According to the internet, the sun rose at 6:02 this morning in Washington. I was awake and when I got around to opening the blinds I could see that the sky was blue. The sheets on the bed are blue too, though not the same blue. They're a few years old and I like the way they feel when I touch them. But the sun doesn't rise, does it? Although centuries ago, people thought it did, they were just wrong. And there isn't really a sky—no dome or roof or thing of any sort. There are sheets, but they're made of atoms, which aren't colored, nor are collections of them. And touching the sheets; don't get me started on that. Except… If someone says the sky is blue, they've said nothing false, nothing wrong. Same goes for telling you the color of their sheets; likewise for telling you they touched them. People may be mistaken about what being a blue sheet amounts to, or a blue sky, or about what's going on under the covers, so to speak, when we touch a sheet, or anything else. But that doesn't make the...

There are interpretations of quantum mechanics that make related claims. There's the transactional interpretation, proposed by John Cramer and developed more recently by Ruth Kastner. It holds that quantum events such as measurement results occur when there is a "handshake" between an advanced wave, traveling from future to past, and a retarded wave, traveling from past to future. The so-called two-state vector formalism, pursued in recent years by Yakir Aharanov and Lev Vaidman, is in some ways similar. Huw Price has long argued that if we allow for backward causation, we can avoid having to posit faster-than-light action at a distance. Some people have argued that in certain cases, quantum teleportation involves information moving from future to past. But all of this is controversial and it would be hard to argue that a consistent understanding of quantum mechanics requires backward causation. To which we should add: these interpretations do not claim that quantum mechanics can exploit any...

I'm sure that Stephen Maitzen will have useful things to say, but I wanted to chime on in this one. You have just given a perfectly consistent description of what actually happens in a simple polarization experiment that I use most every semester as a teaching tool. Classical logic handles this case without breaking a sweat. But there's another point. You've described the phenomenon in terms of light waves. That's fine for many purposes, but note that the wave version of the story of this experiment comes from classical physics, where (for the most part at least) there's no hint of logical paradox. The classical explanation for the result is that a polarizing filter doesn't just respond to a property that the light possesses. It also changes the characteristics of the wave. Up-down polarized light won't pass a left-right filter, but if we put a diagonal filter between the two, the classical story is that the intermediate filter lets the diagonal component of the wave pass, and when it does, the light...

It's not a stupid question. The way that popular accounts "explain" quantum mechanics leads naturally to your question. The moral is that those popular accounts are not to be trusted. Quantum mechanics is unusual in that on the one hand, we understand very well how to apply it and what we should expect to find in experiments if it's correct, but on the other hand there is sharp disagreement over what quantum mechanics is telling us about the nature of the things we use it to predict and explain. The problem you're raising comes from the superposition principle. A quantum system can be in a superposition of being in two different, non-overlapping places, for example. When that happens, there's some probability that if we "look" (make an appropriate measurement) we'll find the system in one of the places, and some probability that we'll find it in the other. However, we can't understand this as a simple case of ignorance --- as a case where the system really is in one place or really is in the other and...

I'm not sure what the difference between the philosophical and the mathematical sense of "determinism" is supposed to be, but I think that the answer will be the same in any case. And that answer is: it depends on how you think quantum theory should be understood. On what we might describe broadly as the "orthodox interpretation" of quantum theory, the answer is no: the decay is not a deterministic event. Roughly put, this means that the state of the world before the decay doesn't determine whether the atom will decay. There are some complications here about relativity and about so-called entangled states, but we can leave them aside. On this way of looking at quantum theory, sometimes the "wave function" or "quantum state" changes unpredictably and discontinuously, and these changes are genuine chance events. Radioactive decay is a special case. According to Bohmian mechanics, the most important of the so-called "hidden variable" views, quantum systems are thoroughly deterministic. What happens in the...

