Is reverse time dilation posssible?

I agree with JesseM: the Casimir Effect proofs the possibility of less energy density than in a vacuum. However, the calculation of the vacuum energy density is not exactly a glorious chapter of modern physics. So I´d say it´s absolutely correct to say that there is no proof for negative energy.

John Baez has a good discussion of the problems with calculating the vacuum energy density here.

(3) If you believe the recent observational data
regarding the accelerating universe, then the SEC [strong energy condition] is violated on cosmological scales right now!

I agree with JesseM: the Casimir Effect proofs the possibility of less energy density than in a vacuum. However, the calculation of the vacuum energy density is not exactly a glorious chapter of modern physics. So I´d say it´s absolutely correct to say that there is no proof for negative energy.

Since we apparently live in an "open" universe which will keep on expanding to infinity, doesn't this violate conservation of energy in a rather big way?

The Casimir Effect shows us that energy can indeed be harnessed for work (pressing two metal plates together)

13. J. Maclay, "Unusual properties of conductive rectangular cavities in the zero point electromagnetic field: Resolving Forward's Casimir energy extraction cycle paradox," PROCEEDINGS of STAIF-99 (Space Technology and Applications International Forum-1999, Albuquerque, NM, January, 1999), edited by M.S. El-Genk, AIP Conference Proceedings 458, American Institute of Physics, New York 1999. Published in hardcopy and CD-ROM by AIP.

This article presents the explanation of why Bob Forwards idea for extracting energy from the vacuum does not work. Usually we think that if the energy density in a box is greater than the energy density outside the box, that there will be an outward force on the walls of the box, which is what Bob’s idea was based on. However, for vacuum energy this it not true!

What do you mean by "harnessed", exactly? I don't know how you'd use the two plates to do work, and even if you could, I'd bet that you couldn't get out more energy than you put in...I did some quick googling and found there was a proposal by physicist Robert Forward to extract energy from the vacuum, but this page says:

Negative energy is related to conservation of enegy because mathematically, one should be able to create energy out of nothing if one also creates an equal amount of negative energy.

My point, which you may or may not have refuted (unfortunately I have very little formal education, so many of the details of that link were lost on me), was that assuming all of empty space has a positive energy value would violate conservation of energy

It's not a matter of extracting useful amounts of power; it's a matter of reducing the amount of zero-point energy in any region of space.

If we accept the QM explanation, then it seems as though zero-point energy should be just strong enough to avoid breaking the Uncertainty Principle by allowing us to be too certain about the speed/position/value of a certain point in space.

My point is that if we reduce the amount of vacuum energy by any means, such as using it to push two small metal plates together (converting it into macroscopic kinetic energy), then that energy MUST be replenished somehow in order to prevent over-certainty. My assumption was that this was done by creating negative energy.

In a quantum mechanical system such as the particle in a box or the quantum harmonic oscillator, the lowest possible energy is called the zero-point energy. According to classical physics, the kinetic energy of a particle in a box or the kinetic energy of the harmonic oscillator may be zero if the velocity is zero. Quantum mechanics with its uncertainty principle implies that if the velocity is measured with certainty to be exactly zero, the uncertainty of the position must be infinite. This either violates the condition that the particle remain in the box, or it brings a new potential energy in the case of the harmonic oscillator. To avoid this paradox, quantum mechanics dictates that the minimal velocity is never equal to zero, and hence the minimal energy is never equal to zero.

But if you're creating an equal amount of negative energy, then you aren't actually violating conservation of energy, right?

Why would a positive vacuum energy violate conservation of energy?

Who said anything about useful? What I'm saying is that I don't think you can extract any energy from the vacuum using the casimir effect, no matter how tiny. I don't understand what connection you're making between reducing the energy density of a given region of empty space and extracting energy to do work from it.

So it appears as though empty space in QM is subject to the same Uncertainty limitations as particles.

This is exactly my point. Creation of positive and negative energy (or matter) in equal amounts does not violate conservation. Creation of positive-only energy, OTOH, does seem to violate conservation, and your explanation of vacuum energy (that all of empty space has some positive energy but never any negative energy) would seem to fall into this catagory.

Well, I thought you said something about always having to "put in" more energy than you'd get out of vacuum energy. My point wasn't getting free energy out of vacuum energy; it was getting ANY energy out of it at all.
If one made microscopic and very light metal plates and put a small amount of pressure on them, not quite enough to move them on its own, but enough to move them after vacuum energy has exterted its influence then wouldn't that be a case of someone turning vacuum energy into kinetic energy? Wouldn't that mean that we must have LESS vacuum energy than we started with?

