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Understanding Wolfram

WolframThere is what I would once have called a Teefal man (for those too young, the reference is to an old TV advert which featured large-headed boffins) currently stirring things up in Physics and Maths.  His name is Stephen Wolfram, and he will be immediately familiar to many, via his commercial computational products, like Mathematica and Alpha, or for his work in mathematics.

Basically, Steve has a, well, sort of, new grand unified theory. That is, he has a model from which everything emerges without any extra tweaking or cherry picking of individual starting conditions/values. In short, he has a single 'theory' from which everything else in science can be derived/understood/described.

Big news, you might think. Indeed.  The trouble is, however, that mathematicians are not supposed to do this sort of thing. Your basic cosmic conundrums are the province of the physicist. Mathematicians are there to invent seemingly useless patterns which might, one day, prove handy when developing some theory or other.  Thus, the media has not been buzzing with the news; it has featured neither regular bulletins on what the BLM response to the new physics is, nor frequent interviews with self-declared experts in everything except the actual maths in question.

I've spent a little time trying to grasp the other edges of this new model, and have decided that the best way to learn new stuff quickly is the tried and trusted method of teaching it. To that end I will try, here, to give an equation-free description, well within reach of any interested reader. (It will, of course, as a result, be grossly inaccurate in some regards, woefully oversimplified in others, and pretty sure to cause apoplexy if read by an actual academic in this field).

OK - A basic persons non-science view of reality in a sentence:

clumps of stuff (some of it squidgy organic stuff, and some generally harder rockier stuff) banging around in space, in some sort of order.

Space is the stage, the interactions (or 'bangings')  are events happening on that stage, in sequence (ie over time).

This model was first dealt a blow by Galileo who showed it was possible for people to disagree about such things as the speed of events.  Since there appears to be no special 'MEASURE FROM THIS POINT' sign, anywhere we can see, how are we to measure speed? Do we measure with regard to a supposedly stationary ground? But the Earth is spinning, and orbiting the sun, which is itself moving through the galactic plane. It would be foolish arrogance for anyone to claim that all speeds should be measured relative to oneself. So, given no special place in the universe from which to measure, we cannot usefully talk about speed as an absolute value, only a RELATIVE one (ie when compared to some other object or point of reference).  Galileo asked, for example, whether a passenger on a ship, deprived of all external references and clues, would be able to tell if he was moving or stationary.  (Anyone who has started to doze-off on a train and been suddenly startled when the whole station apparently starts to move will know the answer). No, there is no way to tell, if moving at constant speed, whether one is moving or not - and in any case the question is not a sensible one, since it can only be asked specifically - ie moving compared to what? The man is surely stationary with regard to his entire surroundings, and so may, justifiably, consider himself at rest, even though those same surroundings are travelling at several knots over the ocean.  Thus the first theory of relativity knocked a rather large hole in the common notion in the above sentence.

In the early 20th Century, another theory of relativity showed that not only speed, but time itself (and, therefore, distance – think about it) are not absolute quantities either –  they, too, are relative.

One way to picture this without maths is to picture everything moving through the universe at the same speed – c(the speed of light). But the universe is space AND time, so the movement is also in space AND time.  Some of the motion is through space, and some of it through time, but it always adds up to a total of  c. If, therefore, you move through space very QUICKLY(relative to some observer), then you move through time correspondingly more SLOWLY(relative to that same observer). That is, a clock, watch and time itself moves more slowly for a fast moving body than for a relatively slower body. (This is the theory of Special Relativity and was just one of three masterpiece papers published by Einstein in a single year – 1905. In fact, when he later won the Nobel Prize, it was for one of the other two papers, not for special relativity).

