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I am a very ordinary art teacher, one who breaks into a rash at the merest

I am a very ordinary art teacher, one who breaks into a rash at the merest glimpse of an equation, and one who is trying to get to grips with the quantum world. Can you answer me this question about the double slit experiment? In the Double Slit experiment, why is it assumed that the particle splits and then reconverges at a point in between the two expected points, rather than a single particle merely bending and curving its trajectory to arrive at the in between point? Yours, Keith

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 mention one important sort of issue: probability is built into quantum theory at the very foundation. But how to understand the probabilities is quite another matter. If we treat them as merely reflecting incomplete description or incomplete knowledge, we run into one set of problems; if we treat them as deeply random behavior in nature itself, we run into other problems. And on it goes.

It's hard to talk about the puzzles of quantum theory with no math at all. One book that at least makes an attempt is the latter part of Peter Kosso's Appearance and Reality. (Actually, there are some simple equations, but not the kind you need to solve. They're just abbreviations.) You might have a look there.

In what sense does the earth rotate around the sun? couldn't the entire universe

In what sense does the earth rotate around the sun? couldn't the entire universe be thought to rotate around any arbitrary point?

In the century and a half following Copernicus, when the debate around this issue was at its height, there were actually several major differences of opinion between those figures (such as Kepler, Bruno, Galileo or Descartes) whom we tend to lump together as adherents of the new astronomy. The debate between Medieval and modern astronomers is usually set up in terms of a pair of interconnected differences of opinion, over (i) whether the Earth or the Sun is stationary or moving, and (ii) whether the Earth or the Sun is at the centre of things. The Medieval view was that the Earth was stationary at the centre of the universe and the Sun revolved around it; the modern view was that the Sun was at the centre and the Earth revolved around that. Except that that's too simplistic. With regard to that notion of a centre, some people (like Bruno) were firmly committed to the notion that the universe was infinite, and they explicitly stressed that no centre could be defined in an infinite universe at all, whether for the Earth or for the Sun. Over on the other side, Nicholas of Cusa, who gets lumped together with the more traditional (so-called) geocentrists, also made exactly the same point. With regard to motion, meanwhile, Descartes (for rather complex reasons of his own, not worth exploring here) believed that both the Earth and the Sun were at rest -- indeed, that if motion in the true sense was going to be ascribed to either of them at all, it would have to be to the Sun.

So why do we classify these figures in the way we do? What did the new astronomers all agree on, to set them apart from the traditionalists? It was that, whatever they decided about the behaviour of the Earth, their account of that case would resemble the account they gave of the behaviour of the other planets, and would differ from the account they gave of the behaviour of the Sun. The Medieval astronomers thought that the Sun moved in a circular orbit around a resting Earth, and (a few epicycles notwithstanding) they thought exactly the same thing about a planet such as Mars. The Earth was the odd one out, the one that did something different from the others. The modern astronomers thought that both the Earth and Mars described the same kind of circular or elliptical orbit around the Sun. For them it was the Sun that was doing something different from the other astral bodies, even if they didn't always agree on precisely what it was doing.

Suppose we do select some arbitrary points, define a frame of reference in relation to them, and then use this as an foundation for defining the motions of bodies. To make things vivid, let's base this alternative frame of reference on the Earth itself: the Earth will then be stationary by definition, and the other astral bodies might indeed, as you suggest, turn out to be revolving around it. But the difference between the Medieval and the modern astronomers will lie in the details of precisely how those other bodies' motions will be defined under this scheme. A Medieval philosopher would be happy to say that both the Sun and Mars were revolving around this stationary Earth, and that these two orbits had the same roughly circular shape. But a modern astronomer, if he could be persuaded to adopt this frame of reference (on the basis that all such selections of frames of reference are arbitrary anyway), might then agree that, looking at things in this way, both the Sun and Mars would indeed be revolving around the Earth: but he would insist that their motions would have very different characters. The relative motion of the Sun would be (roughly) circular or elliptical, but the relative motion of Mars would be much more complex than this. It would involve two components: a shared revolution with the Sun, following the latter's own motion relative to the Earth, plus an independent motion of its own around the Sun itself.

