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Cosmology Talks – To Infinity and Beyond (Probably)

Posted in mathematics, The Universe and Stuff with tags , , , , , , , , , , , , , on March 20, 2024 by telescoper

Here’s an interestingly different talk in the series of Cosmology Talks curated by Shaun Hotchkiss. The speaker, Sylvia Wenmackers, is a philosopher of science. According to the blurb on Youtube:

Her focus is probability and she has worked on a few theories that aim to extend and modify the standard axioms of probability in order to tackle paradoxes related to infinite spaces. In particular there is a paradox of the “infinite fair lottery” where within standard probability it seems impossible to write down a “fair” probability function on the integers. If you give the integers any non-zero probability, the total probability of all integers is unbounded, so the function is not normalisable. If you give the integers zero probability, the total probability of all integers is also zero. No other option seems viable for a fair distribution. This paradox arises in a number of places within cosmology, especially in the context of eternal inflation and a possible multiverse of big bangs bubbling off. If every bubble is to be treated fairly, and there will ultimately be an unbounded number of them, how do we assign probability? The proposed solutions involve hyper-real numbers, such as infinitesimals and infinities with different relative sizes, (reflecting how quickly things converge or diverge respectively). The multiverse has other problems, and other areas of cosmology where this issue arises also have their own problems (e.g. the initial conditions of inflation); however this could very well be part of the way towards fixing the cosmological multiverse.

The paper referred to in the presentation can be found here. There is a lot to digest in this thought-provoking talk, from the starting point on Kolmogorov’s axioms to the application to the multiverse, but this video gives me an excuse to repeat my thoughts on infinities in cosmology.

Most of us – whether scientists or not – have an uncomfortable time coping with the concept of infinity. Physicists have had a particularly difficult relationship with the notion of boundlessness, as various kinds of pesky infinities keep cropping up in calculations. In most cases this this symptomatic of deficiencies in the theoretical foundations of the subject. Think of the ‘ultraviolet catastrophe‘ of classical statistical mechanics, in which the electromagnetic radiation produced by a black body at a finite temperature is calculated to be infinitely intense at infinitely short wavelengths; this signalled the failure of classical statistical mechanics and ushered in the era of quantum mechanics about a hundred years ago. Quantum field theories have other forms of pathological behaviour, with mathematical components of the theory tending to run out of control to infinity unless they are healed using the technique of renormalization. The general theory of relativity predicts that singularities in which physical properties become infinite occur in the centre of black holes and in the Big Bang that kicked our Universe into existence. But even these are regarded as indications that we are missing a piece of the puzzle, rather than implying that somehow infinity is a part of nature itself.

The exception to this rule is the field of cosmology. Somehow it seems natural at least to consider the possibility that our cosmos might be infinite, either in extent or duration, or both, or perhaps even be a multiverse comprising an infinite collection of sub-universes. If the Universe is defined as everything that exists, why should it necessarily be finite? Why should there be some underlying principle that restricts it to a size our human brains can cope with?

On the other hand, there are cosmologists who won’t allow infinity into their view of the Universe. A prominent example is George Ellis, a strong critic of the multiverse idea in particular, who frequently quotes David Hilbert

The final result then is: nowhere is the infinite realized; it is neither present in nature nor admissible as a foundation in our rational thinking—a remarkable harmony between being and thought

But to every Hilbert there’s an equal and opposite Leibniz

I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.

You see that it’s an argument with quite a long pedigree!

Many years ago I attended a lecture by Alex Vilenkin, entitled The Principle of Mediocrity. This was a talk based on some ideas from his book Many Worlds in One: The Search for Other Universes, in which he discusses some of the consequences of the so-called eternal inflation scenario, which leads to a variation of the multiverse idea in which the universe comprises an infinite collection of causally-disconnected “bubbles” with different laws of low-energy physics applying in each. Indeed, in Vilenkin’s vision, all possible configurations of all possible things are realised somewhere in this ensemble of mini-universes.

