Fact and Fiction

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Thursday, February 09, 2006

The cosmic landscape: chapter 2

This is my interpretation of chapter 2 of Leonard Susskind's book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design.

Susskind uses this chapter to introduce the problem that physics has with correctly predicting the value of the cosmological constant. What we naively call the "vacuum" actually contains a seething mass of virtual particles (or vacuum energy), because that is what is implied by our most fundamental theory of how physics operates (i.e. quantum field theory). This mass will affect the gravitational field and thus have observable consequences.

Unfortunately, our fundamental physics theory predicts an infinite (or, at least, very large) vacuum energy, which is not what we observe experimentally. The discrepency is about 120 orders of magnitude!

Susskind then describes the cosmology that was introduced by Einstein (i.e. a static universe governed by the equations of general relativity), by introducing the analogy that space is like the surface of a balloon, where the tension in the ballon is analogous to a gravitational attraction that causes all objects in space (e.g. galaxies) to attract one another. Thus an additional repulsive force is needed to hold the galaxies apart from each other. Einstein noticed this problem, and introduced a suitable term into his equations to provide the necessary repulsive force; this was his famous cosmological constant.

It turned out that Einstein's cosmology was wrong, because the astronomer Edwin Hubble observed that galaxies actually recede from each other, so the universe was not static, so Einstein had no need for a non-zero cosmological constant.

Now, Einstein's cosmological constant is physically the same thing as the vacuum energy mentioned above, so we know that it is non-zero, and in fact we predict (by adding up the effects of all of the virtual particles) that it has a value that is enormously too large. We know the value is too large because this vacuum energy implies the existence of a gravitational field that is not actually observed.

Even calculating this vacuum energy is fraught with problems because a naive calculation gives an infinite result, so we have to make some adjustments to the calculation in order to eliminate the infinity in a "natural" way. The method used is to ignore the contributions from all virtual particles that are so energetic that they would form a black hole if they collided.

One possible way of predicting a zero vacuum energy is to notice that virtual bosons (e.g. photons) have positive vacuum energy, whereas virtual fermions (e.g. electrons) have a negative vacuum energy, so there is the possibility that they produce cancelling effects. Unfortunately, such a cancellation does not materialise for the known types of bosons and fermions. However, if the universe were such that bosons and fermions existed in matched pairs (which they don't!), then cancellation would occur; this is what happens in the so-called supersymmetric theories.

Finally, Susskind points out:
  1. Cosmologists regard the cosmological constant as something with a small non-zero value that needs to be measured.
  2. Physicists (especially string theorists) regard it as something with an exactly zero value that is produced by an as-yet-not-understood cancellation in their theory.

However, there is a Third Way! It is called the Anthropic Principle: some property of the universe must be the way it is, because if it wasn't then we wouldn't be here to observe it. Can this approach be used to explain the values that fundamental physical constants? Should this approach be used, or is it not even science?

Generally, physicists hate the Anthropic Principle for various reasons:

  1. It abandons their cherished hope of deriving everything from first principles. It questions the very root of what science is, and if it turns out to be true it would certainly be a "new kind of science". This possibility cannot be discounted.
  2. It smells suspiciously like an "intelligent design" argument, where the properties of the universe are tuned so that we can exist. In fact, this suspicion is ill-founded, because it fails to recognise the difference between the weak and strong forms of the Anthropic Principle (see the last paragraph below). This possibility is based on a misunderstanding, and can thus be discounted.

Steven Weinberg has looked closely at the Anthropic Principle, and he concluded that a value that is not much larger than the observed upper bound would prevent galaxies, stars and planets from forming from the original very small density fluctuations that existed in the matter distributed throughout the universe. These sorts of arguments can also be used to place a bound on how negative the cosmological constant can be, and again its magnitude has to be extremely small.

Steven Weinberg has thus used the Anthropic Principle to place bounds on the magnitude of the cosmological constant that are consistent with observations. This work has been largely ignored because physicists mistakenly assume that it is necessarily based on an "intelligent design" argument. This is not the case if there is an ensemble of universes each with its own laws of physics, one of which is the fortuitously tuned version that we observe around us

Susskind then describes a thought experiment in which he rediscovers the "natural" (i.e. Planck) units of length, time and mass. These units turn out to be fundamentally important in the unification of quantum theory and Einstein's general theory of relativity, because they tell us where the naive picture of space as being analogous to a smooth rubber sheet breaks down (i.e. Einstein's gravity) to be replaced by a deeply wrinkled and knotted surface (quantum gravity).

