notation is more intuitive. That doesn't stop crackpots from insisting that Maxwell's equations are wishful thinking.

Physicists use Maxwell's vector equations despite the fact that we're well aware of quaternion notation. John Baez even wrote a paper on octonians. As Baez quips, if the noncommutative quaternions are like a shunned eccentric cousin, then the nonassociative octonians are like the crazy old uncle nobody lets out of the attic.

In fact, look at p542 of Griffiths 3rd edition: "Equation 12.136 combines our previous results into a single 4-vector equation-- it represents the most elegant (and the simplest) formulation of Maxwell's equations."

Page 555 of Jackson 3rd edition uses different units to make a similar point. Both graduate and undergraduate electrodynamics courses introduce students to the 4-vector notation, which collapses the four Maxwell's equations into a single 4-vector equation.

Using different notations can be fun, but it shouldn't change the answer to any physical problem. Therefore, caution isn't required when referring to elementary consequences of Maxwell's equations, such as the fact that electric fields are zero in perfect conductors.

It's also strange that you criticize Maxwell's equations for introducing arbitrary constants (with no links or details, as usual). I've previously explained that many physicists think the "zero" in Gauss's law for magnetism should be replaced with the density of hypothetical magnetic monopoles.

Because often what are referred to as "Maxwell's Equations" are actually just Maxwell's simplifications of Heaviside's and Hamilton's quaternion equations, with introductions of arbitrary "constants" to cancel out inconveniences, much like Einstein's "cosmological constant". [Jane Q. Public]

Einstein abandoned the "cosmological constant" in 1931 because of the 1927 discovery by Hubble and Lemaitre that the universe is expanding. Ironically, your 2009 suggestion that "the Universe is not expanding after all" contradicts all the cosmology we've learned since 1927. The last link in that comment evokes yet another feeling of deja vu:

... there is a good bit of evidence that in some cases we may end up having to go back to some of those older ideas: so far dark mass and energy haven't proved out, and there have come up explanations that don't need them. Explanations that go back to some of the old "unadjusted" equations after all. ... We may, for example, be going back to Hamilton's Quaternions, and Heaviside's, analyses as opposed to Maxwell's simplifications. It all depends on how it shakes out. ... [Jane Q. Public, 2011-12-05]

After repeatedly appealing to Heaviside without providing any links or details, perhaps you should read Heaviside's own words?

"... I came later to see that, as far as the vector analysis I required was concerned, the quaternion was not only not required, but was a positive evil of no inconsiderable magnitude; and that by its avoidance the establishment of vector analysis was made quite simple and its working also simplified, and that it could be conveniently harmonised with ordinary Cartesian work. There is not a ghost of a quaternion in any of my papers (except in one, for a special purpose). The vector analysis I use may be described either as a convenient and systematic abbreviation of Cartesian analysis ; or else, as Quaternions without the quaternions, and with a simplified notation harmonising with Cartesians. In this form, it is not more difficult, but easier to work than Cartesians. Of course you must learn how to work it. Initially, unfamiliarity may make it difficult. But no amount of familiarity will make Quaternions an easy subject. Maxwell, in his great treatise on Electricity and Magnetism, whilst pointing out the suitability of vectorial methods to the treatment of his subject, did not go any further than to freely make use of the idea of a vector, in the first place, and to occasionally express his results in vectorial form. In this way his readers became familiarised with the idea of a vector, and also with the appearance of certain formula) when exhibited in the quaternionic notation. ..." [Oliver Heaviside, Electromagnetic Theory, Volume I, pp. 134–135, 1893]

Here, Heaviside echoes the mainstream viewpoint that quaternions and vectors are just two notations for describing electrodynamics. And he doesn't seem to advocate the quaternion notation.