One of the features of this scenario is that it brings the anthropic principle into play as a potential “explanation” for the apparent fine-tuning of our Universe that enables life to be sustained within it. We can only live in a domain wherein the laws of physics are compatible with life so it should be no surprise that’s what we find. There is an infinity of dead universes, but we don’t live there.

I’m not going to go on about the anthropic principle here, although it’s a subject that’s quite fun to write or, better still, give a talk about, especially if you enjoy winding people up! What I did want to say mention, though, is that Vilenkin correctly pointed out that three ingredients are needed to make this work:

  1. An infinite ensemble of realizations
  2. A discretizer
  3. A randomizer

Item 2 involves some sort of principle that ensures that the number of possible states of the system we’re talking about  is not infinite. A very simple example from  quantum physics might be the two spin states of an electron, up (↑) or down(↓). No “in-between” states are allowed, according to our tried-and-tested theories of quantum physics, so the state space is discrete.  In the more general context required for cosmology, the states are the allowed “laws of physics” ( i.e. possible  false vacuum configurations). The space of possible states is very much larger here, of course, and the theory that makes it discrete much less secure. In string theory, the number of false vacua is estimated at 10500. That’s certainly a very big number, but it’s not infinite so will do the job needed.

Item 3 requires a process that realizes every possible configuration across the ensemble in a “random” fashion. The word “random” is a bit problematic for me because I don’t really know what it’s supposed to mean. It’s a word that far too many scientists are content to hide behind, in my opinion. In this context, however, “random” really means that the assigning of states to elements in the ensemble must be ergodic, meaning that it must visit the entire state space with some probability. This is the kind of process that’s needed if an infinite collection of monkeys is indeed to type the (large but finite) complete works of shakespeare. It’s not enough that there be an infinite number and that the works of shakespeare be finite. The process of typing must also be ergodic.

Now it’s by no means obvious that monkeys would type ergodically. If, for example, they always hit two adjoining keys at the same time then the process would not be ergodic. Likewise it is by no means clear to me that the process of realizing the ensemble is ergodic. In fact I’m not even sure that there’s any process at all that “realizes” the string landscape. There’s a long and dangerous road from the (hypothetical) ensembles that exist even in standard quantum field theory to an actually existing “random” collection of observed things…

More generally, the mere fact that a mathematical solution of an equation can be derived does not mean that that equation describes anything that actually exists in nature. In this respect I agree with Alfred North Whitehead:

There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.

It’s a quote I think some string theorists might benefit from reading!

Items 1, 2 and 3 are all needed to ensure that each particular configuration of the system is actually realized in nature. If we had an infinite number of realizations but with either infinite number of possible configurations or a non-ergodic selection mechanism then there’s no guarantee each possibility would actually happen. The success of this explanation consequently rests on quite stringent assumptions.

I’m a sceptic about this whole scheme for many reasons. First, I’m uncomfortable with infinity – that’s what you get for working with George Ellis, I guess. Second, and more importantly, I don’t understand string theory and am in any case unsure of the ontological status of the string landscape. Finally, although a large number of prominent cosmologists have waved their hands with commendable vigour, I have never seen anything even approaching a rigorous proof that eternal inflation does lead to realized infinity of  false vacua. If such a thing exists, I’d really like to hear about it!

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Beyond Falsifiability: Normal Science in a Multiverse

Posted in The Universe and Stuff with tags , , , , , , on January 17, 2018 by telescoper

There’s a new paper on the arXiv by Sean Carroll called Beyond Falsifiability: Normal Science in a Multiverse. The abstract is:

Cosmological models that invoke a multiverse – a collection of unobservable regions of space where conditions are very different from the region around us – are controversial, on the grounds that unobservable phenomena shouldn’t play a crucial role in legitimate scientific theories. I argue that the way we evaluate multiverse models is precisely the same as the way we evaluate any other models, on the basis of abduction, Bayesian inference, and empirical success. There is no scientifically respectable way to do cosmology without taking into account different possibilities for what the universe might be like outside our horizon. Multiverse theories are utterly conventionally scientific, even if evaluating them can be difficult in practice.