The Casimir Effect is a direct consequence of the Uncertainty Principle, and it proves we can convert vacuum energy into another form (kinetic.) BUT, the universe will not allow the reduction of vacuum energy in this manner because this would violate the Uncertainty Principle.

To avoid this paradox, quantum mechanics dictates that the minimal velocity is never equal to zero, and hence the minimal energy is never equal to zero.

You may be right that the increase in kinetic energy of the plates as they are pulled together is balanced by the decreased vacuum energy between them.

(emphasis mine.)
This means that empty space cannot exist, because empty space=0 energy. This is why we have "quantum foam" or zero-point fluctuations instead. And the Casimir Effect is a direct test of the existence these fluctuations. That is the relationship between the Casimir Effect and Uncertainty--zero-point fluctuations are a consequence of Uncertainty, and the Casimir Effect is a consequence of zero-point fluctuations.

Vacuum energy is present to preserve Uncertainty, and to convert it to another form (in essence taking it away from the vacuum) would allow us to be too certain about the value of a particular point in spacetime.

Where else is the kinetic energy coming from, if not a decrease in vacuum energy?

Assuming I'm not horribly wrong about Uncertainty applying to empty space, any vacuum energy converted to another form must be replaced or else we lose that Uncertainty. The idea of negative energy lets us seemlessly replace this lost energy, and no net energy will have been created--thus both Conservation and Uncertainty are preserved.

Ok, but you're not telling me what entity it is that you think is subject to uncertainty here--you said earlier that it was the position/speed of "points in space" which was uncertain, I still think that doesn't make any sense. What I've read in a few places is that different "modes" of the quantum fields which fill empty space carry momentum/energy and are therefore subject to uncertainty, and this is what's responsible for vacuum energy. In between the plates in the Casimir effect, there are fewer possible modes than in free space, therefore the minimum energy is less, without any violation of the uncertainty principle. Are you disagreeing with me about this?

some popularized musings by Fenyman - don't appear to me to actually lead to any experimental predictions.
I could be wrong, perhaps RandallB could cite some papers.

Now if this thread has turned to finding what’s ‘correct’, I don’t think Casimir will do. Entanglement is the only recognized non-circular ‘proof’ for QM/HUP and we already have two or three active threads debating that issue.

SO, for me my money’s on backwards time a la Fenyman’s Diagrams is shown to be real and not a trick before Negative Gravitation is. In fact I’d bet that a Theory proving so would also show QM/HUP to wormholes as wrong.

I don't want anyone to get the impression that I'm pulling stuff out of my ***, so:

Mainstream physicists have said that the Casimir Effect arises as a consequence of Uncertainty, not that it violates it. Mainstream physicists have also brought up the possibility of negative energy or negative mass, and I have heard them use the Casimir Effect as one such example.

My claim that a reduction in energy would result in Uncertainty breaking is my own. Since I have always heard the Casimir Effect explained in terms of the Uncertainty Principle, I assume that the fluctuations are just strong enough to preserve Uncertainty. It may be that there is a margin there, and that it is possible to convert some vacuum energy into other forms but not enough to break Uncertainty, but because of the way it was explained to me, I have no reason to believe that such an excess of vacuum energy exists.

My claim that an increase in vacuum energy (e.g. to replace that loss through the Casimir Effect) violates Conservation is also my own, though I think it is a fairly straightforward assumption.

Interesting. I have never heard this explanation before. I have always read that it is the appearence and disappearence of virtual particles, the kind that are responsible for Hawking Radiation (one particle of the particle/antiparticle virtual pair appears just barely within the event horizon of a black hole and the other one appears just barely outside of it. The one outside escapes to freedom and becomes "real" whereas the other one falls into the black hole and reduces its mass through QM weirdness that I do not fully understand.) It was my understanding that all of empty space was composed of these virtual particle pairs, constantly appearing and annihilating one another--the quantum "foam". They have no mass and usually have no effect, except that Uncertainty commands that they MUST have a mass or energy value, at least sometimes.

The Casimir effect is a small attractive force which acts between two close parallel uncharged conducting plates. It is due to quantum vacuum fluctuations of the electromagnetic field.

The effect was predicted by the Dutch physicist Hendrick Casimir in 1948. According to the quantum theory, the vacuum contains virtual particles which are in a continuous state of fluctuation (see physics FAQ article on virtual particles). Casimir realised that between two plates, only those virtual photons whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy. The energy density decreases as the plates are moved closer which implies there is a small force drawing them together.

Understanding the Casimir force

Although the Casimir force seems completely counterintuitive, it is actually well understood. In the old days of classical mechanics the idea of a vacuum was simple. The vacuum was what remained if you emptied a container of all its particles and lowered the temperature down to absolute zero. The arrival of quantum mechanics, however, completely changed our notion of a vacuum. All fields - in particular electromagnetic fields - have fluctuations. In other words at any given moment their actual value varies around a constant, mean value. Even a perfect vacuum at absolute zero has fluctuating fields known as "vacuum fluctuations", the mean energy of which corresponds to half the energy of a photon.

