Otherwise known as the scientific method, or How Science Works. You were probably taught the basics of this in secondary school/high school/your local equivalent, but the number of physics undergraduates who came through my university not having the first clue about how science works is large enough that I suspect it’s not quite being hammered into people’s brains the way it should be. Which is a shame¹, because not knowing anything about the scientific method is what allows so much anti-science to flourish in the press and media at large. I guarantee you homeopathy – for example — wouldn’t last a second in a world where people were the least bit curious about what was going on under the bonnet, and neither would the hundreds of news “stories” about how chocolate is actually good for us.

So this is going to be a brief précis on how science works with a couple of classic examples thrown in that should hopefully prompt at least a couple of people who read it to not just accept a piece of research’s final conclusions, but instead to spend a second or two looking at their methodology to see if it’s solid and if it adheres to the basic structure of the scientific method. If it doesn’t then there’s a fairly high chance that there’s some commercial bias involved; I know that more than a few of the “chocolate is good for us” pieces are actually funded by chocolate manufacturers who want people to feel less guilty about buying and consuming their product, while the last thing the peddlers of homeopathic pills want is for someone to take a magnifying glass to their method because it makes no scientific sense whatsoever.

Science is an evidence-based discipline. This is the key feature of science, so I’m going to repeat it a couple of times. Science is an evidence-based discipline. Science is an evidence-based discipline. If you don’t have some kind of objective, verifiable evidence that proves what you are saying could be true, what you are doing is not science. Whatever scientific idea you’ve come up with needs to be built on previously existing evidence that provides it with a strong support, otherwise it’s going to collapse alarmingly quickly under the detailed scrutiny of other trained scientists.

Speaking of, science is also based heavily around the concept of peer-review. Scientific research has to be as open as possible, with each stage of the process exhaustively documented so that other people can exactly reproduce that research if they want to. Getting independent confirmation of a result is very important, and so is letting other scientists in the field pick over the details of your research for any flaws. You might have carried out your experiment with the best will in the world and merely reported what you saw at the end of it, but that doesn’t necessarily mean you have done a science. Your apparatus might have been broken in some subtle way. You might have set it up in the wrong place. There might be some other unknown factor at work that you just didn’t think of but which alters the experimental results significantly. Exposing your research method to the rest of scientific establishment means that it’s going to be looked at by dozens of experts in the field² you’re exploring, and vastly decreases the chance of any flaws making it through into the final work.

Anyway, let’s say you do have some kind of coherent scientific idea based on previously-existing evidence. Contrary to what you might think, this is not a theory.  What you have there is a hypothesis, which you might recognise as the thing most experimental research sets out to test. The reason we differentiate hypotheses from theories is because it’s rather easy to tweak a “theory” to fit pre-existing scientific evidence. If you have one cat-shaped jelly mould and somebody uses it to make some jelly, predicting that the jelly is going to come out of the mould in the shape of a cat isn’t exactly going to indicate astounding precognitive abilities on your part because you knew the mould was shaped like that in the first place. It isn’t enough for your nascent hypothesis to make sweeping statements about the universe we already know and think we understand; in order for it to be accepted as a new theory that is better than the currently existing theory, it has to make a unique, experimentally verifiable prediction about the universe that is at odds with – or at least more accurate than – the old theory. It’s easy to come up with a hypothesis that accounts for experimental outcomes that have occurred in the past; it’s rather more difficult to come up with a hypothesis that accounts for experimental outcomes that have yet to occur at all. If you manage it without access to a time machine there’s a very good chance there might be something in your hypothesis.

