## Friday, March 7, 2014

### Quantum mechanics and the Planck-spectrum

[The following is a guest post from Bjoern Malte Schaefer. Bjoern is one of the curators of the Cosmology Question of the Week blog, which is worth checking out. This post is a historical look at some of the early parts in the history of quantum mechanics, in particular, the black-body spectrum. Questions are welcome and I'll make sure he sees any of them. Image captions (and hyper-links, in this case) are, as usual, by me, because guest posters don't ever seem to provide their own.]

Two unusual systems

Quantum mechanics surprises with the statement that the microscopic world works very differently from the macroscopic world. Therefore, it took a while until quantum mechanics was formally established as the theory of the microworld. In particular, despite the fact that two of the natural systems on which theories of quantum mechanics could initially be tested were very simple, even from the point of view of the physicists of the time, one needed to introduce a number of novel concepts for their description. These two physical systems were the hydrogen atom and the spectrum of a thermal radiation source. The hydrogen atom was the lightest of all atoms with the most simply structured spectrum. It exhibited many regularities involving rational numbers relating its discrete energy levels. It could only be ionised once implying that it had only a single electron and from these reasons it was the obvious test case for any theory of mechanics in the quantum regime. Werner Heisenberg was the first to be successful in solving this quantum mechanical analogue of the Kepler-problem, i.e. the equation of motion of a charge moving in a Coulomb-potential, paving the way for a systematic understanding of atomic spectra, their fine structure, the theory of chemical bonds, interactions of atoms with fields and ultimately quantum electrodynamics.

The Planck-spectrum was equally puzzling: It is the distribution of photon energies emitted from a body at thermal equilibrium and does not, in particular, require any further specification of the body apart that it should be black, meaning ideally emitting and absorbing radiation irrespective of wave length: From this point of view it is really the simplest macroscopic body one could imagine because its internal structure does not matter. In contrast to the hydrogen atom it is described with a continuous spectrum. In fact, there are at least two beautiful examples of Planck-spectra in Nature: the thermal spectrum of the Sun and the cosmic microwave background. The solution to the Planck-spectrum involves quantum mechanics, quantum statistics and relativity, and unites three of the four the great constants of Nature: the Planck-quantum h, the Boltzmann-constant $$k_B$$ and the speed of light c.

 The spectrum (basically intensity against wavelength or frequency) of the light from the sun (in yellow) and a blackbody with the same temperature (grey). I'm actually surprised by how similar they are.

Limits of the Planck-spectrum

Although criticised at the time by many physicists as phenomenological, the high energy part of the Planck-spectrum is relatively straightforward to understand, as had been realised by Wilhelm Wien: Starting with the result that photons as relativistic particles carry energies proportional to their frequency as well as momenta inversely proportional to their wave length (the constant of proportionality in both cases being the Planck-constant h), imposing isotropy of the photon momenta and assuming a thermal distribution of energies according to Boltzmann leads directly to Wien's result which is an excellent fit at high photon energies but shows discrepancies at low photon energies, implying that at low temperatures the system exhibits quantum behaviour of some type.

## Monday, February 3, 2014

### The human machine: picoscale engineering

The previous post in this series can be found here.

Over the course of my 'human machine' series of posts I've tried to convey the intricacy and beauty of our biological engineering, and demonstrate that we are incredibly well-engineered machines whose complexity and originality go all the way down to the atomic level. In this week's post, I will be exemplifying this with one of the best cases that I can think of; how we transport oxygen around our bodies. I feel that this is a great story to tell because it is one that most people might think that they know well, but that actually is far more complex and subtle than it may appear, and that demonstrates how our lives are highly dependent on perfectly evolved processes working on the subatomic scale.

"It will have blood, they say."

I'm sure that anyone reading this blog is fully aware that we need oxygen to survive (although if you want a more detail explanation of exactly why then I direct your attention to a previous post of mine available here), and anyone remembering their primary school biology will know that oxygen is transported around the body by the circulatory system, i.e. the blood. Most of the cells within your blood are the famous red blood cells (to distinguish them from the immune cells - the white blood cells), which are, unsurprisingly, responsible for blood's distinctive colour - earning them the respect of horror movie aficionados everywhere. You have roughly 20-30 trillion red blood cells in you as you read this, each of which is about 7 microns (i.e. 7 millionths of a metre) in diameter. They shoot around your body, taking roughly 20 seconds to make one circulation, and have just one job; take oxygen from the lungs (where there's lots of it) to the tissues (where there's not). So specific are they to this job that they don't even bother having a nucleus, thereby removing all possibility of them doing anything else.