I’ve added a link to `abduction’ lest you think it has something to do with aliens!

I haven’t had time to read all of it yet, but thought I’d share it here because it concerns a topic that surfaces on this blog from time to time. I’m not a fan the multiverse because (in my opinion) most of the arguments trotted out in its favour are based on very muddled thinking. On the other hand, I’ve never taken seriously any of the numerous critiques of the multiverse idea based on the Popperian criterion of falsifiability because (again, in my opinion) that falsifiability has very little to do with the way science operates.

Anyway, Sean’s papers are always interesting to read so do have a look if this topic interests you. And feel free to comment through the box below.

4 Comments »

Inflationary Perturbation

Posted in The Universe and Stuff with tags , , , , , , on May 11, 2017 by telescoper

I thought I’d just draw the collective attention of my vast readership (Sid and Doris Bonkers) to a bit of a row that has broken out between two groups of cosmologists concerning the theory of cosmic inflation.

This kerfuffle started with an article entitled Pop Goes The Universe in Scientific American by Anna Ijjas, Paul Steinhardt, and Avi Loeb that (among other things) asserts that inflation “cannot be evaluated using the scientific method” and is consequently not a scientific theory. Another group of cosmologists (including Alan Guth, the author of the paper that launched the inflationay universe model) penned a response that was signed by a long list of leading scientists, thirty-three of them to be precise. The original authors then issued a response to the response. Sean Carroll (who was one of those who signed the response the original paper has written a nice blog post summarizing the points of disagreement.

I’m not going to attempt to post a detailed response to every issue raised in this correspondence, but I will make a few points.

First, I think it’s important to realize that there isn’t a single simple definition of `the scientific method’: there are lots of scientific methods, each of which may employed to a greater or lesser degree in different disciplines. Most scientists would probably agree that some notion of `testability’ has to be included if a theory is said to be scientific, but it seems to me that testability is not an absolute, in the sense that not all predictions of a theory need to be observable for the theory as a whole to be testable to a degree. A theory might predict the existence of a phenomenon A that is impossible for all practical purposes to observe, but if that theory also has another necessary consequence B that is observed then the theory does not deserve to be dismissed as unscientific.

One aspect of modern inflationary theory that is singled out for criticism has been the incorporation of the idea of a multiverse. I have to make the confession here that I don’t like the concept of the multiverse, nor do I like the way it has become fashionably mainstream in the field. I’ve never seen it as a necessary (or even useful) addition to inflation theory. However, suppose you have a model of inflation that leads to something like Linde’s version of the multiverse. Causally disconnected domains of this multiverse may indeed not be observable, but if the theory has other necessary implications for things we can observe in our local universe then it is testable to a degree.

My position (such as it is) is that I like the idea of inflation, largely because: (a) it’s very neat; and (b) it provides a simple mechanism for generating fluctuations of the right form to account for so many of the observable properties of our universe, especially the fluctuations we measure in the cosmic microwave background seen by Planck:

These observations don’t prove that inflation is right, nor do they narrow down the field of possible inflationary models very much, but they do seem to be in accord with the predictions of the simplest versions of the theory. Whether that remains true for planned and future observations remains to be seen. Should someone come up with a different theory that matches existing data and can account for something in future data that inflation can’t then I’m sure cosmologists would shift allegiance. The thing is we don’t have such an alternative at the moment. Inflation is the preferred theory, partly for want of compelling alternatives and partly because we need more data to test its predictions.

That said, there are one or two points on which I agree with Ijjas, Steinhardt and Loeb. In particular there has developed what I consider to be a pathological industry dreaming up countless variations of the basic inflation model. There is now a bewildering variety of such models, few of which have any physical motivation whatsoever. I think this is a particularly a grotesque manifestation of the absurd way we measure scientific `success’ in terms of counting publications and how that has driven unhealthy research practice.

No doubt many of you disagree or wish to comment for other reasons either on the original communications or on my comments. Please feel free to offer your thoughts through the box below!

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George Ellis – Are there multiple universes?