The most dramatic example of a successful theory overturning an old one in this fashion was when Einstein’s general relativity proved more accurate than Newton’s theory of universal gravitation at predicting the deflection of light as it passed close to a large gravitational source – in this case the Sun. General relativity had already accounted for aberrations in the precession of Mercury that Newtonian gravity couldn’t, but the existence of those aberrations had been known for centuries and it was entirely possible that Einstein might have written his theory with the sole purpose of explaining them away. In order to be accepted general relativity had to predict something new that had never been tested before, and in this case Einstein and Arthur Eddington decided to attempt the measurement of the deflection of light waves by the Sun in 1919. Cavendish had predicted this would happen in a Newtonian universe waaaay back in the late 1700s, but the key difference between Newtonian gravity and general relativity was that Newton’s formulation predicted a degree of deflection that was half that predicted by general relativity. Eddington and other collaborators around the world waited for a total solar eclipse (this being the only time that deflected beams of light wouldn’t be completely drowned out by the ambient light from the Sun) and then measured how much the positions of stars close to the edge of the Sun’s disc appeared to shift from their actual, known positions in space. After they’d cranked through the calculations the result was unarguably final: Einstein’s prediction fell within experimental error of the actual observed deflection of light, while Newton’s was a long way outside it. After this result was independently confirmed Newton’s theory wasn’t exactly thrown out, but it was seen as just an approximation of what was really going on with gravity which was more adequately explained by general relativity.

That’s a good example of the scientific method working exactly how it’s supposed to: a hypothesis is formulated, tested, found to be more accurate than the currently existing theory and subsequently supplants it in the scientific lexicon. It’s also possible for negative outcomes to result in this rewriting of the scientific handbook; just look at Michelson and Morley’s interferometer experiment back in 1887. Before we understood that space is a near-total vacuum it was thought that in order for light waves to make it to the Earth from the Sun (as well as other sources) it would need some medium through which it could propagate, like ocean waves propagate through water and sound waves propagate through the air. Scientific orthodoxy therefore held that the entire universe was permeated by a substance called the lumineferous aether through which light could travel. Such a medium would have produced fluctuations in the velocity of light depending on which way the Earth was travelling at a given time, and so Michelson and Morley built an experiment that would show these velocity shifts as an effect of the Earth’s motion against the “aether wind”³. They were rather surprised when they discovered that the speed of light was completely invariant no matter which way the Earth was going, which neatly disproved the whole concept of the lumineferous aether in the first place and directly led to Einstein’s formulation of special relativity two decades later.

Not being able to account for a subsequent experimental result can lead to the death of an old theory even if there’s nothing to replace it. This is the core of the scientific method; not only do theories have to make it through this arduous process of formulation, testing and gradual acceptance into the scientific mainstream, but they have to be on their metaphorical toes even after they’ve made it in life as one null result could end up invalidating the whole thing. Scientific theories are constantly – constantly – being tested in this way to increasingly insane degrees of accuracy, and so you can be sure that anything that still carries the “theory” nomenclature is about as correct as we can make it. Anyone who says “But it’s just a theory!”⁴ is betraying their basic ignorance of how science works and probably has trouble tying their shoelaces in the morning to boot. The Big Bang may have happened 13.7 billion years ago but Big Bang theory has made several crucial predictions about the universe which have subsequently been confirmed experimentally. Evolution is trickier to spot in action, but even there the weight of observed evidence supporting the theory’s case both before and after its formulation is so overwhelming that it is (so far) the only plausible explanation for that observed evidence. The scientific method isn’t without its flaws – there’s an old adage that new theories are only fully accepted once the supporters of the old theory physically die out – but it’s the best we’ve been able to come up with and it is astoundingly successful.

Next week: what happens when people ignore the scientific method, otherwise known as “making stuff up”, otherwise known as “newspapers will print anything because journalists don’t understand how science works,” Hopefully you do now, though.

