The Weakness of the Weak Anthropic Principle A. Snyder 7/14/2016 11:21 AM Version 2.2

What are the odds?

The WAP or ‘Weak Anthropic Principle’ did not bother me. Many physicist object to it as ‘unscientific’, but I thought of it as ‘trigger bias.’ If you design an experiment to ‘trigger’ on a certain kind of event, it can detect only that kind of event, so it’s no surprise (that apart from background) that is the only kind of event you observe.

If evolution ‘designed’ us from the ‘components’ available, it’s no surprise we find ourselves in a ‘world’ where those components exist, even if such ‘worlds’ are rare, they are the only ones we can ‘trigger’ on. There might be other ‘worlds’ with other creatures constructed differently, but creatures like us can only exist in a ‘world’ like ours. Trivial!

My favorite example of ‘fine tuning’ is the neutron-proton mass difference. If neutrons were lighter than protons our ‘world’ would not exist. The matter of the universe would be almost all neutrons (well apart from ‘dark matter’). There’d be nothing to build atoms from. There’d be no Hydrogen or Carbon. There’d be no amino acids or proteins. There’d be no DNA. And the neutron being heavier appears ‘unnatural’ as the proton is charged and has an extra contribution to its mass from squeezing its charge into a small space. And yet the neutron is not too heavy. It’s light enough that when bound in a nucleus it is stable. Otherwise all the neutrons would decay and there’d be no atoms heavier then Hydrogen. The neutron-proton mass difference is ‘just right’ for us to exist! The book below argues this is not a problem:

Fallacy of Fine-Tuning: On the other hand, the masses of the two quarks are estimated to be in the range 1.5 to 3 MeV for the u quark and 2.5 to 5.5

MeV for the d quark. This gives a mass difference range md – mu from 1 to 4 MeV. The neutron-proton mass difference is 1.29 MeV, well within that range. We conclude that the mass difference between the neutron and proton results from the mass difference between the d and u quarks, which, in turn, must result from their electroweak interaction with the Higgs field. No fine-tuning is once again evident. Stenger, Victor J.. The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us (p. 178). Prometheus Books. Kindle Edition.

Stenger’s debunking of neutron-proton mass difference does not work. He’s just moved it off to the Higgs couplings which in the Standard Model are arbitrary. The u- and d-quark masses are obtained from the neutron-proton mass difference not independently estimated in the Standard Model. Ok, maybe a little unfair. There is input from particles other than neutrons and protons, but still u- and d- quark masses have to be picked carefully. In a world where they were different, other particles containing them would have different masses too, though there might not be anybody about to notice or put ‘em in the particle data book because the protons all decayed. Even if quark masses were independently ‘measured’ they are not predicted by the Standard Model.

Indeed, as the u-quark carries more charge (2/3) than the d (-1/3) , their masses also differ in an ‘unnatural’ direction, but their Higgs couplings can be adjusted to get anything you want. If Higgs coupling vary from ‘universe’ to ‘universe’ they have to be in a narrow range to get atoms and us. Stenger is showing his ‘confirmation bias.’ I was hoping for better when I bought his book! I share his bias and was prepared to believe. The answers usually given are ‘God or gods tuned it’ or WAP (‘we wouldn’t be here’). I find WAP more palatable, but it’s got its problems. The ‘it can’t be otherwise’ answer seems to be fading with the super-abundance of string theories, but maybe it will make a comeback someday.

The ‘trigger bias’ analogy is less than perfect. In the case of a trigger we know there’s other interactions going on that we’re choosing not to look out. We know other stuff is happening. We know the flux of incident particles and how often

they interact. In the case of our ‘world’ we don’t know anything about the flux of other worlds or even what that means. How often we ‘trigger’ tells us a lot about the process we are studying. Tegmark’s ‘Mathematical Universe Hypothesis’ (MUH) in his book ‘Our Mathematical Universe’ makes WAP problematic. What the flux of possible universes is becomes total unclear.

Tegmark’s idea is that our universe is ‘just’ mathematics. That mathematical structures are reality and are all there is. You might call it ‘Platonism on steroids.’

I remember joking about this at lunch at SLAC. Suppose we knew the Theory of Everything (ToE) and had the means to solve it. In the solution we could find our selves on a warm winter day outside the SLAC cafeteria Turtles all the way down eating lunch and solving for ourselves. We have a powerful laptop with us and Michael Peskin is showing us his solution to the ToE and finding… Turtles all the way down!

