Goose Report '08

January 6th. Fucking January, fucking 6th, in fucking Canada. The snow's already melting, and the geese are already back, and yet we're not even halfway through what winter is supposed to be yet.

You might remember that last year I clocked the geese returning on March 16. I then went on a bit about Global Warming. Most of my comments there are still valid, so go and read that and the follow-up post if you haven't already. Today, my mind being a little bit blown by seeing the geese back this early, excuse me if I rant a little.

Okay, how the hell can so many seemingly thinking, rational people still doubt Global Warming? I can understand doubt coming from those who have a vested interest in it not being true, along with those who get all of their information form such sources. That's just confirmation bias (or lying) and Garbage In, Garbage Out respectively at work. I don't like it, but it's no surprise.

Particularly on my mind right now is the issue of South Park creators, Matt Stone and Trey Parker, thanks to an episode I saw a couple days ago. They seem to really have it in for Global Warming. Now, they seem to go out of their way to attack any and everything, so an episode or two on it wouldn't be surprising or anything to worry about. I'm not going to pretend her that there aren't some people who go a bit overboard in their zeal and deserve a little mockery for it, but that apparently isn't the extent of Matt and Trey's attacks.

From my count, it seems that South Park has, directly or indirectly, addressed Global Warming in five separate episodes: "Spontaneous Combustion," "Two Days Before the Day After Tomorrow," "ManBearPig," "Terrance and Phillip: Behind the Blow," and "Imaginationland" (episodes II and III). So, it's clear that Matt and Trey really have it in for Global Warming, and it's probably a safe bet they doubt the validity of Anthropogenic Global Warming and/or the possible consequences.

The question then is: Why? The two of them have shown remarkable skepticism in the past, taking down the likes of John Edwards ("The Biggest Douche in the Universe"), psychic detectives ("Carman's Incredible Gift"), and too many aspects of religion to mention. So what's different here?

Getting the obvious possibility out of the way: They're right, we're wrong. I don't really buy this one, of course. Personally, I don't know enough about climate science to study everything and come up with my own, independant conclusion (to any degree of confidence that I could challenge people who study it for a living), so I'm left trusting the experts. And the conclusion among them is that AGW is real and a problem. There are, of course, dissenters, but many of them have corporate ties you'd expect to introduce a bias or are so obviously cranky that I can debunk their claims myself.

So why don't Matt and Trey simply trust the experts here? Well, I'm guessing it's simply because they think the experts are wrong. I'm not going to hazard a guess right now as to why this is, as there are many possible ways they could have come to this conclusion, and I have no evidence for any particular one of them.

What I will bring up here is why they stick to this belief. For this, the chapter from the paperback edition of Michael Sheremer's Why People Believe Weird Things, "Why Smart People Believe Weird Things" gives us a very good answer. If you haven't read that, I'd recommend checking it out for the full story, but to sum it up: Smart people are very good at defending beliefs they arrived at through irrational reasoning.

This raises the issue of how important it is to be willing to change your mind. Personally, I've probably got a ton of beliefs I arrived at for bad reasons. I could well be wrong about many of them, and the issue at stake here, Global Warming, could easily be one.

So I'm opening this up to the commenters. A couple issues here you could address, depending on your own beliefs: 1) Why do you think so many smart people don't believe in AGW? What led them to their initial beliefs? or 2) Try to convince me why I shouldn't trust the expert opinion on this issue. Go for it.

Proceed with your information binge...

Too much information!

The God Hypothesis

I'd like to make a few comments about my recent post, Intelligent Planting. I left the narrative without any comments there, as I figured this was an allegory that worked well enough on its own. I set up a parody of Intelligent Design to better illustrate all the leaps in logic design proponents expect people to make. It starts with jumping from "it doesn't look random" to "it was designed." Then it jumps from "it was designed" to "God/Pete designed it, and he also did all these other things recorded in the Bible." Now, of course, design proponents are all about hiding their religious affiliation, but it's there, and it is their ultimate goal, whether they'll admit it or not. I also then threw in some of the other doggerel they use to justify this for good measure, particularly mocking the appeal to faith.

That all being said, you might be somewhat surprised to learned that Intelligent Design wasn't my initial impetus for writing this story. Instead, this comes from a different argument for God which makes much the same leap in logic (from saying there was someone or something to saying it was God). This was what's known as the Cosmological Argument. When boiled down, it essentially becomes, "There was an ultimate cause for everything, therefore God."

You might want to take a moment to read through the Wikipedia article on this argument, linked above. What I'd like to call to your attention is the simple fact of how many variations on this argument there are. The Cosmological Argument is often presented as being strictly logical, but if that were so, then you wouldn't expect these variations on exactly how the Prime Mover/Uncaused Cause/God started things. Therefore, it would seem that most or all of these arguments are likely making some assumptions behind the scenes (or are just fallacious).

For example, let's take the argument of Thomas Aquinas, one of the more complete versions. From the Wikipedia summary:

1. Every finite and contingent being has a cause.
2. Nothing finite and dependent (contingent) can cause itself.
3. A causal chain cannot be of infinite length.
4. Therefore, there must be a first cause; or, there must be something that is not an effect.

Few would argue with points 1 and 2, but let's take a look at point 3. Why is it that a causal chain cannot be of infinite length? Presumably this is simply stated because the thought of it seems absurd, but is it really? Let's extend things into the future. Under most modern models for the universe and many religious models as well, time will go on infinitely into the future. This means that as long as it keeps going, we'll keep on having a causal chain. Thus, the causal chain will extend infinitely into the future. Ipso, a causal chain of infinite length. (Man, have I been itching to properly use "ipso" in a sentence...)

So, if it can extend infinitely into the future, what's wrong with having a causal chain extend infinitely into the past? It's at this point that it seems a bit more absurd instinctively, but logically it doesn't have to be. All laws of physics we know of are time-reversible, with a single exception that allows us to see order in time, the collapse of a wavefunction. If you compensate for collapse and run things backwards in time, you can see the same theme of causation occurring. Instead of a sperm and egg causing a zygote, you get a zygote causing a sperm and an egg, for instance. Running things this way, it doesn't seem so absurd that things might go on forever.

So here we have the problem with this particular argument: a false premise. The argument may still be technically valid (the conclusion can't be false if all the premises are true), but with a false premise, it's unsound, and we have no reason to believe the conclusion given this argument. Now, this doesn't mean that there wasn't actually some first cause, it only means that this argument doesn't prove it. So, let's entertain the idea that there was a first cause now, for completeness' sake.

What can we say about this first cause? Well, nothing, really. We can't claim it must have been intelligent, or even complex in any way, as it's easily possible for intelligence and complexity to arise from unintelligent, simple conditions, driven by a little randomness. However, we have a lot of religious people pointing to their own god and saying it fits the bill of a first cause. The argument for a first cause, even if it were valid, doesn't give us any reason to believe that the first cause is anything like their god, but that's not necessarily a problem.

What we can do is treat their god as a hypothesis to explain the first cause. A tactic like this is often done by scientists; we have a problem, so we hypothesize something to explain it which is a bit beyond what we know. Since it's beyond what we know, it often comes with the ability to predict other phenomena we haven't tested for yet. So, we then go and test for those phenomena. If they exist, we have evidence that this hypothesis is true. We can do roughly the same thing for the hypothesis that a god was the first cause.

The immediate problem is that invoking a god here is a gross violation of Occam's Razor. An explanation that invokes a particular brings in many interrelated claims, and has many, many predictions beyond the simple creation of the universe. This doesn't mean it isn't true, however; it just means that we're going to need a lot of evidence to support it. Otherwise, a simpler explanation (or less precise god) will be much preferred.

Now, there are many deities we can choose from, so I'll only use a couple examples here, positioned at extremes. Most other deities will fall on the continuum somewhere between these, and a mix of the applicable arguments will apply.

First up, I'm going to take the god believed in by many evangelical Christians in the US. This is the god discussed in the Bible, who did all the things claimed there. He's omnipotent, omniscient, omnipresent, and just generally omni. He also takes a role in our day-to-day lives. He listens to and answers prayers. He smites those who displease him in any way. When people die, their souls are judged by him. If they've led a ridiculously devout life, free from even the slightest pleasure (shadenfreude over thinking about sinners going to hell excepted), they go into heaven, a place of eternal bliss. If they're even slightly off, or believe in a slightly different god, they go to hell, a place of eternal torment. (Aside: I don't particularly care if anyone believes in exactly this god; I'm just using it as an extreme example.)

This the hypothesis to be tested. On the other end, we'll have the null hypothesis, which we'll be comparing this to. At the end, we hope to be able to reject either this or the null hypothesis. In this case, we can use the null hypothesis, "No god exists." If we find sufficient evidence for this god, we'll be able to reject this null hypothesis.

So, what of this is testable? If you say "none of it," scroll down a bit. I've got your untestable god there. This is a god who interferes with the world. If there are natural effects of supernatural causes, they can be tested for. Anyways, there are two big points here that we can test: Intercessory prayer and smiting the heathens. Let's start with prayer. This is something that actually has been scientifically tested. Repeatedly. And then some more. And again, because every time, the results weren't satisfactory. Whey weren't they satisfactory? Because the tests were either poorly done, or they didn't show any effect to prayer. Even if you don't agree that the ones who showed an effect were poorly done, it's still only a marginal improvement. It's nothing compared to the effect you'd think an omnipotent god like this could have.