... Dude. I know you are a scientist. But do you even really know what the Casimir effect is? Of course I expect you will by the time you answer (if you do). And if you do answer, I probably won't reply. But at this very moment, at the time you first read this, from what you have already stated, I suspect that you really don't know what it is. [Jane Q. Public]

In addition to the other reply I wrote two days before your latest accusation of incompetence charming and productive questions, I'd also briefly explained the Casimir effect to Marble three years earlier.

Apologies. I did not see your additional reply until I had already answered. It appears that you do, in fact, know what the Casimir effect is. [Jane Q. Public]

Instead of apologizing, could you please stop spamming humanity with all of this multi-disciplinary misinformation? You may find that doing so reduces your need to apologize in the future.

... "zero point" energy is NOT in fact zero (it is actually pretty huge)... [Jane Q. Public]

While talking with my first research advisor around 2003, I mused that it's unfortunate how the Casimir effect only supresses vacuum fluctuations with wavelengths larger than twice the spacing between the plates. Since fluctuations with shorter wavelengths have more energy, the Casimir effect only depletes a vanishingly small fraction of the vacuum energy between the plates. So I agree that a naive quantum calculation leads to a huge vacuum energy. But as I've just explained, the same theory of general relativity [1] that implies stable wormholes and the Alcubierre drive also seems to renormalize the vacuum energy to zero. So this just means that depleting vacuum energy could potentially lead to very negative energy densities.

In fact I thought it was pretty obvious to most people that the fact that "zero point" energy is NOT in fact zero (it is actually pretty huge), has been the motivation for finding ways to "Maxwell's Demon" the quantum vacuum fluctuations. There is nothing theoretically preventing it; one team this year found a possible means of exploiting it. We shall see. [Jane Q. Public]

I asked which team and you replied:

I looked again, and didn't find anything from this year. So my memory could be incorrect. [Jane Q. Public]

Agreed:

What I am curious about is: assume you get the virtual particles which then tunnel: what is the probability that they will tunnel with the same probability, then recombine properly? It seems to me (without having done the math), that there is some possibility here of ending up with a quantum Goretex, or, in other words, a Maxwell's Demon of sorts, no matter how small its effect might be. [Jane Q. Public, 2009-04-21]

Not having done the math often does lead to quantum Goretex and ironic references to Maxwell's (broken) Demon.

But there's Maclay and Forward, from 2004. There are more recent examples but I will not have time to hunt them up today. [Jane Q. Public]

Maclay and Forward 2004 [2] imagined accelerating a mirror fast enough that the dynamic Casimir effect creates real photons. A more recent example was in 2009, which imagined spinning magneto-electric nanoparticles fast enough that the centripetal acceleration created real photons. At the time, I called this device a photon drive. On page 2 of their 2004 paper, Maclay and Forward point out that more conventional photon drives would arguably be better than their propulsion system.

Granted, it's only a thought experiment, and it doesn't generate practical energy even then, in this form. But hey... fusion isn't practical yet, either. To be clear: I did not claim anybody had found anything practical. Only that there may be ways to do it. [Jane Q. Public]

We know that fusion generates practical energy because the stars shine. We just don't know if we can build fusion reactors that generate more energy than is required to run the containment system that replaces the immense pressure at a star's core. I do like thought experiments about new sources of energy, though. For instance, I just described Greg Egan's suggestion that rotating hoops could provide a more efficient energy source than fusion, which could allow our civilization to outlive the stars. Egan notes that negative pressure (tension) contributes negatively to the stress-energy tensor, which might allow us to beat fusion's ~1% mass defect without violating the weak energy condition.

I've also daydreamed about ways to harness the Casimir force. Suppose one plate is made of vanadium [3], a superconductor cooled to delta_T below its critical temperature (T_c = 5.03K), and the other plate is made of niobium (T_c = 9.26K) which is held at (5.03 + delta_T)K. The Casimir force will pull the two plates together, and when they touch the vanadium plate will lose superconductivity as it's warmed past its critical temperature. This weakens the Casimir effect, allowing the plates to be pulled apart with less force, where the vanadium plate will eventually cool enough to superconduct again. Repeating this process could turn a crankshaft [4] just like a piston in a gas engine. I wish I had time to figure out if this system would actually break the Carnot efficiency limit, but I'm too busy with GRACE research and defending the scientific community against an avalanche of baseless accusations.