But then something else to consider is whether such selections between conflicting frames of reference are arbitrary at all. Some figures in this early modern period (for I must confess that I know this stuff better than I do the General Theory of Relativity and matters arising from that) did indeed regard them as arbitrary, the reason being that they thought that the only available frames of reference, in relation to which places and motions might be defined, were ones based on bodies, and they did not think that any particular body had a privileged status over the rest as the one that defined the 'correct' frame of reference. But others, most notably Newton, thought that there was such a thing as an absolute frame of reference, defined not by bodies at all but rather by an eternal and immutable space in which these bodies were located. He acknowledged that we could never discover by empirical means which objects (if any) in the physical world were at absolute rest, in relation to this absolute space, but he felt that it was reasonable to conjecture that the centre of mass of the solar system might be. Notice that he did not say this of the Sun itself, because his opinion was that the Sun actually jiggled about a little bit. In Newtonian physics, it's not so much that the Earth revolves around the Sun, but more that the Earth and the Sun both revolve around the centre of mass of the two of them taken together; but, since this point is very close to the centre of the Sun alone, the effect on the Sun is very much less pronounced than the effect on the Earth. And then Newton also gave exactly the same account of the interaction between the Sun and Mars. Indeed, it was really Newton's work that signalled the end of this particular debate. The reason why people aren't still arguing about this issue isn't because anyone managed to prove beyond doubt that theirs was the correct answer to the question. Rather, Newton showed that the question itself didn't actually make much sense. The Medieval astronomers would tell one story about the Earth, and a different story about both the Sun and Mars; the modern astronomers up until Newton would tell one story about the Sun, and a different story about both the Earth and Mars. But, as far as Newton was concerned, the Earth and Mars and the Sun were all doing the same thing, all revolving around their common centre of mass. This revolution was less noticeable in some cases than in others, but nevertheless the same cause (namely, gravity) was producing the same effect in, as a matter of fact, every object in the universe.

Many of my science professors have remarked that the law of conservation of mass

Many of my science professors have remarked that the law of conservation of mass and energy is unprovable (or at least unproven); is this really the case, however? Isn't the problem of the conservation law precisely the problem of induction? (I.e., we observe that the mass and energy of every system we have ever examined has remained constant, but how do we know that this will hold true (1) in the future and (2) of all systems?) But presumably when my professors have said that the conservation law is unproven, they didn't mean that this is so because of the problem of induction (after all, if they took this route then all of science would be "unproven"!). I feel as though they are treating the conservation law as exceptional when in fact it is not. -ace

I agree with you that observational evidence for the hypothesis that all processes conserve energy (or mass, or mass-energy) inevitably fails to prove that hypothesis (though succeeds in confirming the hypothesis strongly), just as our observational evidence for the hypothesis that (say) "All bolts of lightning are followed by claps of thunder" inevitably fails to prove that hypothesis. Even if every lightning bolt we have observed so far has been followed by a thunder clap, no contradiction would result from the next lightning bolt occurring without a thunder clap. So the "problem of induction" applies to both examples equally.

Perhaps your science professors had something else in mind in emphasizing the "unprovability" of energy conservation. Suppose we observe a process that apparently fails to conserve energy. The system's energy before the process occurs seems to exceed the system's energy after the process occurs. Rather than rejecting the conservation of energy, couldn't we always respond by saying, "Well, I guess there's an additional form of energy of which we had previously been unaware, which makes up the difference"? The availability of this tactic might make the "law of energy conservation" (or any similar conservation law) seem especially suspicious -- unable to be tested in the same way as other hypotheses. It might seem that a conservation law does not have the status of a hypothesis that gets confirmed by evidence, because the quantity of "energy" is not specified in advance as given by a particular formula, but is just whatever it has to be (with the dimensions of force times distance) in order to be conserved.

