Shahn Majid

This will be my last regular post for a while because of Christmas and teaching three courses next term at my University. These past eleven posts, see here and here, have been my personal take on many of the topics covered in On Space and Time and its now time in this twelfth post to address the larger picture of the volume itself.

In fact the volume is about opening a genuine public debate on the true nature of space and time, starting with a public panel discussion on this topic in 2006 in Cambridge, England. Where this came from was my increasing unease about the portrayal of fundamental physics — quantum gravity in particular — as already solved by string theory when, in fact, theoretical physics is in need of fresh profound ideas and contact with experiment, when these are the most exciting and turbulent of times.

I also insist in the preface to On Space and Time that this debate needs to involve not only scientists but the wider public. The reason is that scientists’ ideas have to come from somewhere, from sitting around in cafes, from contemplation of art. We don’t know where the key revolutionary idea is going to come from. Put another way, to progress, scientists need now to see what Science is, which means they have to step outside it and see it in part as a non-scientist.

In particular, and this being Christmastime, I want you to ask yourself what does someone singing a Christmas carol have to say about quantum gravity? What does that person have in common with a theoretical physicist? What I think they have in common is contemplation of the infinite. I mean a sense of something bigger than ourselves. As a confirmed atheist I won’t call it God, but its a sense of awe at the Universe and a wonder about our place in it. My approach as a theoretical physicist is to use mathematics and the scientific method to explore the issue, while a carol singer is surely using other means to ‘connect’.

In fact it is only since the 17th century Enlightenment that Science somehow replaced religion as the font of physical truth. But the Scientific Method pioneered by Hooke and others replaced religious dogma, good, yet itself is based on certain assumptions and ways of doing things, of dividing knowledge into ‘theory’ and ‘experiment’, in other words some other dogma.

As a scientist I am 1000% committed to the Scientific Method but I see it as a particular way of exploring reality. One that we might now need to understand better by seeing it from the outside.

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Shahn Majid

After last week’s imaginative speculation, I’d better tell you something concrete. How about the solution to quantum gravity that has been eluding us for some 90 years? Here it is … er … with one minor catch. We’ll have to suppose that spacetime is 3 dimensional, i.e. one time and only two space directions rather than three.

He's never heard of this "3rd spatial dimension"!

There is a tradition, starting I think with Edwin A. Abbott’s 1880 tale ‘Flatland’, where we suppose that we are not 3-dimensional beings but, let us say, ants, constrained to live forever on some two-dimensional surface. We tend to visualize a surface — imagine, say, the surface of a sphere or doughnut — within three dimensions, but don’t be fooled by that. That is just an aid to visualization. An ant crawling about on the surface, moving along ’shortest paths’ (the analogue of a straight line on a flat space) could fully map out the geometry of the surface without ever leaving it.

I am speaking here of the spatial geometry. We will assume that time is a further linear dimension, making spacetime 3-dimensional, mapped out as the 2-dimensional surface evolves in time.

Actually, we won’t assume any of this, since as I explained in previous blogs, there is no evidence of an actual spacetime continuum of any dimension. But we will take it as a commonly accepted starting point and then I will explain carefully where we have to make the quantum leap to throw all that away to get to actual quantum gravity. This will also give you a bit of insight into the guts of the way that scientific revolutions work in practice.

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Shahn Majid

So far in these posts we have looked at testable quantum gravity effects, but I have not said much about the ultimate theory of quantum gravity itself. There is a simple reason: I do not think we have a compelling theory yet.

Rather, I think that this deepest and most long-standing of all problems in fundamental physics still needs a revolutionary new idea or two for which we are still grasping. More revolutionary even than time-reversal. Far more revolutionary and imaginative than string theory. In this post I’ll take a personal shot at an idea — a new kind of duality principle that I think might ultimately relate gravity and information.

The idea that gravity and information should be intimately related, or if you like that information is not just a semantic construct but has a physical aspect is not new. It goes back at least some decades to works of Beckenstein and Hawking showing that black holes radiate energy due to quantum effects. As a result it was found that black holes could be viewed has having a certain entropy, proportional to the surface area of the black hole. Lets add to this a `black-holes no-hair theorem’ which says that black holes, within General Relativity, have no structure other than their total mass, spin and charge (in fact, surprisingly like an elementary particle).

What this means is that when something falls into a black hole all of its finer information content is lost forever. This is actually a bit misleading because in our perception of time far from the black hole the object never actually falls in but hovers forever at the edge (the event horizon) of the black hole. But lets gloss over that technicality. Simply put, then, black holes gobble up information and turn it into raw mass, spin and charge. This in turn suggests a kind of interplay between mass or gravity, and information. These are classical gravity or quantum particle arguments, not quantum gravity, but a true theory of quantum gravity should surely explain all this much more deeply.

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First off, newly syndicated readers who want to have access to my previous posts can find them archived here as well as listed on my own site here.

After last week’s speculations on time I would like to ask an even deeper question: why is there time?

My 4 year old daughter would be proud. What I mean is, why do things evolve in the first place? It seems to me that fundamental physics has to answer not only ‘what’ questions but also ‘why’ questions if it claims to provide understanding. I think I have an answer, or a glimpse of one.

The answer has to do with quantum anomalies; no not the large (not very quantum, then) things that seem to turn up in every other episode of Star Trek Voyager, but what physicists mean by this, which I am afraid is much more dry and dusty. In fact, I’m going to have to ask you to dust off your high school calculus books, just for a minute.

I explained in a previous post that even if nobody at the moment knows how to reconcile quantum theory and gravity, quantum spacetime should emerge as an effect coming out of any unknown theory. Typically, the coordinates x,y,z of space would also be quantum variables, so space alone should typically form some kind of symbolic algebra. Due to quantum effects, the order of the variables in this algebra will matter, xy will typically not coincide with yx. One says that the algebra is ‘noncommutative’.

Click to enlarge

Now, what about differential calculus on such a quantum space? If you remember any high school calculus it means things like dx, dy, dz as the ‘infinitesimal differences’. Newton and Leibniz both considered such things as numbers which are then made arbitrarily small. Hands up if your high school calculus class contained a picture like the one shown at left. It defines differentiation of a function f in the x direction as a limit of the slope df/dx of the triangle as dx gets small.

So to develop quantum gravity effects in physics we also need ‘quantum differentials’ dx, dy, dz. They should enjoy the properties that differentials enjoy in Newtons theory except, since xy and yx need not coincide, similarly y dx need not coincide with dx y, etc. Now, here is the remarkable thing one finds as you dig deeper into this world of quantum geometry:

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Shahn Majid

Yikes.

First off, congratulations America! Electing the first black US president has to be significant and already puts Obama into the history books, whatever economic and other problems may loom worryingly in the future. Certainly his work will be cut out for him given the falls in the stock market and some of the dire predictions going forward.

Maybe in such times of history, change and future uncertainty, it is appropriate to reflect, then, what exactly do we mean by past, present and future? What is the cutting edge of modern physics telling us about these important concepts?

So far in these blogs I have focussed on hard science verifiable by experiment. But it is also part of the background to my multiauthored volume On Space and Time that to proceed further with fundamental science may need revolutionary new ideas for which science is still grasping. So this week we are going to let our hair down and extrapolate from what is understood into what is definitely, well, speculative.

Incidentally, I did run these ideas here past a BBC producer for Horizon a few years ago when he called me asking about the possibility of time travel, and obviously I was not controversial enough as he never called me back.

What I propose, as a motion for debate, is:

The direction of time is a spontaneously broken symmetry, in the same way as which side of the road to drive on is a spontaneously broken symmetry.

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