[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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