Posted in The Universe and Stuff with tags , , , on July 18, 2016 by telescoper

So, back to Brighton and a sweltering office on Sussex University Campus. I made it back to pick up the list of names I’ll be reading out at tomorrow afternoon’s graduation ceremony in time to give me a few hours’ practice tonight. On the train back from Cardiff I remembered a discussion I had at the conference last week, especially about the various views about cosmology, especially the idea that we might live in a multiverse. I did a bit of a dig around and found this nice video of esteemed cosmologist  (and erstwhile co-author of mine) George Ellis talking about this, and also about his favourite kind of universe (namely one with a compact topology).

 

2 Comments »

The Map is not the Territory

Posted in History, The Universe and Stuff with tags , , , , , , , , on January 27, 2015 by telescoper

I came across this charming historical map while following one of my favourite Twitter feeds “@Libroantiguo” which publishes fascinating material about books of all kinds, especially old ones. It shows the location of London coffee houses and is itself constructed in the shape of a coffee pot:

Coffee
Although this one is obviously just a bit of fun, maps like this are quite fascinating, not only as practical guides to navigating a transport system but also because they often stand up very well as works of art. It’s also interesting how they evolve with time  because of changes to the network and also changing ideas about stylistic matters.

A familiar example is the London Underground or Tube map. There is a fascinating website depicting the evolutionary history of this famous piece of graphic design. Early versions simply portrayed the railway lines inset into a normal geographical map which made them rather complicated, as the real layout of the lines is far from regular. A geographically accurate depiction of the modern tube network is shown here which makes the point:

tubegeo

A revolution occurred in 1933 when Harry Beck compiled the first “modern” version of the map. His great idea was to simplify the representation of the network around a single unifying feature. To this end he turned the Central Line (in red) into a straight line travelling left to right across the centre of the page, only changing direction at the extremities. All other lines were also distorted to run basically either North-South or East-West and produce a regular pattern, abandoning any attempt to represent the “real” geometry of the system but preserving its topology (i.e. its connectivity).  Here is an early version of his beautiful construction:

Note that although this a “modern” map in terms of how it represents the layout, it does look rather dated in terms of other design elements such as the border and typefaces used. We tend not to notice how much we surround the essential things, which tend to last, with embellishments that date very quickly.

More modern versions of this map that you can get at tube stations and the like rather spoil the idea by introducing a kink in the central line to accommodate the complexity of the interchange between Bank and Monument stations as well as generally buggering about with the predominantly  rectilinear arrangement of the previous design:

I quite often use this map when I’m giving popular talks about physics. I think it illustrates quite nicely some of the philosophical issues related with theoretical representations of nature. I think of theories as being like maps, i.e. as attempts to make a useful representation of some  aspects of external reality. By useful, I mean the things we can use to make tests. However, there is a persistent tendency for some scientists to confuse the theory and the reality it is supposed to describe, especially a tendency to assert there is a one-to-one relationship between all elements of reality and the corresponding elements in the theoretical picture. This confusion was stated most succintly by the Polish scientist Alfred Korzybski in his memorable aphorism :

The map is not the territory.

I see this problem written particularly large with those physicists who persistently identify the landscape of string-theoretical possibilities with a multiverse of physically existing domains in which all these are realised. Of course, the Universe might be like that but it’s by no means clear to me that it has to be. I think we just don’t know what we’re doing well enough to know as much as we like to think we do.

A theory is also surrounded by a penumbra of non-testable elements, including those concepts that we use to translate the mathematical language of physics into everday words. We shouldn’t forget that many equations of physics have survived for a long time, but their interpretation has changed radically over the years.

The inevitable gap that lies between theory and reality does not mean that physics is a useless waste of time, it just means that its scope is limited. The Tube  map is not complete or accurate in all respects, but it’s excellent for what it was made for. Physics goes down the tubes when it loses sight of its key requirement: to be testable.

In any case, an attempt to make a grand unified theory of the London Underground system would no doubt produce a monstrous thing that would be so unwieldly that it would be useless in practice. I think there’s a lesson there for string theorists too…

Now, anyone for a game of Mornington Crescent?