The most important thing to understand in this chapter is the Anthropic Principle, which is not an "intelligent design" argument. None of Susskind's book will make sense until it is appreciated that Susskind is using the weak form of the Anthropic Principle, in which there is no prior tuning of the laws of physics, but rather there is an ensemble of universes each with its own laws of physics, one of which is the fortuitously tuned version that we observe around us.

10 Comments:

At 10 February 2006 at 17:11, Blogger island said...

Hi Steve,

I'll try not to detract from your review too much, but his one really hits home for me, because my understanding is that Einstein wasn't wrong at all if negative energy states as having negative pressure, where...

P=-u=-rho*c2

The energy density of the vacuum is less than the matter density, so particles don't arise until vacuum energy gets condensed down over a finite enough area of space to attain positive matter density. In this case, the antigravity effect of the negative pressure vacuum mimics the effect of Dirac's negative mass states, which takes modern physics all the way back to 1917:

http://www.lns.cornell.edu/spr/2005-06/msg0069755.html

In Einstein's static model, G=0 when there is no matter. The cosmological constant came about because we do have matter, so in order to get rho>0 out of Einstein's matter-less model, you have to condense the matter density from the existing structure, and in doing so the pressure of the vacuum necessarily becomes less than zero, P(less-than)0.

The most obvious way to create new matter in Einstein's model, (the most compatible with the spirit of general relativity), also holds it flat and stable, so any other conclusions that have been made since Einstein abandoned his notion without this knowledge, are therefore subject to suspect review, because he could have rejected arguments against his finite model based on the above.

 
At 11 February 2006 at 21:45, Blogger Steve said...

...you have to condense the matter density from the existing structure...

This is the key assumption in your argument. If this is not the case, then your conclusions do not follow. Yes?

Particle creation/annihilation according to one's favourite time evolution operator is the means by which the universe gets from one state to another, but this doesn't constrain the initial state.

Your argument assumes a very special type of initial state. Yes?

 
At 11 February 2006 at 22:15, Blogger island said...

This is the key assumption in your argument. If this is not the case, then your conclusions do not follow. Yes?

No, this falls directly from Einstein's finite model, and there is no discrepancy with the quantum expectation for the energy of this ground state, because it requires a greater volume of the vacuum each time that you make a particle.

The graviational acceleraton is zero if the density of the static vacuum is -0.5*rho(matter) because,

rho+3P/c^2=0

... so you have no choice, but to condense this energy in order to attain the matter density.

Particle creation/annihilation according to one's favourite time evolution operator is the means by which the universe gets from one state to another, but this doesn't constrain the initial state.

Your argument assumes a very special type of initial state. Yes?


I'll tell you what... here is a very clear but somewhat popularized treatment by Ned Wright, where you can ascertain everything that I've said:

www.astro.ucla.edu/~wright/cosmo_constant.html

I promise you that I would prove this outright, myself, if I could write down the basis of wave functions in this background, including an expansion of the field in corresponding creation and annihilation operators - compute the stress-energy tensor in that background - quantitatively describe the vacua - and then work out the matrix elements of the stress-energy tensor between the vacuum and the one-particle states.

But... I can't, because I don't have nearly enough math for this level of physics... so I try to provoke people like you into doing it... ;)

See Ned's website for yourself, Steve... I'm not wrong about this.

It's very simple...

What happens to the vacuum when you rip out a chunk of its energy to make a real particle with.

 
At 11 February 2006 at 23:06, Blogger island said...

"What happens to the vacuum when you rip out a chunk of its energy to make a real particle with?"

Tension between the vacuum and ordinary matter grows as the vacuum expands, because the increase in negative pressure that results from rarefaction of the vacuum energy, gets offset by the increase in positive gravitational curvature that results from particle creation in this model.

So tension grows until the forces that bind the finite closed spherical universe are compromised and the universe has ANOTHER Big Bang.