But wait! "Absence of evidence isn't evidence of absence!" I hear you cry. Ah, well there's a big exception to that. Absence of evidence can indeed be evidence of absence when you've properly and thoroughly looked for evidence. I call it the Modus Tollens Exception, as you can phrase it in the following logical form:

P1: If A exists and we use method M to search for evidence, we will find evidence E.
P2: We used method M to search for evidence, and did not find evidence E.
C: Therefore, A does not exist.

Boiling it down to the simple logic, this is the valid structure:

P1: If A and M, then E.
P2: M and not E.
C: Not A.

This is essentially the Modus Tollens argument form, with a small complication of an extra requirement in the premise. Since we're using a logical form here, my argument that absence of evidence is in this case evidence of absence is also valid.

It's a bit harder to test the prediction that this god will go around smiting heathens, as we can't really control things here. However, if you look at what happens in the world, there isn't good evidence that this takes place. For instance, many evangelicals claimed that Hurricane Katrina was their god smiting New Orleans for all the debauchery that takes place there. The problem was that the French Quarter, which was where most of the debauchery took place, was one of the least-damaged areas. This particular claim, at least, doesn't hold water. (Ugh... I swear that pun was unintentional.)

In any case, testing prayer alone is sufficient here. We can, of course, add to the evidence for all the other claims about this god, though it's not necessary for the time being. Since we have evidence that prayer to this god doesn't work, we can reject the hypothesis that this god exists. And no, we don't go and accept the null hypothesis that no god exists; we just say that we fail to reject it. It could well be true, but we haven't shown that here.

Alright, now let's switch to the other extreme. Let's take a Deist god. This god created the universe, and then just kind of sat back and watched. Or maybe he went off to create another universe, or just took the next few billion years off to slouch around and watch TV. Or maybe he's a "she," or an "it," or some other gender we don't have a pronoun for. Not much is claimed about this god. In fact, aside from that he created the universe, not anything is claimed about this god. In contrast to the previous case where so much was claimed about the god that it was easy to find evidence against him, here, we don't have anything claimed at all beyond what we know happened. With this, we can't make any testable predictions about him, so we can't scientifically test for his existence.

This is still a hypothesis, though. The problem is that it's a completely useless hypothesis. There's nothing we can do to improve upon it, or get any further evidence that it might be true. There isn't even anything we can do to differentiate it from similar hypotheses, such as saying that instead of a god, a Flying Spaghetti Monster created the universe. Or we could say that the universe spawned yesterday from primordial slood with all the particles in just the right positions and velocities for us to be here with all this evidence for a past and memories of it.

In the end, there's no way to reject this hypothesis. But coupled with that is the fact that there's no way to get evidence for it. There's no reason for you to actually believe in it. The fact that it can't be disproven is no reason to believe, as following that logic would lead you to believe a million contradictory explanations for the beginning of the universe. This is why science doesn't do anything with untestable hypotheses; they're utterly useless.

In the real world, most gods people believe in fall somewhere between these extremes. They try to balance out not contradicting reality with having enough predictions to be useful. However, this doesn't really solve any problems. In order for their to be evidence of a god's existence, it has to make some predictions that later turn out to be true (and of course, can't be adequately explained without him. A god predicting gravity isn't a big deal). Simply throwing away disproven predictions and holding onto untestable ones still doesn't give anyone a reason to believe in this god.

However, I could well be wrong. If I am, if there's some god out there with good evidence for his existence, I would in fact quite like to know about it. I'd expect to have heard of it by now, but you never know. Maybe the right study just hasn't been performed yet. In which case, I challenge any believer who believes they have a testable prediction about their god to go out and perform a study to test it. Perform it well enough, and a positive result could be just what you need to convince me. Until then, I'm happy living my life accepting the null hypothesis as most plausible.

Proceed with your information binge...

Too much information!

Something for nothing and your universe for free

One argument I keep running into that is supposedly evidence for God (sometimes a generic god, sometimes a specific one) is that the universe began, therefore it must have been created. Sometimes it's more elaborate than this, sometimes not. In the cases where it's just this simple, it's effectively a God of the gaps argument. Since that type of argument has been dismantled repeatedly, I'm going to focus on the more elaborate versions today.

The most common elaboration to this argument is that the creation of the universe violates conservation of energy. "It's a well-known fact of science that you can't get something from nothing," they say. Interestingly, it seems that the people who say this sort of thing rarely have any real background in physics, much less a background in theoretical physics or cosmology. Before making big assumptions like this, wouldn't it make sense to check with someone who knows what they're talking about in this area to see if they could explain it?

Now, if only we had a cosmologist on hand... Wait a second, I'm a cosmologist! Well, I guess I'd better try to make some sense of these problems then. So, to the claims that the creation of the universe violates conservation of energy, my response can be summed up in two simple retorts: "Says who?" and "Even if so, so what?" Allow me to elaborate.

The first catch is that we don't know for sure that the creation of the universe actually does violate conservation of energy. First, let's keep to known science, and use an example taking place within our own universe. Let's say that somehow, a massive particle was created. Since mass = energy, this took up energy to create it. Now, what could have happened to allow this creation? A few possibilities:

1. Some physical process took place which resulted in an excess of energy. This extra energy was converted into this particle.
2. Even a vacuum doesn't have zero energy. It's possible that this particle borrowed energy from the vacuum in order to form (possibly along with its antiparticle if it has other properties such as charge which need to be conserved).
3. This particle was created alongside a mirro version of itself which has negative mass, resulting in a net change of zero energy. Note that we've never observed negative mass particles, but our current laws of physics don't bar them from existing.

So, let's expand to the creation of our universe. It turns out that for each of these, there's a nice parallel for the creation of the universe as well:

1. Some physical process took place outside our universe which resulted in an excess of energy. This extra energy was converted into our universe.
2. Whatever medium exists outside our universe might not necessarily have zero energy. It's possible that the creation of our universe simply borrowed some energy from this medium. A parallel anti-universe might also exist to balance quantities which must be conserved.
3. Our universe was created alongside a negative energy version of itself, so the net change in energy is zero.

There's also one more explanation which works for our universe, but not for the particle example:

4. Our universe has a net energy of zero. It is possible that the mysterious phenomenon we've termed "Dark energy" actually has negative energy, and this balances out the positive energy all of the mass in the universe provides. A little catch is that there's likely much more dark energy in the universe than all the other mass, so we'd actually be at an excess if this were true. That's little problem though, as it could easily have just been radiated away or whatever outside our universe.

So there you have it, four possible reasons why the creation of our universe might not violate conservation of energy. But even going into all that isn't really necessary. The catch is, violating conservation of energy isn't necessarily a problem when it comes to the creation of the universe. The reason for this is a bit complicated, but a simple version is as follows: Conservation of energy is an observation we've made which always seems to hold within our universe. We have no evidence that it holds outside our universe, or even that any of our laws of physics are the same out there. Therefore, we don't have reason to believe it must hold at the point of creation.

Now, for the more complicated explanation. We actually do have one explanation for why energy (and other properties, for that matter) is conserved. The reasoning is complicated, so I won't go into it here, but the key point is that it relies on what are known as symmetries. In the physics world, a symmetry is more than simply being able to mirror something and have it be the same. What it means here is that we could move the whole frame of reference in some way, and all the physics would remain the same.

There are three big symmetries of this type you'll know of. There's translational symmetry, which means if you move a foot to the right for instance, physics stays the same. There's rotation symmetry, which means whichever way you turn, the physics is the same. And there's temporal symmetry, which means that physics stays the same over time. There are also some others you probably haven't heard of it you haven't take college physics, such as gauge symmetry, but you don't need to worry about those here.

The important point about this is that there's a law of physics which states that for every symmetry, there must be some conserved quantity. This is completely unintuitive, but it's provable. Not easily provable, and most people reading this probably wouldn't understand the proof in any case, but it is provable, so just trust me on this. When we apply this law, we get the following conservations from the following symmetries:

-Translational symmetry gives us conservation of momentum.
-Rotational symmetry gives us conservation of angular momentum.
-Temporal symmetry gives us conservation of energy.
-Gauge symmetry gives us conservation of charge.

The important one for our purposes is the third: Temporal symmetry gives us conservation of energy. What happens if we no longer have temporal symmetry? Well, we can no longer guarantee conservation of energy. Now, think back to the beginning of the universe. At this point, all of the universe is compressed to a single, zero-dimensional point. Are the laws of physics the same here? Not at all. Temporal symmetry must be broken at this point, so we have no reason to believe that conservation of energy must apply. The instant after it, we start to have temporal symmetry, so whatever energy we start with we're stuck with, but there's no way to say what this might be.

So there you have it: a cosmologist's perspective on conservation of energy at the beginning of the universe. We don't know that the beginning of the universe violates conservation of energy at all. Even if it does, this isn't necessarily a problem. Even if all this is a problem, it's still at best a God of the gaps argument, and that's really no reason to believe at all.

Proceed with your information binge...

Too much information!

Pseudodebate

Continuing on the theme of "pseudoskepticism" over the past few weeks (see here and here), I've come upon some of Marcello Truzzi's original comments on the subject and have decided to give some specific responses. You can read the article, originally published in his Skeptical Inquirer, here.

After a brief introduction, Truzzi starts out with discussing the burden of proof of evidence. Most of his article follows on this theme, so I'll just quote this to give the summary. (All italics is his original emphasis.)

In science, the burden of proof falls upon the claimant; and the more extraordinary a claim, the heavier is the burden of proof demanded. The true skeptic takes an agnostic position, one that says the claim is not proved rather than disproved. He asserts that the claimant has not borne the burden of proof and that science must continue to build its cognitive map of reality without incorporating the extraordinary claim as a new "fact." Since the true skeptic does not assert a claim, he has no burden to prove anything. He just goes on using the established theories of "conventional science" as usual. But if a critic asserts that there is evidence for disproof, that he has a negative hypothesis --saying, for instance, that a seeming psi result was actually due to an artifact--he is making a claim and therefore also has to bear a burden of proof.

