Let's start with a quick comment about string theory. My knowledge is only journalistic, but it's clear that string theory is a mathematical theory and states its hypotheses about extra dimensions using mathematics. And as your comment about additional variables already suggests, there's nothing mathematically esoteric about higher dimensions. When variables have the right sort of independence, they represent distinct mathematical dimensions in a mathematical space, though not necessarily a physical space. (Quantum theory uses abstract spaces called Hilbert spaces that can have infinitely many dimensions. But these mathematical spaces don't represent space as we usually think of it.) Of course, it might be that getting the right physics will call for the development of new branches of math. Remember, for example, that Newtonian physics called for the invention of Calculus, and though earlier thinkers had insights that helped pave the way, Calculus was something new. Just what sort of new...

It's certainly true that Bohr and Heisenberg, among others, interpreted quantum theory in a way that put the knowing subject center stage, but this is just one part of a controversy that continues to this day. Einstein and Schrödinger, for rather different reasons, resisted these more epistemic interpretations, and while some would say that Einstein lost in the wake of the investigations of Bell's inequality, Bell himself was very attracted to realist interpretations of quantum theory. "Collapse" interpretations, such as the so-called GRW theory, are not epistemological interpretations, nor is Bohmian mechanics (a development of de Broglie's pilot wave idea), nor, for that matter, is the Everett interpretation (roughly, the "many-worlds" interpretation.) So the simplest thing to say is that there partisans on both sides and the controversy is ongoing. If you'd like to read more, you could do worse than to get a copy of Alistair Rae's Quantum Physics: Illusion or Reality? or John Polkinghorne's ...

The obvious response is that there isn't a single response, and for a simple reason: quantum theory doesn't have anything to say (or not obviously, anyway) about souls -- at least not if a soul is some non-material thing that doesn't fit into the equations we use to do physics. There is a view that's rather like many worlds and that allows for something soul-like. It's called the Many Minds interpretation, and you can read a short account of it (and get further references) by following this link: http://plato.stanford.edu/entries/qm-everett/#6 However, this won't address your worries about the afterlife. And since this is a topic that physics has even less to say about than it says about souls, it's even clearer that there's no good answer. That said, a handful of extra thoughts. The first is that IF there is a non-physical soul (a very big "if), then we can start by asking what happens to it after death on our usual non-quantum picture. And then we could say that whatever the story...

The answer to the general question is that indeterminism at the "lower" level doesn't have to mean indeterminism at "higher" levels. Here's an abstract way to think about it. Suppose some theory has a set of possible states -- call it S -- and a strict deterministic law governing how the states change over time. Let's suppose that this theory is both true and know to be true. But suppose, unbeknownst to us, each of the states in S can be realized in many different ways, at some sub-microscopic level that we don't have access to. And suppose that even though the law that tells us how we get from one state in S to another is deterministic, there's no deterministic law governing exactlywhich way states in S will be realized as the system moves from one state to another.We might never have any reason to believe any such thing, but it could be true all the same. That's one story about how indeterminism at the micro level might not infect the macro level. Another way is a "for all practical...

My closet. More seriously, it isn't expanding into anything. The universe contains all of space-time. If it's expanding, this is a fact about the stuff that makes up the universe itself, and not about its relation to some other place/thing/void. So what does it mean to say that the universe is expanding? At least this: that distances between things (on average) are getting larger. One common analogy: think about the surface of a balloon that's being blown up. Imagine the ballon as covered with little dots. Then as the balloon expands, each dot will get further away from each other dot. The obvious objection is that the balloon is expanding into the space around it -- there's more than just the surface of the balloon. That's true. But that's why it's an analogy rather than a perfect fit. Although it puzzles the imagination, the math of space-time doesn't call for positing a container space for the expanding universe. The geometry is internal to the universe itself.

We normally assume that causes can't precede their effects, but this isn't a logical truth, and in fact it's possible to tell coherent stories where the principle fails. By "tell coherent stories," I don't just mean tell science fiction. As your author may point out (I haven't read the book), it's possible to say how causal loops and backward causation might fit into physical theory, even though there's no strong case for saying that such things actually happen. So there's no issue about the "logic" of causality being violated. As for your Christmas shopping, this isn't really an example of the future affecting the present. Your present intentions do the causing. You want to make sure that come Christmas day, Granny gets that gorgeous pair of Manolo Blahniks, and it's that present desire and intention that gets you to head off to the shoe store. Granny's beaming grin isn't reaching back from the future to get you to the mall.

I'll have to confess that I'm one of those people who was early on seduced by a particular sort of solution to this sort of problem, and since then I've never been able to feel the force of the puzzle. Here's a somewhat fanciful example that conveys the idea. Suppose that we have a body whose temperature at 12:00 midnite is o° Celsius. And imagine that the body's temperature is increasing at a steady rate as follows. Let T t be the body's temperature at time t. And let the temperature at any given time over the hour after midnite be given by T t = t where t is the number of minutes after midnite. In other words, the temperature rises steadily at the rate of one degree Celsius per minute. It goes through all the intermediate values in finite time. If the arithmetic of real numbers makes sense, so does this. And so I can't find the puzzle. Pick any time you like over that one hour period. There's an answer to the question "What is the body's temperature at that instant?" And in...

Hi Keith. A perfectly good question. The short answer is that any such assumption is, to put it mildly, controversial. There are respectable ways of thinking about quantum theory that look at it in more or less the way you suggest. Those ways, however, come at a price: they require us to assume that there are influences on the particile that propogate faster than light. They also go beyond what the theory itself has to say, and add some extra physical/interpretive machinery. That's not a criticism of such views; it's just a remark. Quantum theory, alas, is a topic that leaves us in a peculiar lurch. As physics, it's fantastically well-confirmed and scientists and engineers make use of it in a vast number of ways that give us things like cell phones, laptop computers, MRI machines and a good deal else. But there are weird things about the math of the theory (I'll spare you any equations) that make it quite different from "classical" theories in ways that are still enormously controversial. Just to...