Zero point energy

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The zero point energy (also ground state energy or vacuum energy or quantum vacuum ) is the difference between the energy that a quantum mechanical system has in the ground state and the energy minimum that the system would have if it were described in a classic way. In thermodynamic systems that exchange energy with their environment, the zero point energy is therefore also the same as the energy of the system at absolute temperature zero .

Potential function of the harmonic oscillator (red).
A particle in this potential can only take on certain energies (blue), the lowest possible of these energies is above the minimum potential

One-dimensional single-particle systems

The zero point energy is usually introduced on the basis of one-dimensional systems of a particle in a potential . In classical (that is, non-quantum mechanical) physics, the lowest energy state is that in which the particle is at rest in the minimum potential. In quantum mechanics, the smallest achievable energy can be above the value of the minimum potential. For given example systems, this can be verified by explicitly determining the energy eigenstates .

Alternatively, this result can be obtained by using the uncertainty relation: A finite positional uncertainty, e.g. B. present in bound states , generally requires a pulse uncertainty greater than zero. Hence the momentum and kinetic energy cannot be exactly zero. Since the kinetic energy cannot become negative:

the total energy, the sum of potential energy and kinetic energy, must therefore be greater than the minimum of the potential energy:

Harmonic oscillator

The standard example of zero point energy is the quantum mechanical harmonic oscillator . This one has the potential energy

With

This potential has a minimum at and leads to an energy spectrum

With

Even in the energetically lowest state, the basic state with , there is an energy different from zero:

In the classical case of the lowest energy state is the one in which the particle at rest, ie . In quantum mechanics, however, the uncertainty relation between position and momentum forbids that both quantities have exact values. The more precisely the location is known, the less precisely the impulse is known and vice versa. The zero point energy clearly results as the mean value of these fluctuations.

Observations

The Casimir effect and the Lamb shift are often interpreted as experimental evidence for the zero point energy and the vacuum fluctuations caused by it . However, it is possible to derive the Casimir effect without resorting to vacuum fluctuations. The Lamb shift is a phenomenon in an interacting quantum field theory , which accordingly cannot be traced back to the vacuum energy; The misunderstanding arises from the fact that although it is a sequence of virtual particles - antiparticles - pair formation , which does not take place from the vacuum, but is based on interactions between fields.

The vacuum energy is considered a possible candidate for the dark energy , which in astronomy would offer an explanation for the observed accelerated expansion of the universe . In this context, the amount of vacuum energy represents one of the greatest problems of modern physics, since the experimentally found and the theoretically predicted values ​​for the vacuum energy as dark energy differ from each other: Based on observations, the energy density of the vacuum is reduced to a value of the order of 10 - 9 to 10 −11  J / m³, which is around a factor of 10 120 lower than in the theoretical calculations.

Historical development

After abandoning the aether filling empty space as a medium for the propagation of waves and a frame of reference for the movement of bodies, the idea of ​​a vacuum containing neither matter nor any form of energy prevailed in classical physics .

However, the radiation law of his "second theory" discovered by Max Planck in 1911 suggested zero-point energy of the electromagnetic field in a vacuum, since a variable ½ was independent  of temperature . However, Planck initially did not consider this to be of any significance in terms of experimental evidence.

With similar considerations came Albert Einstein and Otto Stern in 1913 to the conclusion that the zero point fluctuations of the electromagnetic field at the absolute zero of temperature at BE REDUCED.

Building on Planck's work, Walther Nernst proposed zero point fluctuations for the electromagnetic field around the value ½  on the one hand and that the entire universe was filled with zero point energy on the other.

In 1927 Werner Heisenberg formulated his uncertainty principle , which is considered the basis of the zero-point energy in every quantum mechanical system.

Georges Lemaître , who had done pioneering theoretical work on the Big Bang and the expansion of the universe, found in 1934 a match between the vacuum energy and Einstein's cosmological constant (1917), the introduction of which Einstein later described as the "greatest donkey" of his life.

In an investigation of the Van der Waals forces in colloid solutions, Hendrik Casimir and Dirk Polder used a quantum mechanical approach in 1947, which led to a discussion with Niels Bohr . Bohr commented on this, "that must have something to do with zero point fluctuations". Casimir pursued the idea that the attraction between neutral atoms might only be based on vacuum fluctuations, and in 1948 published his seminal work On the Attraction Between Two Perfectly Conducting Plates . In it he described a theoretical test arrangement with two metal plates in a vacuum, which according to his calculations should attract each other due to the vacuum energy of the electromagnetic quantum field (Casimir effect).