I will confess that I don't see the charm of Tegmark's view. I quite literally find it unintelligible, and I find the "advantages" not to be advantages at all. You suggest a few possible attractions of the view. One is that "atomic and subatomic particles have only mathematical properties (mass, spin, wavelength, etc.) and hence we might as well see them as nothing but math. Any proton, for example, is quite interchangeable with any other." But first, the fact that we only have mathematical characterizations of these properties is both false and irrelevant insofar as it's true. It's false because knowing something about the mass or the spin or whatever of a particle has experimental consequences. It tells us that one thing rather than another will happen in real time in a real lab. If that weren't true, we'd have no reason to take theories that talk about these things seriously; we'd cheat ourselves of any possible evidence. Of course, we may not know what spin is "in itself," and perhaps to that...

My short answer is that we don't need to be able to visualize higher-dimensional spaces in order to reason about them. I'd be quite astonished if Stephen Hawking could visualize 11 or 26 or even 5 dimensions. In fact, visualizing even three dimensions is not as easy as people think, as one realizes when trying to think through certain "ordinary" geometrical descriptions. But there are tricks that can sometimes give you the sense of visualizing higher dimensions, as with various diagrams of a four-dimensional "hypercube." Here's an example: https://plus.google.com/117663015413546257905/posts/VteWm45DCff Turns out that what I've said is more or less what the well-known physicist Sean Carroll says here: http://www.preposterousuniverse.com/blog/2009/03/30/why-cant-we-visualize-more-than-three-dimensions/ though he adds some speculations that you can evaluate for yourself. But on the question you ask, it's (1) you can't, (2) you don't need to, and (3) there are all the same some tricks.

The rule of thumb when you hear someone claim that quantum mechanics explains or underwrites something about minds is to be very, very suspicious. Let's suppose that two particles within some microtubule get entangled. (Caveat: I know more or less nothing about microtubules, but that won't matter for what follows.) Now suppose that these particles get dispersed into spacetime. The chance that these particles will remain entangled for any significant length of time at all is near enough to zero that the difference isn't worth arguing about. That's because if anything else interacts with either particle, the entanglement will be destroyed. Entanglement is very fragile. In entanglement experiments, physicists have to go to great lengths to prevent decoherence—the process by which interaction with the environment destroys entanglement, or more accurately, disperses it into the environment, in effect diluting it. But even if the two particles somehow stayed entangled, this wouldn't give us any special...

There's no simple uncontroversial answer to your question, but perhaps a couple of points will be at least somewhat helpful. "Wave-particle duality" is ultimately too narrow a way to think about what you're interested in. The things that get described as illustrating "wave-particle duality" are special cases of the phenomenon of quantum interference, and that, in turn, is a manifestation of the fact that quantum states obey a superposition principle . At the end of the day, there's no substitute for thinking of this mathematically, but I'll do my best to avoid that here. You probably know at least a bit about polarization. If we hold a polarizing filter (e.g., a lens from good sunglasses) up to a light source, the light that gets past it is polarized along a common axis—let's say the vertical axis. In principle, with the right kind of light source, we can turn the intensity down so that only one photon is emitted at a time. If such a photon passes the filter, it will hit a screen in one spot—like a...

I'm not quite as happy with Prof. Kraus's way of putting things. I'd suggest having a look at this review by philosopher/physicist David Albert: http://www.nytimes.com/2012/03/25/books/review/a-universe-from-nothing-by-lawrence-m-krauss.html As for whether something has always existed, Prof. Maitzen and I may well agree, but there's some ambiguity here that's worth thinking about. If we say that something has always existed, the most plausible way to understand that is that there has never been a time when nothing existed. If there's no time before the Big Bang, then we can say that something or other has always existed. Suppose, however, that there are times earlier than the Big Bang. One possibility is that what there was is an earlier cycle in an oscillating universe. In that case, the "something" was the sort of thing that's around in this phase of cosmic history. Another possibility is that what was around was the vacuum of quantum field theory. The vacuum, indeed, is not matter, but it's...