So here's the situation: Some experiment somewhere did a test for the presence of psi. They came back with results and claimed that these constituted evidence for psi. What is a skeptic to do? Truzzi's strawman of a skeptic would immediately say that the result must have been an artifact or due to some explanation other than psi, and then give no justification for this. But just because no justification is given doesn't mean no justification exists.

Let me illustrate this, once again with the example of "slood," a postulated substance with ill-defined properties. In our world, we can explain almost everything without appealing to slood. Any events that people have attempted to explain with slood are just as easily - if not more easily - explained by known phenomena. There are many models of the underworkings of the universe, and not one of them predicts the existence of slood. In fact, fitting it in to any of these models would require a drastic reworking. Simply put, there's absolutely no reason to believe that slood exists.

Now, let's say one group of never-say-die scientists designs an experiment to test for the presence of slood. If slood exists, this experiment would be expected to give Result A (which is generally a statistically significant deviation from what we would expect in a sloodless universe). The experiment is performed, and Result A is found. The scientists then claim this is evidence of slood.

So what's a skeptic to do here? Accepting slood would require a drastic reworking of known science, and up to now there's been no reason to believe it exists. On the other hand, there are many other possibilities to explain why the experiment resulted in the way it did:

1. A statistical fluke - Generally, statistical significance requires 95% certainty. This means that there's a 5% chance this result was obtained purely as a matter of chance. Of course, some results can be more extreme, and the chance of them happening randomly is less (though never zero).
2. A known mechanism - The experiment might have failed to control for (or properly control for) the possibility that some known physical phenomenon influenced the result. In this case, the result could just mean that this phenomenon was coming into play.
3. An unknown mechanism - Maybe it wasn't slood that caused the result of the experiment. Maybe it was dools, a substance which no one has even thought of yet (but which doesn't require a drastic reworking of science to fit in). Or maybe our universe is all a giant simulation and the designer decided to toy with us by changing the results.
4. Fraud - Many "scientists" make a living promoting the existence of slood, and finding evidence that it exists would be in their benefit. Some such scientists might have been involved in this experiment and had a chance to cheat. Also, it's known from past experiments to test for slood that fraud has indeed occurred.

Adding these four possibilities in, we've got a total of five ways this result could have occurred, only one of which implies the existence of slood. Now, the number of ways it could have occurred alone doesn't give us the chances that it's any one way. To get this, we have to look at the likelihood. From the beginning, we know that accepting slood would require a drastic reworking of science and we've seen very little prior reason to believe it exists. This makes this possibility very unlikely, so it's much more likely that instead one of the other possibilities came into play.

So even despite this experiment's results, it's still most likely that slood doesn't exist. Many amateur skeptics will stop there and simply say the evidence isn't convincing enough. However, some skeptics will then go a step further and analyze the experimental protocols to judge the plausibility of alternatives 2 and 4. Some scientists might even see if they can come up with a theory for a new phenomenon to meet alternative 3.

Generally, the result of these will be the skeptics coming up with ways the experimental controls can be tightened and the scientists with ways to change it to rule out alternative theories. If the original experimenters are serious, they'll then take these changes to heart and perform another, better-designed experiment with a few checks against fraud. If they aren't serious, they'll whine about "pseudoskeptics" and make no progress towards a better experiment.

Sometimes, in the real world, investigators do indeed take recommendations to heart. For instance, this happened in the case of the Ganzfeld experiments. What's happened in every one of these cases I've come across is that the results take a sudden plunge back towards the expected results. Sometimes the significance fades away completely, while other times it remains. In either case, this gives evidence that the skeptics were right in that there were some problems with the experiment.

The next step of inquiry will generally have skeptics and scientists looking over the experimental controls again to see if there are any remaining flaws. If some are found, the process is repeated. If none are, slood proponents will then dance on the rooftops claiming slood is proved to exist, but one important step is still left. This step is replication. What is done here is that a completely independent group should recreate the experiment from scratch, and see if they get the same results. Preferably, no one involved with the first experiment should be involved in the replications, and if possible, those involved in the replications should be neutral on the matter or even negatively biased.

The point of replication is to provide another level of checking against design flaws and fraud. The replicators can start off with all the recommendations over how to keep it tight, and shouldn't have any bias which would lead them to consciously or subconsciously influence the results. It also provides another check against statistical flukes, as it's less likely the same fluke would occur twice. Only once the experiment has been independently replicated do we truly have a reason to believe that slood exists - though we can never rule out alternative explanations. Further experiments should likely be performed to test other proposed properties of slood and to see if alternatives can be ruled out. After a long time has gone on with many tests of slood, none of which it fails, it will eventually become accepted science.

A single experimental result is never enough to change scientific consensus, and considering it most likely that an unusual result is due to an artifact, poor experimental design, or fraud is simply the default position. It takes work to overturn the current scientific consensus, and paranormal enthusiasts rarely want to put in this work. When they actually do, it tends not to work out for them. Skeptics are there to make sure they follow proper procedure and don't try to short-circuit the system, not to bar the way to new findings. If some claim has truth behind it, it can make its way in through the standard system. Accusations of skeptics being pseudoskeptics really just amount to giving up and fighting the wrong the battle.

Proceed with your information binge...

Too much information!

No place left for God

From a story via Bad Astronomy, it looks like there's an interesting new theory coming out which might explain what happened prior to the Big Bang. Essentially, it turns into another universe contracting down to almost nothing, then undergoing a Big Bounce to come back out again.

Anyone else thing that if this theory gains ground, it's going to drive religious people crazy? If the universe had no beginning, the concept of a God creating it goes right out the window. Sure, some of them might come up with ideas like a secondary temporal axis, but this isn't going to be tractable to the public. What they're going to have to do is deny, deny, deny. If this theory becomes commonly accepted, expect it to see just as much controversy as evolution.

Proceed with your information binge...

Too much information!

Physics Q&A #2: The Fundamental Forces (part 2)

(Note: I have some diagrams I want to add in, but I don't have access to them on this computer. I'll put them in when I get home from work.)

Welcome back to the concluding part of this 3-part Physics Q&A. If you haven't already, I recommend you go back and read the first two parts of this entry. If you haven't read them, you'll likely be quite lost.

This time, we're going to tackle the two most complicated forces: The strong and weak nuclear forces. Of these two, the strong is the simpler one, so let's start there.

The Strong Nuclear Force

While electromagnetism works off of the electric charge of particles, the strong nuclear force works off of color charge. Of all the existing particles, only quarks and gluons have color charge, so these are the only particles that participate in strong nuclear interactions. A few brief notes on color charge:

• Color is conserved in all interactions


• All quarks have one of three colors: red, blue, and green


• All anti-quarks have one of the opposite three colors: anti-red, anti-blue, and anti-green


• Gluons have eight possible color charges (and one ninth theoretical charge that we've never observed). All of these are linear combinations of the typical quark and anti-quark charges, such as red-antiblue or red-antired + blue-antiblue


• Different colors attract, like colors can't interact with each other


• Only color-neutral particles can actually exist in stable states

The reason only color-neutral particles can exist is a bit complicated, but it has to do with symmetry. Essentially, any observable particles must be what are known as "color-singlets" (due to theory on symmetry and Lie Groups I won't get into here), which means that any color-swapping we perform on the gluons that make it up must result back in the same particle. Since we could do swapping such as Red <-> Blue or Blue <-> Green, any particle that shows any imbalance in color at all wouldn't be a singlet. This leaves only color-neutral combinations being allowed.

So, let's get down to how gluons and quarks interact, which gives us the fundamental nature of the strong nuclear force. The strong nuclear force has three possible vertices for interaction. The first and most important one happens when a quark goes along and emits a gluon. Since gluons must carry some color and color is conserved, this means that the quark must change color at the vertex. So for instance, we could start off with a red quark, which emits a red-antiblue gluon and becomes a blue quark. The other two vertices don't matter as much here, but for completeness sake, one of them is where a gluon emits another gluon, and the other is where two gluons directly interact (respectively, a vertex of three gluons and a vertex of four gluons).

Now, let's use this to try to put together a particle. First, let's start off with a baryon, which is made up of one red quark, one blue quark, and one green quark. A possible interaction here is for the red quark to emit a red-antiblue gluon and become blue, and then for the blue quark to absorb this gluon and become red. This leaves us with a color-neutral quark like we started with, so the interaction can and will occur, pulling the red and blue (now blue and red) quarks together. Of course, the third quark will also have to get pulled towards the other two to keep the baryon from splitting apart, so there will be interactions with it as well.

The other type of particle we can make is a meson, which consists of a quark bonded to an antiquark. For instance, let's say we start off with a red quark and an antired antiquark. The red quark can emit a red-antiblue gluon and become blue, and then the antired quark can absorb this gluon and become antiblue, leaving us with a blue-antiblue meson. This can then happen again, switching over to green-antigreen or back to red-antired.

However, there's a little quirk here. Red and antired don't actually cancel out with each other, and so don't actually qualify as color-neutral. So how is it that mesons exist at all? The trick here is that gluons undergo tons of these interactions and cycle through all the possible color combinations very rapidly. In fact, they can't really be described as oscillating but instead in a superposition of quantum states representing the possible color combinations. This means that at any given time, the "actual" color of a meson is red-antired + blue-antiblue + green-antigreen, and all of these do add up to neutral.

