Zero-point field

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In quantum field theory, the zero-point field is the lowest energy state of a field, i.e. its ground state, which is non zero.^[1] This phenomenon gives the quantum vacuum a complex structure, which can be probed experimentally; see, for example, the Casimir effect. The term "zero-point field" is sometimes used as a synonym for the vacuum state of an individual quantized field. The electromagnetic zero-point field is loosely considered as a sea of background electromagnetic energy that fills the vacuum of space, and is often regarded merely as a curious outcome of the quantum mechanical requirement, namely the Heisenberg uncertainty principle, that the lowest allowable energy level in a harmonic oscillator mode is not zero but ħw /2, where w is the characteristic frequency of the oscillator.^[2]

Contents 1 Overview 2 History 3 Zero-point energy and conservation of energy 4 Quantum fluctuations versus quantum pathways 5 Curvature of space and the physical vacuum 6 Andrei Sakharov and the elasticity of space 7 Related 8 References in popular culture 9 References

[edit] Overview

It is believed that an electromagnetic field exists in a vacuum even when the temperature of the surrounding material is reduced towards absolute zero.^[3] The existence of such a zero-point field has been confirmed experimentally by the Casimir experiment, i.e. the measurement of the attractive force between two parallel plates in an evacuated, near-zero temperature enclosure.^[3] That force is found to be proportional to the inverse fourth power of the distance apart of the plates; it has been shown that such a result can only be produced by a zero-point field whose spectral energy density has a frequency dependence of ρ(ν) = kν³.^[3] It has been assumed until recently, though without any experimental evidence, that there are zero-point energies for the strong, and weak forces as well as the electromagnetic force. More recently it has been understood that since the electromagnetic force, expressed by the Lorentz force equation, does not require mass that the electromagnetic zero-point field is probably fundamental to all three forces.

[edit] History

Quantum mechanics predicts the existence of what are usually called zero-point energies for the strong, the weak and the electromagnetic interactions, where zero-point refers to the energy of the system at temperature T=0, or the lowest quantized energy level of a quantum mechanical system. Specifically, in 1900, Max Planck derived the formula for the energy of a single "energy radiator", i.e. a vibrating atomic unit, as:

Here, h is Planck's constant, ν is the frequency, k is Boltzmann's constant, and T is the temperature.

In 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero. They called this "residual energy" and then Nullpunktsenergie (in German), which later became translated as zero-point energy. They carried out an analysis of the specific heat of hydrogen gas at low temperature, and concluded that the data are best represented if the vibrational energy is taken to have the form:^[4]

Thus, according to this expression, even at absolute zero the energy of an atomic system has the value ½hν.^[5] Although the term zero-point energy applies to all three of these interactions in nature, customarily it is used in reference only to the electromagnetic case.^[6] Because the zero-point field has the property of being Lorentz invariant, the zero-point field becomes detectable only when a body is accelerated through space.^[6]

Some experiments in 1992 have demonstrated experimentally that the familiar spontaneous emission process in atoms may be regarded as stimulated emission by zero-point field radiation.^[7] In recent years, it has been suggested that the electromagnetic zero-point field is not merely an artifact of quantum mechanics, but a real entity with major implications for gravity, astrophysics and technology. This view is shared by a number of researchers, including Boyer (1980), McCrea (1986), Puthoff (1987) and Rueda and Haisch (1998).^{[8][9][10][11]}

[edit] Zero-point energy and conservation of energy

Traditionally it has been assumed that the electromagnetic zpf energy density for each quantum space equals the sum of the quantum oscillatory energy at all possible frequencies in each of the three spatial dimensions all the way up to the Planck frequency. Using this historical measure of energy density it has been estimated that there is enough zero point energy contained in one cubic meter of space to boil all of the oceans of the world.

However, the historical analysis of the zpf energy density just described appears to contradict the first law of thermodynamics and our understanding of the cosmology of the universe. The physical evidence is extensive that the universe has expanded from an origin containing essentially no space and infinite energy density in the event called the Big Bang. If our universe is defined as all that has the potential of being known to us and interacted with, then it is defined as a "closed system". A closed system retains causality because its total energy is finite and always conserved. This is not a contradiction with the universe at time (t) = 0 because the concept of infinite energy "density" in "zero" occupied space does not equal "infinite energy" for the universe. The historical analysis of the zpf energy density used in the example of energy in one cubic meter of space does not account for the expansion of the universe. It simply increments this expanding space over time and assigns each new additional quantum space with the maximum energy density.

