Thanks for the time and effort.

Regards,

JBMjr.

I think in the next couple of decades some work with deep space astronomy and some new particle physics experiments is going to lead to data supporting an emergent theory of quantum gravity and cosmology. What does emerge might be different from what is now thought. We will just have to see how things develop.

Lawrence B. Crowell

The cosmological constant is due to an inherent curvature to spacetime.

Presumably an opposite curvature then that commonly associated with gravity. Sort of like a hill is the opposite of a valley?

p is the momentum, q the position, f the frequency, and the mass term has been absorbed in these.

So you don’t think there is any possibility that radiation can have the effect of curving space, as recorded by light, such as redshifting it, without having equal effect on the position of emitting objects? I should point out that light passing through a gravity field is curved, but that doesn’t mean the source is moved by this effect. At least there would be no need for ZPE, or dark energy, to explain why space appears to expand, if this is a possibility.

The recent posting by Sean, on the article by Dennis Overbye about Boltzmann brains, is a pretty graphic example of the problems cosmology is having in trying to fit together all the current concepts that are considered resolved. Do you think the answers will suddenly become clear, or is cosmology headed down the path of becoming a scientific laughingstock?

H = 1/2(p^2 + f^2q^2)

where p is the momentum, q the position, f the frequency, and the mass term has been absorbed in these. Now if I add a term i(qp - pq) [i = sqrt{-1}] classically by commutivity this is zero. Yet if I write the momentum and position variables in quantum operator form this commutator is not zero. The hamiltonian for the Harmonic osciilator is

H = hbar-f/2(a^*a + aa^*) = hbar-f(a^*a + 1/2)

where I have added a^*a - a^*a = 0 and this gives a commutator

[a, a^*] = aa^* - a^*a = 1.

Now if I do this quantization on the classical level with the zero commutator added in with the classical variables

[p, q] = pq- qp = 0

and then quantized I can eliminate the ZPE term hbar-f/2. Classical mechanics has commutivity of variables, but when quantized that commutivity is lost, such as [q, p] = i hbar.

A common way of doing this is something called normal ordering. This is somewhat justified by the fact there is no classical content to the ZPE. This is what I have just argued for. The traditional approach to the cosmological constant is to take a ZPE vacuum energy and construct the cosmological constant from a momentum-energy tensor constructed from ZPE terms. This causes all sorts of problems. A straight ZPE constructed this way predicts a cosmological constant 123 orders of magnitude larger than what is observed. Other horrors rear their head, and in a way they are related to this problem of the “dark misleading force.”

The cosmological constant is due to an inherent curvature to spacetime. It is not due to a source, such as a “dark misleading force.” Yet if we pause for a minute we might think of a ZPE energy as having a mass-energy content and that this is something which could couple to a spacetime manifold. So is this inherent curvature induced by the cosmological constant related in some way to a quantum ZPE? Probably, but not quite in the naive way we do this. To work on this involves walking through a minefield. Huge amounts of confusion lies here, such as ideas that virtual loops and the like are some real aspect of the vacuum and so forth. Yet this does indicate some subtle connection between general relativity and quantum field theory. Yet I think this connection is far more subtle than what is thought by most.

Lawrence B. Crowell

a|n) = sqrt{n}|n-1) —> reduces the number of particles

and

a^*|n) = sqrt{n+1}|n+1).

The Hamiltonian or energy operator turns out to be

H = hbar-freq(a^*a + 1/2).

These operators are derived from the form of the classical Hamitlonian for the harmonic oscillator, such as a spring of a pendulum with small oscillations. This Hamiltonian operator then acts on a state |n) as

H|n> = hbar-freq(n + 1/2)|n),

and there is this energy for the vacuum state |0). This is sometimes called the zero point energy (ZPE), which is an artifact of quantization. It can be removed by various techniques.

There is a lot of nonsense about the ZPE, such as people who think it is a source of free energy. But anyway this is what I was meaning by the vacuum state. In the case I wrote this morning I am referring to a vacuum state associated with a quantum wave function(al) for a metric spacetime configuration variable. A vacuum for this state means the spacetime in a sense does not exist.

BTW, normally the state vector is written with the horizontal carrot instead of a paranthesis, but this system seems to not like them.