Before moving on to the weak force, there's one more quirk with the strong force I'd like to address: Why does it have limited range? Gluons, like photons, are massless and so have infinite lifetime, so why can't they travel out far?

The answer to this is complicated, but it starts with the fact that gluons also carry color charge, and since the second vertex which I mentioned briefly allows gluons to emit or absorb other gluons, then two gluons with different colors can attract each other. In general, you won't just have one gluon being exchanged between two quarks at a time; you'll have many. And all these gluons attract each other, compressing down into what's known as a "flux tube" between the two quarks. Any other gluons that are emitted will also be caught by this flux tube and will then travel over to the other quark.

The reason the electromagnetic force gets weaker with distance is that fewer photons emitted are going in the right direction to interact with the other particle (think of shooting a laser in a random direction with a target a close distance away. If you move farther from the target, its profile is smaller and you have a lower chance of hitting it). However, due to the effects of the flux tube, all gluons get pulled into the right direction so the number that interact doesn't decrease with distance, and the force stays the same.

So, shouldn't this imply that the force should be unbound rather than bound, if it doesn't decrease with distance? At first it seems so. The problem has to do with energy. Pulling quarks apart takes a ton of energy, and particles want to go to states with less energy. Eventually, you'll pull the two quarks so far apart that they'll find other quarks closer than each other and latch onto them instead (quarks only mate in pairs or triplets), emitting some energy and getting pulled in. Even if you had a perfect vaccuum, you're pumping a lot of energy into this pair by pulling them apart, and this is likely to result in pair production before long, giving two new quarks for each to attach to. So although the force could work at a large distance, it won't.

The Weak Nuclear Force

And finally, onto the last and most complicated of the fundamental forces. Part of its complication is that it further breaks down into two other types of interactions: Charged Weak interactions, which exchange a lot of properties between properties, and Weak Neutral interactions, which exchange only spin and momentum. Don't ask me about the adjective order; I didn't come up with it. Of these two, Weak Neutral interactions are a fair bit simpler and can sometimes actually act like a simple force, so I'll talk about them first.

Weak Neutral interactions are mediated by the Z boson, which is chargeless, high mass (so it decays rapidly and the force is short-range), and has a spin of 1. The allowed interactions are when a lepton or quark emits or absorbs a Z. The particle's type and charge are unchanged, but it gives some of its spin and momentum to the Z, which could then pass it on to another particle or decay into a particle-antiparticle pair.

This type of interaction is responsible for electron-neutrino scattering, which is where an electron and neutrino get deflected off of each other. Since neutrinos are chargeless, they can't be affected through the electromagnetic force, and since we do see this type of interaction in the lab, we know that Weak Neutral interactions are occuring.

And now, we get on to Charged Weak interactions. These interactions are mediated by W bosons, which are spin 1 and high mass like the Z, but unlike it have an electric charge of +1 or -1 and an isospin of +1 or -1 (respectively). As you may recall from my last post, isospin is a property that differentiates electrons from their neutrinos and the negatively-charged quarks from the positively charged ones.

The primary vertex for a Charged Weak interaction has some lepton or quark emitting or absorbing a W⁺ or W^-. Since charge and isospin are conserved, this causes it to flip over to its counterpart in the same generation. For instance, an electron (charge -1, isospin -1/2) could come along and emit a W^- (charge -1, isospin -1) and turn into an electron neutrino (charge 0, isospin +1/2). This W could then decay or it interact with another particle.

One common example of a Charged Weak interaction is Beta Decay, in which a neutron turns into a proton, an electron, and an electron-antineutrino. The neutron is made up of two Down quarks and an Up quark, while the proton is made up of one Down quark and two Up quarks. In the reaction, first, one of the neutron's Down quarks (charge -1/3, isospin -1/2) emits a W^- (charge -1, isospin -1) and turns into an up quark (charge 2/3, isospin +1/2). Now we have a proton and a W^-. Since the W^- is unstable, it quickly decays. Its favored method of decay at these energies is into an electron (charge -1, isospin -1/2) and an electron-antineutrino (charge 0, isospin -1/2), so this is what we see happening. One simple variant on this reaction is that instead of an antineutrino coming out at the end, one comes into the system at the beginning and triggers the decay.

Now, you might be wondering how exactly this serves to work as a force (since it's grouped into the four fundamental forces). The simple answer is, it doesn't. Calling these "forces" is just bad terminology, and careful particle physicists use the term "interaction" to describe them all. It might seem weird that this never acts like a force, but let me remind you that the other interactions don't always act like forces either. For instance, in an electromagnetic interaction you can have an electron and a positron annihilate each other into a pair of photons. No forciness here, just a change in the types of particles. This is just the case for Charged Weak interactions, except Charged Weak ones don't have any options that leave the reactants and products unchanged.

So that's it for this overly-long answer to a question no one asked. If you have any questions on this or future questions you'd like me to address, leave a note in the comments.

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Quantum Mechanics for Dummies #2: Observation

Well, it's been a while, but an e-mail exchange not long ago prompted me to get back to this series. If you haven't yet read it (or need a refresher), I recommend you go back and read my first post, on the Wave Nature of Matter. This time, I'm going to be talking about something that can happen to waves and is a very important part of Quantum Mechanics: the collapse (which is closely tied into the concepts of a measurement and an observation).

But before that, we need to cover the concept of eigenstates. (For anyone who already knows about it, this is a vastly simplified explanation, so you're probably safe just skipping past.) Unlike particles, waves don't have discrete positions they'll be in, but rather a range of possible positions they could be found at at any time. Since waves travel, the probability distribution of where it will end up will often change with time. However, there are ways to trap waves, such as a beam of light between two mirrors. In these cases, the wave can only take on discrete stable patterns so that it doesn't end up interfering with itself. These discrete patterns are what are known as eigenstates.

But the probability distribution for a wave won't always fall perfectly into one eigenstate. Often its probability distribution will be a linear sum of multiple eigenstates. Due to interference between the waves of the different states, this pattern won't be perfectly stable and will change somewhat with time, but it will generally do so in a periodic fashion.

This also isn't limited to cases such as light waves. For instance, all particles have a property known as "spin" (if you take that exactly as it sounds, you're close enough). If you measure the spin of a particle such as an electron, you will always get one of only two values, regardless of the orientation of your measuring device: +h/(4π) and -h/(4π) (called "spin up" and "spin down." Think of it as spinning clockwise or counterclockwise).

Both spin up and spin down are eigenstates of the electrons spin, but it's not necessary for the electron to be exactly in one of these states. To generate this, say you take an electron that you just measured to be spin up, then made a second measurement at a right angle to the first. Classically, you would expect to measure a spin of zero, but this isn't one the allowable results. Instead, you'll end up with a 50% chance to measure spin up and a 50% chance to measure spin down.

And here's where things get a bit strange: After you measure it once, if you go back and measure it the same way, you'll always get the same result. It's no longer a 50/50 split. However, if you go and measure it back in the initial direction, it's a 50/50 split here. The implication here is that by measuring the spin of the electron, you somehow changed it - in this case so that it was in a spin up eigenstate with respect to your new measurement.

What's happened here is known as wavefunction collapse. After your first measurement, the electron was spin up in the first direction, which corresponded to a 50/50 split when measuring from the second direction. This 50/50 split was a combination of two eigenstates for the electron. When you then measured it in this direction, one of those states was randomly selected and the electron then became 100% in that state.

And this when the misinterpretations start to happen. The reason for the misinterpretations is the fact that quantum physicists happened to use one particular word in describing it: "observation." In the sense of what happens, an observation simply entails measuring the wavefunction of something, causing said wavefunction to collapse.

But that's not how the word "observation" sounds to the layman. When many hear it, they then think, "So, does this mean that reality is unresolved until I look at it?" People started to believe that quantum states wouldn't resolve until the information from them had filtered its way to a human mind. Even when it came to quantum physics, people wanted to put the human mind on some special pedestal in the universe.

This argument wasn't limited to laymen however. At first, the best quantum theorists couldn't decide themselves what exactly caused the wavefunction to collapse. All they knew was that if they weren't measuring particles, the wavefunction wouldn't collapse, and if you were, then it would. (They tested this by means of the double-slit experiment, which I mentioned in my previous post in this series.)

So, you have scientists not knowing the answer and using a word which heavily implies that human consciousness actually is the answer, and what do you expect happens? People pick it up and start extrapolating, saying that we then must create reality with our minds and be able to control it as we see fit. Even if we were to accept the premise (that being processed by a human mind is what caused the collapse of a wavefunction), this in no way implies that the human mind actually creates or can control reality. The results are still inherently random, whatver the processing mind may wish.

Beyond that, there's actually good reason to believe that it isn't a human mind that causes the collapse of a wavefunction. Let's go back to the case of the double slit experiment, which is our best way of determining whether or not a wavefunction has collapsed. In this case, we'll be shooting electrons from an initial source through one of two slits. One foot beyond the slits is a detector screen. We know that if the electron's wavefunction is uncollapsed at the slits, we'll end up seeing an interference pattern on the screen, while if it's collapsed, we'll see the sum of two diffraction patterns.

If we just let the experiment run, without any detectors, we end up seeing the interference pattern (nothing's causing the wavefunction to collapse). If, instead, we put in detectors at each slit that will notify us if the electron passes through (say by blinking a light on the left or right side), we see the sum of diffraction patterns on the detector screen. Now, what if you were to try this: Have the detectors at the slits and turned on, but don't look at the lights. You could simply disable the feature that has it flashing the lights on the detectors and not store data of which slit the electron passed through, so no human could ever know which way it went.