So I also like to speculate about energy sources that aren't practical yet. But a photon drive isn't a source of energy. It converts energy to photons like a flashlight does. Understanding physics could help you to avoid mistaking flashlights for energy sources, and might dissuade you and Lonny Eachus from cheerleading Fleischmann–Pons cold fusion long after physicists dismissed it because it can't be replicated and has no plausible mechanism.

Footnotes

[1] A complete answer awaits quantum gravity. back

[2] Also, note that equation 8 from Brown and Maclay 1969 (PDF) and equation 1 from Forward 1984 both say the energy density between Casimir plates is negative. back

[3] Pinto 1999 (patented) considers plates made of semiconductors, which have finite conductivity and a correspondingly large skin depth. Semiconductors are created by doping a silicon crystal lattice with impurities like phosphorous, which also makes their properties non-uniform at the atomic scale. Superconductors made of just one element would address both concerns. Type II superconductors have second order phase transitions, so passing the critical temperature (T_c) doesn't involve latent heat. There are just two stable elemental type II superconductors: niobium (T_c = 9.26K) and vanadium (T_c = 5.03K). The niobium plate's heat capacity should be larger than the vanadium's, so the vanadium plate is warmed past its critical temperature upon contact. The niobium plate remains below its T_c, so it could also be a type I superconductor like lead or beta-lanthanum. back

[4] The plate motion could also be turned into electricity via piezoelectric crystals or molecular motors. The plate temperatures could be controlled with Peltier coolers. Fortunately, Vanadium's critical temperature is higher than 2.73K, so its heat can be radiated to space. In practice, one "plate" should probably be part of a sphere, because aligning parallel flat plates is difficult when they're very small. back

I will add a tidbit that I picked up last night shortly after I wrote the above. You mentioned that since the ground state (not your exact words) of the vacuum is "defined" to be 0, then the energy must be negative. I understand that logic. The problem is that the premise is incorrect. Planck's equations, as refined by Einstein et al. in 1913, show that in fact the vacuum energy of a quantum system must always be above its "potential well", or the theoretical zero state. Thus, "zero-point" energy is NOT "defined" to be zero, but in fact is always positive, and the Casimir effect then, even using your own framework, is not "negative energy". [Jane Q. Public]

If you really did "understand that logic" then you wouldn't have written all that nonsense about vectors. Instead, you'd have skipped immediately to this point, which now implicitly acknowledges that the Casimir vacuum has lower energy than the standard vacuum.

Remember that spacetime is curved near large masses, but ~flat far away from masses where only vacuum energy is present. This implies that vacuum energy exerts ~zero gravitational force, so its stress-energy tensor must be ~zero, so the standard vacuum has ~zero energy.

If you're interested in the details, John Baez summarizes several vacuum energy density calculations. A naive quantum field theory calculation yields a vacuum energy with a mass density of +10^96 kg/m^3, which would've ripped the universe apart [1] before galaxies could form. On the other hand, general relativity and observations of our nearly-flat universe place a more rigorous upper bound at +10^(-26) kg/m^3. It seems like [2] gravity renormalizes vacuum energy to zero, within about one part in 10^122. Even though renormalization was harshly criticized at first, it's necessary to explain why galaxies (and thus humans!) exist.

