[Paleopsych] SW: Einstein and the Cosmological Constant

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History of Physics: Einstein and the Cosmological Constant
http://scienceweek.com/2005/sw051230-2.htm

    The following points are made by Steven Weinberg (Physics Today 2005 
November):
    1) The mistakes made by leading scientists often provide a better insight 
into
    the spirit and presuppositions of their times than do their successes. In
    thinking of Einstein's mistakes, one immediately recalls what Einstein (in a
    conversation with George Gamow) called the biggest blunder he had made in 
his
    life: the introduction of the cosmological constant. After Einstein had 
completed
    the formulation of his theory of space, time, and gravitation -- the general
    theory of relativity -- he turned in 1917 to a consideration of the 
spacetime
    structure of the whole Universe. He then encountered a problem. Einstein was
    assuming that, when suitably averaged over many stars, the Universe is 
uniform
    and essentially static, but the equations of general relativity did not seem 
to
    allow a time-independent solution for a universe with a uniform distribution 
of
    matter. So Einstein modified his equations, by including a new term 
involving a
    quantity that he called the cosmological constant. Then it was discovered 
that
    the Universe is not static, but expanding. Einstein came to regret that he 
had
    needlessly mutilated his original theory. It may also have bothered him that 
he
    had missed predicting the expansion of the universe.
    2) This story involves a tangle of mistakes, but not the one that Einstein
    thought he had made. First, the author (Weinberg) does not think that it can
    count against Einstein that he had assumed the Universe is static. With rare
    exceptions, theorists have to take the world as it is presented to them by
    observers. The relatively low observed velocities of stars made it almost
    irresistible in 1917 to suppose that the universe is static. Thus when 
Willem de
    Sitter (1872-1934) proposed an alternative solution to the Einstein 
equations in
    1917, he took care to use coordinates for which the metric tensor is
    time-independent. However, the physical meaning of those coordinates is not
    transparent, and the realization that de Sitter's alternate cosmology was 
not
    static -- that matter particles in his model would accelerate away from each
    other -- was considered to be a drawback of the theory.
    3) It is true that Vesto Melvin Slipher (1875-1969), while observing the 
spectra
    of spiral nebulae in the 1910s, had found a preponderance of redshifts of 
the
    sort that would be produced in an expansion by the Doppler effect, but no 
one
    then knew what the spiral nebulae were; it was not until Edwin Hubble 
(1889-1953)
    found faint Cepheid variables in the Andromeda Nebula in 1923 that it became
    clear that spiral nebulae were distant galaxies, clusters of stars far 
outside
    our own galaxy. The author (Weinberg) does not know if Einstein had heard of
    Slipher's redshifts by 1917, but in any case he knew very well about at 
least one
    other thing that could produce a redshift of spectral lines: a gravitational
    field.
    4) It should be acknowledged here that Arthur Eddington (1882-1944), who had
    learned about general relativity during World War I from de Sitter, did in 
1923
    interpret Slipher's redshifts as due to the expansion of the Universe in the 
de
    Sitter model. Nevertheless, the expansion of the Universe was not generally
    accepted until Hubble announced in 1929 -- and actually showed in 1931 -- 
that
    the redshifts of distant galaxies increase in proportion to their distance, 
as
    would be expected for a uniform expansion. Only then was much attention 
given to
    the expanding-universe models introduced in 1922 by Alexander Friedmann
    (1888-1925), in which no cosmological constant is needed. In 1917 it was 
quite
    reasonable for Einstein to assume that the Universe is static.
    Physics Today http://www.physicstoday.org
    --------------------------------
    Related Material:
    ON QUINTESSENCE AND THE EVOLUTION OF THE COSMOLOGICAL CONSTANT
    The following points are made by P.J.E. Peebles (Nature 1999 398:25):
    1) Contrary to expectations, the evidence is that the Universe is expanding 
at
    approximately twice the velocity required to overcome the gravitational pull 
of
    all the matter the Universe contains. The implication of this is that in the 
past
    the greater density of mass in the Universe gravitationally slowed the 
expansion,
    while in the future the expansion rate will be close to constant or perhaps
    increasing under the influence of a new type of matter that some call
    "quintessence".
    2) Quintessence began as Einstein's cosmological constant, Lambda. It has
    negative gravitational mass: its gravity pushes things apart.
    3) Particle physicists later adopted Einstein's Lambda as a good model for 
the
    gravitational effect of the active vacuum of quantum physics, although the 
idea
    is at odds with the small value of Lambda indicated by cosmology.
    4) Theoretical cosmologists have noted that as the Universe expands and 
cools,
    Lambda tends to decrease. As the Universe cools, symmetries among forces are
    broken, particles acquire masses, and these processes tend to release an 
analogue
    of latent heat. The vacuum energy density accordingly decreases, and with it 
the
    value of Lambda. Perhaps an enormous Lambda drove an early rapid expansion 
that
    smoothed the primeval chaos to make the near uniform Universe we see today, 
with
    a decrease in Lambda over time to its current value. This is the 
cosmological
    inflation concept.
    5) The author suggests that the recent great advances in detectors, 
telescopes,
    and observatories on the ground and in space have given us a rough picture 
of
    what happened as our Universe evolved from a dense, hot, and perhaps quite 
simple
    early state to its present complexity. Observations in progress are filling 
in
    the details, and that in turn is driving intense debate on how the behavior 
of
    our Universe can be understood within fundamental physics.
    Nature http://www.nature.com/nature