 Human red blood cells - you make 2 million every second!

## Wednesday, January 22, 2014

### Particle Fever

The video above is a trailer of an upcoming documentary about CERN and the discovery of the Higgs particle. This documentary looks wonderful and important. CERN has triumphed again at outreach and is simply leagues ahead of basically everyone else in science when it comes to this sort of thing. If anyone is surprised or wonders how CERN is able to get such a relatively large sum of science funding (though only relative to other science funding) then don't be. This sort of thing matters and makes a difference. People care about CERN because they know about CERN and they know about CERN because documentaries like this are made, made well, marketed well and received well.

The documentary itself will be released March 5, in New York, and hopefully will be viewable in most major locations, eventually, after that.

My only gripe is that it is coming 18 months after the Higgs discovery. I know that part of the motivation for this is that people want to make sure the science is definitely true before disseminating it, otherwise things can become confusing for the less engaged viewer. However, in July 2012 those guys were reasonably sure that they'd found something. This research is owned as much by the public as it is by the researchers. CERN did do a great job on that day by holding press releases, announcing the discovery live, with live web-streams, and with public level discussions, at the moment, of what the implications were. And, of course, this is all great, and I love CERN for it. But maybe it can be done even better.

Here's (potentially) how...

This documentary will probably be reasonably widely viewed. It looks like it is potentially headed for some major awards and it is being reviewed very favourably by a bunch of major newspapers and film critics.

Imagine if the film had been released, and widely viewed, immediately prior to the discovery's announcement, and the climax of the film was all the researchers, scientists, students, engineers, and everyone involved in this experiment waiting, full of anticipation, not knowing the result. The viewer now has a reasonable understanding of what the researchers were looking for and how they were hoping to find it. Now everyone is waiting, full of anticipation, not knowing the result. Then, we cut to the actual, live, not even the majority of the scientists know the result, announcement of the detection. The general viewer will now share in this discovery, that their taxes paid for (and who's future taxes will pay for future experiments) in the moment.

That's not just great for science outreach, it is genuinely good theatre for everyone involved (even if there isn't a detection). But most importantly it allows this sharing of not just the result, but the acquisition of the result. The public feels like they were there, like they took part, like it is also their discovery. And, to bring back the bottom line, when funding is next being decided, they want to be able to contribute to, and participate in, more discoveries like this.

Instead, people could tune in to the discovery, and see the researchers and scientists, etc, and their excitement, without being able to share in it.

Having said all of that, 18 months isn't that long. So, when the documentary is released, go watch it, and remember that this stuff happened less than two years ago. This is the present.

## Tuesday, January 14, 2014

### A few more comments on inflation and the multiverse

[This carries on from a post yesterday where I attempted to explain what inflation has to do with a multiverse]

Is that it?

You might be thinking: "OK, that's a toy-toy model about how a multiverse might come from an inflationary model. Cool. But are there any non-toy models?"

As far as I'm aware, no. And this is where I definitely agree with Peter that, although it is certainly possible to generate a multiverse, it definitely isn't inevitable. In fact, if anyone reading this does know of any full models where a multiverse is generated, with a set of vacua with different energies, please let me know (even if it's just a complete toy model).

In which case, you might now be wondering why is there so much excitement amongst some cosmologists about multiverses? Why do some physicists want it so much? There are two reasons I can think of. The first is that the multiverse, coupled with an anthropic principle, can explain why the cosmological constant has the value it does. If the true model of inflation generated Big Bangs in many vacua (i.e. more than 10^130 vacua), then, even though most of them will have large vacuum energies, the Big Bangs that occur in them also can't support life. Therefore we would expect to find ourselves in a Big Bang bubble where the cosmological constant was small, but just big enough to be detected. And this is actually exactly what we see. [Edit: As Sesh points out in a comment, an additional assumption is required to conclude that the cosmological constant should be both small and measurable. This assumption is that the distribution of vacuum energies in the multiverse favours large energies. See the comment and replies for discussion. Thanks Sesh.]

The second reason multiverses are popular is that there is a candidate for where this absurdly large number of possible minima could come from and this is string theory. In fact, string theory predicts many more than 10^130 possible vacua.

Summary

So, that's it. A multiverse needs two things: a way that multiple possible types of universe are possible; and a way to make sure that these universes all actually come into existence. String theory suggests that there may indeed be multiple possible types of "universe" (i.e. sets of laws of physics), but it is eternal inflation that would cause many Big Bangs to occur and thus, potentially, to populate these "universes".