Here's another, purely quantum-based, argument [3] for renormalization:

"As there is no lower energy state than the ground state, there is no energy level transition available to release the ZPE. Therefore, it can be argued that hf/2 should be dropped before integration of the quantum expression. This procedure is an example of renormalization, which basically redefines the zero of energy." [Abbott et al. 1996]

Footnotes

[1] One might assume that a large positive vacuum energy would collapse the universe just like a large amount of positive mass-energy would. This doesn't happen because in general relativity gravity depends on energy and pressure. In natural units, vacuum energy has pressure equal and opposite to its energy density. Because the stress-energy tensor has three pressure terms (for x,y,z) and only one energy density term, the negative pressure of positive vacuum energy dominates, causing the expansion of the universe to accelerate. back

[2] It's also vaguely possible that zero point energy doesn't gravitate at all (see question 2 here), but that would violate the equivalence principle. Also, during inflation, the vacuum energy density has been estimated at +10^74 kg/m^3. It's almost as though the universe stopped renormalizing some of the vacuum's zero point energy for a tiny fraction of a second just after the birth of the universe... back

[3] Notice that section 8 on page 7 has interesting skeptical remarks about the Casimir effect, its relationship to vacuum energy, and the question of whether vacuum energy is "available for grilling steaks." Furthermore, Jaffe 2005 presents an alternative explanation for the Casimir effect that doesn't involve vacuum energy at all. back

Because those fluctuations do exist in the vacuum outside the plates (which is defined to have zero energy), the energy inside the plates is actually negative. The attractive force implies negative energy between the plates because force is the negative gradient of potential energy.

A force being applied in the context of the Casimir effect is definitely a vector. It has direction. Neither a positive or negative vector implies "negative energy": it simply defines the physical direction in which the energy is directed. The coordinates are arbitrary according to vector calculus. There are circumstances in which energy can also be considered a vector, but this is not one of them. The Casimir effect is definitely a measurable vector in a particular direction, and he clear implication then is positive energy. [Jane Q. Public]

Good grief, you're arguing with the definition of potential energy. I was referring to the fact that all conservative forces can be described as the negative vector gradient of a potential energy function. Many of your statements on this topic are confusing:

A force being applied in the context of the Casimir effect is definitely a vector. It has direction. [Jane Q. Public]

Yeah, forces are vectors...

Neither a positive or negative vector implies "negative energy": it simply defines the physical direction in which the energy is directed. [Jane Q. Public]

The force vector points from a region with high potential energy to a region with lower potential energy. That's why an attractive force implies that the Casimir vacuum has less energy than the standard vacuum. No energy is "directed" anywhere because we're talking about potential energy, not calculating Poynting vectors.

"Because those fluctuations do exist in the vacuum outside the plates (which is defined to have zero energy), the energy inside the plates is actually negative."

You're trying to get my goat. Haha. That isn't what it says. According to the article, the force is negative, in relation to the chosen physical framework, which (as it clearly says in the article) merely implies that the energy is lowered when the physical substrates come together. [Jane Q. Public]

The Casimir force between two parallel conducting plates is negative/attractive. Period. More complicated geometries can have repulsive Casimir forces, but that doesn't affect the attractive force between parallel plates any more than your meaningless caveat does. Perhaps you meant to say "According to the article, the energy is negative..."

The same phenomenon can be demonstrated with magnets. No "negative energy" is implied. [Jane Q. Public]

In my opinion, electrostatics (or gravity) would be a better analogy than magnetism. Moving two oppositely-charged particles together does make their electrostatic potential energies more negative, just like their gravitational potential energies become more negative. The article I originally linked even explains why gravitational potential energies are negative, which also explains the values I've calculated for the Earth-Moon system.

But in the Casimir effect the classical fields that usually cause negative potential energies are zero (or negligible, like gravity). Instead, energy is removed from the vacuum itself.

The coordinates are arbitrary according to vector calculus. [Jane Q. Public]

By your logic, I could demonstrate "negative energy" with a child on a playground swing. All I have to do is choose my coordinates appropriately. [Jane Q. Public]

As discussed below LINK LATER, my logic is that gravity itself seems to have chosen coordinates that renormalize vacuum energy to zero, which means the Casimir vacuum has negative energy.