 

12 Comments »

Has BICEP2 bitten the dust?

Posted in The Universe and Stuff with tags , , , , , , , , , , on June 5, 2014 by telescoper

Time for yet another update on twists and turns of the ongoing saga of  BICEP2 and in particular the growing suspicion that the measurements could be accounted for by Galactic dust rather than primordial gravitational waves; see various posts on this blog.

First there is a Nature News and Views article by Paul Steinhardt with the title Big Bang blunder bursts the multiverse bubble. As the title suggests, this piece is pretty scathing about the whole affair, for two main reasons. The first is to do with the manner of the release of the result via a press conference before the results had been subjected to peer review. Steinhardt argues that future announcements of “discoveries” in this area

should be made after submission to journals and vetting by expert referees. If there must be a press conference, hopefully the scientific community and the media will demand that it is accompanied by a complete set of documents, including details of the systematic analysis and sufficient data to enable objective verification.

I also have reservations about the way the communication of this result was handled but I wouldn’t go as far as Steinhardt did. I think it’s quite clear that the BICEP2 team have detected something and that they published their findings in good faith. The fact that the media pushed the result as being a definitive detection of primordial gravitational waves wasn’t entirely their fault; most of the hype was probably down to other cosmologists (especially theorists) who got a bit over-excited.

It is true that if it turns out that the BICEP2 signal is due to dust rather than primordial gravitational waves then the cosmology community will have a certain amount of egg on its face. On the other hand, this is actually what happens in science all the time. If we scientists want the general public to understand better how science actually works we should not pretend that it is about absolute certainties but that it is a process, and because it is a process operated by human beings it is sometimes rather messy. The lesson to be learned is not about hiding the mess from the public but about communicating the uncertainties more accurately and more honestly.

Steinhardt’s other main point is one with which I disagree very strongly. Here is the core of his argument about inflation:

The common view is that it is a highly predictive theory. If that was the case and the detection of gravitational waves was the ‘smoking gun’ proof of inflation, one would think that non-detection means that the theory fails. Such is the nature of normal science. Yet some proponents of inflation who celebrated the BICEP2 announcement already insist that the theory is equally valid whether or not gravitational waves are detected. How is this possible?

The answer given by proponents is alarming: the inflationary paradigm is so flexible that it is immune to experimental and observational tests.

This is extremely disingenuous. There’s a real difference between a theory that is “immune to experimental and observational tests” and one which is just very difficult to test in that way. For a start, the failure of a given experiment to detect gravitational waves  does not prove that gravitational waves don’t exist at some level; a more sensitive experiment might be needed. More generally, the inflationary paradigm is not completely specified as a theory; it is a complex entity which contains a number of free parameters that can be adjusted in the light of empirical data. The same is also true, for example, of the standard model of particle physics. The presence of these adjustable degrees of freedom makes it much harder to test the hypothesis than would be the case if there were no such wiggle room. Normal science often proceeds via the progressive tightening of the theoretical slack until there is no more room for manoeuvre. This process can take some time.

Inflation will probably be very difficult to test, but then there’s no reason why we should expect a definitive theoretical understanding of the very early Universe to come easily to us. Indeed, there is almost certainly a limit to the extent that we can understand the Universe with “normal science” but I don’t think we’ve reached it yet. We need to be more patient. So what if we can’t test inflation with our current technology? That doesn’t mean that the idea is unscientific. It just means that the Universe is playing hard to get.

Steinhardt continues with an argument about the multiverse. He states that inflation

almost inevitably leads to a multiverse with an infinite number of bubbles, in which the cosmic and physical properties vary from bubble to bubble. The part of the multiverse that we observe corresponds to a piece of just one such bubble. Scanning over all possible bubbles in the multi­verse, every­thing that can physically happen does happen an infinite number of times. No experiment can rule out a theory that allows for all possible outcomes. Hence, the paradigm of inflation is unfalsifiable.