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1. Actually what I want to say here is that it’s a tragic shortcoming in our societal attitudes that science is perceived as a “hard” subject and something that should be mostly left to experts, which allows anyone who can dress themselves up like an expert to peddle whatever crap they want under the guise of science.
2. Peer-review isn’t perfect by any means, as the various scientific paper databases are set up so that they’ll prioritise research that is referred to a lot by other people. This is reasonable, as a paper that gets mentioned a hundred times in the reference sections of other papers is probably a very important piece of work, but it can also turn the submission process into a Kafkaesque version of social media where some of the people commenting on the work you’ve done have a vested interest in getting you to mention their research at some point in order to increase their pageviews. You would be amazed at how petty things can get, especially in niche areas of research.
3. The lumineferous aether was supposed to be moving relative to the Sun’s motion around the Milky Way, meaning that the Earth’s motion around the Sun should have produced apparent shifts in the relative velocity in the aether wind – think running down a track on a still day and nevertheless feeling the movement of air around your body. By taking measurements six months apart when the Earth was travelling in completely different directions through space it was expected that this would produce a large shift in the relative velocity of the aether wind that would be reflected in the light waves that travelled through it and showed up on an interferometer. It didn’t.
4. The notable exception here being string theory. I’ve gone over my objections to string theory before and I’m not entirely sure how it’s ended up with the “theory” moniker since it is entirely based on pre-existing scientific evidence and has never – and probably will never – be experimentally verified in any way that counts.

The post The Theory Of Theories. appeared first on The Scientific Gamer.

(Click on that for the full picture. DO IT. DO IT NOW.)

This question plopped into my inbox like a month ago now.

Name: Justin M.
Question: How can physicists determine the shape of the universe, and what implications might the different speculated shapes of the universe have?

And I’ve been avoiding it ever since, because if you mean what I think you mean it’s an insanely hard subject to try to explain to somebody who hasn’t done, say, three years of an undergraduate physics degree course.

Now, if I’m lucky you just want to know about the old open/closed/flat conundrum. That I can do. We will start with this picture, swiped from the usual source:

These are the three possible candidates for the general shape of the fabric of the universe: football, pringle or bedsheet. Other scientists call these closed, open and flat respectively. I call them boring. Exactly what is going on here is quite easy to visualise in my head but as soon as I try to put it into words bad things happen, but I’ll have a go just for you.

When Einstein first worked out the fundamental concept of general relativity he also came up with a bunch of equations – called the Einstein field equations – which describe how gravity works in a universe where the fabric of spacetime is warped and curved by the presence of matter and energy. Einstein did his general relativity work before Edwin Hubble showed that the universe was expanding through galactic redshift measurements and the Big Bang had yet to be accepted as common scientific orthodoxy, so he assumed we lived in a static universe (i.e. one that is not expanding or contracting) just like the rest of the scientific establishment. The problem with this was that if you start off with a universe that is in perfect static equilibrium, general relativity says that that universe will inevitably start to contract due to the mutual gravitational attraction of everything in it. As it stood general relativity simply didn’t allow for the concept of a static universe, so in order to make his field equations work he fudged them slightly by adding in something called the cosmological constant which provided the universe with a fundamental internal pressure that resisted the contraction due to gravity.

This may have made Einstein’s equations balance and allowed him to model his static universe, but it was bad science and he knew it. After the expansion of the universe was proven he famously referred to the cosmological constant as the biggest blunder of his life; if he’d had faith in the robustness of his theory he could have predicted an expanding universe long before it was confirmed experimentally. Anyway, in an expanding universe the cosmological constant was nothing more than a curio, a simple artefact of the maths. It didn’t have any relevance to anything that was actually physically happening and a lot of people simply ignored it.

That was up until 1998, when it was discovered through redshift measurements of Type 1a supernovae in distant galaxies (have I talked about standard candles before? I’m sure I must have) that those galaxies were actually moving away from us far faster than a simple model of a continually expanding universe would seem to imply, and that the most distant parts of the universe were accelerating in their rate of expansion. This accelerating universe model has since been confirmed by, amongst other things, observations of fluctuations in the cosmic background radiation by the Wilkinson Microwave Anisotropy Probe (WMAP) in the 2000s. An imperfect way of describing this CMB anisotropy is as an “echo” of the Big Bang – the CMB is leftover radiation from the formation of the universe, and the fluctuations in its structure essentially make up a record of the distribution of matter in the universe just after the Big Bang. Circumstances have changed a bit since then, of course, and by comparing the positions and velocities of galaxies now to the CMB rest frame we can get the closest thing possible to an “absolute” measure of galactic velocity. These velocity measurements appear to show that the universe is indeed accelerating in its expansion.

