discrete physics, a more general concept. Let me return to this topic – and change the focus somewhat – in the wake of a sensible text at a German physics blog,
The simulation hypothesis and other things I don’t believeAs David Tong explained using different words in his Silver Prize Winning Essay written for a crackpot foundation whose basic mission does include the promotion of the "Simulation Hypothesis", there is strong scientific evidence today that the world isn't discrete (and it isn't simulated).
We do encounter integers and discrete mathematical structures in physics but in all the cases, we may see that they're derived or emergent. They're just limited discrete aspects of a more general and more fundamental underlying continuous structure, or they're a rewriting of a continuous structure into discrete variables (eigenstates in a discrete spectrum) which makes it impossible to understand the value of certain parameters.
Quite generally, if the Universe were fundamentally discontinuous, it couldn't have continuous symmetries such as the rotational symmetry, the Lorentz symmetry, and even descriptions in terms of gauge symmetries (which aren't real full-fledged symmetries but redundancies) would be impossible. In a fundamentally discrete world, many (or infinitely many) continuous parameters would have to be precisely fine-tuned for the product to "look" invariant under the continuous transformations.
I am not saying that it is "impossible" for all these parameters to be fine-tuned for the product to look e.g. Lorentz-invariant; I just say it is very unlikely. The scientific theory that requires this huge unexplained fine-tuning is less likely than scientific theories that work with no fine-tuning (or less fine-tuning). It's less likely simply because given any sensible, quasi-uniform a priori distribution of the parameters, it is insanely unlikely that they will have the "right" values if there are so many wrong values.
EPR-style experiments show that local realism is incompatible with the observations. Locality must be fundamentally respected because it may only follow from the Lorentz invariance, the Lorentz invariance is observed to hold as well, and making it accidentally hold in a fundamentally Lorentz-violating theory would require the nearly infinite amount of luck and fine-tuning, as explained in the previous paragraph. So the reality is local but non-realist. It is quantum, stupid.
It means that the proposal that our Universe is a simulation run on a classical computer is ruled out immediately. This is a very naive idea, indeed. Again, I am not saying that it is "impossible" to write a computer program that behaves in a way that resembles the reality. It may have a wave function treated as a collection of classical degrees of freedom; it can make the wave function "objectively collapse" at various points (although this guarantees that some disagreement with the observations is inevitable, as I have often emphasized). But it may look "more or less OK".
But when a simulation may "look OK", it's a different statement than the statement that the simulation may "be" the reality. These are totally different questions. The simulation may do a good job in emulating Nature around us. However, we may still prove by the scientific method that it must be a simulation, not the real deal!
I wrote a lot about the flawed idea of discrete physics. But in this blog entry, I want to write a few more words about a more ambitious aspect of this reasoning, the idea of an "Overlord". We are a simulation that a more intelligent "Overlord" is playing with. This is such a childish and mathless idea that we are really leaving proper physics. The first thing I would say – in agreement a Western European blogger – is that this idea is just religion in "modernized clothes" and its details reveal unusually naive anthropomorphism that we usually associate with very primitive forms of religions.
But some people apparently think that if they replace the old Gentleman floating on the cloud by a modern (or slightly futuristic) computer with its data floating in the cloud, it's not only much cooler but also much more scientific. Well, it's not. The decoration and makeup may look modern, technological, and geeky but the central idea in this scenario is still the same primitive religion.
(Some IT companies may think that their cloud technology is the newest state-of-the-art invention but clouds have been a basic tool used by the Overlords for thousands of years.)
Brian Greene promoted these ideas in the last 2 chapters of his latest major popular book, The Hidden Reality. It's a fun reading that tries to suggest that it's connecting physics with the ideas of science-fiction movies and books. However, it is not. These ideas are pure science-fiction. They don't contain any "physical added value" whatsoever. They show a physicist trying to make an excursion to the world of science-fiction.
Don't get me wrong. I do like many of these books and movies. I think that some of them are clever in the ways how the rules of the game are sketched. I have watched some of these movies many times, thought about them, and I have perhaps tried to write my own science-fiction novels, too. Those activities may require some thinking. However, it is important to realize that this thinking is certainly not scientific thinking.
The Ultragirl who plays with the simulation is usually visualized in a totally anthropomorphic way. She is a girl so she just wants to have some fun. She may be bored. She doesn't want to be bored. She may have bought the device with the simulation in the mall. She may even be sexy and tease you. She may even look like a human babe.