In this case, we can expect to see one of two outcomes: Either we see an interference pattern, which means that without a human observing it, the wavefunction wouldn't collapse, or we could see a sum of diffraction patterns, which would mean the interaction of the electron with the detector (or some process within the detector after the detection) caused the collapse. This has in fact been done, many times. Very frequently, scientists did experiments using a detector but didn't care which slit was detected, and so they didn't set it up to tell them this data. The result of these tests? The wavefunction collapsed anyways, so human consciousness is not necessary to cause the collapse of a wavefunction.

Why then, do we still see people claiming that it is? Mostly it's do to a poor understanding of the subject. They see words like "observation" and interpret it to mean human observation. Even some professors of quantum physics (including one I had as an undergrad) made this mistake, and then taught it as accepted fact to their students. The only way you can really know for sure on something like this is to go to the experiments themselves. Fortunately, this particular phenomenon is testable, and it has been tested.* Unfortunately, this won't stop some people; I raised this issue up with my professor at one point, and he said testing it was a waste of time because he knew that human consciousness had to be involved. Well, you can't convince everyone.

*Edit to add: Unfortunately, no one seems to have a link to the studies that actually test this, most likely because they were done so long ago that they were never published online anywhere. Actual science has moved on far past this point, while popular science is just starting to get interested in it. I've asked a few people in the know about it, and while some, like the professor mentioned above, still hold to the view that it's human consciousness that does the collapsing, the consensus is pretty clear that the collapse happens long before any human mind looks at whether the particle was detected in either slit.

In fact, even when humans are looking at this, there's so much processing that goes on in the technology that interprets the data that the particle as already traveled and hit the plate at the end before information about which slit it passed through reaches the mind of a human (the "flashing light" is just a metaphor, it's not what's actually done in these experiments). So if it was human thought that was controlling these outcomes, then this result would also have to reach back in time to collapse the particle's wavefunction at some point before it hit the plate.

* * * * *

Other posts in this series:

Quantum Mechanics for Dummies #1: Wave Nature of Matter

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Physics Q&A #2: The Fundamental Forces (part 1.5)

(If you haven't read the first post on this subject, check it out here.)

Before I get into the latter two of the fundamental forces, I realized that one aspect of physics I take for granted probably isn't well understood by most who haven't done much with particle physics. This aspect is the fundamental particles of the universe; the basic building blocks of everything. I'm making an interlude post here to explain that to everyone, since the knowledge of it is critical to understanding the strong and weak nuclear forces.

There are many dividing lines between the fundamental particles, and I'll go through them one at a time to best sort them out. The first dividing line is between what are known as "Bosons" and "Fermions." Fermions are like solid matter, in that you can never put two of them into the same place (or quantum state). Bosons, on the other hand, can be stacked up without limit in the same place/state. Fermions tend to make up the bulk of matter, while bosons work to mediate forces. There also tend to be conservation laws about the number of Fermions, so you can't just go and create or destroy them. Bosons, however, have no such conservation laws.

Bosons

First, I'll go over the Bosons seeing as there are fewer of them and no more divisions between them (among the fundamental ones, that is. Many bound groups of particles can also be bosons, and there are extra divisions here). We know that the following fundamental bosons exist:

• Photon: Photons are little quantum pieces of light, and mediate the electromagnetic force. They have no mass and never decay, so the electromagnetic force has unlimited range. Photons are all their own antiparticles.
• W⁺, W^-, and Z: The W and Z particles mediate the weak nuclear force. They have very high mass (each ways about as much as an iron atom), and short lifetimes, leading to the weak force having only short range. The W⁺ and W^- are each other's antiparticle, and the Z is its own antiparticle.
• Gluons: Gluons mediate the strong nuclear force. They have zero mass and don't decay, but the strong nuclear force is still limited to short range for reasons I'll cover in the next part of this mini-series. Gluons are electrically neutral, but have "color charge" which determines attraction from the the strong nuclear force.

There are also two other theoretical bosons that deserve a mention here. The first is the Higgs particle (H), which is a massive uncharged particle predicted to exist by the Standard Model and which is currently being tested for. You might have heard that the Higgs particle is what "gives other particles mass," but this is a common misinterpretation of the theory. It's actually the Higgs field which gives particles mass. The W⁺, W^-, Z, and H particles are all quanta (fundamental pieces, like photons are of light) of this field. If the H particle exists, we might expect to see it interacting through the weak force in a similar way to the Z boson, except working at different energies due to its different mass.

The other theoretical boson is known as the graviton, and it was predicted to mediate the gravitational force similar to how photons mediate the electromagnetic force (see my previous post for exactly how). However, no direct evidence of its existence could be found, and Einstein's model of General Relativity did a much better job of explaining the how and why of gravity, so the graviton has generally been given up on.

Fermions

Fundamental fermions, unlike bosons, come with another dividing line into two more families: leptons and quarks. The difference here is that quarks feel the strong nuclear force while leptons don't. There also appears to be a nice symmetry between leptons and quarks, as they each have six particles which can be further divided up into three pairs (called "generations," an important concept for the weak nuclear force). For convenience of envisioning how the forces work, we then introduce a property called "isospin" which is equal to +1/2 for one particle of each pair and -1/2 for the other.

Additionally, each of these fermions has a distinct antimatter counterpart to it. These antiparticles have the same mass as the normal particles, but opposite isospin, charge, and color.

Leptons

Among the leptons is one you've likely heard of: The electron. It also has a light, neutrally charged particle called a neutrino which corresponds to it. There's also the muon and the tau, plus their corresponding neutrinos. However, if your only goal is to understand how the weak force works, you really only need to worry about the electron and its neutrino. A quick fact sheet on them:

Generation 1

Electron
Isospin: -1/2
Charge: -1
Mass: Very Low

Electron-neutrino
Isospin: +1/2
Charge: 0
Mass: Extremely low

Generation 2

Muon
Isospin: -1/2
Charge: -1
Mass: Medium

Muon-neutrino
Isospin: +1/2
Charge: 0
Mass: Extremely low

Generation 3

Tau
Isospin: -1/2
Charge: -1
Mass: High

Tau-neutrino
Isospin: +1/2
Charge: 0
Mass: Extremely low

Quarks

Quarks are the building blocks of protons, neutrons, and other similar particles. They bind in groups of 2 or 3 through the strong nuclear force to form these particles. Like leptons, there are 6 types of quarks, but to understand the weak and strong forces, you only need to know about the first two (subsequent generations work essentially the same way).

Quarks are affected by the strong nuclear force because they carry what's known as "color charge." Quarks can have one of three colors: red, green, and blue. Quarks of different colors are then attracted to each other. However, there appears to be a law of nature that no particle can exist alone unless it's color-neutral, so you can never see individual quarks. Instead, you see them either in groups of three with one of each color (known as "baryons") or in pairs of one normal quark and one antiquark (antiquarks have opposite colors of regular quarks, anti-red, anti-green, and anti-blue, and these alone cancel out the regular color). Also, unlike electric charge, color charge isn't innate to the type of particle; each quark can have any color (and antiquarks any anticolor), and even oscillate through different colors.

A quick fact sheet on quarks:

Generation 1

Down Quark
Isospin: -1/2
Charge: -1/3
Mass: Low

Up Quark
Isospin: +1/2
Charge: +2/3
Mass: Low

Generation 2

Strange Quark
Isospin: -1/2
Charge: -1/3
Mass: Medium

Charm Quark
Isospin: +1/2
Charge: +2/3
Mass: High

Generation 3

Bottom Quark
Isospin: -1/2
Charge: -1/3
Mass: High

Top Quark
Isospin: +1/2
Charge: +2/3
Mass: Very High (in fact, the highest of any particle known; about the mass of a gold atom)

If you want a convenient chart of these particles, there's one very popular poster you might have seen in your high school physics room which Wikipedia has gotten permission to host online for their article on the Standard Model. It's a bit dated and doesn't mention the Higgs particle, but other than that it's a great reference on the basic properties of the fundamental particles and forces (at least until you're at the point where you've got it memorized).

As before, if you have any questions on any of this, please ask. I'm doing this purely to help your understanding, so be sure to let me know of anything I haven't explained well enough.

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Why Blogism?

(Hey, it worked for Skepticism!)

Well I got tagged for this by TheBrummell (yes, it did get around to me), so here goes, a list of reasons why I blog:

• It's something to do. Honestly, this might actually have been the biggest reason for my starting this blog. I had a ton of free time at work (what can I say? I was so good at my job they couldn't find enough for me to do), and I needed something to do. So I blogged. I still have lots of free time around school, and I'm on a short vacation right now, so I still need something to do.
• Community. When I started this blog, I was just losing touch with all my friends from high school. I didn't plan on using this blog to make new friends online, but when it started to happen, it became a reason to keep going.
• Interacting with "famous" people. Sure, anyone can go and post on the blog of someone moderately famous in the blogosphere, but it's an entirely different feeling when they come and post a comment on your blog. (Yes, he was correcting a minor mistake I'd made, but I've corrected him on occasion too, and I maintain that I'd prefer to be corrected than leave a mistake up.)
• I can help grease the wheels of skepticism. I noticed early on that most of the big swaths of skepticism are already covered in various places by very good bloggers. I've found a few subjects that went unmentioned and covered them myself, but that's not my primary contribution to the cause. The most popular posts I've done have actually been what I call "Greasing" posts, where I talk more about the philosophical side of what we're doing. This includes my Why Skepticism? posts and the Distilled Wisdom series, which give explanations of why this is important and how you can argue better, respectively. While these posts aren't directly attacking woo, they serve the purpose of helping other bloggers attack it better. For instance, my second Why Skepticism? post showed how Godel's Incompleteness Theorem actually serves to help disprove faith rather than put a limit on science, as many woos are prone to claim.
• I can teach people about science. One thing I've noticed is that many people are genuinely interested in learning about the scientific picture of the world. The problem is that they see huge barriers such as having to be great at math and studying and getting an undergraduate degree before they can even be told qualitatively what's going on. With this blog, I can create a bridge out to them to teach them roughly what's going on without having to drown them in math. It's no coincidence that my Quantum Mechanics for Dummies post is the most frequent target of Google hits (beating out Faith no More lyrics and Bible quotes by a wide margin).
• I get to randomly reference Terry Pratchett, this note included.
  