There is a major drive in physics to create a more realistic zpf energy density model that still allows for causality and conservation of energy in the universe. There is substantial evidence in quantum physics, via the de Broglie relations, the Casimir effect, and the Zitterbewegung action of electrons that this field of energy acts as an energy intermediary in the dynamic actions of all particles. Electrons orbiting a nucleus, as one specific example, may use this energy source to move up in an orbit, and then contribute back to this energy source when they relax back into a lower orbit around the nucleus. The de Broglie relations show that the wavelength is inversely proportional to the momentum of an electron and that the frequency is directly proportional to the electron's kinetic energy. As long as the electron does not increase its average kinetic energy over time through acceleration or heating of the atom as a whole, then this wave-like movement of electrons can be seen as a direct interaction of electrons with the zpf.

A potentially promising area for research is the fact that if particles become more energetic as they are heated or accelerated their gravitational field increases. Changes in gravity can perhaps be attributed to a change in a spherical zpf energy density gradient surrounding an accelerated or decelerated massive particle. This dynamic action is just an extension of the static orbiting electron wave model to a dynamic model in which the "average" kinetic energy of a particle no longer remains constant over time and energy is drawn in from the quantum vacuum but not returned. If a massive particle's ground state is defined as it's inertial reference frame at the instant of its creation, then when a particle or body returns to this reference frame, or ground state, from an accelerated state that energy is returned to the quantum vacuum as a decrease in gravity surrounding the particle. This would be in accord with the rules of gravity on accelerated bodies as we know them, and most importantly, maintains conservation of the combined energy of both particles and the zpf, while still allowing for dynamic interaction between the two.

[edit] Quantum fluctuations versus quantum pathways

The essential character of the zpf was originally described by John Archibald Wheeler^[12] as a foamy sea of constantly emerging virtual particles and anti-particles which would come into existence spontaneously and then annihilate themselves. This description originated because it was the only way to consolidate the disparity between the enormous projected energy density of the quantum vacuum with the much smaller energy predicted from the Cosmological Constant. Because the mathematics of oscillators was the origin of our understanding of the zpf it has been described as "fluctuating" in the absence of any outside force. But this seems to be a fundamental error in logic. An individual oscillator can fluctuate just as an electron's orbital wave motion can fluctuate between two different orbits. However, in both cases there should be no "change" in fluctuation as long as the energy does not change. At zero degrees Kelvin the energy from one quantum oscillator should not propagate between quantum spaces, nor should there be any change in any single quantum oscillator's strength, absent an outside force, as this would violate conservation of energy.

A static, but plastic quantum foam is a better analogy to the character of the quantum vacuum, and not the kind of foam Wheeler described. For example, in the cold reaches of space between galaxies photons from distant galaxies arrive rarely. If by chance a rare photon passes through one of these cold dark spaces it will leave a quantum signature on the oscillatory energy of each quantum space it passes through. If a quantum space has experienced a photon passing through it and no further photons pass through, then that area of space will retain a memory of the last photon it experienced. In effect, a pathway has been produced by this single photon. The fact that this pathway cannot be maintained in its unaltered form after measuring it, as the Heisenberg Uncertainty Principle predicts, does not alter the fact that this pathway is retained in space until the next photon passing through creates an interference with this pathway. The appearance of fluctuation is the transformation of energy and information as it travels through space, but the total energy and information of the universe are always maintained. Acts of measurement represent an exchange of photons between the "observer" and the "observed" and are synonymous with local changes in energy. The "observed" can be an actual particle or just the pathway in space created by the particle. So it is seen that this quantum foam is not the kind of foam that springs back, but is more like milk foam on top of a cup of cappuccino - a straw can be pushed through the foam and a hole in the foam will remain for a time after the straw is withdrawn. But in the case of quantum foam the impression left behind is not of a hole, but rather the impression of the photon or particle with mass that passed through it.^[13].

[edit] Curvature of space and the physical vacuum

Zero-point field theory originated from the application of thermodynamics to the problem of Black Body radiation. This knowledge was later used by Albert Einstein to calculate the energy density of the vacuum required to keep the electron in the hydrogen atom from collapsing into the nucleus. Much later the energy density of empty space was calculated to have a spectral density of p = kv³. This energy density is an enormous figure and is approximately 10^120 times higher than the cosmological constant predicts. The total energy of the universe does not seem to be conserved unless laws of physics are invoked that cannot be understood at the classical level. In other words, the observed expansion of the universe leads to a discrepancy from quantum physics derived vacuum energy of the order of 10^120 times. Even now, quantum theory's contradiction with the conservation of the total energy of the universe and the first law of thermodynamics, is not universally understood among the scientific community. A man that did understand this problem was Andrei Sakharov, the famous Russian physicist and political dissident.