Needless to say, all these ideas are preposterous. If there were a totally new fundamental layer beneath our Universe, and I have argued it can't exist, it would not only have no reason to include beings that are physically similar to humans with the same kind of lust. Even broader feelings such as fun and boredom would almost certainly be irrelevant. They're as silly as they are in the case of Moses and the Lord who apparently created the Solar System within a week some 6,000 years ago but who needed to relax on the sixth or seventh day (sorry, I am really uncertain at this point!) because all the workers want their weekends to be relaxing.
But the anthropocentric delusions don't stop with fun and boredom. Some people, including Brian Greene, are even promoting a scenario in which the simulation runs on a limited device that only simulates something or uses rougher, approximate algorithms to simulate things that aren't too important because the simulated beings aren't observing these aspects too accurately (or they don't observe them at all).
It may be a good idea for you to buy a cheaper computer if you don't need the most powerful one. You may have good reasons to save some electricity and run simpler programs if you don't need the state-of-the-art ones. You may pay smaller bills and you may save some money for other things. But to imagine that the underlying Overlords are trying to save the money in the same sense as we do is the ultimate anthropomorphic naivite. It's not just anthropomorphic: it's an idea that envisions a layer underlying the whole observable Universe to resemble the early 21st century culture of the U.S. urbanite teenagers.
Holy Christ and Saint Simulator, we must ask: Why? All these assumptions about the Overlords are completely irrational. There is absolutely no reason to assume that the beings underlying our existence would resemble the U.S. urbanite teenagers of 2007. In fact, if we have some experience and if we can imagine a reasonable "landscape of possible ideas", we must agree that the probability that the underlying reality respects these principles is virtually zero.
Brian Greene faithfully yet uncritically sketched many other arguments in favor of the "Simulation Hypothesis" that I find utterly idiotic. One of them is a sort of the anthropic propaganda. He says that in the asymptotic future (of our particular Universe or perhaps the whole multiverse), there will probably be so many computers with so much power that the number of simulated TRF readers will be vastly greater than the number of biological TRF reader. For this reason, Brian thinks, it's far more likely that you are a simulated being, not a physical or biological one.
There are several reasons why this argument is dumb. One of them is that there is no such a law that the probability that you belong to a subset S of the whole set W is equal to the ratio of the number of elements N(S)/N(W). In most cases, the ratio isn't even well-defined because both the numerator and denominator are infinite. But even when they're finite, there's absolutely no reason why the probability should be equal to the ratio and in almost all cases, it is not equal. Only if all elements of W are equally likely – and that pretty much occurs only when there is a reason why they are equally likely (thermalization balancing all the microstates, for example) – the probabilities may be represented by the ratio. But it is a negligible fraction of the situations. There isn't any symmetry or democracy between biological and simulated beings because they're qualitatively different objects so there can't be any justification of the "equal odds" assumptions.
Regardless of the number of simulated beings "somewhere", we may still present scientific evidence that there is no "simulated layer" in our reality. The continuous symmetries are such an example. If you want to deny this argument, you may deny it by saying that your meme that "the number of simulated beings is vastly greater than the number of genuine beings" is so powerful (because the number of simulated beings is so high) that it may render the smallness of the "we are simulated beings" prior probabilities irrelevant.
But such a method to render rational arguments and calculations irrelevant is just a sleight-of-hand. It is exactly equivalent to the statement that all scientists and atheists are deluded a*s*oles because God is infinite and by His infinite powers, He may neutralize any scientist, his arguments, and inflate an arbitrarily unlikely possibility into the most likely outcome. To argue in this way means to totally abandon rational discourse and replace it by a kindergarten boys' pissing contest trying to find out whose God or Father is more infinite. You're just showing that your faith is infinite and won't be affected by any finite evidence, however extensive. But this only proves your bigotry. It doesn't prove anything about Nature.
Moreover, one may conjecture equally convincingly that in the future world, the number of biological beings will be vastly dominant; yes, I am just saying that the other side could be active in the pissing contest, too. I don't want to spend too much time with these anthropic arguments because they're just totally unjustifiable. In fact, there aren't any infinite numbers in physics that could ever "strengthen an argument". All physically meaningful numbers are always finite (some renormalization etc. is sometimes needed to see it) and if you think about possible infinite numbers such as the volume of our not-only-observable Universe, they never affect probabilities of observable propositions. The latter are only affected by intensive or local, and therefore finite, quantities. Someone's infinite size as the "ultimate argument" belongs to religion, not to physics.