There are circumstances in which energy can also be considered a vector, but this is not one of them. [Jane Q. Public]

Ironically, the potential "energy" of a magnetic field is usually a vector potential, which makes magnetism a poor analogy for simpler forces that can be described using scalar potentials. (Permanent magnets can be described with a scalar potential, but electrostatic and gravitational potential energies are used as examples far more often, because ferromagnetism is so complicated that most intro physics courses only cover free currents.)

The Casimir effect is definitely a measurable vector in a particular direction, and he clear implication then is positive energy. [Jane Q. Public]

So... neither a positive or negative vector implies negative energy, but a vector in any direction clearly implies positive energy? That's just nonsense.

"The Casimir effect is the best known example of negative energy:" [Dumb Scientist]

This is going to be one of my rare responses to your posts. Prepare to be ignored for the most part, from here on in. ... Get a clue. If you are seriously using that link as a citation, then you lose. You did not properly comprehend what it said. ... Dude. I know you are a scientist. But do you even really know what the Casimir effect is? Of course I expect you will by the time you answer (if you do). And if you do answer, I probably won't reply. But at this very moment, at the time you first read this, from what you have already stated, I suspect that you really don't know what it is. [Jane Q. Public]

Comments like these suggest that you're not really interested in studying physics. On the other hand, John Cramer's Alternate View columns inspired me to study physics in high school. In 1998, FTL Photons introduced me to the Casimir effect. In 2001, I made an offhand remark about these faster-than-light (FTL) implications to my experimental physics professor, and he asked me to give a presentation to the class.

The next comment I wrote summarized the first part of my presentation. The second part showed that virtual particles actually slow down light in the standard vacuum, because photons spend some of their time as electron-positron pairs that travel slower than "true" lightspeed. Because the Casimir effect suppresses some of these virtual particles, light actually travels faster between the plates (perpendicular to the plates) than in the standard vacuum. This is called the Scharnhorst effect.

The Casimir effect can be modeled mathematically as a negative-mass region; Hawking showed that negative energy is necessary for certain effects on WORMHOLES to take place in conjunction with such a negative mass. But he did not claim that the negative energy was supplied by it. But that does not establish a direct relationship between the two. It is a very FAR cry from equating negative energy with the Casimir effect. [Jane Q. Public]

Why are you talking about Hawking? I already pointed you to "Wormholes, Time Machines, and the Weak Energy Condition":

"The following model explores the use of the 'Casimir vacuum'[12] (a quantum state of the electromagnetic field that violates the unaveraged weak energy condition[11]) to support a wormhole..." [Morris, Thorne, and Yurtsever, 1988]

Nevertheless, Hawking's findings did not point at Casimir effect as a source of negative energy; they merely indicated that negative energy was necessary for the negative mass to have the calculated effect. Not the same thing. [Jane Q. Public]

Again, why are you talking about Hawking? You might want [1] to read "FTL Photons":

"Since the energy density of normal vacuum is defined to be zero, the vacuum between the metal plates actually becomes a region of negative energy density." [John Cramer, 1990]

Again, granted: Hawking showed that negative energy might be required for negative mass effects in relation to wormholes. But I have never seen any science indicating that this negative energy is actually related to or a result of the Casimir effect. That is a rather large leap that is not supported in any of the science I have read. The only relationship I have seen is that negative energy is required for certain predicted phenomena; nowhere have I seen any claim that anything related to the Casismir effect is the actual source of that negative energy. [Jane Q. Public]

Then you might want to see the claim in "The warp drive: hyper-fast travel within general relativity":

"We see then that, just as it happens with wormholes, one needs exotic matter to travel faster than the speed of light. However, even if one believes that exotic matter is forbidden classically, it is well known that quantum field theory permits the existence of regions with negative energy densities in some special circumstances (as, for example, in the Casimir effect [4]). The need of exotic matter therefore doesn’t necessarily eliminate the possibility of using a spacetime distortion like the one described above for hyper-fast interstellar travel." [Miguel Alcubierre, 1994]

You might also want to see Hawking's claim in "Space and Time Warps" regarding the Casimir effect:

"So the energy density in the region between the plates, must be negative." [Stephen Hawking]

Your inexplicable references to Hawking's research might have been prompted by this sentence shortly after the part I quoted: "Stephen Hawking has proved that negative energy is a necessary condition for the creation of a closed timelike curve by manipulation of gravitational fields within a finite region of space;[6] this proves, for example, that a finite Tipler cylinder cannot be used as a time machine."