Some parting words...

There are some (perhaps even many) scientists who hate the idea of a multiverse and demand that multiverses are stricken from science for being "unfalsifiable" or "unpredictive" (because we can't ever access the other Big Bangs).

I don't understand this mentality.

Forgetting about whether a multiverse is "scientific" or not, what if it is true? What if we do live in a universe that, it just so happens, is part of a multiverse? Would we not want whatever method we use to try to learn about our existence to be able to deal with it? If we want "science" to be something that examines reality, then (if we are in a multiverse) should it not be able to deal with a multiverse? We might not be able to directly measure other Big Bangs, but we can infer their probable existence by measuring other things. [Edit(06/02): I just want to clarify that I'm not meaning to suggest here that science needs changed to be able to talk about untestable things, but instead that scientists are justified when trying hard to find ways to test this idea. And that there are ways to test it.]

Suppose we all lived 500 years ago and wanted to know why the Earth is exactly the right distance from the sun to allow life to occur. What explanations could we come up with for why this is true?

What is the real reason?

## Monday, January 13, 2014

### On inflation and the multiverse

[Note: in the following, and in the title, I have used the word multiverse a lot. When I do I am exclusively referring to this type of multiverse, which has, for example, been used to try to explain why the cosmological constant it so small. If you have any questions then please do ask them.]

About a week ago, Peter Coles, another cosmology blogger (who also happens to be my boss' boss' boss - or something), wrote a post expressing confusion about the association of inflation with the multiverse. His post was a reaction to a copy of a set of lectures posted on the arXiv by Alan Guth, one of the inventors of inflation (and discoverer of the name). Guth's lectures claimed, in title and abstract, that there is a very obvious link between inflation and a multiverse. Peter had some strong comments to make about this, including the assertion that at some points he's inclined to believe that any association between inflation and a multiverse is no different to a thought pattern of: quantum physics ---> woo ---> a multiverse!

I have some sympathy for Peter's frustration when people over-sell their articles/papers, and I would agree that inflation does not require a multiverse to exist, nor does inflation itself necessarily make a multiverse seem particularly likely/obvious. However, it is also true that, in a certain context, inflation and a multiverse are related. Put simply, through "eternal inflation", inflation provides a mechanism to create many Big Bangs. To get the sort of multiverse this post is about, these different Big Bangs need to have different laws of physics, which is not generic. However it can occur if the laws of physics depend on how inflation ends, in a way which I will describe below.

As with Peter though, I am unaware of any complete inflationary model that will generate a multiverse. We could both have a blindspot on this, but my understanding is that the situation is that people expect (or hope?) that complete models of inflation derived from string theory are likely to generate a multiverse for reasons that I will describe below.

Before that, you're probably wondering what this inflation thing is...

Inflation

The inflationary epoch is a (proposed - although the evidence for it is reasonably convincing) period in the past where the energy density of the universe was almost exactly constant and homogeneous (i.e. the same everywhere) and the expansion of the universe was accelerating. After this inflationary epoch ended, the expansion was decelerating (which isn't surprising given that gravity is normally attractive) and the universe gradually became less and less homogeneous, until it looked like it does today. We like inflation for all sorts of reasons, but for the purpose of this post, the preceding two sentences are all you need to know.

 This is the "potential energy density" stored by a hypothetical inflationary field, $$\phi$$. The x-axis is the value of $$\phi$$. The y-axis is the energy density. The hatched region is where the conditions for "eternal inflation" would be satisfied.

## Monday, December 9, 2013

### Cubism. Realism. Sciencism.

 Post-impressionist carcinoma.

This week's post from me will be relatively brief as I am currently on honeymoon, and although Shaun somehow manages to find time on his travels to blog about his conference experiences I doubt my new wife would be too happy if I did likewise! So, in lieu of my intended Human Machine series post (which will be coming early in the new year), I wanted to bring your attention to something wonderful going on at the Cell Picture Show.