Another would-be scientific yet unscientific line of defense that the champions of the Simulated Universe Hypothesis often employ are the demands of loyalty towards our Overlord. Some of them are as dead serious about this line as the most hopeless religious fundamentalists. They say that the Overlord may be deliberately trying to mislead us and we must just stay humble and respect Her great power because we're such tiny insects.
Well, let me say that I know that this Overlord doesn't exist but even if I had doubts about Her existence, as a scientist, I don't have and can't have any respect towards Her "authority" that would affect my reasoning. Such an influence of fear on reasoning is just not kosher for a scientist – and I would surely extend this moral principle to North Korean scientists and simulated scientists, too. It's just about the most important, defining features of science. So even if the Overlord exists, she may politely have a romantic relationship with Her own openings, or whatever other parts of the body She is expected to have. Give me a break with this stuff. Worshiping a being, especially one that doesn't exist according to all the rational reasoning, is just plain stupid.
When She is presented as omnipotent in this way, the champions of Her dominion over the world have no problem to say that She may fine-tune things to values I find unlikely because it's Her right. She has the right to confuse me, too. Because these folks live in a mental world that assumes that She exists as if it were the most reliable and universal axiom of science – in a complete analogy with religious bigots in Christianity, Islam, and perhaps other old-fashioned religions – they consider their uncritical faith to be a sign of their being scientific.
But it's exactly the opposite. In religion, one can make assumptions (such as the Simulator's omnipotence) and require that everyone else worships these assumptions and treats them as facts. All other facts must be distorted, adjusted, or completely overlooked so that they become compatible with the basic religious axioms and of course that if you're willing to say awkward things, it's possible to a large extent. However, this approach is unacceptable in science.
In science, we always question the assumptions. We're comparing competing theories whose assumptions differ. That's really another defining feature of science. So feel free to create a personality cult around the Female Simulator but a person who is thinking scientifically will always question it and will always try to estimate the probability (and probable truth values of various assumptions) using the most rational, indirectly empirically based, arguments that are available.
Let me phrase this point about "Her right to confuse" differently. Some champions of the Simulation Hypothesis (and religions) think that if they postulate that "She" can arrange things in such a way that scientific strategies to investigate the foundations of the Universe become misleading or impossible, they make their Simulation Hypothesis more likely because they "hurt" the other hypotheses. But the answer is the opposite one. They only hurt their own, Simulation Hypothesis because they are adding additional unnatural assumptions to it: they are making it less likely. The probabilities of the competing (scientific) explanations can't be lowered by axioms done within the Simulation Hypothesis because – with apologies to the Overlord – the competing scientific explanations lie beyond the Overlord's power. So if the Simulation Hypothesis contains additional axioms that "hurt the Overlord-free scientific explanations" and if someone believes that the scientific explanations really become less likely because of that, he is a victim of circular reasoning. He can only prove what he wants (scientific explanations are disfavored or impossible) if he assumes it from the beginning, anyway.
For the question of fine-tuning, a rational argument is that the fine-tuning of 40+ parameters of the Lorentz-breaking Standard Model to the Lorentz-preserving values is almost infinitely unlikely, so a fundamental theory that doesn't respect the Lorentz symmetry is almost fully excluded. That's true for the Sexy Simulator Hypothesis, Loop Quantum Gravity, or any other silly fairy-tale of this sort. It doesn't matter that you may imagine that such an unlikely scenario is true and you may collect a billion of gullible simpletons around the religion that it is actually true. Science is still saying what it is saying and it is saying that the probability that such an assumption about the Simulator holds is basically zero. It's the strongest way how science may disfavor a hypothesis. So science is against you in the most violent way that the cautious and peaceful structure of science admits.
To summarize, I think that if you admit that there is a difference between science and religion, the proponents of the Simulated Universe Hypothesis are squarely on the religious side and all the feelings that their theories are modern, geeky, technological, and advanced are just about the makeup, not about the essence of the hypothesis that is the same primitive religion that the mankind has played with at least for thousands of years.
And that's the memo.