## Posts Tagged ‘**infinity**’

## reading matters 2

The beginning of infinity by David Deutsch (quantum physicist and philosopher, as nerdy as he looks)

Content hints

- science as explanations with most reach, conjecture as origin of knowledge, fallibilism, the solubility of problems, the open-endedness of explanation, inspiration is human but perspiration can be automated, all explanations give birth to new problems, emergent phenomena provide clues about other emergent phenomena, the jump to universality as systems converge and cross-fertilise, AI and the essential problem of creativity, don’t be afraid of infinity and the unlimited growth of knowledge, optimism is the needful option, better Athens than Sparta any day, there is a multiverse, the Copenhagen interpretation and positivism as bad philosophy, political institutions need to create new options, maybe beauty really is objective, static societies use anti-rational memes (e.g gods) while dynamic societies develop richer, critically valuable ones, creativity has enabled us to transcend biological evolution and to attain new estates of knowledge, Jacob Bronowski
*The Ascent of**Man*and Karl Popper as inspirations, the beginning….

## the reveries of a solitary wa*ker: wa*k 4 (universal matters)

The universe is more turbulent than we imagined. It’s a quantum computer. It’s nothing but information. Where’s all the lithium? Is it really spinning, and are we anywhere near the axis? What was in the beginning? Pure energy? What does that mean? Energy without particles? The energy coalesced into particles, so I’ve read. Sounds a bit miraculous to me. The fundamental particles being quarks and electrons. Leptons? But quarks aren’t leptons, they’re fermions but leptons are also fermions but these are but names. Quarks came together in triplets via a strong force, but from whence this force? Something to do with electromagnetism, but that’s just a name. I’m guessing that physicists don’t know how these forces and particles emerged, they can only deduce and describe them mathematically. Quarks and leptons are elementary fermions, that’s to say particles with half-integer spin, according to the spin-statistics theorem. Only one fermion can occupy a particular quantumstate at one time, that’s according to the Pauli exclusion principle. Fermions include more than just quarks and leptons (electrons and neutrinos), they can be composite particles made up of an odd number of quarks and leptons, hence baryons made up of quark triplets. Fermions are often opposed to bosons in the sense that they’re associated with particles (matter) but bosons are more associated with force, but the intimate relation between matter and energy blurs this distinction. Anyway this strong force pulled quarks together to form protons and neutrons, while an electromagnetic force pulled together protons and electrons and voila, hydrogen atoms. All this in the turbulent immediate post-bang time. Hydrogen fused with hydrogen to form helium and so on all the way up to lithium, but that’s not far up because lithium comes after helium in the periodic table. The amount of hydrogen and helium in the universe fits precisely big bang expectations, and in fact is bestevidence for that theory but where’s all the lithium? There’s only a third as much lithium isotope 7 (with four neutrons) as there should be, but that’s okay cause there’s a superabundance of lithium-6. No, not okay. Some argue that it’s a big problem for the big bang theory, others not, surprise surprise. The period of creation of hydrogen and helium is called the primordial nucleosynthesis period, and it covers the time from a few seconds to 20 minutes or so after the bang. More precisely, the heavier isotopes of hydrogen, as well as helium and some lithium and beryllium, the next one in complexity, were created then and everything else was created much later, in stellar evolution and dissolution. Obviously the big bang released a serious amount of energy, and then things quickly cooled, permitting somehow the creation of elementary leptons such as electrons and electron neutrinos. During these first instances there was also a huge degree of inflation. The earliest instants of theuniverse are referred to as the Planck epoch, and it’s fair to say that what we know for certain about that minuscule epoch is equally minuscule, but it’s believed that the different fundamental forces posited today were then unified, and gravitation, the weakest of those forces in the present universe, was then much stronger, and maybe subject to quantum effects, which is interesting because though I know little of all this stuff largely due to mathematical ignorance, and of course inattention, I do know that gravity and the quantum world have proved irreconcilable since first theorised. Needless to say the Planck epoch is very different from ours, and it’s at this scale that quantum gravitational effects may be realised. We can’t test this though even with our best particle accelerators. It’s one for the future. Meanwhile, the renormalisation problem. Well actually renormalisation began as a provisional solution to the problem of infinities.

We describe space-time as a continuum. So there are three dimensions of space, what we call Euclidean space, and a dimension of time. But how does that actually work? Perhaps not very well. I’m talking about a classic-mechanical picture, but in relativistic contexts time is enmeshed with space and velocity and gravity. Cosmologists combine the lot into a single manifold called a Minkowski space. All I know of this is that it involves an independent notion of spacetime intervals and is mathematically more complicated than I can begin to comprehend, though supposedly it’s a relatively simple special case of a Lorentzian manifold, which itself is a special case of a pseudo-Riemannian manifold. I’m engaging in mathematics, not humour. Or vice versa. All this is beside the point, it’s just that trying to reconcile quantum theory and relativity is impossible without the creation of infinities, and infinities are much disliked by many cosmologists, being far too messy, and time is out of fashion too, the quantum world simply ignores it. And we still don’t know what happened to the lithium.

Mathematics has so far been absolutely central to our understanding of the universe. So is the universe or multiverse no more than a mathematical construct? If it is, it’s one that we’ve not yet figured out, and it’s unlikely that we ever will, it just gets more complicated as we develop more sophisticated tools to examine it. I’ve always suspected that the universe/multiverse is as complex as we are capable, with our increasingly ‘precise’ tools and increasingly sophisticated maths, of making it, and so will continue to get more complex, but that’s a sort of sacrilegious solipsism, isn’t it? The universe as increasingly complex projection of an increasingly complex collective consciousness? Is that what they mean when they say it’s a hologram? Probably not.

One more point about infinity. Max Tegmark says that the idea of a finite universe never made sense to him. How could the universe have a boundary, and if so, what’s on the other side? Another way of thinking about this is, if the big bang involved an explosion or, more accurately, a massive, near-instantaneous expansion, what did it expand into? Did this expansion involve a contraction on the other side of the boundary? It’s said that space-time began with the big bang, so there’s no outside. How can we really know that though? Of course if you believe that absolutely everything began with the big bang, then you’ll believe in a finite universe, as the bang began with a particular mass-energy point-bundle, which would have to be finite, and could not be added to or subtracted from, according to what I know about conservation laws. Anyway, enough of all this paddling in the shallows. It’s funny, though, I’ve recently encountered people who are extremely reluctant to talk about such matters, even in my shallow way. They actually suffer from ‘cosmological fear’ (my invention). Something to do with existential lostness, and mortality.