The hole in the edifice had become a gaping canyon.  Within a decade Quantum Physics flattened the remaining ramparts. Now it seemed that even 'obvious' certainties - such as

one cannot be in two places at one time
one moves through time only one way
one exists at a specific place in space, at any specific instant of time

no longer hold. This is roughly the current state of play in physics. The overall picture is split into the very small, where Quantum Theory accurately models’ events, and scales larger than atoms/molecules, where General Relativity describes events.  Both of these models/theories have been, are being, and will continue to be widely and rigorously tested. Both pass every test with flying colours. This doesn’t make them correct but it does mean they are not wrong, perhaps simply incomplete or part of a wider model – a Grand Unified Theory (GUT). The only problem is that the two models absolutely refuse to play nice together, so we can’t currently combine them into a GUT for an easy win – either the universe really does behave completely differently at very small scales or our current two models are still missing something crucial. 

Anyhoo……In this modern picture, the universe consists of different fields (picture the iron filings picture you surely made at some point with a magnet), and that is it – just fields.  Particles of matter are actually vibrations in these fields, equivalent to the energy contained in that vibration (e=mc2). One field, the Higgs field, acts as a drag on vibrations in other fields, and this is what we perceive as mass. Fields unaffected by the Higgs field, such as the electromagnetic field, vibrate such that the resulting particles have no mass. The fields, and vibrations in those fields, obey fixed and well understood laws - the Schrödinger Wave Equation is one way of expressing this. I do not intend, here, to stray into the complexities and weirdness of quantum theory – that is for another posting.

So….what might a GUT look like? The most widely known candidate is string theory which has, for over 3 decades, held out promise of being the long-sought GUT. Unfortunately, despite huge efforts and the development of entire new branches of physics and mathematics, current consensus seems to be that string theory has failed – certainly as a potential GUT. It turns out to be more an entire landscape of theories, rather than a single theory – a sort of meta-theory from which one can select a particular set of conditions to suit.  Needless to say, as a theory, it fails basic considerations of testability and repeatability and many physicists are coming to see it as a mathematically beautiful dead end.  A major problem is that string theory is not background independent. This is crucial but not widely understood.  General Relativity is background independent – it needs no ‘stage’, no ‘background’ on which to happen. In general relativity, mass tells space how to bend, and space tells mass how to move – both are dynamic, and the overall model is self-contained and complete.  String theory is background dependent – ie one needs to specify some background against which the equations can be applied. This is tantamount to setting starting conditions, and naturally leads to the question of why those conditions applied – ie the theory cannot truly be held as a complete and accurate model of observed reality, requiring something other than itself. Lee Smolin insists that any true candidate for a GUT must be background independent. It should not require special numbers to be plugged in, or parameters to be altered, or unexplained values to arise. It should be complete and values should arise as a necessity of the theory rather than a desperate attempt to save the appearance. I tend to agree with Smolin. For further suggested reading, I recommend his books ‘The Trouble with Physics’ and ‘Time Reborn’. Smolin is, himself, closely associated with another candidate GUT – loop quantum gravity. Another way to think about the differences between GR and QT is that in GR things are smooth and continuous, whereas in QT things are chunky and ‘bitty’.  GR is our best model of gravity, but gravity itself is just a type of field, which vibrates to produce particles – called gravitons – in the way that the electromagnetic field produces particles called photons. Both particles are believed to be massless (they don’t interact with the Higgs field), but observing a graviton, as opposed to a photon, is beyond our abilities for the foreseeable future due to the huge differences in scale between the two. The electromagnetic field is many orders of magnitude more powerful than any gravitational field – consider that a tiny amount of static electricity is able to pull against the entire gravitational field produced by the earth when things stick to a recently head-rubbed balloon or passes a recently used comb over small pieces of paper.  The energy involved when gravitons interact with other particles (the only way to detect them) is so tiny that it is beyond current and any conceivable measurement ability.

For context, a detector with the mass of Jupiter, in orbit round an extremely powerful gravitational field, such as produced by a black hole or neutron star, would produce roughly one observable graviton per 10 years – even if imagined to function at 100% efficiency.


I realise that this posting is going to be pretty huge, so I'll do it in parts.

Here endeth Part 1.

(to be continued soon).....................................

A view on Caster Semenya

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