This is interesting for a number of reasons, but the one we’re mainly concerned about is that in the basic expanding universe model without a cosmological constant there are two factors governing the rate of expansion: the inertia of expansion provided by the Big Bang, and the gravitational attraction of all the matter inside the universe counteracting that. Depending on how much stuff there is in the universe and how closely it’s packed together (density), there are three possible outcomes for this basic model.

1)     There is enough gravity to overcome the expansion inertia. The expansion of the universe will gradually stop and reverse itself, and everything will collapse into a Big Crunch. This is a closed universe.

2)     There isn’t enough gravity to overcome the expansion inertia. The universe continues to expand, everything becomes more and more spread out and diffuse, and things inevitably end in widespread entropy and heat death. This is an open universe.

3)     There is just enough gravity to counterbalance the expansion inertia. The expansion rate of the universe will continually slow, gradually approaching zero without ever quite getting there. This is a flat universe.

Note that in none of these three models is there any room for the expansion of the universe accelerating somehow. Clearly there’s something up with it that needs fixing. Serendipitously, though, if you drop Einstein’s previously-defunct cosmological constant back into the cosmological model, it turns out that you can model the accelerating expansion of the universe. The acceleration is driven by the outwards pressure that the cosmological constant represents. And by fiddling with the parameters of the cosmological constant, we can describe something approximating the universe we see today.

What is the cosmological constant, though? Where is this outwards pressure it describes coming from in physical terms? The short answer is: dark energy. Exactly what that is nobody really knows; all we know for sure is that there must be some sort of intrinsic energy permeating all of space (sometimes called vacuum energy if you’re particularly into sci-fi) that counterbalances gravity and causes this acceleration in expansion. I can’t give you a great explanation of dark energy since it really is at the cutting edge of theoretical cosmology, so if you want to find out about it I recommend you read this bit on Wikipedia and then go from there. All I can tell you is that while we cannot perceive the dark energy itself, we can certainly perceive its effects: accelerating expansion, which requires some tinkering with the basic cosmological model I described above in order to accommodate it.

When you dump the cosmological constant back into the model you end up with what is today called the Lambda-CDM model of the universe, which is the currently-accepted model of How Things Are. It’s called Lambda-CDM because lambda is the mathematical symbol representing the cosmological constant, while CDM stands for Cold Dark Matter. Both of these things are needed to explain inadequacies in the previously-accepted model of the universe, the FLRW metric. Lambda-CDM is FLRW on steroids; it doesn’t replace FLRW so much as it supplements it and makes it work with the current observational evidence. The expansion of the universe is governed by lambda, the cosmological constant, as well as baryonic and dark matter (for gravity). The idea is that you add the shit out of all these subcomponents and you get a final number, omega, which tells you what is going to happen to the universe at the end of time, and also incidentally what it happens to be shaped like.

Hey, I knew we’d get back here eventually. That number to the bottom left of each possible universe shape is omega, or Ω. Omega is the observed density of all the stuff in the universe divided by the theoretical critical density required for a perfectly flat universe. If Ω adds up to be bigger than one, then you get the closed beachball universe. If it’s less than one then you get an open pringle universe. If it happens to be exactly one, then you get a flat bathtowel universe. The outcomes are roughly the same as described above, except with the addition of the cosmological constant the pressure due to dark energy eventually overcomes gravitational attraction in the flat model, causing the universe to first slow down in its expansion and then speed back up again once gravity has been smacked down sufficiently, and things end up just like an open universe: in entropy and heat death. The role this shape — or geometry — plays beyond being linked to the expansion and fate of the universe is somewhat explained here if you read the bits about triangles and angles and parallel lines.