I can't think of the expected five people to tag with this that haven't already been hit, but I'll send out a couple to Akusai and Tom Foss. Let's see what you've got.

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Physics Q&A #2: The Fundamental Forces (part 1)

Welcome back to Physics Q&A, where I answer physics questions sent in by readers in order to help give you all an understanding of how the universe works. This week I'll be addressing the fundamental forces of nature, explaining how they work and how they differ.

First, let me just give you a brief overview of the forces, before we get into the details of how they work:

Gravity
Acts on: Everything that has either mass or energy
Effect: Weak attraction between objects with mass or energy

Electromagnetic Force
Acts on: All charged particles and light
Effect: Attractive force between objects of opposite charge, repulsive force between objects of same charge. Acceleration caused by and/or causes light waves. Effects of special relativity give rise to magnetic effects between moving charged particles.

Weak Nuclear Force
Acts on: Leptons, quarks, and neutrinos
Effect: A bit complicated. Basically, the trick here is that all Weak interactions change the form of the particles involved. As such, it's really not a good idea to characterize this as a force, but more as an "interaction." Some people extend this to all the fundamental "forces."

Strong Nuclear Force
Acts on: Quarks
Effect: Binds quarks together to form baryons, or binds baryons together to form nuclei.

That's the essentials of it. If you want to get into the nitty-gritty of how they work, head below the fold.

Gravity

Let's start out with the oddball force: Gravity. As far as modern physics can tell, gravity acts in no way like the other forces. While the other three fit well under a model of interchanging particles (called "Gauge bosons"), Gravity fits best under the model of General Relativity.

So, at this point, you're likely wondering exactly how this model works and how it differs from Newtonian gravity. Of course, the actual equations aren't simple, but I can still explain it in qualitative terms.

The key realization that gravity worked differently than other forces was the fact that a particle's acceleration due to gravity was independant of its own mass. This then tied in with a law of mechanics you may or may not have heard: The path an object takes when under the influence of no outside forces is independant of its property. But, does this mean that the converse (If an object's path is independant of its properties, it's under the influence of no outside forces) must be true?

Logically, it doesn't have to be, but it's something at least worth investigating, and that's what Einstein did, leading to his formulation for General Relativity. In doing this, he realized that, for instance, a person standing on a surface in a gravitational field would feel a normal force pushing out from the surface that would be exactly the same as a person outside a gravitational field would feel if that surface were being accelerated upwards. This formed what is known as the Equivalence Principle - that a gravitational field is equivalent to an "acceleration" of space.

So, he set up equations as if an object in freefall (a path independant of its properties) were in a natural path, and holding it out against gravity were unnatural. This led to the formulation of what's known as the Schwarzschild metric, the fundamental equation of GR. (If you've forgotten what a metric is, I recommend you check my last Physics Q&A post.)

That's the history of it, but what does it all mean? In essence, the presence of any type of energy warps space such that the natural path of objects through time now curves towards it. You can picture this as matter sitting on a giant rubber sheet, with "time" pulling downwards. Objects like Earth then warp the sheet around them:



Someone standing on the surface of Earth also feels time pulling them downwards, but now they also see that space under them is slanted towards the center of Earth. This means that if their path goes that way, they'll get ahead in time faster, so they're also pulled inwards. Now, this isn't exactly how it works, but it's good for visualization.

The Electromagnetic Force

Let's proceed onto the simplest of the three forces that can be explained from the Particle Physics model: Electromagnetism. I'll just be focusing on the electric side of it for this post, as it's all that's actually needed for the fundamental model (magnetism is just the interaction of it with special relativity).

First, the basics of it: Objects have one type of charge, which can be either positive or negative. Objects with the same sign of this charge feel a repulsive force between each other, objects with the opposite sign of this charge are attracted to each other. The force of this repulsion or attraction is proportional to the magnitude of each charge and the inverse-square of the distance between the particles to a first-order approximation.

On very small scales, electromagnetism works through what's pictured as an exchange of particles (in this case, photons). To picture this, imagine you and a friend are standing on a sheet of ice. You have a heavy ball, and you throw it over to your friend. As you release it, conservation of momentum pushes you back. Then, as your friend catches it, conservation of momentum pushes them away from you as well.

That works for the repulsive case, though the attractive case is a bit more difficult. For this case, you have to imagine that the ball you're throwing has negative mass. This way, when you throw it out, it's momentum is like it's going backwards, so you're pulled forwards too. And when your friend catches it, they get pulled closer to you as well.

Since this is the simplest case, I'll take this chance to introduce you to Feynman diagrams, which are what we use to chart this exchange of particles. In these diagrams, we start out by writing out the initial particles at the bottom and the final particles at the top. For instance, if it's an interaction between two electrons, this step would look like:

Then, we draw some possible connection between the beginning and end. In this case, the simplest is simply each of the electrons at the beginning making a straight path to one of the end ones, but this represents no interaction between them, so it's not very interesting. If we want to do some actual interactions, we need to first define what type of vertices are allowed. For EM interactions, there's only one basic type of vertex: Some charged particle comes in, emits or absorbs a photon, then goes out:

A few notes on the lines:

• Straight, solid lines represent massive particles (such as electrons)
• Other types of lines represent gauge bosons. For instance, photons are represented by squiggly lines as seen above.
• The arrow on the line represents the direction of travel of a normal particle. If it points in a direction opposite that of the momentum of the particle, this is considered to be the corresponding anti-particle.

We don't need to worry about the last point for this interaction, since no antiparticles are involved. So, using this type of vertex, we end up getting two possible interactions that only include two vertices:



Once we go through a ton of complicated math using these two interactions, we can come with equations to govern it. However, it turns out that there are also a ton of possibilities (infinitely many) that use more than two vertices, but they're much less likely to occur. In the end, you get an infinite series of interactions which you can sum up, and the convergence is how things will end up behaving in the real world.

One of the big strengths of this manner of handling physics is that it doesn't only govern forces between two unchanging particles. For instance, we can also use it to represent an electron and a positron annihilating each other. To do this, we use the last point of my explanation of what the lines mean above. This way, we could make a reaction where an electron and a positron come together and turn into a photon. However, we run into a problem with this reaction in that it turns out to be impossible for momentum to be conserved. It is possible to conserve it, though, in a somewhat more complicated reaction that produces two photons:


But wait! If we can't conserve momentum for a single vertex, how come we can use that vertex within the chart? The trick here is that the internal lines we're using don't represent actual particles - there's no point in time you could freeze the interaction and see an intermediate electron. These are what we call "virtual" particles. They never actually exist in real space, but travel through imaginary space to help mediate the reaction. As such, they don't have to obey standard equations of motion, so they're allowed to have imaginary momentum or negative energy and other crazy stuff.

Now, I'm getting the feeling that a lot of you likely aren't completely following at this point, so before I continue on to finish up with the even more complicated forces, I'm going to stop the post here and open it up to questions.

Proceed with your information binge...

Too much information!

Physics Q&A #1: Curved Space

Welcome to my premier post of Physics Q&A, where I answer physics questions sent in by readers in order to help give you all an understanding of how the universe works. This week I'll be covering the question of what it means for space to be curved. I was also planning to cover the four fundamental forces here, but it got long enough I decided to just put it up and get at that in the next few days.

Q: What does it mean for space to be curved?

Warning: High math content below. Feel free to skim down to where I've marked "*****" if that's not your thing.

Before getting into this, it's helpful for you to understand what a metric is. Basically, it's a mathematical tool we use to measure distances in space. It takes a form like the following for normal, Cartesian space:

ds² = dx² + dy² + dz²

You might recognize this as being similar to the Pythagorean theorem for three dimensions, and that's no coincidence. For short intervals, you can calculate the distance between two points from the metric by:

Δs² = Δx² + Δy² + Δz²

In fact, in Cartesian space, this works exactly even for large distances, but this isn't the case in general. Most of the time we have to integrate along a line segment in order to find the length of it. For an example of a more complicated line segment, take a look at the metric for polar coordinates:

ds² = dr² + r²dθ²

Once we expand to three dimensions, we can add in another angle, φ, to get the spherical metric:

ds² = dr² + r²dθ² + r²sin²θdφ²

Then, for brevity's sake, as we won't be doing many complicated things with the angles here, we combine the two angles into a single angular portion Ω, getting our final spherical metric:

ds² = dr² + r²dΩ²

This is the basic form metric generally used by astronomers for flat space. However, it turns out we can modify it to cover curved space as well by changing the r² factor into some other function of r, which we'll call f²(r). We could choose virtually anything for it, but observationally we have a few limitations. Basically, on a cosmic scale, space appears to be roughly the same in every direction (it's isotropic), and we would expect it to appear the same from when viewed from any point (it's homogenous).

