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Planck scale

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In particle physics and physical cosmology, the Planck scale (named after Max Planck) is an energy scale around 1.22 × 1019 GeV (the Planck energy, corresponding to the mass–energy equivalence of the Planck mass, 2.17645 × 10−8 kg) at which quantum effects of gravity become strong. At this scale, present descriptions and theories of sub-atomic particle interactions in terms of quantum field theory break down and become inadequate, due to the impact of the apparent non-renormalizability of gravity within current theories.


Relationship to gravity

At the Planck scale, the strength of gravity is expected to become comparable with the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown. The Planck scale is therefore the point where the effects of quantum gravity can no longer be ignored in other fundamental interactions, and where current calculations and approaches begin to break down, and a means to take account of its impact is required.[citation needed]

While physicists have a fairly good understanding of the other fundamental interactions of forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics at very high energies using the usual framework of quantum field theory. At lesser energy levels it is usually ignored, while for energies approaching or exceeding the Planck scale, a new theory of quantum gravity is required. Other approaches to this problem include string theory and M-theory, loop quantum gravity, noncommutative geometry, scale relativity, causal set theory and P-adic quantum mechanics.[1]

Cosmology

In Big Bang cosmology, the Planck epoch or Planck era refers to the earliest stage of the Big Bang, before the time passed was equal to the Planck time, approximately 10−43 seconds. There is no currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time. It is generally assumed that quantum effects of gravity dominate physical interactions at this time scale. At this scale, the unified force of the Standard Model is assumed to be unified with gravitation. Inconceivably hot and dense, the state of the Planck epoch was succeded by the Grand unification epoch, where gravitation is separated from the unified force of the Standard Model, in turn followed by the Inflationary epoch, which ended after about 10−32 seconds (i.e. ten billion times the Planck time).[2]

Expressing fundamental constants in terms of the Planck scale may lead to insights into cosmology.[3] After the measurement of the cosmological constant in 1998, estimated at 10−122 in Planck units, it was noted that this is suggestively close to the reciprocal of the Age of the Universe squared.[4] Barrow and Shaw (2011) proposed a modified theory in which Λ is a field evolving in such a way that its value remains Λ ~ T-2 throughout the history of the universe.[5]

Other uses

The term Planck scale can also refer to a length scale or time scale.

Quantity SI equivalent
Planck time 5.39121 × 10−44 s
Planck mass 2.17645 × 10−8 kg
Planck length (ℓP) 1.616252×10−35 m

The Planck length is related to Planck energy by the uncertainty principle. At this scale, the concepts of size and distance break down, as quantum indeterminacy becomes virtually absolute. Because the Schwarzschild radius of a black hole is roughly equal to the Compton wavelength at the Planck scale, a photon with sufficient energy to probe this realm would yield no information whatsoever. Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole (a.k.a. Planck particle), thus completely distorting that region of space, and swallowing the photon. This is the most extreme example possible of the uncertainty principle, and explains why only a quantum gravity theory reconciling general relativity with quantum mechanics will allow us to understand the dynamics of space-time at this scale. Planck scale dynamics are important for cosmology because if we trace the evolution of the cosmos back to the very beginning, at some very early stage the universe should have been so hot that processes involving energies as high as the Planck energy (corresponding to distances as short as the Planck length) may have occurred. This period is therefore called the Planck era or Planck epoch.

See also

References

  1. ^ Number Theory as the Ultimate Physical Theory, Igor V. Volovich, empslocal.ex.ac.uk/~mwatkins/zeta/volovich1.pdf, 10.1134/S2070046610010061
  2. ^ Edward W. Kolb; Michael S. Turner (1994). The Early Universe. Basic Books. p. 447. ISBN 978-0-201-62674-2. Retrieved 10 April 2010.
  3. ^ P.A.M. Dirac (1938). "A New Basis for Cosmology". Proceedings of the Royal Society A. 165 (921): 199–208. Bibcode:1938RSPSA.165..199D. doi:10.1098/rspa.1938.0053.
  4. ^ J.D. Barrow and F.J. Tipler, The Anthropic Cosmological Principle, Oxford UP, Oxford (1986), chapter 6.9.
  5. ^ John D. Barrow, Douglas J. Shaw, "The Value of the Cosmological Constant", General Relativity and Gravitation 43, 2555-2560 (2011) DOI: 10.1007/s10714-011-1199-1, arXiv:1105.3105.
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