This may seem confusing given the hundreds of theoretical papers on the predictions of this or that inflationary model. What these papers typically fail to acknowledge is that they ignore the multiverse and that, even with this unjustified choice, there exists a spectrum of other models which produce all manner of diverse cosmological outcomes. Taking this into account, it is clear that the inflationary paradigm is fundamentally untestable, and hence scientifically meaningless.

I don’t accept the argument that “inflation almost inevitably leads to a multiverse” but even if you do the rest of the argument is false. Infinitely many outcomes may be possible, but are they equally probable? There is a well-defined Bayesian framework within which one could answer this question, with sufficient understanding of the underlying physics. I don’t think we know how to do this yet but that doesn’t mean that it can’t be done in principle.

For similar discussion of this issue see Ted Bunn’s Blog.

Steinhardt’s diatribe was accompanied  yesterday by a sceptical news piece in the Grauniad entitled Gravitational waves turn to dust after claims of flawed analysis. This piece is basically a rehash of the argument that the BICEP2 results may be accounted for by dust rather than primordial gravitational waves, which definitely a possibility, and that the BICEP2 analysis involved a fairly dubious analysis of the foregrounds. In my opinion it’s an unnecessarily aggressive piece, but mentioning it here gives me the excuse to post the following screen grab from the science section of today’s Guardian website:

BICEP_thenandnow

Aficionados of Private Eye will probably think of the Just Fancy That section!

Where do I stand? I can hear you all asking that question so I’ll make it clear that my view hasn’t really changed at all since March. I wouldn’t offer any more than even money on a bet that BICEP2 has detected primordial gravitational waves at all and I’d offer good odds that, if the detection does stand, the value of the tensor-to-scalar ratio is significantly lower than the value of 0.2 claimed by BICEP2.  In other words, I don’t know. Sometimes that’s the only really accurate statement a scientist can make.

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Inflation and the Multiverse

Posted in Astrohype, The Universe and Stuff with tags , , , , , , on January 6, 2014 by telescoper

I was quite excited when I discovered, via Twitter, a paper on the arXiv with the title Quantum Fluctuations in Cosmology and How They Lead to a Multiverse, which was written by one of the architects of the inflationary universe scenario, Alan Guth. Despite numerous attempts to understand the argument how inflation leads to a Multiverse I’ve never really succeeded. To me it always seemed like  a version of the Mind Projection Fallacy inspired by a frequentist interpretation of probability: the construction of notional ensembles for the purposes of calculation in quantum mechanics does not imply that such ensembles are realized in nature. In fact I’ve never found much more substance in articles about this issue than the assertion that Quantum Physics = Woo! = Multiverse.

Anyway, since the paper I found is a review article I hoped it would help teach me the error of my ways. Here is the abstract

This article discusses density perturbations in inflationary models, offering a pedagogical description of how these perturbations are generated by quantum fluctuations in the early universe. A key feature of inflation is that that rapid expansion can stretch microscopic fluctuations to cosmological proportions. I discuss also another important conseqence of quantum fluctuations: the fact that almost all inflationary models become eternal, so that once inflation starts, it never stops.

My eye was drawn to the phrase “almost all inflationary models”.  I had hoped to see “almost all” used in its strict mathematical sense, ie “apart from a set of measure zero” with the measure being fully specified. Disappointingly, it isn’t.   Guth discusses the consequences of the tail  the inflationary potential V (for large values of the inflaton field ϕ) on the long-term evolution of inflationary dynamics and then states

Since V3/2/|V ′| grows without bound as ϕ → ∞ for most potentials under consideration, almost all models allow for eternal inflation.

This means, to me, most models people have constructed but doesn’t mean all possible models. I don’t doubt that some inflationary models  become eternal, but would have preferred a more rigorous statement.  This is particularly strange because Guth spends the last section of his paper discussing the “measure problem”:

While the multiverse picture looks very plausible in the context of inflationary cosmology — at least to me — it raises a thorny and unsolved problem, known as the “measure problem.” Specifically, we do not know how to define probabilities in the multiverse.