Actually deriving the possibilities for f(r) takes some work that you probably don't care about, so I'll just skip to the three solutions:

f(r) = r - This standard, flat space.
f(r) = R*sin(r/R) - This is known as positively curved space
f(r) = R*sinh(r/R) - This is known as negatively curved space

(In case you aren't familiar with it, sinh is the hyperbolic sine defined by sinh(x) = (e^x - e^-x)/2)

It turns out that if R is sufficiently large, then for small values of r, the metric for positively-curved and negatively-curved space behaves just like for flat space, so the difference wouldn't be perceptible to us. Note that when r becomes a significant portion of R, f(r) for positively-curved space increases more slowly than for flat space (angular distances correspond to less physical distance), while for negatively-curved space, f(r) increases faster (angular distances correspond to more physical distance).

***** (High-math content ends here)

So now the question is, what does space in these three different models actually look like? It's very difficult to picture in your mind how 3-dimensional space can warp, but if we bump it down a level, to 2-dimensional space, we can use a trick called "embedding" it into 3-dimensional space. What we do here is just take a 2-dimensional membrane and somehow bend it around so it has the curvature we want.

Case 1: Flat Space

This is the simplest case. Here, we just have a flat plane representing our space:



Everything in here is perfectly sane. If you draw a circle with radius r, you'll measure its circumference to be 2πr. Nothing interesting to see, move along.

Case 2: Positively-Curved Space

A bit more complicated, but still manageable. In this case, space ends up being represented as the surface of a sphere:



Now things are a bit more strange. If you draw a circle of radius r, you'll find that its radius is a bit less than 2πr. Additionally, the entire space is finite, and you can walk all the way around it given enough time. It's kind of like being on the surface of Earth if you pretend "up" and "down" don't exist. This type of space can be extended to three dimensions rather easily; just imagine that you can travel in space in any direction, and if you go long enough, you'll loop around to where you started. Additionally, at half that distance, no matter what direction you traveled, you'll end up at the same point, polar to where you started.

Case 3: Negatively-Curved Space

Here's where things go to hell. Negatively-curved space is a bitch, and we frankly have no way to give an entire representation of it using our tool of embedding it in higher-dimensional space. But, we can give a few local representations. The notable feature to negatively-curved space is that it has what's known as a "saddle" shape locally:



As you can see, if you travel off in the x-direction either way, space curves up, while if you travel off in the y-direction either way, space curves down. This has the result of stretching out space, so if you were to draw a circle of radius r, you'll find that it will have a circumference greater than 2πr.

Now, unfortunately we run into problems when we try to find a representation of negatively-curved space that has constant curvature everywhere. A simple hyperbolic representation which I used to generate the graph above doesn't have constant curvature everywhere. Another common negatively-curved surface is what's known as the pseudosphere:



The problem with using a pseudosphere to represent space is that it isn't isotropic - one dimension extends out to infinity and goes imaginary at one point, while the other wraps around. However, it does have constant negative curvature. In the end, it turns out to be impossible to find a representation of isotropic negatively-curved space in this manner.

If we try to extend things to three dimensions, things get even worse. With our 2-dimensional membrane, we could have the x- and y-directions curve opposite ways, but if we add another dimension, we have no opposite left for it to curve in. To resolve this, we have to go up to at least 5-dimensional space to embed it. This allows us to have each dimension's curving go in a direction 120 degrees off from the other two dimensions:



This allows us to give a partial representation of how it looks (I'll spare your minds the 5-d graph). Unfortunately, we still run into a problem with coming up with a representation for infinite, isotropic, constant-curvature space. The lesson we have to take from this is one of two things:

1. An embedded representation might not be necessary. It could be that space just has a fundamental law about how distances in it work determined by the metric, and embedding is just a sometimes-convenient way of looking at it.

2. Negative space just won't work. This would be the case if the real way things were made in the meta-universe was with our universe being embedded in some higher-dimensional Cartesian space. It's possible that things would work out this way, but we can never know for sure. This possibility might imply that our universe can't be negatively curved, but we can't know for sure.

Proceed with your information binge...

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Convenient Myths

I promised you guys last time I'd get to debunking some of the arguments against Global Warming, but I figured I'd go a step further and also debunk some of the bad arguments made in favor of it (oddly enough, I couldn't find nearly as many of these). Onto the myths!

Note: This post was so long I decided to get into the habit of using a "fold" to hide the bulk of it. Don't want to overload everyone's browser unnecessarily.

The Myth: The Earth goes through warming and cooling cycles, causing ice ages and warm periods. It's simply been warming since the last ice age.

The Truth: It is true that the Earth goes through cycles, but there are a couple of problems here. The first of these is the linear assumption, which is where people assume that since it was at point A in the past and point B now, it followed a linear path between them and will continue on it. In truth, the cycles are anything but linear. Let's take a look at what they actually look like:



Okay, first of all there's a lot of random variance at any time, but ignore that for now and look at the overall pattern. It's pretty cyclical alright, but it's not like a simple sine wave or saw blade. Rather, we see a pattern of a sharp rise in temperature of around 10°C taking place in a span of around 10,000 years followed by a gradual cooling over the next 100,000 years or so.

Now, let's look at our recent history on the far right side of the graph. We see that we've just come off of a spike which has stayed strangely level afterwards. (The timescale of the graph is too much to attribute this leveling to human activities.) What we would expect to happen next judging from the long-term cycles is that the temperature would plunge back down into another ice age.

There's another variant to this myth, however, that relates to a more recent cooling period: the "Little Ice Age," which took place within the last millenium. See the following image:
During the Medieval Warm Period you can see on this graph, Greenland was actually temperate enough that colonies were set up there, but they had to be abandoned in the later years. We're now approaching those temperatures again in the recent century. Does this mean we're due for a melting of it? Time will tell... (well, hopefully not)

But anyways, onto the claim they're making. They say that the present warming is simply the Earth correcting itself after that Little Ice Age. But wait, as seen on the previous image, which way should the Earth be correcting itself next? That's right, it should be going downwards. Looking at historical trends, we don't see as much of short-term (on the scale of a few centuries) cycles as we do just random fluctuations, so we don't really have any reason to assume that from a short-term trend we're due to come back up.

In fact, if you want to be really pessimistic, you could argue that the escape from the Little Ice Age occured in the middle of the world's industrialization, and it's possible that this is what caused us to come back to a peak, and possibly rise some more. But that's just speculation.

There's one other problem here, with the Medieval Warm Period itself. It's hard to accurately gauge temperatures that far back in time, and when we can, it's often only in a few places in the world. The best evidence we have shows that outside of Europe, it was indeed probable that many areas experienced the warm period, but it's not conclusive. In fact, Antarctic Ice Core samples showed an additional cold period from 1000-1100 AD.

But there's another big problem with using the Medieval Warm Period to extrapolate anything about cycles in the Earth's climate: It was also the time of an extremely hyperactive phase of solar activity known as the Medieval Maximum. The relationship between the sun's activity and the temperature on Earth is well-accepted, especially by Global Warming skeptics who try to use it to explain the rise now. You know what they fail to point out? We're at the same temperature as in the Medieval Warm Period now, but the sun is not in a hyperactive phase (at least, nowhere near how it was back then).

The Myth: Temperature causes the CO2 levels, rather than CO2 causing the temperature levels.

The Truth: While it is true that temperature plays a role in changing the CO2 levels in the atmosphere (higher temperatures decrease the solubility of gasses in liquids, so CO2 is released from the oceans. The opposite happens as temperatures decrease, though not as quickly), it's also true that CO2 plays a role in affecting global temperatures. This latter process happens through the greenhouse effect, where CO2 in the atmosphere allows more heat to enter than to leave. Just because A can cause B doesn't mean B can't cause A as well.

In fact, the truth is even more frightening: Once the temperature starts to move up for some reason, it will cause more CO2 to be released from the oceans, which will cause the temperature to increase even more, which will cause even more CO2 to be released, and so on. With this in mind, it's easy to see why the upward spikes on the first chart were so sharp. The reason the downward trends weren't so sharp was because the process of the oceans reabsorbing CO2 in low temperatures is much slower than the process by which it releases it in high temperatures (only the interface between the atmosphere and water allows reabsorbtion, so it takes a long time for the water to get back up to its saturation point).

Now, there are a few big things we don't know: Why did the spikes stop? It's possible the oceans ran out of CO2 to contribute to the atmosphere, so the temperature leveled out. But then there's the problem of what caused the decline (this might also cover what caused the stop in the spike). And there's also the problem of what started the spike in the first place.

While these questions are intriguing, they're not necessarily relevant. In the current situation, the critical factors are that: 1. We're releasing huge amounts of CO2 into the atmosphere (no dispute here), 2. CO2 in the atmosphere plays a role to warm the Earth, and 3. This warming can cause a cascading effect resulting in sharp spikes in temperature. What caused the warming that brought us out of the ice ages isn't relevant here; the important factor is what might cause warming today.

I'll make one final note on this subject: It appears that the warming trends hit a maximum of around 2°C higher than our current average. This might imply we don't have to worry about unlimited warming, but we still do have those 2 degrees to worry about. And, as I mentioned a bit earlier, even a rise of half a degree could drastically change the face of Greenland, which is one of the biggest threats to us.

The Myth: Thermal expansion of water in the oceans could cause as much sea level rise as glacial melting, if not more.

The Truth: Water's a peculiar material in many ways. Part of its peculiarity is how its density changes with temperature and phase. Unlike most substances, its solid form is actually less dense than its liquid form (that's why ice floats in water). Additionally, for a region between 0°C and 4°C, water's density actually increases with temperature, in contrast to the general trend of most substances to decrease their density with temperature. This point is actually very important here, as the average temperature of the water in the oceans is 3.5°C - where an increase in temperature would cause it to contract.