That reminds me...

"No, nothing can go faster than the speed of light because it will violate causality. Which is more or less forbidden by the entirety of physics." [Nyrath the nearly wi]

Incorrect. There is nothing we know of that actually works to prevent the violation of causality. There are a number of ways it can theoretically be done. See Tipler, "Rotating Cylinders and the Possibility of Global Causality Violation". All rhetoric (like the post at that link) aside, all we really have about it is guesses. The fact that we have never observed anything, so far, that would violate causality says absolutely nothing about the possibility. Further, it is not necessarily true that limited instances of causality violation would render the entirety of physics invalid, any more than relativistic situations render Newton "invalid". They are "special cases". That is all. [Jane Q. Public]

I've argued that violating causality isn't impossible if the many worlds interpretation is right, and explained why FTL travel is equivalent to time travel. However, Hawking's research actually seems to show that a finite [2] Tipler cylinder wouldn't even work in theory.

Hawking's chronology protection conjecture also poses problems for warp drive. For instance, Hawking radiation could destroy anything inside an FTL warp bubble, or its stress-energy tensor could blow up.

Krasnikov and Everett and Roman pointed out that the spacecraft would be causally separated [3] from an FTL warp bubble, so the spacecraft couldn't activate or deactivate the warp bubble.

So the Alcubierre and Natario drives might "just" be reactionless sublight propulsion systems where arbitrarily high acceleration isn't felt [4] aboard the spacecraft, and where relativistic speed doesn't cause time dilation.

"Exotic matter, by definition, requires violations of the known laws of physics." [Someone]

No, it doesn't. Antimatter is one valid type of "exotic matter", and it has been manufactured in labs in various (small) amounts for many decades now, without a physics violation in sight. [Jane Q. Public]

Antimatter certainly isn't common, but it's not "exotic matter". Stable wormholes and the Alcubierre drive require using exotic matter that has negative mass-energy, which would violate the weak energy condition. [Dumb Scientist]

Okay, I will concede that point, although it is about a Wikipedia entry. If you really want to argue about those... But my point is still valid, since Bose-Einstein condensates of macro-size have been manufactured in laboratories since 1998. Thus, "exotic matter" IS being manufactured, in significant quantities, right here in the real world, for 14 years now with no physics violations in sight. ("Exotic Matter", according to your own citation.) [Jane Q. Public]

Many physicists, including the inventor of warp drive, use the term "exotic matter" [5] to refer to matter with negative mass-energy. I tried (and apparently failed) to make this explicit. BEC's are qualitatively similar to lasers, superconductors and superfluids; none of them have negative mass-energy.

Note that I'm not claiming the weak energy condition is a law of nature. In fact, all these physicists point to the Casimir effect's negative energy as experimental evidence [6] that the weak energy condition can be violated. However, in theory the weak energy condition is supported by "quantum inequalities" that limit the magnitude and duration [7] of negative energy densities.

That's why this Slashdot article focuses on ways to reduce the unphysically large amount of negative energy required for a warp bubble. That's also why John Cramer mused that warp drive is outlawed and celebrated Van Den Broeck's 1999 insight that the required negative energy could be reduced by making the interior of the warp bubble larger [8] than its exterior.