However, it seems to me that this view of energy conservation is mistaken. Of course, new forms of energy have occasionally been discovered. And they have sometimes been ascertained by figuring out what it would take to "balance the books." Still, faced with a case that appears to violate energy conservation, it would be utterly ad hoc simply to reply, "Well, there must be some unknown form of energy out there, sufficient to make energy conserved." Rather, scientists work to figure out a general formula for the quantity of this new kind of energy, and to find other situations where the posited new kind of energy makes a difference. Scientists seek some other, independent ways to test for the existence of this new kind of energy. So the law of energy conservation is as testable as any other general scientific hypothesis, despite the fact that there may always turn out to be further types of energy that have not yet been found.

(A case in point was the discovery of the neutrino. The particle was posited precisely to restore the mass-energy and momentum balance in beta decays. The story of how evidence was accumulated for this highly elusive particle is a good example of how scientists cannot justly save a conservation principle simply by adding to the equation whatever new term is needed to balance the books.)

It seems that most astronomers and theoretical physicists believe that time only

It seems that most astronomers and theoretical physicists believe that time only began at the formation of the universe with the "big bang". Assuming that this is correct, is it possible for time to end (to no longer exist)? If so, what conditions would be necessary for this to occur? JW (Australia)

The easiest way to think of this may be in terms of some regular relation between time and the size of the universe. Expressing this regular relation as some mathematical formula, it may turn out that, going back from the present in accordance with this formula, we get to a past point of time at which the size of the universe is zero. We would have reason to postulate such a starting point as the origin of the universe if all we know about the universe supports or is at least consistent with our backward extrapolation. Big bang theorists believe that this is (by and large) the case.

The same mathematical formula may be such that, going forward from the present, we get to a future point of time at which the size of the universe is zero once more. We would have reason to postulate such an end point of the universe if all we know about the universe supports or is at least consistent with our forward extrapolation.

There are other conceivable end-of-time scenarios. The amount of stuff in the universe might be declining in accordance with some regular formula which predicts that there will be no stuff left at some future point in time. Or the amount of motion in the universe might be declining in accordance with some regular formula which predicts that all motion will cease at some future point in time. Again, if all we know about the universe supported or were at least consistent with such a forward extrapolation, we might have reason to postulate such an end of time.

To sum up. The passage of time presupposes that something is happening. Something happening in turn presupposes stuff moving in space (or some analogues, on which see Peter Strawson's book Individuals). Time can end by any of these three presuppositions ceasing to hold. We cannot experience such cessation. But we can have reason to postulate it by forward extrapolation -- just as we can have reason to postulate a beginning of time (big bang) by backward extrapolation.

Such extrapolation raises further philosophical issues: What can support our assumption that any mathematical formula (any laws of nature) supported by the evidence we have near the present will continue to hold? And likewise backwards: What supports a big-bang theorist's assumption that the laws of nature she relies on did not evolve but rather held all the way back in time so as to sustain her extrapolation?

If the universe has existed forever, i.e. if the universe did not have a

If the universe has existed forever, i.e. if the universe did not have a beginning, would the present time be possible? That is, if an infinite amount of time was necessary to get to the present time? And if this is so, does this mean the universe necessarily had a beginning?

Short answer: You say: "That is, if an infinite amount of time was necessary to get to the present time?" But to get to the present time from when? The natural impulse is to say: to get here from the first moment. But, of course, the hypothesis of an infinite past means precisely that there was no first moment. So, again, where are we going to start counting? To get here from a time ten years ago will take ten years. To get here from a time twenty years ago will take twenty years. So, given an infinite past, we can pick a time infinitely long ago, and it will take infinitely many years to get to here from there, right? Wrong. The hypothesis of an infinite past does not mean that there was a time infinitely distant from the present. What it means is that there are infinitely many past moments of time, each one of which is some finite distance from the present. Now, this hypothesis may well be false (I take it that both the physicists and the theologians would agree that it is, albeit for very different reasons): but I'm not persuaded that it's logically incoherent.