As it happens the WMAP probe also measured the overall geometry of the universe (if you want a “how?” then you can start with this), and it came back with the answer that Ω was equal to 1 with less than 0.5% error. In other words the part of the universe that we can see appears to be almost perfectly flat with very little local curvature. However, since we don’t know how much of the universe we can see it could be that this only holds true for our little corner of it. Saying that the universe is flat now would be like ancient civilisations saying that the world was flat; it certainly looked flat, but that was just because they could only see part of it and it was actually way bigger than they thought.

So yes. After like a hundred years of modern astronomy and cosmology, we can finally say that the bit of the universe we live in is probably mostly flat. QED.

(Christ I just realised I managed to get all the way through this post without mentioning Friedmann at all. That’s a massive fault on my part.)

PS – I’m out of questions now so feel free to send more in. I mean, you don’t have to if you don’t want to. But it would be nice.

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Josh asks

 String theory. What the very fuck is it.

I was going to chide you for swearing on this blog, Josh; it’s a family space and a small child could happen by and have their brain infected with that nasty language. Then I remembered that I fucking hate string theory – I truly detest it – and that a sizeable percentage of the next thousand words I write describing it are going to be swear words. On this one occasion, therefore, you are forgiven.

String theory is what happens when theoretical mathematicians have too much time on their hands and decide they want to make a contribution to the world of physics. It arises from a fundamental incompatibility between our two main theories of the universe, quantum mechanics and gravity. Quantum mechanics is the physics of the very small and encompasses three of the four fundamental forces: strong nuclear, weak nuclear, and electromagnetic. General relativity is the physics of the very large and deals with the fourth fundamental force, gravity.

If the universe were a well-ordered, logical place these four forces would all be different aspects of a single unified force that could be described by a single set of rules: this is the fabled Theory of Everything. Unfortunately as things stand they really can’t. The three quantum forces coexist happily in something called the Standard Model which is essentially a basic physics toolkit for understanding the universe; if you like, we can say that we can describe those three forces using the same physical language even if the specific mechanisms governing each are different. Wee have successfully combined the weak nuclear and electromagnetic theories into electroweak theory, and while we’re some way off managing to combine the third quantum force – the strong nuclear – with electroweak it’s not something that’s fundamentally incompatible with the theory. The same, alas, cannot be said of general relativity. The Standard Model doesn’t even attempt to explain gravity or general relativity; all attempts to do so using quantum field theory have broken down long before reaching the Planck scale where quantum gravity becomes relevant¹, which is where they’d need to go in order to be compatible with both general relativity and the Standard Model².

Why is the Planck scale important? Well, we have general relativity for describing very heavy stuff. We have quantum mechanics for describing very small stuff. The Planck scale, though, is a region of physics where the two blur into each other; very heavy, very small stuff. For why this is wacky see the Wikipedia articles on Planck scales and Planck particles (this is actually a joke, I barely understand those articles and I don’t expect you guys to either) but neither general relativity nor quantum mechanics can predict what the hell is going on at these scales indicating that those theories are incomplete in some way. The reason they’ve made it this far is that the things described by quantum mechanics and the things described by general relatively are, on the whole, completely separate worlds with little direct interaction. We can use quantum mechanics to model particle behaviour because gravity is mostly not important at quantum mechanical scales. We can use general relativity to model the curvature of space time because quantum mechanical effects are mostly not relevant at relativistic scales. But saying “Well, these theories work for 99% of situations so they’re good enough” really doesn’t fly in science, hence the search for a Theory of Everything, and hence string theory.

String theory states… actually you know what, I’m not actually going to paraphrase this Wikipedia article, I’m just going to copy and paste from the source:

String theory posits that the electrons and quarks within an atom are not 0-dimensional objects, but made up of 1-dimensional strings. These strings can oscillate, giving the observed particles their flavor, charge, mass and spin. Among the modes of oscillation of the string is a massless, spin-two state—a graviton. The existence of this graviton state and the fact that the equations describing string theory include Einstein’s equations for general relativity mean that string theory is a quantum theory of gravity. Since string theory is widely believed^[7] to be mathematically consistent, many hope that it fully describes our universe, making it a theory of everything.