The first corresponding tests to prove the Casimir force in a vacuum were carried out by Marcus Sparnaay in 1958 , but with a measurement error of around 100%. Gradually the measurements of the Casimir force (value for two mirrors of 1 cm² area at a distance of 1 µm: 10 −7  N) achieved a higher accuracy, e.g. For example, the measurement error for van Bloklands and Oveerbeeks in 1978 was 25% and for Steven Lamoreaux in 1996 it was only 5%.

In recent years, the cosmological constant, which is closely related to the curvature of space-time , has again received more attention, especially since it is now viewed as a small positive energy density of the vacuum. A more recent explanation for the cosmological constant provides, for example, a cyclic universe.

Popular culture

In various film- pean works the zero-point energy is the energy source or shape described:

Individual evidence

  1. Harald Lesch: Zero point energy (also vacuum energy) . Retrieved January 20, 2017.
  2. Martin Bäker: The vacuum energy and the Casimir effect .
  3. F. Schwabl: Quantenmechanik , 6th edition, chapter 3.1.3, ISBN 3-540-43106-3 (google books)
  4. ^ RL Jaffe: The Casimir Effect and the Quantum Vacuum . In: Physical Review D . Volume 72, 2005 ( arxiv : hep-th / 0503158 )
  5. J. Baez. What's the energy density of the vacuum? , 2006.
  6. SM Carroll: The Cosmological Constant ( Memento of the original from August 29, 2016 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. , 2001. @1@ 2Template: Webachiv / IABot / relativity.livingreviews.org
  7. A. Tillemans. Plato's allegory of the cave and the vacuum energy of the universe. In: Wissenschaft.de. August 19, 2002, accessed September 8, 2019 .
  8. Max Planck : A new radiation hypothesis . In: Negotiations of the German Physical Society . Volume 13, 1911, pp. 138-148.
  9. a b c B. Haisch, A. Rueda and Y. Dobyns: Inertial mass and the quantum vacuum fields . In: Annals of Physics . Volume 10, 2000, pp. 393-414. arxiv : gr-qc / 0009036 .
  10. Walther Nernst : About an attempt to return from quantum theoretical considerations to the assumption of constant energy changes . In: Negotiations of the German Physical Society . Volume 4, 1916, p. 83.
  11. Werner Heisenberg : About the descriptive content of quantum theoretical kinematics and mechanics . In: Journal of Physics . Volume 43, 1927, pp. 172-198. doi : 10.1007 / BF01397280 .
  12. J.-P. Luminet: The Rise of Big Bang Models, from Myth to Theory and Observations . 2007, arxiv : 0704.3579 .
  13. a b A. Lambrecht: The vacuum gains strength . In: Physics in Our Time . Volume 2, 2005, pp. 85–91, bibcode : 2005PhuZ ... 36 ... 85L .
  14. Hendrik Casimir : On the attraction between two perfectly conducting plates . In: Proc. Con. Ned. Akad. Van Wetensch . B51 (7), 1948, pp. 793-796. reprint online
  15. ^ MJ Sparnaay: Measurements of attractive forces between flat plates. In: Physica. 24, 1958, p. 751, doi: 10.1016 / S0031-8914 (58) 80090-7 .
  16. ^ R. Onofrio: Casimir forces and non-Newtonian gravitation . In: New Journal of Physics . Volume 8, 2006, p. 237 Abstract .
  17. PHG M van Blokland and JTG Oveerbeek: The measurement of the van der Waals dispersion forces in the range 1.5 to 130 nm . In: Journal of the Chemical Society Faraday Transactions . Volume I74, 1978, p. 2637.
  18. SK Lamoreaux: Demonstration of the Casimir force in the 0.6 to 6 µm range . Physical Review Letters . Volume 78, No. 1, 1997, pp. 5-8 Abstract .
  19. SM Carroll: The Cosmological Constant ( Memento of the original dated August 29, 2016 in the Internet Archive ) Info: The @1@ 2Template: Webachiv / IABot / relativity.livingreviews.org archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. . 2001.
  20. ^ Paul Steinhardt and N. Turok: A Cyclic Model of the Universe . In: Science . Volume 296, No. 5572, 2002, pp. 1436-1439 abstract .
  21. Zero point module. The German-language Stargate Lexicon. In: Stargate Wiki. Retrieved February 9, 2016 .
  22. ^ Herman Zimmerman , Rick Sternbach , Doug Drexler : Star Trek: Deep Space Nine - The Technical Manual, Simon & Schuster POCKET BOOKS, New York 1998, p. 85.