In the West the scientific description of gravity remains centered on Einstein's original conception as described in General Relativity, i.e. gravity is the geometry of space, or geometrodynamics. In this description space can curve not only around a large massive object but it can also be made to curve similarly around a much, much less massive object that has been accelerated close to the speed of light. This is a perfectly accurate description , but "space" in this description is an amorphous element that is similar to the classical elements of earth, water, fire, and air, as described by early Greek, Japanese, and Hindu civilizations - there is no granularity or definition of what that space represents.

Sakharov was able to see that the geometrodynamics of gravity could just as easily be subsumed within a larger description of the geometry of the energy density of the zpf. In this way gravity can be described similarly to the geometry of isobaric lines of equal air pressure in the atmosphere, but in the case of gravity these lines would instead be spherical surfaces of equal zpf energy density around a massive object. In this conception the spherical surfaces of lowest zpf energy density would be those closest to the massive object or particle and the energy density in space would increase at the rate equal to p − (1 / r²), where r is the distance from the massive object or particle. Here p would be the average density of the zpf over the entire universe at any given moment in the life of the universe. At sufficient distances in open space from the massive body p − (1 / r²) would approximate p.

[edit] Andrei Sakharov and the elasticity of space

It is a fact that Albert Einstein's equation in General Relativity for the geometrodynamics of space is one of the most beautiful equations in physics. Unfortunately, its beauty has resulted in a fixation in the West on the mathematics of geometry, including the geometry of hyper-dimensional space. This focus has resulted in Western mainstream physics ignoring the need for a mathematical definition that connects the classical 4-space, or perhaps 5-space, derived theories of the geometry of space with new quantum mechanical derived ideas that will better correlate with them. Until an explicit mathematical equation is robustly proven to link these two disparate interpretations of physics the first law of thermodynamics for our universe appears to be conceptually violated.

Andrei Sakharov's conception of the elasticity of space, though incomplete, seems to point towards an ultimate resolution of this problem. In his cosmological model space is elastic like the surface of a balloon and thins out as the volume of the universe expands over time. If the three dimensional volume of the universe is represented as a 3-space surface of a balloon, then in its collapsed state at the beginning of time the zpf energy density of the universe is greatest. In approximately the first pico-pico second in the life of the universe the zpf energy density would be extremely high, high enough to create the proton in the hydrogen atom. The proton represents approximately 99.9 percent of the mass of the entire hydrogen atom. The estimated energy density of the physical vacuum at the instant of the proton creation would then represent approximately the amount of energy density recently calculated for the hydrogen atom using stochastic electrodynamics. However, in this conceptual framework this zpf energy density would only exist at precisely this one moment in the life of the universe. Sakharov conceived that at the instant of the creation of fundamental massive particles that the elastic zpf energy required for their mass was transformed into inelastic energy.

Though Sakharov didn't know this when he conceptualized this idea, today our experimental knowledge indicates the proton, which itself is made up of three quarks, is the only fundamental massive particle that does not undergo transformation through radioactive decay if given a long enough time of observation or a large enough quantity of protons being observed.(In the case of neutrinos, they simply transform into other kinds of neutrinos). So his idea seems to fit in with the idea of a type of "absolute" inelasticity that the Standard Model cannot account for.

So a question similar to the question Einstein proposed concerning the non-collapse of the electron into the hydrogen nucleus can be posed for the proton: Why doesn't the proton radioactively decay if the energy density of the physical vacuum is now a tiny fraction of what it was when the proton was created? The principle of asking why is exactly the same even though they apply to different processes. If the zpf energy density decreases over time the statistical probability of both processes occurring should increase. If the proton composes 99.9 percent of the energy of the hydrogen atom, is itself a composite elementary particle, an even more pertinent question would be to ask why the proton doesn't radioactively decay?

Sakharov imagined that spin and its associated angular momentum provided this inelasticity. Spin is a part of 5-space definition that closely correlates with gravity in Kaluza-Klein theory. If one maintains the balloon metaphor then we sew in a round piece of inelastic material into our balloon while it is still in its collapsed state. We are careful to select a piece of inelastic material that has exactly the same density as the same equivalent elastic material surrounding it at that point in its expansion. As we continue to blow up the balloon its elastic material thins out symmetrically except where the inelastic patch is located. Because the area of the inelastic patch does not stretch and thin out the elastic material surrounding it must compensate by stretching and thinning even more than it otherwise would. The greatest thinning will be right on the periphery of the patch in the elastic material because this is the part of the elastic material that has the greatest concentration of stress. If we translate this idea to physics the greatest zpf stress, or thinning out, will be right on the periphery of any massive body and this is where gravity is greatest.