The measure problem to my mind also extends to the space of all possible inflationary theories.

And then there’s the title, which, I remind you, is Quantum Fluctuations in Cosmology and How They Lead to a Multiverse. Guth’s argument consists of going through the (standard) calculation of the spectrum of cosmological density fluctuations (which does fit a host of observational data). He then states:

Since the density perturbation calculations have been incredibly successful, it seems to make sense to take seriously the assumptions behind these calculations, and follow them where they lead. I have to admit that there is no clear consensus among cosmologists, but to many of us the assumptions seem to be pointing to eternal inflation, and the multiverse.

I have to admit that I get a bit annoyed when I read a paper in which the actual conclusions are much weaker than implied by the title, but that seems to be par for the course in this field.

For the record, I’ll state that I am an agnostic about the multiverse. It may be a correct idea, it may not. I will say, however, that I still haven’t found any article that puts it on a firm scientific footing. That may well, of course, just be a measure of my ignorance. If you know of one, please let me know through the comments box.

4 Comments »

The Inflationary Bubble

Posted in The Universe and Stuff with tags , , , , on July 9, 2013 by telescoper

The Summer School I’m attending on Inflation and the CMB got under way yesterday morning with a couple of lectures (90 minutes each) by Andrei Linde, one of the pioneers of the theory of cosmic inflation. I enjoyed the first part of the session, but then he went off into the technical details of a specific model for which there seemed previous little in the way of physical motivation or testable consequences. There’s an occupational hazard for people working on inflation which is that they become so absorbed by their calculations that they forget that they’re supposed to be doing science. It sometimes appears that this field has reached a critical density of activity which means that it’s in danger of forming a closed universe completely incapable of communicating with the world outside and perhaps of collapsing in on itself.

The other thing I didn’t like was the evangelism about the multiverse, which is widespread amongst theorists these days. I’ve stated my position about this before so I won’t repeat my objections here. I will, however, lodge an objection to the way Prof. Linde answered a question about whether the multiverse theory was a testable of various fine-tuning problems in cosmology by saying

Ihe multiverse is the only known explanation so in a sense it has already been tested.

I don’t mind particularly if theories are not testable with current technology. New ideas often have to wait a very long time before equipment and techniques are developed to test them, but Linde’s response is rather symptomatic of a frame of mind that does not consider testability important at all. The worst offenders in this regard are certain string theorists who seem to thing string theory is so compelling in its own right that it just has to be the one true description of how the Universe works, even if the framework it provides is unable to make any predictions at all.

IMG-20130708-00145

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All models are wrong

Posted in The Universe and Stuff with tags , , , , , , , , , on May 17, 2013 by telescoper

I’m back in Cardiff for the day, mainly for the purpose of attending presentations by a group of final-year project students (two of them under my supervision, albeit now remotely).  One of the talks featured a famous quote by the statistician George E.P. Box:

Essentially, all models are wrong, but some are useful.

I agree with this, actually, but only if it’s not interpreted in a way that suggests that there’s no such thing as reality and/or that science is just a game.  We may never achieve a perfect understanding of how the Universe works, but that’s not the same as not knowing anything at all. 

A familiar example that nicely illustrates my point  is the London Underground or Tube map. There is a fascinating website depicting the evolutionary history of this famous piece of graphic design. Early versions simply portrayed the railway lines inset into a normal geographical map which made them rather complicated, as the real layout of the lines is far from regular. A geographically accurate depiction of the modern tube network is shown here which makes the point:

geo_tubemap

A revolution occurred in 1933 when Harry Beck compiled the first “modern” version of the map. His great idea was to simplify the representation of the network around a single unifying feature. To this end he turned the Central Line (in red) into a straight line travelling left to right across the centre of the page, only changing direction at the extremities. All other lines were also distorted to run basically either North-South or East-West and produce a much more regular pattern, abandoning any attempt to represent the “real” geometry of the system but preserving its topology (i.e. its connectivity).  Here is an early version of his beautiful construction:

Note that although this a “modern” map in terms of how it represents the layout, it does look rather dated in terms of other design elements such as the border and typefaces used. We tend not to notice how much we surround the essential things with embellishments that date very quickly.

