I just finished Isaac Asimov’s “The Gods Themselves,” and was wondering: just how many constants and natural laws are necessary to construct a universe? Say I want to build myself a new universe next door. Well, I’ll need to define the charge and weight of an electron, but what about the other fundamental particles? Do I have to specify the wieghts and charges of all of them, or can they be worked out from that of the electron? And what about the laws of physics? Can every other law be derived from Maxwell’s field equations, or do you have to throw in F=ma as well? (Using the equations we know today, of course – no Grand Unified Theory yet.)
To put it another way, if I want to make a t-shirt of the variety:
“And God said:
c=299,792,458 m/s
G=6.673 x 10^-11 m^3/kg/s^2
h=6.62606876 x 10^-34 Js
electron charge=1.602176462 x 10^-19 C
electron mass=9.10938188 x 10^-31 kg Maxwell’s four field equations
…and there was light!”
Just how many lines am I going to have to put on the shirt so that a sufficiently talented physicist could derive all of physics as we know it today?
But presumably one could conceive of different laws of physics with different sorts of constants. If you imagine an infinite space containing a number of point particles, of equal mass, interacting only by newtonian gravity, you’ve got a complete theroy once you specify G.
(Of course, you could imagine a super theory which would describe this universe and ours, depending on some other constant, but this may or may not be useful.)
There is an article in this month’s Scientific American that says there are 17. Or maybe it was 17 masses. But that so many parameters have to be specified is certainly regarded as a flaw in the so-called standard model. So the writer certainly hopes and expects that a super theory (such as string theory or supersymmetry) will come along to drastically reduce that number. But it is logically possible that every time the universal dice are rolled, all these numbers come up differently and it is only once in a googleplex that it results in an interesting universe, where life can form, etc., etc. In all of infinite time, it will eventually happen. In fact, infinitely often.
dylan_73 – interesting. It is disappointing that you have to specify each mass explicitly. Can you really not experimentally determine the mass of, say, one quark, one lepton, and one neutrino, and calculate the others from those? Also, where is the gravitational coupling constant in that list?
dylan_73 the Standard model can’t tell you anything about gravity as it doesn’t seem to behave like the other forces. No, when we replace the model (say m-branes etc.) then gravity should emerge as a property. I’d suggest getting this month’s scientific american as it has this question all laid out.
To take the last question first, Grey’s correct that the SU(3)xSU(2)xU(1) Standard Model doesn’t describe gravity. However, the list has been compiled assuming a set of units determined by the speed of light, the charge of the electron and the gravitational constant (rather than specifying units of length, mass and time). In such units, G=1 by convention and is not a free parameter.
And, yes, currently nobody can do better than measure all these masses separately.
However, these are clearly not all randomly chosen numbers. In particular, there are very evident patterns within the set of 26. The main one is the idea that there are 3 families. Thus the strange and charmed quarks are somehow just heavier copies of the down and up quarks respectively. So we talk of a family consisting of electron neutrino, electron, down quark and up quark and a family made up of the muon neutrino, muon, strange quark and charmed quark. Not only are most of the non-free properties of a particle in one family the same as that in another, comparing masses give patterns. In these instances, all the particles in the second family are heavier than those in the first family. And masses increase within families in the same way in all three.
These patterns suggest that we should be able to understand the relationship between families. Thus we should be able to say something like that the second family is just the first family with one parameter twiddled. And that difference in one (unknown) parameter should explain all the parameters currently associated with the second family. Which is the sort of explanation that should partially satisfy bryanmcc.
If there were only one family, the list would collapse to about a dozen parameters. So understanding the patterns that can already be picked out within the set of 26 would be a big step forward. State-of-play is that there are plenty of tentative proposals for approximate explanations, but nothing totally convincing so far.
Sure, the situation is disappointing. It’s also puzzling, frustrating, tantalising, exciting, confusing, fascinating, hopeful, seductive …
