Penrose and the Road to Reality

[Matt the Poet]

Hi,

Thought I'd start off with a query to any physicists out there. I've just managed to clear Penrose's 'Road to Reality' on my second attempt. It's been a stimulating ride - I used to be a biologist so phyiscs and maths were not my strong suit, but I was aware that you could only go so far with friendly rubber-sheet and cat metaphors.

Thing is, I know that Penrose has some, ah, unconventional ideas about certain things, particularly quantum physics and consciousness, that verge on the wacky and unsubstantiated. He claims to have been pretty clear on where he's entering these areas, but obviously he's going to have a certain amount of bias.

Have I internalised anything that's dodgier than it looks? Particularly in the realms of mathematical philosophy...

 

[Paulhoff]

If you can, buy Scientific American July issue. There is an article about memory in it. Even if it has nothing to do with quantum physics and consciousness I'm sure that it is still good reading. As for quantum physics and consciousness, that is just so much woo-woo.

Paul

 

[shpalman]

I didn't really like The Road to Reality. I'm a physicist but not a mathematical one, so I didn't like his tone of "if only x (some physics genius) [had had access to some of this mathematical framework / had expressed himself in a better way so that mathematicians could have understood him / had been as clever as I am]..." and I didn't understand what's to be gained by the extra levels of abstraction he introduces. Furthermore, I notice how he derides String Theory for having only come up with the graviton so far, and then presents his Spinor theory which has so far only come up with half a graviton. I don't agree with his "gravity fixes everything" idea either, and you should see Tegmark regarding quantum conciousness.

 

[Cuddles]

I haven't read that book, but from my experience of Penrose I'd say the mathematics is all very good but the physics should generally be ignored. Penrose is very much a mathematician and most of his views on physics and philosophy seem to be based more on mathematical possibilities rather than actual reality. It is important to remember that mathematics is a tool that can be used to describe reality, but maths does not tell us what reality is.

 

[shpalman]

Incidentally, for those of us who like our science freely available through university physics department subscriptions, there's William Marshall, Christoph Simon, Roger Penrose, and Dik Bouwmeester. Towards Quantum Superpositions of a Mirror. Phys. Rev. Lett. 91 (13) 130401 (2003).

 

[Matt the Poet]

Shpalman: Thanks for the Tegmark. I won't cough up for the whole thing, as the abstract seems to make the point quite well. I always suspected that the whole quantum consciousness thing was an extension of the whole "The brain works like [the most complex thing we know about at the present time]" paradigm.

Cuddles: OK, that's interesting, because the deepest and most satisfying insights I got from the books were all about what the maths was doing in terms of describing 'what reality is'?

I used to have this sense that there was an 'underlying reality' that the mathematics was overlaid on like a framework, thanks to RtoR I'm leaning towards the idea that the maths is all there is, plopping out results and models that happen to work in the outside world (a correspondence which, incidentally, freaks me the out far more than any incidental 'quantum weirdness' you'd care to name). It's not that space is 11 (or whatever) dimensional, it's just that you need 11 dimensional maths to describe it properly.

I mean, if we go any deeper than mathematical models into 'what reality is', aren't we hitting the fluffy bedrock of metaphysics?

 

[shpalman]

The thing which impresses me most regarding the correspondence between maths and physics is the way that propagating waves can be written as complex exponentials and non-propagating "evanescent" waves can be written as real exponentials - complex exponentials with imaginary wavenumbers obtained by taking the square root of a negative energy.

But regarding quantum weirdness, there's Simon Gröblacher, Tomasz Paterek, Rainer Kaltenbaek, Caslav Brukner, Marek Zukowski, Markus Aspelmeyer, and Anton Zeilinger. An experimental test of non-local realism. Nature 446 (7138) 871-875 (2007).

 

[Cuddles]

Cuddles: OK, that's interesting, because the deepest and most satisfying insights I got from the books were all about what the maths was doing in terms of describing 'what reality is'?

I used to have this sense that there was an 'underlying reality' that the mathematics was overlaid on like a framework, thanks to RtoR I'm leaning towards the idea that the maths is all there is, plopping out results and models that happen to work in the outside world (a correspondence which, incidentally, freaks me the out far more than any incidental 'quantum weirdness' you'd care to name). It's not that space is 11 (or whatever) dimensional, it's just that you need 11 dimensional maths to describe it properly.