Footnotes

[1] You might also want to read "Averaged Energy Conditions and Quantum Inequalities" and "The Energy Density in the Casimir Effect":

"... AWEC is violated in both two and four dimensions for a static timelike observer in a Casimir vacuum state, with either type of boundary conditions, since such an observer simply sits in a region of constant negative energy density for all time. ..." [Ford and Roman, 1995]

"... we have also found that it is possible for the net energy density in the region between the plates to be negative ... It should not come as a surprise that there is a regime of negative energy density. ..." [Sopova and Ford, 2002] back

[2] If cosmic strings exist, they could be literally infinite- stretching across the entire universe. In Stephen Baxter's Ring, the Great Northern travels into the past by repeatedly looping around a pair of cosmic strings. On a related note, the Great Northern's 5,000,000 year voyage was obviously based on figure 2 from Morris, Thorne, and Yurtsever 1988 ("spacetime diagram for conversion of a wormhole into a time machine"), as was the 1,500 year voyage of the Cauchy in Timelike Infinity. back

[3] Alastair Reynold suggests that the Waynet in his Merlin stories was created when the Waymakers tried to build a network of Krasnikov tubes. back

[4] That sounds like the impulse drive from Star Trek, the gravity polarizers/thrusters from Larry Niven's Known Space, and the parametric/frameshift drives from Alastair Reynolds's House of Suns and Pushing Ice. Even a sublight warp field requires lots of negative energy, so the diametric drive proposed by Robert Forward and Jamie Woodward is a sublight alternative. The diametric drive relies on the peculiar effects that Rei mentioned, which were discussed by Geoffrey Landis (small world, eh?). back

[5] Stephen Baxter also calls matter with negative mass-energy "exotic matter". back

[6] Squeezed vacuum experiments also involve negative energy, along with the energy-time uncertainty principle and Hawking radiation. On a related note, the Casimir effect stabilized the first bulky generation of wormholes generators in The Light of Other Days by Arthur C. Clarke and Stephen Baxter. Then squeezed vacuum technology miniaturized the generators until they were the size of wristwatches. back

[7] In 2002, the same authors who introduced "quantum inequalities" showed that arbitrarily large negative energy densities are possible, though their duration still seems restricted. As Cramer notes, renormalization makes it difficult to take quantum field theory's bounds on energy density seriously. back

[8] Van Den Broeck might have been inspired by Doctor Who's TARDIS. back

What does the Casimir effect have to do with it? That is merely a demonstration of so-called "zero point" fluctuations. It isn't "negative energy", except to the extent that you have particles and their counter-particles spontaneously arising at the same time. Even so, in the case of the Casimir effect it exerts a net positive energy on the affected mass.

The AC is terse but correct. The Casimir effect occurs because vacuum fluctuations are suppressed between two parallel conducting plates that are placed very close together. Maxwell's equations force E=0 inside perfect conductors, which means that vacuum fluctuations with a half-wavelength longer than the separation between the plates can't exist between the plates. Because they exist in the vacuum outside the plates (which is defined to have zero energy), the energy inside the plates is actually negative. The attractive force implies negative energy between the plates because force is the negative gradient of potential energy.

"Exotic matter, by definition, requires violations of the known laws of physics."

No, it doesn't. Antimatter is one valid type of "exotic matter", and it has been manufactured in labs in various (small) amounts for many decades now, without a physics violation in sight.

Antimatter certainly isn't common, but it's not "exotic matter". Stable wormholes and the Alcubierre drive require using exotic matter that has negative mass-energy, which would violate the weak energy condition.

"... we can see it in certain configurations of regular matter, such as the Casimir effect."

What does the Casimir effect have to do with it? That is merely a demonstration of so-called "zero point" fluctuations. It isn't "negative energy", except to the extent that you have particles and their counter-particles spontaneously arising at the same time. Even so, in the case of the Casimir effect it exerts a net positive energy on the affected mass.

The Casimir effect is the best known example of negative energy:

Morris, Thorne and Yurtsever[4] pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time. In this article, and subsequent work by others, they showed that negative matter could be used to stabilize a wormhole.