There are lots of mathematical structures. The real numbers, the integers, Euclidean geometry. These seem unlikely to harbor life. At a minimum time or the ‘illusion’ of time is needed. The ToE would have to be more complex -- field theory, string-theory, branes or something like that. Tegmark includes ‘many worlds’ quantum mechanics; that multiplies the number of possibilities endlessly… It’s not clear to me that the number of ‘worlds’ is even as small as a countable infinity…

Anyway the consequences are horrific. In some ‘worlds’ I might live forever (though likely in misery in ‘most’ of them). On-the-other hand in some worlds my finger just tunneled into the ‘G’ key and this essay comes to abrupt end. Let me know if your world is like that ([email protected], I’ll try to answer even with an injured finger)!

One possibility for our universe is that it is a Friedman solution to General Relativity (plus QM with strings or something). The Friedman universe has a fine tuning problem. It needs regions that have never been in thermal context to be at the same temperature and look the same on large scales. When we look back 13 Billion years using the micro wave background, the universe looks pretty much the same whichever way we look. In the mathematical structure based on the Cosmic Micro Wave Background (CMB) Friedman solution these regions have never been in causal contact. How did they come to equilibrium? Sheer luck? This is called the ‘Horizon Problem.’

The CMB has a thermal black body spectrum at a temperature of 2.72548±0.00057 K and that is pretty close to the same in every direction. i

Steven Weinberg came up with a solution – the weak anthropic principle. The paper is in PRL. Here’s the abstract.

In recent cosmological models, there is an "anthropic" upper bound on the cosmological constant Λ. It is argued here that in universes that do not recollapse, the only such bound on Λ is that it should not be so large as to prevent the formation of gravitationally bound states. It turns out that the bound is quite large. A cosmological constant that is within 1 or 2 orders of magnitude of its upper bound would help with the missing-mass and age problems, but may be ruled out by galaxy number counts. If so, we may conclude that anthropic considerations do not explain the smallness of the cosmological constant

So do we need to look any deeper? It’s a ‘mathematical structure.’ It works. Are we there yet? Well, no. Alan Guth game up with inflation which explained the uniformity w/o resorting to WAP. Fortunately, he ignored the WAP explanation. Inflation explained not just the uniformity of the universe, but other stuff as well.    

The monopole problem Ω 1 – almost Seeding galaxy formation (fluctuations) And, of course, the Horizon problem

The WAP is down, but not out.

It’s back, or rather Andrei Linde is!

The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of lowenergy laws of physics. Since these parts are extremely large, the interior of each of them behaves as if it were a separate universe, practically unaffected by the rest of the world. This picture, combined with the theory of eternal inflation and anthropic considerations, may help to solve many difficult problems of modern physics, including the cosmological constant problem. In this article I will briefly describe this theory and provide links to the some hard to find papers written during the first few years of the development of the inflationary multiverse scenario. See also http://web.stanford.edu/~alinde/1982.pdf

So while Guth disposed of the WAP Andrei Linde and his eternal inflation brought it back with a vengeance…with even more constants and the very laws of physics to be settled by appeal to WAP. Are we there yet?

WAP is particularly problematic for Mathematical Universe Hypothesis. The Friedman universe is a mathematical structure. All possible variants and initial conditions for it ‘exist’ as possibilities and we just find ourselves in one that can support us. Why bother to look further? All those Linde universes are mathematical structures too. WTH? It seems like nonsense, but…

Linde: An advanced version of this scenario describes our world as an eternally growing self-reproducing fractal consisting of many locally homogeneous parts (mini-universes). If the fundamental theory of all interactions has many different vacuum states, or allows different types of compactification, the laws of the low-energy physics and even the dimensionality of space in each of these mini-universes may be different. This provided, for the first time, a simple scientific interpretation of the anthropic principle, which did not rely on the possible existence of ‘other universes’: We can live only in those parts of the world which can support life as we know it, so there is a correlation between our own properties, and the properties of the part of the world that we can observe

If there’s something ‘real out there’ WAP is easier to swallow. If there are many universes with assorted laws, we could have ‘triggered’ on one of them. They provide the ‘other’ interactions we don’t see because we can’t.

So I don’t know how to disprove WAP. It seems likely it has some role. It doesn’t seem like a good idea to give up on explaining things though. The Weakness of WAP is that could cause us to stop looking and settle for what we’ve got. It is a thought stopper. Are we there yet? “No, shut up and keep swimming!”

The newest experiments like WMAP see slight variations which tell us a good deal about the universe and its formation and structure. i