However, vacuum fluctuations are not some abstraction of a physicist's mind. They have observable consequences that can be directly visualized in experiments on a microscopic scale. For example, an atom in an excited state will not remain there infinitely long, but will return to its ground state by spontaneously emitting a photon. This phenomenon is a consequence of vacuum fluctuations. Imagine trying to hold a pencil upright on the end of your finger. It will stay there if your hand is perfectly stable and nothing perturbs the equilibrium. But the slightest perturbation will make the pencil fall into a more stable equilibrium position. Similarly, vacuum fluctuations cause an excited atom to fall into its ground state.

The Casimir force is the most famous mechanical effect of vacuum fluctuations. Consider the gap between two plane mirrors as a cavity (figure 1). All electromagnetic fields have a characteristic "spectrum" containing many different frequencies. In a free vacuum all of the frequencies are of equal importance. But inside a cavity, where the field is reflected back and forth between the mirrors, the situation is different. The field is amplified if integer multiples of half a wavelength can fit exactly inside the cavity. This wavelength corresponds to a "cavity resonance". At other wavelengths, in contrast, the field is suppressed. Vacuum fluctuations are suppressed or enhanced depending on whether their frequency corresponds to a cavity resonance or not.

An important physical quantity when discussing the Casimir force is the "field radiation pressure". Every field - even the vacuum field - carries energy. As all electromagnetic fields can propagate in space they also exert pressure on surfaces, just as a flowing river pushes on a floodgate. This radiation pressure increases with the energy - and hence the frequency - of the electromagnetic field. At a cavity-resonance frequency the radiation pressure inside the cavity is stronger than outside and the mirrors are therefore pushed apart. Out of resonance, in contrast, the radiation pressure inside the cavity is smaller than outside and the mirrors are drawn towards each other.

It turns out that, on balance, the attractive components have a slightly stronger impact than the repulsive ones. For two perfect, plane, parallel mirrors the Casimir force is therefore attractive and the mirrors are pulled together. The force, F, is proportional to the cross-sectional area, A, of the mirrors and increases 16-fold every time the distance, d, between the mirrors is halved: F ~ A/d^4. Apart from these geometrical quantities the force depends only on fundamental values - Planck's constant and the speed of light.

The basis of zero-point energy is the Heisenberg uncertainty principle, one of the fundamental laws of quantum physics. According to this principle, the more precisely one measures the position of a moving particle, such as an electron, the less exact the best possible measurement of momentum (mass times velocity) will be, and vice versa. The least possible uncertainty of position times momentum is specified by Planck's constant, h. A parallel uncertainty exists between measurements involving time and energy. This minimum uncertainty is not due to any correctable flaws in measurement, but rather reflects an intrinsic quantum fuzziness in the very nature of energy and matter.

A useful calculational tool in physics is the ideal harmonic oscillator: a hypothetical mass on a perfect spring moving back and forth. The Heisenberg uncertainty principle dictates that such an ideal harmonic oscillator -- one small enough to be subject to quantum laws -- can never come entirely to rest, since that would be a state of exactly zero energy, which is forbidden. In this case the average minimum energy is one-half h times the frequency, hf/2.

Radio waves, light, X-rays, and gamma rays are all forms of electromagnetic radiation. Classically, electromagnetic radiation can be pictured as waves flowing through space at the speed of light. The waves are not waves of anything substantive, but are in fact ripples in a state of a field. These waves do carry energy, and each wave has a specific direction, frequency and polarization state. This is called a "propagating mode of the electromagnetic field."

Each mode is subject to the Heisenberg uncertainty principle. To understand the meaning of this, the theory of electromagnetic radiation is quantized by treating each mode as an equivalent harmonic oscillator. From this analogy, every mode of the field must have hf/2 as its average minimum energy. That is a tiny amount of energy, but the number of modes is enormous, and indeed increases as the square of the frequency. The product of the tiny energy per mode times the huge spatial density of modes yields a very high theoretical energy density per cubic centimeter.

From this line of reasoning, quantum physics predicts that all of space must be filled with electromagnetic zero-point fluctuations (also called the zero-point field) creating a universal sea of zero-point energy.

So I wonder, can the energy density between plates in the casimir effect go below the vacuum energy density by significantly more than 10^-9 joules per cubic meter? Does anyone know the equation for calculating the energy density between plates in terms of their size and separation? I found a bunch of pages that give an equation for the force (see here, for example), but I'm not sure how to translate this into energy density.