....And Its Limitations in a World That is Large, Technologically Interesting, or of the Quantum Kind
The orthodox view with its notion of fundamental physical world works perfectly fine—in a certain regime. Namely, it applies perfectly to a rather small universe which does not contain too powerful technology and in which we can ignore quantum theory most of the time.
It is in this regime where we can easily implement the solid arrow at the left of Fig. 1c: starting from the laws of that physical world, and our ability to predict its evolution, we can compute (probabilistic) predictions for the first-person perspective. That is, we can use our physical theories to predict what we, as observers, will see in certain situations. For example, if we pick up a stone, lift it with our hand, and release it, we can predict that we will (much) more likely see it subsequently fall down than see it fall up, using the laws of mechanics. This is crucial because this is what allows us to test our theories, comparing predictions with actual observations.Nevertheless, this way of thinking leads to problems and paradoxes if our universe is very large, like in certain scenarios involving eternal inflation. In this case, there are cosmological models in which the universe is full of very improbable but (due to its size) numerous thermodynamic fluctuations [6, 7]. What, then, tells us that we are not one of those fluctuations (the infamous “Boltzmann brains”) who have just come into existence by a combinatorial accident? All the memories of our past lives in an ordered, planetary, low-entropic environment would then be mere illusions, and in the next moment, we would make a very scary and unexpected experience before evaporating forever in the midst of nowhere. Shouldn’t we assign much higher probability to such a shocking experience than to an ordinary continuation of our lives if our cosmological models tell us that the universe contains much more Boltzmann brains than ordinary brains?
Note that I am not claiming that this is the right way to think about the problem; I am simply pointing out that it is a problem in the first place, one that makes cosmologists wonder and argue.
The orthodox view itself does not tell us (at least not directly) how to deal with questions like this because we have no idea how we should reduce this question to a question about the physical world.We need not believe in eternal inflation or turn to cosmology to run into problems of this kind; we can create our own “Boltzmann brain problems” with technology. For example, imagine that some scientists put you to sleep and scan your brain in great detail (while unfortunately destroying it), only to create a near-perfect computer simulation [8] of your brain, connected to a simulated body in some simulated environment. Moreover, suppose that the scientists create a large number of slightly different copies, running on different types of computers, possibly delayed in time. Would you “wake up” in a simulation? If so, in which one? Shortly before the experiment, what probability should you assign to finding yourself in any given simulation? It seems that physics must be silent about this question in principle, which is odd: isn’t the very essence of physics that it tells us what we will see next given what we have seen before?
Or is this demand misguided, and the essence of physics is “to tell us what is really going on in the world”? Not if we live in a quantum world. Contextuality [9] tells us that it is impossible to assign truth values to all propositions (represented by projection operators) such that a measurement simply reveals the corresponding value; thus, in a nutshell, it is inconsistent to assume that the world has (only) well- defined properties that we are able to uncover by inspection or measurement. This insight can be cast into many different precise mathematical statements, from Bell’s theorem [10, 11] to no-go theorems about “facts of the world” [12, 13]. The upshot is that quantum physics only tells us what results to expect with which probability if we decide to perform a certain measurement. In this sense, quantum physics, the most accurate and successful theory we have ever had, talks directly about what we see (conditional on how we observe) and not what there is (in a naive sense).
From an orthodox perspective, this is highly surprising.It would not be so surprising if we reversed the arrow in Fig. 1c, and considered an abstract, information-theoretic notion of first-person perspective (not consciousness!) as more fundamental. Then the physical world would be an emergent, less fundamental notion, and we should expect our most fundamental theories to talk about what is seen and not what there is. Then we should also be prepared to find phenomena comparable to those in noncommutative geometry: while the latter leads to “something close to ordinary space, but not quite”, we should analogously expect to obtain “something close to an ordinary world, but not quite”. Which in some sense we do—we live in a quantum world.
But if we take this idea of “reversing the arrow” seriously, how can we concretely make this work?
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