The Cell Picture Show has appeared in the Trenches before (here and here), but this recent instalment is to me even more original and interesting than anything they've had before. The image above has two halves, both of which are strikingly reminiscent of Van Gogh's famous and beautiful Starry Night. They look like the product of some brilliant mind with an extraordinary mastery of colour and texture. In fact, the image on the left is a cross section of mouse skin containing basal skin carcinoma, with various components stained different colours and imaged using a fluorescence microscope. The image on the right is an artist's rendering of the same image using different coloured fabrics stitched together. This is part of Cell's exhibition 'Art Under the Microscope', in which images of biological samples are recreated into works of art by professional artists. The image above is just one example, but there are many others of similar standard available in the exhibition. The technical prowess of the researchers who obtained the original images is impressive, as are the aesthetic abilities of the artists who recreated them.

 A fire-like network of neural stem cells in the human brain (left) and their artistic equivalent (right).
What I find so exciting about this exhibition is that it is redefining what can be the subject of art, and what can be the source of artistic inspiration. Nature has been inspiring artists for thousands of years, why should that be restricted to what we can see with our own eyes? We are now at a level of technology that we can begin to unveil many of the secrets that nature had previously been hiding from art. This should be exciting to both scientists and artists. Artists can be excited by the wealth of new subject matter that is beginning to open up to them, and scientists can be excited by the prospect of art adding to the ever-growing popularity and appreciation of science. Perhaps one day there will be great debates in artistic circles about new avant-garde artists who paint their proteins in a controversial way, much like the debates between the surrealists and romanticists on how to depict more macroscopic areas of nature.

Although 'Art Under the Microscope' is a small exhibition, it nonetheless marks a growing trend in the use of science as inspiration for art. I sincerely hope that this continues as it will enrich both science and art, and help to blur the boundaries between them. Art has been very successful in entering many concious aspects of our daily lives, and we are the better for it. Science is still catching up in many regards, although to be fair it hasn't had all that long to make up the difference. If science were as exposed in the public conciousness and as everyday as art is, then I believe we would benefit similarly as we have from the ubiquity of art. The fusion of the two is a match made in heaven that is finally beginning to take hold. I look forward to the days when parks are adorned with pieces of science-based public art, and the spectrum of human endeavour is appreciated as single entity rather than as the separated, delineated pigeon holes of 'art' and 'science' as discrete subjects.

## Monday, November 25, 2013

### How does one measure the mass of a neutrino, using cosmology?

I'm going to tell you how, soon, humanity might measure the masses of neutrinos just by observing past events in the universe. I like this topic because it is one of the few situations in fundamental physics where a measurement of the greater universe might detect something about fundamental particles and/or their interactions, before we manage to measure it in a lab. Another example is the existence of dark matter; however the mass of dark matter will almost certainly be first measured in a lab. Perhaps with neutrinos it will go in the other direction?

What is a neutrino?

I guess that before telling you how to measure a neutrino's mass, it might be pertinent to tell you what a neutrino is and how we can know it has mass before we've measured that mass. Well...

When an atomic nucleus decays, the decay products we see are other nuclei, electrons and/or positrons. These visible products always carry less energy and momentum than the amount that the initial nucleus had. This suggests strongly that some unknown other particle is also being created in the decay and that we just can't see it. This hypothetical particle was dubbed the neutrino and when theories were developed for the force responsible for nuclear decays, the neutrino became an important part of them. And, eventually, neutrinos were detected directly. It took a while because neutrinos interact incredibly weakly, which means you need either a lot of neutrinos or a lot of transparent stuff for the neutrino to interact with (or both) before you will see them.

Initially, it was assumed that neutrinos are massless. They don't need to be massless, but for a long time there was no evidence that they did have mass, so the simplest assumption was that they didn't. There are three types of neutrinos: those emitted in interactions with electrons, those emitted in interactions with muons and those emitted in interactions with tau particles. If neutrinos were massless, then a neutrino emitted as an electron neutrino would always remain an electron neutrino. Similarly, a muon neutrino would always remain a muon neutrino. However, if neutrinos do have mass, then a neutrino emitted in an interaction with an electron will actually travel as a superposition of an electron neutrino, muon neutrino and tau neutrino. The net result being that this neutrino could be detected as a different type of neutrino. Therefore, a smoking gun thing to look for when determining whether neutrinos have mass is this characteristic signal whereby one type of neutrino appears to oscillate into another type of neutrino.

This effect was then seen and seen and seen again. Neutrinos appear to have mass. From the perspective of particle physics this is a bit weird. Neutrinos must have really small masses and it is unclear why these masses are so small. Unfortunately, this mechanism of neutrino oscillations doesn't directly give the masses of the neutrinos. Although, it can be used to measure the differences of the masses of the neutrinos, thus setting lower bounds on the possible masses of the neutrinos.

What has this got to do with cosmology?