Longer answer: Philosophers will often draw a distinction between two different ways of thinking about time, which they call the 'A-series' and the 'B-series'. (This distinction has its origins in work done by John McTaggart about a hundred years ago). The two series differ in the way they pick out different moments of time: both are equally common in ordinary discourse, but philosophers will disagree over which gets more to the heart of what is really going on at a metaphysical level. The A-series specifies moments of time through their relation to the present; while the B-series specifies them according to the order they have amongst themselves, without giving any privileged status to any one moment in particular. Thus, "now", "yesterday", "ten years in the future", "soon", "a long time ago" and the like would all be A-series expressions; while dates such as "15 May" or "the ides of March, 44 BC", together with comparative terms like "earlier than" or "ten years after" all belong to the B-series. Note that, in the A-series, the same expressions are continually changing their reference from one moment to another. Tomorrow, the word "today" will refer to a different day than the one to which it currently refers. "It is not raining" is true now, but it was false a few hours ago, and the chances are that it will be false again pretty soon. In the B-series, by contrast, there is no such change: thus, the B-series sentence "The date of Julius Caesar's death is the ides of March, 44 BC" is just as true today as it was when it happened. Indeed, as the seer saw, it was already true that he would die on that day, even before the fateful day arrived.

Now, with this distinction in mind, let's think about your question again. Suppose, first, that we decide that the right way to think about time is with the A-series. But, with the A-series, we have no need to "get to" the present, because we're already here. The present is our starting point: not in a physical sense, but rather in the sense that all other times, past as well as future, are defined in relation to the present. And so, if we begin defining the following sequence of times: "one year ago", "two years ago", "three years ago", we will notice that there is no finite point at which we are logically required to draw this sequence to a close. This should not be thought to imply that an infinite past is physically possible, just that it is logically possible. No matter how large a number n one opts to insert into the specification "n years ago", one can always replace it with n+1. It's up to the physicists (or, if this should be more to anyone's taste, the theologians) to decide whether there actually is any number n such that "n+1 years ago" doesn't refer to any genuine moment of time. But at least the question makes sense, and that's enough to settle the philosophical issue.

But then, what if the B-series is a better way of specifying different moments of time? Well, then it should be even more readily apparent that there will be no logical impediment to an infinite past, because the B-series doesn't recognise the notion of "past" at all. In the terms of the B-series, take any date d you like: there is no number n such that another date n+1 years earlier than d cannot be defined. (Though, again, it's for others to decide whether or not all such specifications will actually refer to really existing moments of time).

It's also worth just noting that all of the same points can be made about future time as about past time.

If science is based on observable, measurable data, what is the basis of science

If science is based on observable, measurable data, what is the basis of science's belief of the origins of the 'Big Bang'? Even religions talk of the cataclysmic beginnings of the Universe, but they don't claim the Bang was of Nothing. Observable, mathematical data suggests nothing begets nothing.

This gets a bit beyond my expertise, but I suppose like you I find these sorts of issues irresistible. (Kant thought that part of that irresistibility was a feature of our being rational beings, by the way. Perhaps he was right.)

Anyway, I'm not exactly sure what you mean by "origins of the 'Big Bang'," but I'm unaware of any scientific theories advance any position at all on any cause or originary reason for the big bang. The bang itself, perhaps from an original singularity, is as far back as natural science goes. Indeed, in a sense, it makes no sense to speak about any time before the big bang, since as I understand it time began with the big bang, too.

Now, I have encountered speculation about the big bang being one in a 'series' of big bangs--where a bang would be followed by a period of expansion, which would be followed by a contraction back to a singularity, which would be followed by another big bang. But that still wouldn't offer an explanation about why this cycle exists in the first place. And, anyway, my understanding is that calculations of the mass and rate of expansion of the universe indicate that the universe is not expected to contract. Instead, it's expected to expand forever until entropy leads everything to decay into a kind of very low level radiation. Some have called this cold-state hell.