More modern versions of this map that you can get at tube stations and the like rather spoil the idea by introducing a kink in the central line to accommodate the complexity of the interchange between Bank and Monument stations as well as generally buggering about with the predominantly  rectilinear arrangement of the previous design:

I quite often use this map when I’m giving popular talks about physics. I think it illustrates quite nicely some of the philosophical issues related with theoretical representations of nature. I think of theories or models as being like maps, i.e. as attempts to make a useful representation of some  aspects of external reality. By useful, I mean the things we can use to make tests. However, there is a persistent tendency for some scientists to confuse the theory and the reality it is supposed to describe, especially a tendency to assert there is a one-to-one relationship between all elements of reality and the corresponding elements in the theoretical picture. This confusion was stated most succintly by the Polish scientist Alfred Korzybski in his memorable aphorism :

The map is not the territory.

I see this problem written particularly large with those physicists who persistently identify the landscape of string-theoretical possibilities with a multiverse of physically existing domains in which all these are realised. Of course, the Universe might be like that but it’s by no means clear to me that it has to be. I think we just don’t know what we’re doing well enough to know as much as we like to think we do.

A theory is also surrounded by a penumbra of non-testable elements, including those concepts that we use to translate the mathematical language of physics into everday words. We shouldn’t forget that many equations of physics have survived for a long time, but their interpretation has changed radically over the years.

The inevitable gap that lies between theory and reality does not mean that physics is a useless waste of time, it just means that its scope is limited. The Tube  map is not complete or accurate in all respects, but it’s excellent for what it was made for. Physics goes down the tubes when it loses sight of its key requirement, i.e. to be testable, and in order to be testable it has to be simple enough to calculate things to be compared with observations. In many cases that means a simplified model is perfectly adequete.

Another quote by George Box expands upon this point:

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

In any case, an attempt to make a grand unified theory of the London Underground system would no doubt produce a monstrous thing so unwieldly that it would be useless in practice. I think there’s a lesson there for string theorists too…

Many modern-day physicists are obsessed with the idea of a “Theory of Everything” (or TOE). Such a theory would entail the unification of all physical theories – all laws of Nature, if you like – into a single principle. An equally accurate description would then be available, in a single formula, of phenomena that are currently described by distinct theories with separate sets of parameters. Instead of textbooks on mechanics, quantum theory, gravity, electromagnetism, and so on, physics students would need just one book. But would such a theory somehow be  physical reality, as some physicists assert? I don’t think so. In fact it’s by no means clear to me that it would even be useful..

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Infinities in Cosmology

Posted in The Universe and Stuff with tags , , , , on February 7, 2013 by telescoper

Only time to post a quick advertisement I received in an email from the one of the organizers of a 4-day series of talks on Infinities in Cosmology, at the Department of Applied Mathematics and Theoretical Physics (DAMTP), Centre for Mathematical Sciences, Cambridge, from 18-21 March 2013.

This is one in a series of thematic programmes on Cosmology and Philosophy organised by a collaboration of cosmologists and philosophers of science at Oxford and Cambridge Universities. Speakers include A. Aguirre, M. Dafermos, M.R. Douglas, G.F.R. Ellis, M. Hogarth, and S. Saunders.

This is taken from the conference website:

Cosmology involves infinities, or at least the prospect of infinities, in various ways: the most obvious being the potentially infinite age and size of the universe, and the possible occurrence of actual infinities at local spacetime singularities or at the beginning of the Universe. But there are also other kinds of infinity to consider; for example, the possibility of enhanced spatiotemporal scope for computation, or the unlimited proliferation inherent in the concept of the multiverse and the problems encountered in defining probabilities in this context. These topics will be explored in this three-day series and the following full-day workshop.

Looks quite interesting to me, although I don’t think I’ll be able to make time to go!

Further details and online registration for the conference are now available at

http://www.damtp.cam.ac.uk/events/infinities2013/

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