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Question
Can quantum fluctuation create something from "nothing" (a vacuum)? In quantum cannot electrons and photons (which are waves and particles) go in and out of existence and also be created at different places at the same time?

Answer
Hello, Charles

First, 'nothing' in physics terms is generally taken to refer to a negative energy quantum vacuum. Perhaps one of the best recent books on the topic is: 'The Quantum Vacuum' by Luciano Boi (Johns Hopkins University Press, 2011) who notes on page 62:

"The vacuum state is not an empty state but rather a sea filled with negative energy electrons. The sea as a universal background is itself unobservable"

The above concept known as the "Dirac Vacuum" has since been extended to modern cosmology and invoked for assorted models (e.g. Padmanabhan, T. 1983, ‘Universe Before Planck Time – A Quantum Gravity Model, in Physical Review D, Vol. 28, No. 4, p. 756.)

In his paper, Padmanabhan showed the instantaneous formation of the universe is feasible from a quantum fluctuation when the conformal part of space-time is treated as a *quantum variable*.

Without going into all the complex mathematics entailed, Padmanabhan employed integrals related to the “action” (J) as a function of time. He proceeded by solving for the expansion factor S(t) using two separate energy equations, one of which (2.15 in his paper) bears a remarkable resemblance to the basic quantum wave equation. The potential energy term is remarkably similar to that for the quantum harmonic oscillator.

The most masterful section in his paper is III. ‘Geometry of the Quantum Universe’ wherein spacetime itself is taken to be in a particular quantum state F(q, t). He then assumes “stationary states” (given by the variable Q) for the early universe that are independent of time and for which all the dynamics “are contained in S(t)” (ibid., p. 28). The form of the expression for his “energy content” of the universe,  (t) also bears a remarkable structural similarity to the equation given earlier for total energy in an expanding cosmos.

The conformal factor Padmanabhan uses is alpha, which is a purely quantum mechanical parameter, defined from his equation (2.24. Physically, it is found that the conformal factor  contributes a negative energy density consistent with Boi's thesis.


While this paper is highly technical, a much more accessible introduction to these concepts can be gained from Lawrence Krauss' book, 'A Universe From Nothing'. Especially Chapters 4, 9 and 10. I definitely recommend this book to you for a more complete understanding than is possible to give in an All Experts format.


Regarding your question of particles (electrons, photons) "going in and out of existence, you are referring here to particle production - wherein particles are created then quickly destroyed with energy release. For example, the typical pi meson (call it pi) lasts 10^-16 sec then vanishes yielding two gamma ray photons in its wake, viz.

Pi -> gamma + gamma

Thus, rest energy is real energy and is capable of doing work. In the case of the pion above, the total mass 2.4 x 10^-28 kg, is converted to electromagnetic energy.

The amount of the energy can be estimated using the Heisenberg Uncertainty Principle in the energy-time format:

Delta (E) Delta (t) less than h/bar

Where h-bar = h/ 2 pi with h = 6.62 x 10^-34 J-s (the Planck constant)

Thus – if the time uncertainty for disappearance of the pi meson is dt = 10^-16s

Then the energy available that comes off, using the energy-time uncertainty principle, is:

Delta (E) = (h-bar)/ delta t = 1.054 x 10^-18 J = 6.5 eV

In the same manner, a number of theoreticians (e.g. T. Padmanabhan) have speculated the universe could have emerged like the pi meson using the same basis for energy arising out of “nothing”. The difference is that the emergence of the cosmos would be from a negative energy background.

Again, these are difficult concepts - especially if you've never taken physics courses-   which is why getting Krauss' book is so important to your more complete understanding.  

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I specialize in stellar and solar astrophysics. Can answer questions pertaining to these areas, including: stellar structure and evolution, HR diagrams, binary systems, collapsars (black holes, neutron stars) stellar atmospheres and the spectroscopic analysis of stars – as well as the magnetohydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions. No nonsense questions accepted, i.e. pertaining to astrology, or 'UFOs' or overly speculative questions: 'traveling through or near black holes, worm holes, time travel etc. Absolutely NO questions based on the twaddle at this Canadian site: http://members.shaw.ca/warmbeach/FAQ.htm purporting to show a "new physics". Do not waste my time or yours by wasting bandwidith with reference to such bunkum.

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Have constructed computerized stellar models; MHD research. Gave workshops in astrophysics (stellar spectroscopy, analysis) at Harry Bayley Observatory, Barbados. More than twenty years spent in solar physics research, including discovery of SID flares. Developed first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Developed first ever loop-based solar flare model using double layers and incorporating cavity resonators. (Paper presented at Joint AGU/AAS Meeting in Baltimore, MD, May 1994)

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American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

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Papers appearing in Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Fundamentals of Solar Physics', 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level', 'Astronomy & Astrophysics: Notes, Problems and Solutions', 'Modern Physics: Notes, Problems and Solutions'

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B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

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Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society. Barbados Astronomical Society award for service (1977-91) as Journal editor.

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