On my top ten list there is the question whether the parameters of the standard model (SM) can be derived from within a yet-to-be-found theory of everything (TOE). And if so, how. Can we make sense out of this collection of numbers? Lately, this question has been dominated by a topic I still can't make any sense out of: the Anthropic Principle (AP).
In this post I want to share some of my thoughts on the AP, and its sense or non-sense. You might also want to read my earlier post The Principle of Finite Imagination (alias: The Liver Post).
I want to state at the beginning that I don't want to discuss whether life on earth is 'intelligent' or 'civilized', so you might want to replace 'life' with 'intelligent life' or 'civilization' if you feel like it.
Below you find my thoughts on the following four statements that I have encountered:
- A: The conditions we observe in our universe are such that they allow the existence of life. (Or, equivalently: If the conditions were such that they didn't allow the existence of life, we wouldn't be here to observe them.)
- B: If we assume that the conditions are according to some random distribution function then we live in a typical sample, and we are typical for the universe we life in.
- C: The conditions we observe in our universe are optimal for the existence of life.
- D: The conditions we observe in our universe are optimal in some other sense.
Is usually called the weak Anthropic Principle (AP). It's scientific content has been debated over and over again, see e.g. Lee Smolin's paper and the following argument with Leonard Susskind. The AP is not a theory, and I honestly have no idea what the scientific status of 'principle' is supposed to be. I think the main issue for the physicist is whether or not the AP allows to make predictions, and whether it is scientifically useful. Or at least this should be the main issue for us.
Without any doubt, A is a true statement. That means not only it can't be falsified: it can't be false. But this does not mean it can't also be useful. It's a device one can use to draw conclusions. And indeed, one can use it to derive constraints on observables. However, this is no more a scientific theory than the use of mathematically true statements.
E.g. consider you compute a prediction for the lifetime of muons at relativistic speed with Lorentz-transformations and use cosh2 - sinh2 = 1. If your prediction is correct, you'd not claim that this is due to the use of a trigonometric identity. Instead, the agreement of your computation with the observed value it a confirmation that Special Relativity is a successful description of reality.
Likewise with Weinberg's bound on the cosmological constant. In a nutshell the argument is: when the cosmological constant was larger than some value, then galaxies would not have formed and we would not be here. Deriving this bound thereby using A, and finding it fulfilled by the observed value is a confirmation of having properly used a sensible theory for gravity and an appropriate model for density fluctuations. If the derived bound would have turned out not to be fulfilled, we'd not have concluded that A is wrong. Instead, we'd have concluded there is something wrong with our understanding of structure formation.
So, A can be used in the context of a theory or a model to make predictions, just that any conclusions drawn from this are not about A, but about the theory or the model.
Is also called the Principle of Mediocrity. For me, one of two crucial question here is the distribution of the parameters. This has to be given (preferably motivated, maybe just postulated) through some kind of a model. From this, one can then find out the most probable configurations. Since we are typical, we belong to one of these. If the parameters in this configuration do agree with our observations we could conclude that the distribution of the random parameters was in accordance with the expectation B that we live in a typical universe.
However, the randomness of the distribution always leaves a sneaky way out. If we measure some parameters, then the distribution of parameters as evaluated from the model will agree with some probability. How small do we allow this probability to be still acceptable, i.e. typical? Or, how natural is natural? Let's say we set this acceptable probability to a value X. Then, we'd have to discard the model leading to the distribution when the observed values would have a smaller probability.
One can do this. This is basically a search for random distributions that have maxima not at the observed values, but sufficiently close around them to be in accordance to our acceptance limit X.
A second huge problem of this approach which I see is obviously what it means for the universe that we are 'typical'. What of our universe has to be typical, and at which stage of the evolution does it have to be typical? I have no idea how the notion of being typical could be put on solid feet.