    --------------------------------
    Notes by ScienceWeek:
    Active vacuum of quantum physics: This refers to the idea that the vacuum 
state
    in quantum mechanics has a zero-point energy (minimum energy) which gives 
rise to
    vacuum fluctuations, so the vacuum state does not mean a state of nothing, 
but is
    instead an active state.
    If a theory or process does not change when certain operations are performed 
on
    it, the theory or process is said to possess a symmetry with respect to 
those
    operations. For example, a circle remains unchanged under rotation or 
reflection,
    and a circle therefore has rotational and reflection symmetry. The term 
"symmetry
    breaking" refers to the deviation from exact symmetry exhibited by many 
physical
    systems, and in general, symmetry breaking encompasses both "explicit" 
symmetry
    breaking and "spontaneous" symmetry breaking. Explicit symmetry breaking is 
a
    phenomenon in which a system is not quite, but almost, the same for two
    configurations related by exact symmetry. Spontaneous symmetry breaking 
refers to
    a situation in which the solution of a set of physical equations fails to 
exhibit
    a symmetry possessed by the equations themselves.
    In general, the term "latent heat" refers to the quantity of heat absorbed 
or
    released when a substance changes its physical phase (e.g., solid to liquid) 
at
    constant temperature.
    The inflationary model, first proposed by Alan Guth in 1980, proposes that
    quantum fluctuations in the time period 10^(-35) to 10^(-32) seconds after 
time
    zero were quickly amplified into large density variations during the
    "inflationary" 10^(50) expansion of the Universe in that time frame.
    --------------------------------
    Related Material:
    COSMOLOGY: ON THE COSMOLOGICAL CONSTANT PROBLEM
    The following points are made by Thomas Banks (Physics Today 2004 March):
    1) Since the mid-1980s, astronomers and astrophysicists have been 
accumulating
    evidence that the expansion of the universe is accelerating. The simplest 
way to
    incorporate that acceleration into the description of cosmology, within the
    framework of general relativity, is to add a cosmological constant (CC) term 
to
    the Einstein equations. Before Edwin Hubble discovered the expansion of the
    universe, Albert Einstein had originally introduced such a term to obtain a
    static solution of his cosmological equations. After the cosmic expansion 
was
    discovered, Einstein considered his introduction of the CC to be the 
greatest
    mistake of his career.
    2) Many physicists were reluctant to consider the CC as an explanation for
    astronomical data, because the value it would need to have is ridiculously 
small
    compared to current theoretical expectations -- some 10^(120) times too 
small.
    Theorists interpreted that discrepancy as an indication that they would one 
day
    find an elegant explanation for why the parameter was exactly zero. Although 
some
    still cling to that hope, the author concludes that observation has once 
again
    upset the expectations of overconfident theorists.
    3) The framework that gives rise to the enormous mismatch between 
calculation and
    observation is called "effective quantum field theory in background 
spacetime",
    or EFT for short. EFT always involves a short distance cutoff scale below 
which
    the approximations of EFT break down. The natural length scale introduced by
    quantum gravity (QG) is the Planck length -- the combination of Newton's
    gravitational constant, Planck's constant, and the speed of light that has 
units
    of length. Naive dimensional analysis and explicit calculations in EFT 
suggest
    that the cosmological constant should be proportional to the fourth power of 
the
    corresponding Planck energy of about 10^(28) eV. That is 10^(120) times too 
big.
    4) Any dynamical solution of the CC problem within EFT should involve 
particles
    whose mass is on the order of the energy scale of the CC, about 10^(-3) eV. 
There
    have been many published attempts to resolve the problem by invoking such
    particles, but all of them have failed. EFT does provide a loophole for 
resolving
    the CC problem: Apart from calculable contributions, there are contributions 
from
    energy scales higher than those corresponding to the cutoff. In principle, 
those
    two types of contributions can cancel, but from the EFT point of view, the
    cancellation to 1 part in 10^(120) would be incredibly fortuitous. The 
author
    believes that the resolution of the CC problem does not involve some clever 
trick
    in EFT. Rather, QG will force on theorists a fundamental revision of the 
rules of
    the game. This belief is not yet the accepted dogma of the field. There are 
as
    many ideas about how to solve the CC problem as there are theorists who 
think
    about it.(1-5)
    References (abridged):
    1. G. 't Hooft, in Salamfestschrift: A Collection of Talks From the 
Conference on
    Highlights of Particle and Condensed Matter Physics, A. Ali, J. Ellis, S.
    Randjbar-Daemi eds., World Scientific, River Edge, NJ (1994), available at
    http://www.arXiv.org/abs/gr-qc/9310026; L. Susskind, J. Math. Phys. 36, 6377
    (1995)
    2. J. H. Schwarz, in Quantum Aspects of Gauge Theories, Supersymmetry, and
    Unification, A. Ceresole, C. Kounnas, D. Loest, S. Theisen, eds.,
    Springer-Verlag, New York (1999), available at
    http://www.arXiv.org/abs/hep-th/9812037
    3. T. Banks, in Strings, Branes, and Gravity: TASI 99, J. Harvey, S. Kachru, 
E.
    Silverstein, eds., World Scientific, River Edge, NJ (2001), available at
    http://www.arXiv.org/abs/hep-th/9911068; D. Bigatti, L. Susskind,
    http://www.arXiv.org/abs/hep-th/9712072; O. Aharony et al., Phys. Rep. 323, 
183
    (2000)
    4. L. Susskind, in The Black Hole: 25 Years After, C. Teitelboim, J. 
Zanelli,
    eds., World Scientific, River Edge, NJ, (1998), available at
    http://www.arXiv.org/abs/hep-th/9309145; A. Sen, Nucl. Phys. B 440, 421 
(1995);
    A. Strominger, C. Vafa, Phys. Lett. B 379, 99 (1996)
    5. J. Bekenstein, Phys. Rev. D 7, 2333 (1973); 9, 3292 (1974); S. Hawking 
Phys.
    Rev. D 13, 191 (1976)
    Physics Today http://www.physicstoday.org



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