I mean, if we go any deeper than mathematical models into 'what reality is', aren't we hitting the fluffy bedrock of metaphysics?

The trouble with all this kind of maths is that you can make up maths that describes pretty much any kind of universe you care to think of. OK, so current theories prefer using somewhere around 11 dimensions. But it is just as easy to set up a universe with 12, or 200. The problem with a lot of the mathematical sort of philosophy of the type you talk of is that it seems to start off with a reasonably valid mathematical model but then carries on working maths on it without ever stopping to compare it to the real world again.

In fact, string theory is quite a good example here. String theory started as a purely mathematical idea. The basics were worked out and compared to reality and matched quite well, so it was considered a valid theory to be worked on. From there, huge amounts of maths has been done to expand the theories in different directions, predicting all kinds of things. But none of it has been tested. The maths is all perfectly valid, but we cannot say anything about it's relevance to the real world because no-one has checked if it actually matches the real world. (Please note that this does not mean it is not good science. String theory does make predictions that can be tested, it is just that they have not been tested yet, and many may not be able to be tested for some time.)

The problem with Penrose, and many others, is that they don't seem to take any notice of this final step of going back and looking at reality again. They start with something that seems valid and the mathematics is valid all the way through, but that doesn't mean the physics is. If a theory predicts, for example, that a certain particle should exist then if that particle doesn't exist then that theory does not describe reality, no matter how good the maths seems.

In the end, maths is a language. It can be used to describe reality, but it is not reality. It can also be used to describe things that aren't real, but that does not make them real.

 

[becomingagodo]

The trouble with all this kind of maths is that you can make up maths that describes pretty much any kind of universe you care to think of. OK, so current theories prefer using somewhere around 11 dimensions. But it is just as easy to set up a universe with 12, or 200.

Didn't Hawking and Penrose prove mathematically that a universe with a dimension higher then 5 is unstable.

In fact, string theory is quite a good example here. String theory started as a purely mathematical idea.

According to Penrose in his book, string theory started out with mathematics to describe hadrons. Bad example too, as special relativity started out only mathematical and quantum physics, the expriments to varify them came later. Plus string theorist are nuts, so not a good example.

Sorry, but string theory is psudeoscience, so the nuts comment stands.

The problem with Penrose, and many others, is that they don't seem to take any notice of this final step of going back and looking at reality again. They start with something that seems valid and the mathematics is valid all the way through, but that doesn't mean the physics is. If a theory predicts, for example, that a certain particle should exist then if that particle doesn't exist then that theory does not describe reality, no matter how good the maths seems.

The standard model predicts Higgs particles, now where is the test saying the Higgs particle is true. See people in physics can get it wrong and believe in something with no proof.

In the end, maths is a language. It can be used to describe reality, but it is not reality. It can also be used to describe things that aren't real, but that does not make them real.

No this is wrong. Math is more then a language. Imaginary numbers are a good example, now imaginary number don't possibly happen in nature, then why does it appear in equations of quantum mechanics?

Well, if something does not exsist, then I'm pretty sure their would be no logic behind it and it will be easy to disprove. Things have to have mathematical proof before it is considered mathematical.

 

[Matt the Poet]

Didn't Hawking and Penrose prove mathematically that a universe with a dimension higher then 5 is unstable

I was never clear on this - he said it would require lots of degrees of freedom, does that mean the same thing?

The standard model predicts Higgs particles, now where is the test saying the Higgs particle is true. See people in physics can get it wrong and believe in something with no proof

Aren't they doing the test right now in Switzerland somewhere? I don't think physicists 'believe in' the Higgs particle as such (well, some might, I can't see inside their heads). It's more a question of the model that predicts a load of stuff they've already tested really well also predicts a Higgs particle. They wouldn't be building colliders if they actually believed, they'd just be making brightly coloured blogs at each other.

No this is wrong. Math is more then a language. Imaginary numbers are a good example, now imaginary number don't possibly happen in nature, then why does it appear in equations of quantum mechanics?