So, in my eyes B is the construction of models within which the observed parameters of the SM have a certain probability. The higher this probability, the better the model. (Hopefully, the model itself has less free parameters than the SM itself). The central statement of being typical is very ill defined and vague.
Approaches to describe nature like this were essentially the reason why I left Heavy Ion Physics (replace 'acceptable probability' with 'errorbars').
Is a more sophisticated version of B, where being typical is replaced with being optimal. It suffers from the same problem of dealing with a very vague quantity, that is the 'optimalness for the existence of life'.
To underlay this with a physical approach, what we really want is some function of these parameters that we aim to predict -- a function which is optimal for the actually observed values. For the case C, this function would have to be
Optimalness-for-Life(Parameters of the SM)
Applying a variational principle to this 'function' seems to be hopeless, but what one can do instead is tuning the variables (parameters of SM) up and down to see whether the optimalness decreases. I.e. the poor man's way to determining a minimum. This is essentially what has been done in a huge amount of examples, and results typically in statements like: When the size of my cellphone was just 2% smaller, then life would not be possible.
Despite the fact that this way one can only check for local minima, and that one can not really draw conclusions when keeping some parameters fixed and varying only a few, imo the largest problem is the absence of a reasonable definition of Optimalness-for-Life. There is way too much ambiguity attached to it. What can we possibly learn from this? Only that - assuming we live in a universe optimal for life - our idea of being optimal is not in disagreement with observation.
So, in my eyes C is an improvement over B but the central point of 'being optimal for life' is too vague to allow sensible insights into the secrets of nature.
Can abstractly be formulated as: there is some function of the parameters to be determined that is optimal for the observed values. The question then is what this function is. Apparently, the universe is not such that it optimizes the amount of US$ on my bank account. Too bad.
Lee Smolin proposes that the number of black holes could be such a function (Cosmological Natural Selection), whose value is maximized for our universe. Though the function Number-of-black-holes(parameters of the SM + LambdaCDM) itself is unknown, at least it's a well defined quantity. Here again, one can test whether we are in a local extremum by tuning around parameters and estimate the effect. It seems, the number of black holes is not such a bad guess (to me this is really surprising.)
Imo, it's in this regard not even important whether or not all the universes that belong to the non-optimal parameters actually 'really' exist. When I make a variation over the metric in GR to find the optimal and realized configuration, I don't think of the other ones as being alternative universes. However, in Lee's scenario the other universes do 'really' exist, and the claim is then that we are likely to live in a universe where the number of black holes is as large as possible. This then has the additional virtue of providing a reason why the number of black holes is the function to be extremal (for further details, see hep-th/0407213 or The Life of the Cosmos) .
One way or the other, D comes down to the question whether there is a function that is optimized when the parameters of the SM have the values we observe. And which in addition to reproducing known number allows us to learn something new (i.e. make at least one falsifiable prediction).
But then, the question lying at hand is whether this function can be derived from the fundamental principles of the TOE. It might be that this is not the case, but that e.g. the initial conditions play a central role. An example that has been used elsewhere (sorry, forgot where) are the orbits of planets in the solar system, which have historically been thought to arise from some symmetric construction. Today we'd say the orbits of the planets follow when we have given the initial stress-energy distribution, and the quantity to be optimised is the Lagrangian of GR plus that of the matter field. We would not expect the orbits of the planets to be predictable from the SM of particle physics plus GR. Or from putting Dodecahedrons inside Icosahedrons (see Platonic Solids).
But even if the function to be optimized can be derived from the TOE, in practice it might not be a useful way to deal with it in the full context. Just like we don't explain liver growth starting from the SM of particle physics, I find it a reasonable expectation that a macroscopic description of our universe might be more useful to determine the parameters of the SM.
However, I'd say our insights about a possible TOE are not yet deep enough to let us conclude that not even some of the parameters in the SM might be explained within such a fundamental theory.
TAGS: SCIENCE, PHYSICS, ANTHROPIC PRINCIPLE