Now, things are actually a bit more complicated. The surface temperature of water is around 10°C, and this is the water which gets warmed up first. This means that we'd actually start to see some expansion in this region. However, although the water in this region would expand, the thermal expansion coefficient is still pretty small at the temperature, so we won't likely see the predicted 5 meters of rise which was calculated using the expansion coefficient at 20°C. Instead, according to one model I've looked at, we could expect the next rise of a degree Celsius to only contribute a few centimeters. This degree could, however, cause significant glacial melting, and this would contribute a lot more than thermal expansion.

The Myth: Water vapor is the more important greenhouse gas, not CO2.

The Truth: Some estimates give the following proportions for how much different gases contribute to the greenhouse effect:

• Water vapor: 36-70%
• CO2: 9-26%
• Methane: 4-9%
• Ozone: 3-7%

So, in an average scenario, we have CO2 contributing about a third as much as water vapor, and methane about a third as much as CO2. Let's throw in some more numbers to make a probably-not-at-all-accurate estimate:

• CO2 levels have increased by 31% in the last 250 years.
• Methane levels have increased by 149% in the last 250 years.
• So, if we assume a linear relationship, the greenhouse strength has increased by about 17% * 31% + 6.5% * 149% = 15%
• The total effect of the greenhouse gases is to raise the atmospheric temperature by around 14°C.
• If we again assume a linear relation, we get an increase caused by man of about 15% * 14°C = 2°C.

That's big. Let's go back to the chart of recent temperature cycles:The rise at the end of the Little Ice Age was around .6°C. Given that our rough estimate was 2°C, mankind causing a .6°C rise in this timeframe is well within reason. As for water vapor being the main greenhouse gas... does it matter? Raising the CO2 and methane levels alone is easily sufficient to cause significant change.

(Note though that there's far from a scientific consensus that that rise in temperature was actually caused by human activity; more so than other claims of global warming. I'm just pointing out its plausibility here, so don't take my word on faith.)

Now, that was just using a really simple model. Climate scientists have of course come up with better models. One model which a lot of them favor actually shows that the presence of water vapor in the atmosphere actually amplifies the effect of increased CO2 and methane. Another model that a lot of the Global Warming dissenters favor argues that instead the water vapor will dampen the effects of increased CO2. To me, both models seem like they're favored by the applicable groups of people mostly because they predict the same thing as the hypothesis they already favor. If both of their models have good points, the true answer probably lies somewhere in the middle. And as I showed above, estimates in the middle are still pretty damn bad.

The Myth: The "Hockey Stick Graph," which was used to show the sharp spike in Global Warming recently, is critically flawed and has been debunked.

The Truth: The graph of course has its share of statistical errors, as you'd expect from any chart of scientific data, particularly when delving this far into the past and then trying to average the entire planet's temperature. This does not equate, however, to it being "critically flawed." Let's take a look at the (in)famous graph:


The first big complaint about this graph is that it doesn't show the Medieval Warm Period at all. However, I'd like you to take a look at a part of the graph most people ignore: The error bars, which in this case are the shaded grey regions. A shift up in the early second millenium by a half a degree would account for the Medieval Warm Period and would be within statistical error. Also, it appears the before the 20th century, the temperature did appear to be on a slow decline, and it's possible that the very slightly warm temperatures at the left side of the chart in fact were the Medieval Warm Period.

Aside from this, there were a lot of criticisms of the statistics used to create this graph, and alternate models proposed. I'm not going to go into the actual criticisms here, as that's likely far out of the scope of my average reader's expertise, but I'll just point out a couple of things. First of all, remember that Global Warming is a politically controversial subject, and even a flawless paper that supports it is going to be criticized. The presence of a criticism doesn't imply the presence of flaws.

Secondly, there was a big independant review of the report performed by the National Research Council at the prompting of the US Congress over the last few years which published their results in 2006. Specifically, they summarized their results as:

• Large-scale surface temperature reconstructions yield a generally consistent picture of temperature trends during the preceding millennium, including relatively warm conditions centered around A.D. 1000 (identified by some as the “Medieval Warm Period”) and a relatively cold period (or “Little Ice Age”) centered around 1700. The existence and extent of a Little Ice Age from roughly 1500 to 1850 is supported by a wide variety of evidence including ice cores, tree rings, borehole temperatures, glacier length records, and historical documents. Evidence for regional warmth during medieval times can be found in a diverse but more limited set of records including ice cores, tree rings, marine sediments, and historical sources from Europe and Asia, but the exact timing and duration of warm periods may have varied from region to region, and the magnitude and geographic extent of the warmth are uncertain.
• It can be said with a high level of confidence that global mean surface temperature was higher during the last few decades of the 20th century than during any comparable period during the preceding four centuries. This statement is justified by the consistency of the evidence from a wide variety of geographically diverse proxies.
• Less confidence can be placed in large-scale surface temperature reconstructions for the period from A.D. 900 to 1600. Presently available proxy evidence indicates that temperatures at many, but not all, individual locations were higher during the past 25 years than during any period of comparable length since A.D. 900. The uncertainties associated with reconstructing hemispheric mean or global mean temperatures from these data increase substantially backward in time through this period and are not yet fully quantified.

...

The basic conclusion of Mann et al. (1998, 1999) was that the late 20th century warmth in the Northern Hemisphere was unprecedented during at least the last 1,000 years. This conclusion has subsequently been supported by an array of evidence that includes both additional large-scale surface temperature reconstructions and pronounced changes in a variety of local proxy indicators, such as melting on icecaps and the retreat of glaciers around the world, which in many cases appear to be unprecedented during at least the last 2,000 years. Not all individual proxy records indicate that the recent warmth is unprecedented, although a larger fraction of geographically diverse sites experienced exceptional warmth during the late 20th century than during any other extended period from A.D. 900 onward.

Based on the analyses presented in the original papers by Mann et al. and this newer supporting evidence, the committee fi nds it plausible that the Northern Hemisphere was warmer during the last few decades of the 20th century than during any comparable period over the preceding millennium. The substantial uncertainties currently present in the quantitative assessment of large-scale surface temperature changes prior to about A.D. 1600 lower our confi dence in this conclusion compared to the high level of confidence we place in the Little Ice Age cooling and 20th century warming. Even less confidence can be placed in the original conclusions by Mann et al. (1999) that “the 1990s are likely the warmest decade, and 1998 the warmest year, in at least a millennium” because the uncertainties inherent in temperature reconstructions for individual years and decades are larger than those for longer time periods, and because not all of the available proxies record temperature information on such short timescales.

Scientist-to-Lay translation: Yes, there are statistical uncertainties. However, they are not significant enough to change the conclusion. It's hot in here and it's not just me.

I'll remind you that this came out from a committee commissioned by the Republican-controlled congress of the time under the (ongoing) censorship of scientists who espoused views or came up with results the administration doesn't like. Despite all that, the report was in favor of the validity of the Hockey Stick Graph. Must be some strong science if it can make it through those barriers.

Oh yeah, there was also one other review done. This one (known as the Wegner Report) was performed at the instigation of Representative Joe Barton, an outspoken Global Warming "skeptic" (don't worry, we're doing our best to steal that word back from them). The report also wasn't subject to peer review, and it didn't even result in changing the shape of the graph after fixing supposed errors. Compare: (The "Hockey Stick Graph" on the left, the graphs the Wegner Report came up with on the right)

(Source: NY Times)

Is it just me, or is the spike even more profound on the new graphs? And they had the gall to use this as evidence against Global Warming?

The Myth: Scientists were going just as crazy back in the 1970's about Global Cooling. And now they think it's Global Warming. Why should we believe them?

The Truth: There was speculation about Global Cooling back in the 1970's (though it wasn't called that back then. The term was invited by Global Warming "skeptics" who wanted to make it look like a comparable theory was proposed back then), but it was only by a few scientists and never got close to the amount of research that's been done on Warming. It never gained the consensus of scientific support that Warming did, so it's unfair to imply that the mass of "Scientists" believed in it.

In fact, since there was so little actual "hysteria" about it, let's go over every scientific paper published on Cooling:

Rasool and Schneider (1971) - Examined the possible effects of greenhouse gases and particulate pollution (such as from aerosols) on the climate. They found that greenhouse gases would result in warming the Earth and particulate pollution in cooling it, and guessed the latter to be more likely. They estimated that sustained effects of particulate polluntants could decrease the temperature of Earth by up to 3.5°C, and if this went on for long enough, it could cause Earth to drop into another ice age. Note that they didn't actually predict this would happen, they just proposed it as a possible future scenario. Nowadays, most scientists are indeed predicting that the Earth is going to warm up.

National Academy of Sciences Report (1975) - Often claimed to show fear of Global Cooling. In fact, all it said was that it's possible for the climate to change, they didn't know in which way it might, and so we should research it more. No big fears there.

Okay, we have one actual paper which shows any support at all for the hypothesis of Global Cooling. That's it. Some hysteria, eh?

Oh yeah, I'd be remiss if I didn't mention that this is just a fallacious appeal to "Science was wrong before."

The Myth: This is the end of the post.

The Truth: Well, it may be all I'm putting up now, but I'm nowhere near closing the book on this subject. Feel free to argue in the comments, and if there's anything worthwhile that comes up, I'll add it in here (or edit one of the above sections). Particularly, I know that my conclusion about thermal expansion is contrary to what TheBrummell heard. If you've heard of some better model which does show significant expansion, I'd be interested in seeing it.

Proceed with your information binge...

Too much information!