Perhaps some of my colleagues can offer more on this topic.

Keep this in mind, however: while it's true that atural science can only tell us about the natural order, it can make claims about things unobserved and even unobservable. Like in times past the dark side of the moon, many parts of other planets are at present unobserved, yet science makes certain claims about them. (For example, that the laws of physics apply to them; that objects there are composed of the same elements as objects here, etc.) Many sub-atomic particles (quarks, for example, perhaps even electrons) can never be observed directly. Forces are not themselves observed. What scientists observe are their effects--or anyway observable events that scientists believe are their effects. What business does natural science have in positing the existence of unobservables? Well, it's a complex story, but basically science is warranted in positing the existence of things that have never or can never been observed on the basis things that can be observed. Moreover, claims about those unobservables can be discliplined and even overthrown in science by observations of observables. That can't or anyway need not be the case in religion. In the case of religion, unobservables are posited irregardless of observation and the character and standing of those unobservables may well be (and is often) little disciplined by observation.

This may be a silly question displaying only my ignorance on the subject. My

This may be a silly question displaying only my ignorance on the subject. My question has to do with point-particles and spatiality. Physicists say that point particles have causal powers, i.e. photons striking someone’s eyes at certain wavelengths cause them to see. Perhaps photons are only contributory causes to one’s seeing. Physicists also say point particles are objects that are both concrete and physical. That is, they can be located in space which entails they are spatial objects too. However, by definition a point-particle lacks width, length, and depth, the three spatial dimensions. My question is how can this be? Is this a conceptual incoherence, or am I missing something? Does spatiality entail physicality or conversely, does physicality entail spatiality? Alternatively, is it that these two concepts have no intimate connection? Please explain. Thanks.

Your question seems to concern the connections between being spatial, being concrete, and being physical. Part of your question seems also to concern the idea of point particles.

Now it might be that ordinary material objects really do consist of point particles. If that's true, then point particles are concrete, physical, spatial entites. (That a point body has no dimensions does not keep it from being spatial: it has a location in space.)

On the other hand, it might be that the fundamental, elementary objects that physics seeks are not point sized. (Perhaps they are strings or whatever.) In that case, it might still be that certain physical theories that invoke point bodies do a pretty good job for certain purposes. Point bodies would then be idealizations -- useful ones. They would be abstract rather than concrete objects, in one sense of "abstract." (It could work the other way too: hydrodynamical theories that treat water as a continuous fluid may work very well even if a body of water is, in fact, a collection of mass points, or at least molecules rather than a continuous substance.)

Of course, an abstract object can still be spatial. For instance, a perfect geometrical sphere is an abstract object, unrealized (I presume) in the actual world -- merely ideal. However, it is spatial.

The notion of a thing being "physical" is not easy to unpack. Some objects that might seem to qualify as 'physical' do not have causal powers. If Newton was correct, then there was absolute space and absolute time. They would be described by theories in physics, so to that extent, they would be physical. But they would have no causal powers. The same applies to the laws of nature. They are not causes, but they help to explain facts and events. Are they "physical"? They are not concrete, of course, since they do not have spatiotemporal locations.

Is the universe infinite? And if it isn't, what is outside it? Are there lots of

Is the universe infinite? And if it isn't, what is outside it? Are there lots of universes, or is it all just fractals? And what about other dimensions? Is it possible that time and laws of physics work differently in other universes? Helen from Worcester, age 12

Hello Helen from Worcester! Thank you for your excellent questions!

Let's start with whether the universe is infinite. The answer is: We don't know! But suppse it is NOT infinite. Then what is outside of it? Perhaps the answer is that there is no such thing as "outside" of it. The universe consists of all of space and time. An "outside" would be a location -- in space -- that is outside of the universe -- and so outside of all space. That is a contradiction, right? (It would be in space and outside of space at the same, um, time.)