So everything is made up of strings that vibrate giving them the appearance of particles, right? I don’t pretend to understand anything more than the very broadest details of string theory so I can’t explain it in detail. What I can do is explain why string theory is a crock of shit.

The modern scientific method is based around a process of formulating a theory, testing it experimentally, publishing the results and then letting other people have a go to see if they can do the same thing. The experimental part is very important; we do not simply test something once and then go “Welp, guess that proves it!”, but instead we test it constantly and repeatedly to ensure that it works in all possible situations. Science works by negative proof: it is never possible to definitively prove a scientific theory is true, but you can prove it is false by turning up results that are fundamentally incompatible with the basic tenets of the theory. Then you toss it out and come up with a new one that explains both the old results of the old paradigm and the contradictory results that caused you to get rid of it in the first place. This ensures that the theories we have are as robust as they can possibly be since they have to withstand constant experimental assault.

The scientific method has worked very well, even for theories that we can’t test directly. General relativity predicted phenomena gravitational lensing and time dilation before they were observed, while the Standard Model predicted the existence of several high-energy particles that were subsequently found in particle accelerators. We know these theories are incomplete, but we keep them around because they’ve otherwise had unparalleled success in explaining the things that we see going on around us. Quantum mechanics is ridiculously counterintuitive and hurts my head to even think about, but it too has predicted many wacky experimental outcomes that were subsequently confirmed in the laboratory so I have to grudgingly concede that it’s a kosher scientific theory. Not so with string theory, however. For an explanation as to why, I’ll turn things over to noted womaniser, self-aggrandising charlatan and Nobel Laureate Richard Feynman.

I don’t like that they’re not calculating anything. I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with a n experiment, they cook up an explanation—a fix-up to say, “Well, it might be true.” For example, the theory requires ten dimensions. Well, maybe there’s a way of wrapping up six of the dimensions. Yes, that’s all possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there’s no reason whatsoever in superstring theory that it isn’t eight out of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn’t produce anything; it has to be excused most of the time. It doesn’t look right.

In a nutshell, every time an experimental result confirms a prediction made by string theory, string theorists claim it as a great success for string theory. Every time an experimental result doesn’t confirm a prediction made by string theory, string theorists simply rewrite string theory. It’s a classic case of post hoc ergo propter hoc. Nobody is ever going to be able to peer all the way down to the Planck length to see if these strings actually exist or not so we can’t ever say string theory is definitively not true, and I would argue that if a phenomena is not experimentally verifiable then the existence of that phenomena is ultimately irrelevant, scientifically speaking. Nobody takes the existence of God seriously as a scientific theory because it’s not something that can ever be proven or disproven, so why should I treat string theory any differently?

1. The Planck scale is a very small scale at which quantum effects dominate, and this wouldn’t be a problem except… well, you’ve heard of micro-black holes, right? Imagine a black hole so small that its Schwarzchild radius (or event horizon) is the same size as the Planck scale. This can only be probed by photons whose Compton wavelength is also equivalent to the Planck scale. However, if they had a wavelength this small their mass-energy would be so great that they would also form micro-black holes, thwarting our theoretical attempt to resolve the Planck scale. General relativity cannot describe these micro-black holes because they lie within the regime governed by quantum mechanics, but quantum mechanics can’t do it either because gravity keeps getting in the way, hence the need for a theory of quantum gravity.

2. I don’t even pretend to understand this but: dealing with quantum field theory is, mathematically, incredibly gnarly. You tend to get a lot of inconvenient terms popping out of your equations that usually can’t be dealt with using conventional mathematics, like infinity. A system of techniques have been developed to purge quantum mechanical equations of these horrible infinities, and these techniques are collectively referred to as “renormalization”. However, they do not work when applied to quantum theories of gravity. Infinities work their way into the maths and cannot be removed, and so these theories break down before they can be applied to scales where a theory of quantum gravity would be useful. Makes me glad I never studied quantum mechanics in a big way, really.

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