Causality... and the second law of thermodynamics is never violated when you make massive particles from negative pressure energy.

Boom, what happens to the need for inflationary theory if the universe has volume when a big bang occurs?

It becomes null and void.

This simple physics very simply resolves ALL of the problems on this page if you think about it for about two seconds:

http://zebu.uoregon.edu/~imamura/209/mar31/anthropic.html

... and it also solves all of the problems on this page, with just a little more thought:

http://math.ucr.edu/home/baez/physics/General/open_questions.html

 
At 11 February 2006 at 23:11, Blogger island said...

Sorry for the broken links:

zebu.uoregon.edu/~imamura/
209/mar31/anthropic.html

math.ucr.edu/home/baez/physics/
General/open_questions.html

 
At 12 February 2006 at 00:47, Blogger Steve said...

I never believe "popularised" or "intuitive" arguments about the type of physics that is governed by quantum field theory (or by general relativity). I prefer to see what the field operators are doing, so I can understand the physics from the bottom-up.

Anyway, none of the above is really necessary here, because the original point that prompted all of this was:

It turned out that Einstein's cosmology was wrong, because the astronomer Edwin Hubble observed that galaxies actually recede from each other, so the universe was not static, so Einstein had no need for a non-zero cosmological constant.

If you are disagreeing with this statement, then you will have to take it up with Susskind, not me, because in that part of what I wrote I was merely paraphrasing what he says in his book. This is usually regarded as fairly uncontroversial material!

 
At 12 February 2006 at 01:02, Blogger island said...

If you are disagreeing with this statement, then you will have to take it up with Susskind, not me...

I don't disagree with the logic that was used, but Einstein didn't know that he had need for a non-zero cosmological constant, because he didn't even know about the particle potential of the quatum vacuum in 1917.

I never believe "popularised"...

I'm sorry, I shouldn't have shown that much disrespect for Ned Wright's work on this, which includes all the necessary physics to make for a valid scientific paper.

There is nothing wrong with thought experiments that apply this hard established physics.

Get into a sealed jar and remove all pressure. Now, "super"-compress some of the remaining vapor pressure, until you attain the matter density.

You can only generate matter from this energy by increasing negative pressure.

Antiparticles don't fall up because antimatter no longer has negative pressure.

Too obvious, sorry.

 
At 12 February 2006 at 01:41, Blogger island said...

Just to cover my butt with you, Steve, I'll retract everything beyond the following that was made in direct response to your question, so as not to further detract from your review.

The following physics stands alone, without need for appeal to any other references or elaboration:

You asked:
This is the key assumption in your argument. If this is not the case, then your conclusions do not follow. Yes?

No, this falls directly from Einstein's finite model, and there is no discrepancy with the quantum expectation for the energy of this ground state, because it requires a greater volume of the vacuum each time that you make a particle.

The graviational acceleraton is zero if the density of the static vacuum is -0.5*rho(matter) because,

rho+3P/c^2=0

... so you have no choice, but to condense this energy in order to attain the matter density.

Einstein was not wrong until somebody does the math to prove that I am.

Sorry for the interruption.

 
At 27 June 2006 at 00:31, Blogger caterpillar said...

Hi Steve,

I must say I loved your exposition on Kate Bush's Pi. I'm thinking of heading over to Cornwall to take a look around myself. But to get to matters more germane, you might not know about this story of anthropic physics:

Guardian | Open minds reap rewards

PS. Did you throw that KB SL bit into the Pi story just for fits and giggles?

 
At 27 June 2006 at 17:08, Blogger Steve said...

I knew about Fred Hoyle's anthropic argument for the Carbon-12 state. There are other examples in the literature, such as Steven Weinberg's bounds on the cosmological constant.

To reiterate, the weak anthropic principle might well turn out to be the "way things are". This would fit in with the idea that there is an enormous "landscape" of possible universes, so we should not be surprised to find ourselves in one that suits life so well.

As for your off-topic comments about KB: My Bertie posting about KB/SL was posted on 1st April 2006. However, there is so much interesting and repeated structure in "Bertie" (which I have not commented on yet) that I am certain that KB has been hiding information in "Bertie".

 

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