Suppose that the universe is not infinite. Suppose you head off in your spaceship in a particular direction, and just keep going straight. Since the universe is not infinite, will you eventually get to a wall that you cannot penetrate: the edge of the universe? No! Instead, you might just find yourself approaching the place from which you started, but from the opposite direction. Space might be curved so that there is only a finite amount of it, but there is no edge to it. (Suppose you were a flat creature living on the surface of a very large balloon. If you headed off in one direction on the balloon's surface, you would eventually arrive back where you began, even though you never reversed the direction of your travel at any point in your trip.)

Finally, you asked whether the laws of physics might work differently in other universes. I don't know whether there are any other universes besides the one in which we live. Some cosmologists think that there are. In fact, some cosmologists and philosophers think that every possible universe exists. (That would nicely explain why our particular universe exists: because every possible universe exists. On the other hand, it would leave us with the question: Why does every possible universe exist?) If every possible universe exists, then of course, the laws of physics in some of those universes are different from the laws in our universe.

On the other hand, perhaps there is only our universe. In that case, the fundamental laws of physics would seem to be arbitrary, brute facts: they could have been different, and there is no reason why they aren't diffferent. They just aren't.

Some philosophers and physicists have speculated that the fundamental laws of physics (whatever they really are) could not have been just a *little bit* different from the way they actually are. If you tried to make them just a little bit different, then the differences would have various consequences, and those consequences would have consequences, and ultimately, you would find yourself dividing by zero, or with probabilities that are greater than 1 or less than 0, or something logically impossible like that. If that's right, then the fundamental laws of physics could not have been a little bit different. But they still could have been a lot different. They just aren't.

Hope that gives you something to think about! Thanks so much for your questions.

If having two dimensions, height and width, means that a diagonal line is just a

If having two dimensions, height and width, means that a diagonal line is just a tiny line up connected to a tiny line across, repeated on a level so small we don't notice and the line appears diagonal, does that mean that everything in our 3D world is almost 'pixelated' at a really microscopic level? Sorry, I'm having problems describing what I mean but see if you can make any sense of that. =) Thanks.

There may be a debate over whether spacetime is continuous or granular: I will have to leave that to others. But there seems to be a problem with saying that a diagonal line is a microscopic staircase. If it was, then the diagonal of a one inch square would be two inches long, when in fact its length is the square root of two.


Hello, I wonder how laws of physics, mathematics and logic influence each other. What I mean is the following: In Quantum Mechanics (probably even in general physics), only very few non-linear problems can be explicitly solved. The most important ones are 1.the harmonic oscillator (potential r^2) and 2. the Hydrogen atom (potential 1/r). This is the reason why almost any other non-linear problem is first reduced to a r^2 or 1/r-potential problem. This seems like lucky coincidence or a divine act or whatever you might call it: 2 very basic physical problems can be expressed and solved in a very basic mathematical way. Now I keep on wondering: If our mathematics was based on some different algebra than the one it actually is, say, elliptic functions (=objects that are reasonably hard to express in "our" mathematics), would our understanding of physics be different? (For example: would we better understand physical facts that are now "too complicated" (because of their mathematical complexity), and ...

Very interesting query. But is it necessarily a 'lucky coincidenceor divine act' that basic physical problems can be solved using basicmathematics? Maybe the reason is that is that our mathematics has beendeveloped in order to deal with the physical world.

True, thereare many familiar cases where techniques which were were firstdeveloped by pure mathematicians later turned out to be useful fornovel physical applications. For example, complex numbers are great fordealing with alternating currents in electrical circuits. This may make it seem that the physical applicability of these bits of mathematics is a coincidence after all.

But it may still be true that, at a more general level, mathematics is designed to analyse the kinds of patterns that are displayed by physical phenomena. The same kinds of patterns often repeat themselves in nature, as your question implies, so it is scarcely surprising that we have developed mathematics to deal with these patterns.

Of course, none of the above rules out the possibility that some 'alternative' mathematics would enable us to deal with problems that are present mathematically intractable.