I presented a version of this argument to Sean Carroll (prominent physicist/blogger) in his December 2022 AMA (for context, the past hypothesis is just the quantitative way to state the assumption that the universe began low entropy, thus throwing out all universes that emerged randomly from fluctuations and predict Boltzman brains):
Q: In the October AMA, you said there was “No experiment you can do” to prove the past hypothesis. However, it seems any universe where the laws of thermodynamics are true and the past hypothesis is false should makes some very strong, very falsifiable predictions! The theory would say that, with overwhelming probability, our experiences are explained by a small world fluctuating from equilibrium, and by illusory stuff outside that world, just enough to make us think the universe is bigger and explain what we’ve observed so far.
So, every time we see stars continue to shine, or take a walk to a new street in town, or otherwise fail to shatter the illusion of the outside world, that is a result not predicted in a universe without a past hypothesis! Given how incredibly thermodynamically unlikely these coincidences would be, are we not gaining several sigmas of certainty per second that the past hypothesis is true?
A: All that’s true, but it does not get you the result, Kevin, that you want to get because you have to distinguish between asking, given this universe, in other words a universe where there really just are random fluctuations and we don’t have the past hypothesis, what would you expect to see next? That is a question you can ask and that is what you’re talking about. But the theory choice question about doing an experiment to prove the past hypothesis is not that question. That’s just calculating the likelihood function in Bayes’ theorem. To choose between the theories, you have to multiply that likelihood function by the prior. So the question is not given this theory, what do you expect to see next? But given what you see, what is the most likely theory?
And given a universe that is randomly fluctuating, it is true that given what we see now, the next thing we should see is just some thermal equilibrium random fluctuations. But given that the next thing we see is not thermal equilibrium random fluctuations, if that universe were real, it would still be overwhelmingly likely that all that stuff had just fluctuated into existence, okay? So that’s why you need to assume the past hypothesis. You can’t actually be a good Bayesian and rule it out by data because under that set of assumptions that all configurations of stuff in the universe are equally likely, the prior probability that you’re seeing things randomly fluctuate into existence is so overwhelmingly large that you can’t beat it down just by likelihood functions and collecting new data.
I don’t like his answer. I think it probably comes out of repeated arguments of the form “Boltzman brains wouldn’t experience X” “Granted, but you’ll still see way more Boltzman brains+X than real coherent universes”, or of the form “Here’s this info about the early universe from data we collected” “That info assumes the past hypothesis, since you discount the overwhelming numbers of ways your data could be produced from thermodynamically incoherent universes”. He’s comfortable saying everyone’s ultimately assuming the past hypothesis somewhere, so we need to be able to say that’s fine.
There’s arguably only a semantic difference here: Is being willing to assume the past hypothesis is practically any different from accepting the evidence of the past hypothesis?
I think it’s worth calling evidence evidence. The past hypothesis is a theory, the null past hypothesis (allowing fluctuated universes) is another theory. You can imagine many different acceptable priors on the credence of those theories. The past hypothesis is possibly less natural and possibly should have much weaker weight due to that unnaturalness. It should not however, have a much weaker weight because the other theory thermodynamically assigns it that weaker weight. That’s just backwards: Assign prior likelihoods, then consider the evidence.
The evidence we see in favor of the past hypothesis is strong enough to overwhelm any reasonable naturalness weighting. It is not enough to overwhelm the other theory’s thermodynamic naturalness weighting, but that was never the question.
I presented a version of this argument to Sean Carroll (prominent physicist/blogger) in his December 2022 AMA (for context, the past hypothesis is just the quantitative way to state the assumption that the universe began low entropy, thus throwing out all universes that emerged randomly from fluctuations and predict Boltzman brains):
Q: In the October AMA, you said there was “No experiment you can do” to prove the past hypothesis. However, it seems any universe where the laws of thermodynamics are true and the past hypothesis is false should makes some very strong, very falsifiable predictions! The theory would say that, with overwhelming probability, our experiences are explained by a small world fluctuating from equilibrium, and by illusory stuff outside that world, just enough to make us think the universe is bigger and explain what we’ve observed so far.
So, every time we see stars continue to shine, or take a walk to a new street in town, or otherwise fail to shatter the illusion of the outside world, that is a result not predicted in a universe without a past hypothesis! Given how incredibly thermodynamically unlikely these coincidences would be, are we not gaining several sigmas of certainty per second that the past hypothesis is true?
A: All that’s true, but it does not get you the result, Kevin, that you want to get because you have to distinguish between asking, given this universe, in other words a universe where there really just are random fluctuations and we don’t have the past hypothesis, what would you expect to see next? That is a question you can ask and that is what you’re talking about. But the theory choice question about doing an experiment to prove the past hypothesis is not that question. That’s just calculating the likelihood function in Bayes’ theorem. To choose between the theories, you have to multiply that likelihood function by the prior. So the question is not given this theory, what do you expect to see next? But given what you see, what is the most likely theory?
And given a universe that is randomly fluctuating, it is true that given what we see now, the next thing we should see is just some thermal equilibrium random fluctuations. But given that the next thing we see is not thermal equilibrium random fluctuations, if that universe were real, it would still be overwhelmingly likely that all that stuff had just fluctuated into existence, okay? So that’s why you need to assume the past hypothesis. You can’t actually be a good Bayesian and rule it out by data because under that set of assumptions that all configurations of stuff in the universe are equally likely, the prior probability that you’re seeing things randomly fluctuate into existence is so overwhelmingly large that you can’t beat it down just by likelihood functions and collecting new data.
I don’t like his answer. I think it probably comes out of repeated arguments of the form “Boltzman brains wouldn’t experience X” “Granted, but you’ll still see way more Boltzman brains+X than real coherent universes”, or of the form “Here’s this info about the early universe from data we collected” “That info assumes the past hypothesis, since you discount the overwhelming numbers of ways your data could be produced from thermodynamically incoherent universes”. He’s comfortable saying everyone’s ultimately assuming the past hypothesis somewhere, so we need to be able to say that’s fine.
There’s arguably only a semantic difference here: Is being willing to assume the past hypothesis is practically any different from accepting the evidence of the past hypothesis?
I think it’s worth calling evidence evidence. The past hypothesis is a theory, the null past hypothesis (allowing fluctuated universes) is another theory. You can imagine many different acceptable priors on the credence of those theories. The past hypothesis is possibly less natural and possibly should have much weaker weight due to that unnaturalness. It should not however, have a much weaker weight because the other theory thermodynamically assigns it that weaker weight. That’s just backwards: Assign prior likelihoods, then consider the evidence.
The evidence we see in favor of the past hypothesis is strong enough to overwhelm any reasonable naturalness weighting. It is not enough to overwhelm the other theory’s thermodynamic naturalness weighting, but that was never the question.