Ah, well this gets to the heart of what I'm wondering. In my limited, Penrose-driven understanding, imaginary numbers appear in quantum (and all sorts of other) equations because they turn out to be a neat way to describe complicated wave phenomena - the fact that when you take a logarithm of a complex number you turn it into a 'cyclical' kind of quantity (sorry for making proper maths people wince) makes it ideal for talking about 'real' things that have similar properties.

Although I'm with Cuddles that this doesn't mean a whole lot unless it tells us something about how the world we percieve should behave.

I don't know enough about string theory to comment. On the one hand, I'm not sure that it's playing fair with the notion of 'testable hypothesis' to demand a particle accelerator the size of Saturn. On the other, it describes a fair chunk of reality better than some of the other models, and why shouldn't 'elegance' be a factor in cosmological or particle physics models - especially if you don't claim an interest in some sort of 'underlying reality' that the maths might describe?

 

[becomingagodo]

Ah, well this gets to the heart of what I'm wondering. In my limited, Penrose-driven understanding, imaginary numbers appear in quantum (and all sorts of other) equations because they turn out to be a neat way to describe complicated wave phenomena - the fact that when you take a logarithm of a complex number you turn it into a 'cyclical' kind of quantity (sorry for making proper maths people wince) makes it ideal for talking about 'real' things that have similar properties.

Well, no look up Paul Dirac's work. From using mathematics and combining that with quantum physics and special relativity he could only combined it when you let something called a anti-particle exist, so from mathematics Paul Dirac predicted the anti-particle.

It's more a question of the model that predicts a load of stuff they've already tested really well also predicts a Higgs particle. They wouldn't be building colliders if they actually believed, they'd just be making brightly coloured blogs at each other.

No, the mass problem is avoided by introducing the Higgs particle, now if the Higgs did not exist then it would put lots of problems with the standard model. So theorticle physician said what if this particle exist it would solve the problem, which is the same as a string theorist however dimensions equal particle in this case.

Mathematics beats physics every time, thats why physics people hate it. Mathematics is also harder thats why it is hard for people in other science areas to appreciate it.

Also the mathematics does advance physics understanding, a good example is with poincare conjecture, which now makes it possible to figure out the shape of the universe better.

 

[PixyMisa]

Didn't Hawking and Penrose prove mathematically that a universe with a dimension higher then 5 is unstable.

Unless the extra dimensions are curled up very small (which they are in string theory). As I understand it, there are no stable orbits in a universe with more than 3 large spatial dimensions.

 

[Paulhoff]

As I understand it, there are no stable orbits in a universe with more than 3 large spatial dimensions.

I never heard that before, and of course never thought about it, that is interesting.

Paul

 

[Jekyll]

I used to have this sense that there was an 'underlying reality' that the mathematics was overlaid on like a framework, thanks to RtoR I'm leaning towards the idea that the maths is all there is, plopping out results and models that happen to work in the outside world (a correspondence which, incidentally, freaks me the out far more than any incidental 'quantum weirdness' you'd care to name).

Well you'll get that feeling from Penrose's writtings, as he is very much a Platonist. But as Cuddles' says there are so many possible models all with parameters that can be tweaked.

Marvelling over models that happen to fit reality is a lot like marvelling that you went to this lovely bespoke tailors down the road, and he found you the perfect suit that matched your hair style and your shoes and fits like a glove.

I mean its very nice that it all worked out, but its hardly surprising.

 

[Matt the Poet]

Marvelling over models that happen to fit reality is a lot like marvelling that you went to this lovely bespoke tailors down the road, and he found you the perfect suit that matched your hair style and your shoes and fits like a glove.

Hello again...

I'm always wary of analogous thinking. Isn't it more like you wandered into a likely looking building nearby, with the vague intention that you might get a new suit and it just happened to be not aonly a bespoke tailors, but a better bespoke taiors than any there has been in the world before?

Although it's also as though, when you asked for a business suit, there was a chance that they would give you some massively elaborate piece of pimpwear which they somehow convinced you was the best suit in the world, until you went for a job interview...

 

[illogical]

the section on spacetime: Aristotlean, Galilean, Newton-Cartan, Minkowskian, and Einsteinian. wow! the stuff is pretty exciting, although i don't understand fibre bundles.

John Baez suggests reading RtR while studying GR and QFT.

 

[Cuddles]

Didn't Hawking and Penrose prove mathematically that a universe with a dimension higher then 5 is unstable.

No.

