Questioning the cosmological principle

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  • #76
Chalnoth
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Question: do you think that one model is "more likely", "more reasonable", "simpler" in the sense of Ockhams razor than the other? How do you calculate and compare the probability of a cosmological constant having a certain value with the probability of sitting near the center of a huge void?
It's not really that difficult. First, you compare the free parameters in the theory used to explain the acceleration.

The cosmological constant has one free parameter.

The void model has three free parameters (our position in three spatial dimensions).

Things aren't looking so good for the void model already.

To do this in more detail, it makes sense to compare the fraction of parameter space that is consistent with the model to the entire parameter space. With the void model, this requires some estimate of the frequency of such nearly-spherical large voids, but we can easily provide an extremely pessimistic estimate by taking the maximum value of this frequency that is still consistent with the void model explaining acceleration. We then compare the number of galaxies that lie close enough to the center of such a void to explain the observed acceleration to the total number of galaxies. This gives a rough estimate of how likely the model is.

To contrast this, we can compare the current error bars on the cosmological constant to the available parameter space for the cosmological constant that is consistent with an old universe that forms galaxies.

Now, I haven't done the numbers here, but I'd be willing to bet that the void model will end up with a much, much lower likelihood than the cosmological constant.

Bear in mind that the numerator of this fraction that makes up the likelihood depends upon experimental precision, so we can't take the likelihood itself as being physical, just a means of comparing between different models.

Using this sort of analysis, it is not at all difficult to compare models even when the experimental support for two competing models is identical. The result may, in some cases, be ambiguous, but it's still possible to do the comparison, and certainly not outside of the realm of science.
 
  • #77
Chalnoth
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Congratulations! You are questioning what most research programs did over the last few hundred years.
Er, no. I'm not saying it wouldn't be nice to directly detect the dark matter particle, for instance. Rather I'm saying that what we test in science isn't things. We test theories. And there is no a priori reason to select one specific sort of data as being the only kind that is acceptable to accept a theory. Instead, we use well-tested epistemological tools to determine whether or not a theory is likely to be at least approximately true.

The tool of interest where dark matter is concerned is this: we know that we make mistakes. We expect it. So a good test of any theory is an independent test. We have different scientists examine the same data in order to reduce the possibility of individual errors impacting the results. We have different groups of scientists collect the same class of data using different instrumentation in order to make sure there is not some problem with the instruments. We have different groups of scientists collect entirely different sorts of data to test the same model predictions, or very different model predictions.

The first couple of types of error-checking are just verifications that we didn't make any dumb mistakes. These sorts of mistakes are pretty frequent when a scientific field is new, but tend to become less and less common as a field matures and scientists learn from the mistakes of their predecessors. But it is the last type of error checking that really gets into the meat of the issue and checks whether or not a particular theory is likely to describe reality, at least at an approximate level.

And with dark matter, today we have such a diverse and varied body of evidence that it is highly, highly unlikely that what we interpret as dark matter is not a WIMP of some sort or other.

I am refering to theories like Maxwell's theory of electromagnetism using electromagnetic waves to explain certain phenoma (which have been detected experimentally); I am refering to the standard model of elementary particles introducing the idea of particles living in representations of certain symmetry groups (the success of the SM was not to postulate the existence of these particles but to detect them :-)
And guess what? Almost none of those particles have been directly detected, in the sense of having a more-or-less direct measurement of their charge and mass. Your objections seem to me to be identical to, in the particle physics sense, not accepting the existence of a particle unless you can see its tracks in a bubble chamber (or equivalent detector that independently measures charge and mass).
 
  • #78
tom.stoer
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Yes, I am coming from the particle physics community and therefore my statement is rather simple:

Any claim that a certain class of elementary particles (WIMPs, SUSY, ...) exists and is responsible for a certain class of phenomena must be tested according to principles valid in the domain of elementary particle physics. B/c people working in elementary particle physics do not claim to have proven SUSY to exist, any claim tat SUSY is realized in nature is lacking experimental support (even if it's highly "reasonable" or "evident" looking at results from cosmology).

I think this is a fair and reasonable statement.
 
  • #79
tom.stoer
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It's not really that difficult. ...
It is not difficult, it's impossible.

You would have to define the probability of having the cc in a certain interval on the real axis. But there is no well-defined probability measure on "theory spaces" and there is no probability measure on the real numbers. I am sorry for that, but mathematically it's impossible to do what you have in mind.

What I am saying is that "likely", "reasonable", "evidence" etc. cannot be defined rigorously.

The main problem is that physics today is partially confronted with the the situation that certain physical theories may bot be verifiable or falsifiable (especially in cosmology this is very likely). My conclusion is that it's better to admit that according to scientific principles the decision is not yet possible instead of weakening scientific principles in order to come to a decision.
 
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  • #80
Chalnoth
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Yes, I am coming from the particle physics community and therefore my statement is rather simple:

Any claim that a certain class of elementary particles (WIMPs, SUSY, ...) exists and is responsible for a certain class of phenomena must be tested according to principles valid in the domain of elementary particle physics. B/c people working in elementary particle physics do not claim to have proven SUSY to exist, any claim tat SUSY is realized in nature is lacking experimental support (even if it's highly "reasonable" or "evident" looking at results from cosmology).

I think this is a fair and reasonable statement.
Given the current status of the evidence, any claim that the dark matter evidence supports any particular particle physics theory is ridiculous. However, the evidence that there is some kind of WIMP not in the standard model is quite strong.
 
  • #81
Chalnoth
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You would have to define the probability of having the cc in a certain interval on the real axis. But there is no well-defined probability measure on "theory spaces" and there is no probability measure on the real numbers. I am sorry for that, but mathematically it's impossible to do what you have in mind.
No, not at all. A first step would be to merely assume a constant probability density within the allowable region. If somebody wants to propose a particular physical model for the cosmological constant, then we can take things one step further and ask about what the probability density is within the allowable region for that particular model. But absent a physical model, a constant probability density is reasonable.

There's no real reason to worry about theory spaces when simple model comparisons are good enough.

The main problem is that physics today is partially confronted with the the situation that certain physical theories may bot be verifiable or falsifiable (especially in cosmology this is very likely). My conclusion is that it's better to admit that according to scientific principles the decision is not yet possible instead of weakening scientific principles in order to come to a decision.
1) There is no reason whatsoever to avoid investigations regarding whether a particular model is more or less likely than another given current evidence.
2) The situation for dark energy may well fall in the position of "not enough to make a decision", but dark matter long ago passed that point.
 
  • #82
tom.stoer
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I will stop responding; thanks for the discussion, but further progress seems to be impossible.
 
  • #83
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While true, the statement that the center of a void is the most favorable place for life to emerge is manifestly unlikely. After all, the distances between galaxies are great, so there is unlikely to be much of an effect of the overall density on the behavior of galaxies, and the centers of voids will have fewer galaxies and thus fewer chances for life to appear.
We have no clue what are conditions that are necessary for life to emerge, beside obvious ones (energy, water, etc). I for sure, can't think of any reason why one part of universe will be more fertile for life than the other, providing same local conditions, and taking the premise of homogeneity seriously. But if you abandon large scale homogeneity, then it is quite possible that life will favour some parts more then others.

Remember that there is the fact that we are "sitting" on the special place on a(t) curve, which may be coincidence, or may be necessity for which we have no obvious explanation.

Point is - we should exercise caution, and remain open.
 

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