One now returns to the question of where the missing energy went to that is required to support the proton in today's greatly expanded universe. Using pure logic it appears that the proton still has it in the form of energy pulled in from the surrounding physical vacuum. Though the inelasticity between a proton's quarks can by no means account for all the gravity in the universe it certainly can account for nearly all the gravity of nucleons, i.e., protons and neutrons. (A neutron can be included in this because it has very slightly more energy than a proton and will decay into a proton after fifteen minutes if separated from protons.) It seems that the energy density in the universe from that first pico-pico second, at least for protons, is equal to 99.9 percent of the original energy density calculated for the hydrogen atom from stochastic electrodynamics and the Casimir effect. If one accounts only for the gravity of nucleons, which is a very large proportion of the gravity implicitly assigned within the cosmological constant, then a significant proportion of the 10^120 difference between it and the traditional vacuum energy can be resolved simply by subtracting that energy in nucleons from the vacuum energy. Gravity is what makes up this deficit. This is not gravity as we are used to understanding it, but gravity as an energy density gradient in the vacuum spreading out smoothly around any massive object. So it can be seen that the reason the proton does not decay in today's universe is because energy is pulled in from the surrounding physical vacuum. We experience that reduction in energy as gravity.

[edit] Related

In recent years, a number of new age books have begun to appear propounding the view that the zero-point field of physics is the secret force of the universe being used to explain such phenomena as intention, remote viewing, paranormal ability, etc.^[14][15] One of the main purveyors of this view is Stanford physicist Harold Puthoff who spent more than thirty years examining the zero-point field.^[16] Books that promote this view include:

• Lynne McTaggart's 2001 The Field - the Quest for the Secret Force of the Universe.
• Ervin Laszlo's 2004 Science and the Akashic Field - an Integral Theory of Everything.
• Brenda Anderson's 2006 Playing the Quantum Field - How Changing Your Choices Can Change Your Life.

Another popular book that propounds this view in a loose sense is Masaru Emoto's 2005 The Hidden Messages in Water. These views do not, however, have the support of the general scientific community and are typically considered by them to be pseudoscience.^[17]

[edit] References in popular culture

Though seldom used in fiction, the most notable reference to the Zero-point field is the use of ZPMs in the Stargate universe, devices which extract huge amounts of energy from a Zero-point field. In the video game Half-Life 2, there is also a weapon called the Zero-Point Energy Field Manipulator, more commonly known as the "Gravity Gun". In their 1996 fictional book, Encounter With Tiber, Buzz Aldrin and John Barnes have Alpha Centaurians visit Earth in 7200BC using laserable Zero-Point Field-based propulsion to achieve near-light speed travel. In the 2004 animated film The Incredibles, Syndrome's basic weapon is a zero-point energy field.

[edit] References

1. ^ Gribbin, John (1998). Q is for Quantum - An Encyclopedia of Particle Physics. Touchstone Books. ISBN 0-684-86315-4. 
2. ^ H.E. Puthoff,, Scott Little, Michael Ibison, (2000). Ground States and the Zero-Point Field, Earthtech International, Inc
3. ^ ^{a b c} Dodd, John, H. (1991). Atoms and Light: Interactions. Springer, (217). ISBN 0306437414. 
4. ^ Laidler, Keith, J. (2001). The World of Physical Chemistry. Oxford University Press. ISBN 0198559194. 
5. ^ Introduction to Zero-Point Energy - Calphysics Institute
6. ^ ^{a b} Zero-point Energy and Zero-point Field – Calphysics Institute
7. ^ S. Haroche and J.-M. Raimond, “Cavity Quantum Electrodynamics,” Sci. Am., pp. 54-62 (April 1993). Also H. Yokoyama, “Physics and Device Applications,” Science 256, pp. 66-70 (1992).
8. ^ Boyer, T.H. (1980). In Foundations of Radiation Theory and Quantum Electrodynamics (ed. Barut, A.O.), Plenum, New York, 49.
9. ^ McCrea, W.H. (1986). Quart. J. Roy. Astr. Soc. 27, 137.
10. ^ Puthoff, H.E. (1987). Phys. Rev. D. 35, 3266.
11. ^ Rueda, A., Haisch, B. (1998). Found. Phys. 28, 1057.
12. ^ Wheeler, John (1998). Geons, Black Holes, and Quantum Foam: A Life In Physics. Norton & Company. ISBN 0393319911. 
13. ^ Habegger, E.J., Quantum Vacuum Pathway Theory, Space Technology and Applications International Forum, (STAIF 2005), AIP Conference Proceedings 746 , 1379.
14. ^ Brilliant Disguise: Light, Matter and the Zero-Point Field – Bernard Haisch, 2001 Science & Spirit Magazine
15. ^ The Field: The Quest For The Secret Force Of The Universe – Lynne McTaggart, Book Synopsis.
16. ^ McTaggart, Lynne (2007). The Intention Experiment. Free Press, (13). ISBN 0743276957. 
17. ^ Exploiting Zero-point Energy – Philip Yam, Scientific American Magazine, December 1997, pp. 82-85.