According to Penrose in his book, string theory started out with mathematics to describe hadrons. Bad example too, as special relativity started out only mathematical and quantum physics, the expriments to varify them came later. Plus string theorist are nuts, so not a good example.

Sorry, but string theory is psudeoscience, so the nuts comment stands.

Clearly you have absolutely no idea what you are talking about. String theory is science. It makes predictions that can be tested. It makes predictions that are being tested.

The standard model predicts Higgs particles, now where is the test saying the Higgs particle is true. See people in physics can get it wrong and believe in something with no proof.

Get it wrong? Are you really trying to claim that you have proof that the Higgs particle doesn't exist? I'm sure the nice folk over at the LHC would be quite interested to here about that.

No this is wrong. Math is more then a language. Imaginary numbers are a good example, now imaginary number don't possibly happen in nature, then why does it appear in equations of quantum mechanics?

No, maths is a language. That is all. Invisible pink unicorns don't exist in nature, does that mean that English isn't a language? Imaginary numbers also appear in electronics, does that mean electricity doesn't exist.

Seriously, please go out a read a book about science or maths that has more than six words per page and doesn't involve a dog called "Spot". If you carry on insulting large groups of scientists while so obviously not knowing a single thing about what you are talking about you will just embarass yourself.

 

[Cuddles]

No, the mass problem is avoided by introducing the Higgs particle, now if the Higgs did not exist then it would put lots of problems with the standard model. So theorticle physician said what if this particle exist it would solve the problem, which is the same as a string theorist however dimensions equal particle in this case.

Actually I think you'll find that most theories predict the Higgs particle or its equivalent. String theory also predicts it. As does supersymmetry, superstring, M-theory. It is not, as you imply, something made up to try to force the standard model to work, it is something that is predicted by our best scientific knowledge.

Mathematics beats physics every time, thats why physics people hate it. Mathematics is also harder thats why it is hard for people in other science areas to appreciate it.

This just made me giggle. Physicists hating maths? You must be absolutely insane. That's like a swimmer not liking water. Many, if not most, scientists don't enjoy doing maths simply for the sake of the maths, but that does not mean they hate it or that they find it hard, it is just that they apply maths to things rather than looking at it all by itself.

Also the mathematics does advance physics understanding, a good example is with poincare conjecture, which now makes it possible to figure out the shape of the universe better.

A perfect example of maths being a tool of science. As I said. Yes, the maths can describe the shape of the universe. Now trying describing the universe without there being a universe to describe. The universe is physics, maths is the language used to describe it.

 

[Jekyll]

Marvelling over models that happen to fit reality is a lot like marvelling that you went to this lovely bespoke tailors down the road, and he found you the perfect suit that matched your hair style and your shoes and fits like a glove.

Hello again...

I'm always wary of analogous thinking. Isn't it more like you wandered into a likely looking building nearby, with the vague intention that you might get a new suit and it just happened to be not aonly a bespoke tailors, but a better bespoke taiors than any there has been in the world before?

Ok, this is a different question.

We've gone from "Isn't it amazing that a piece of mathematics happens to describe some part the world exactly?" (well as far as we can tell), to "Isn't it amazing how mathematics lets us create a description of the world?".

Now externally, from the point of view of science, it doesn't matter that its mathematics which happens to describe the world so well and so consistently. It could be poetry or philosophy or some strange Jungian theology instead and science would then be using that instead.*

To stick to this some what tortured analogy, science will always go to the tailors.

So why is it a "better bespoke tailors than any there has been in the world before"?
Because mathematics (in the way you're using the word) isn't just what one mathematician does, but its the cumulative effort of all the mathematicians in the world to build on the work of those who have come before them.

So it's guaranteed that, with civilisation the way it is, scientists will always turn to maths and maths will keep getting incrementally better.
It's not a fantastic coincidence any more than all the pieces of a jigsaw managing to fit together.

*Of course nature would have to be stupid not to rely on maths.

 

[Yllanes]

We've gone from "Isn't it amazing that a piece of mathematics happens to describe some part the world exactly?" (well as far as we can tell), to "Isn't it amazing how mathematics lets us create a description of the world?".

If we are going to talk about those things, I recommend E. Wigner's The Unreasonable Effectiveness of Mathematics in the Natural Sciences.