Lawrence B. Crowell

Lemaitre was working as an honest theoretical physicist, and said the origin of the big bang was something similar to the radioactive decay of an atom. Replace atom with an unstable vacuum configuration and this statement was not too far off the mark.

Pardon my conceptual immaturity, but I see the difference between a primordial atom and unstable vacuum, as that between a dimensionless point and unstable, but otherwise featureless, space. In other words, is the initial state bound up in a single point, from which everything grew/expanded, or does it rise from an infinite, unstable vacuum?

The origin of entropy in the universe I think comes from the self-squeezing of the vacuum state for gravitation.

Since this unstable vacuum would have to expand, otherwise it wouldn’t be unstable, the reaction is that at a certain level, it collapses and this effect builds on itself, creating ever larger regions of collapse. They then reach a state of density caused by this collapse not efficiently neutralizing the instability and bouncing back out as radiation. This radiation further destablizes the vacuum, causing it to continue expanding and so on….

Lemaitre did not propose the big bang as a support for Genesis. In fact he admonished Pope Pius XII not to encorporate this into an infallibility doctrine supporting the Church’s theology on creation. Lemaitre was working as an honest theoretical physicist, and said the origin of the big bang was something similar to the radioactive decay of an atom. Replace atom with an unstable vacuum configuration and this statement was not too far off the mark.

Back to the origin of entropy. The conformal group su(4) ~ so(4,2) contains the deSitter (dS) and Anti-deSitter (AdS) group. The AdS exists in a five dimensional space with two timelike directions, and as a result it has cyclic timelike solutions. So one selects out a patch with a pi cycle on the timelike directions. The conformal infinity of this is a Minkowski spacetime. The rub with this is that no amount of data on a spatial surface in AdS can uniquely give this conformal infinity. So additional data or boundary conditions are needed. I think this additional data is given by black holes and their brane dual as condensates of gauge fields, similar to the quark-gluon plasmas being probed at RHIC. This determines the cosmological constant /\ = /\_0 + k*F^{ab}F_{ab}, where phi is the dilaton field with a quartic potential, k = constant, and F^{ab} a Yang-Mills field tensor. This data then provides the conformal completeness of the S \subset AdS, or S = pi-cycle patch.

The initial state of the universe consisted of some set of unitarily inequivalent vacua, which under a coarse graining define an entropy to spacetime. This initial entropy was low, where by initial I mean during the inflationary period. The entropy increases until the cosmos expands as time “goes to” infinity to a deSitter space with the cosmological constant /\ and horizon radius r = sqrt{3/ /\}. Hawking-Gibbon radiation will cause this to decay, similar to the emission of radiation from black holes, so that /\ approaches zero value and the spacetime is a flat Minkowski spacetime with nothing. This matches the dS with the AdS at conformal infinity, is a state with a single vacuum, but at maximal entropy. I think that how the universe started out with minimal entropy and with the structure of elementary particles we observe is in order to give this conformal completeness on AdS, and further to define the conformal group su(4) with a single vacuum states “at infinity.”

In spite of the 13.7 billion year age of the universe it is an infant compared to the time left in the future, which is infinite or “nearly so.” Things are going to get cold and dark and eventually everything will fade into nothingness and a complete void defined by a Minkowski spacetime. This is the endpoint of the Feynman path integral of the universe, while the initial state with a set of inequivalent set of vacua is the initial point. The path integral has a finite meaning when the conformal infinity is “mapped” to a finite value.

Lawrence B. Crowell

So this low entropy state just sprang into existance with the singularity and we are not supposed to look behind that curtain. That would be like questioning, uh…God!

I have no fear that Big Bang Theory is going anywhere anytime soon, because the basic premises on which it is based go back to the roots of western civilization. We would literally have to throw out the Bible, go back to before the time the Greeks were seduced by monotheism and reopen the debate between Plato and Aristotle. The absolute isn’t one, it’s zero. It’s not an ideal from which we fell, but the essence out of which we rise. It’s not the singularity, but the vacuum. Not the dimensionless point, but empty space. That an incredibly complex mathematics has been developed to support it, isn’t proof it’s right. Remember epi-cycles?

Time is not a linear dimension from start to finish, Genesis to Armageddon, birth to death, prologue to epilogue. It’s a cycle. Expansion, contraction. Mass/order collapses. Energy expands. Order falls away into the past, as energy moves into the future.