What is governing the laws of physics? [closed]

Question

What makes all the laws of physics do what they do? What is the governor of all of those laws?

Answer 1

What makes all the laws of physics do what they do?

But what do they do, really? They allow us to reproduce on paper observed events and predict future events.

Do they have a "deeper meaning", some absolute "truth" in them. No. At least that is not necessary to do physics. Laws simply "match" what we observe.

What is the governor of all of those laws?

A governor? What makes them actually work, you mean? We (humans) invented them! We are their governors. We found laws that turned out to match observations. And nobody should claim that these laws are absolute ... they will most likely turn out to be wrong eventually, as most physical laws have in the past.

Answer 2

Your question is mostly one of philosophy. But a physics component of it is the question "Is there a physical metalaw - a law of physics that accounts for the structure of the other fundamental laws". This quest is near to the idea of seeking a "Theory of Everything".

As far as we know, there is none. But there are recurrent themes: mathematical and physical principles that express themselves in many of the fundamental physics law sets at once and can thus be said to have at least some of the characteristics of what we would reasonably call a "meta-law". I would sum them up in the four notions: "(1) Symmetry, (2) Analyticity/Continuity, (3) Causality/Locality and (4) Maximum Likelihood". Of course, one can then ask "why" to these four and, in principle, we're back to your same question, but I think these four as much more "visceral", "intuitive" and "fundamental" than the usually stated fundamental physics laws they beget insofar that they are highly accessible from our everyday World. From the time we are small children, we observe many times a day manifestations of these four notions so that they are far more natural to us than law-sets like Maxwells Equations that are more wontedly cited as "fundamental".

Let's go through how these four notions give rise to our physical laws. Note carefully that they do not fully and uniquely define all physical laws as a full Theory of Everything would need to to be accepted as such. However, they do establish fairly tight tethers on what forms these fundamental laws can take.

The first three are tightly woven together. Symmetry, in the guise of homogeneity and isotropy of spacetime together with Analyticity/Continuity show the transformation between inertial reference frames to be linear and homogeneous. These latter are then either pure rotations or boosts, but a notion of causality (see also my answer here) rules rotations out as the rule that mixes time and space co-ordinates, so now all of special relativity is established aside from the actual value of the invariant speed $c$. At the same time, we are forced by these notions to postulate that no signal can go faster than $c$ so as to save the notion of causality - it would seem impossible otherwise because faster than $c$ signalling implies that the time order of physical processes can change between inertial observers: so we could eat boiled eggs before we cook them, from the standpoint of some observers!

Following from relativistic causality we see that in physical laws, quantities pertaining to an event cannot depend on quantities pertaining to other events with nonzero spatial separation from the initial event if the two events have the same time co-ordinate. Otherwise, again, the time ordering of events can be reversed by transformation between inertial frames. This means that either (1) physical laws are differential equations connecting quantities and their derivatives at the same spacetime point or (2) discrete recurrence relations between quantites at different spacetime events with timelike separation. However, since a gradient operator generates nonzero length, discrete spacetime translations (as expressed by Taylor's theorem that $f(t+h) = \exp\left(h\, \frac{\mathrm{d}}{\mathrm{d} t}\right)\,f(t)$ for analytic $f$), and given the uniform convergence of partial sums in Taylor's theorem for suitable analyticity assumptions, we see that a finite order differential equation can express physical laws governed by (1) Symmetry, (2) Analyticity/Continuity, (3) Causality/Locality to within any wished-for accuracy. In particular, this accuracy can be as small as one likes compared to contemporary experimental measurement capabilities. That is, experimentally, a finite order differential equation in principle can yield predictions indistinguishable from experimental results. This is roughly what physicists mean when they say that physical law must be local - it must uphold causality and this means it must be expressible as a differential equation.

So the notions of Symmetry, Analyticity/Continuity, Causality/Locality validate the use of differential equations as the universal language for expressing physical law. This is hardly a unique prescription of physical law, but nonetheless it is significant. Moreover, we can go further: not all differential equations comply with our Symmerty-Analyticity-Causality constraints. For example, the heat conduction / diffusion equation, as wontedly written in a nonrelativistic form, cannot be valid aside from as an approximation because a disturbance at a point makes itself felt throughout the whole medium at once. That is, it allows faster than light signalling. Only certain kinds of differential equations are allowed: those which encode a less than or equal to lightspeed delay between disturbances and their effects at other points in the medium. If we restrict ourselves to linear differential equations, this needfully means that the equations must be hyperbolic (see my answer here).

Symmetry makes itself felt as the metaprinciple that governs many conservation laws. For example, the accepted explanation for the laws of conservation of energy, momentum and angular momentum is that these quantities are the Conserved Noether Charges that arise from the invariance of Lagrangian formulations of physical laws with with resepect to translation in time, space and to rotation.

Lastly we reach the notion of "Maximum Likelihood": this is the idea of statistical mechanics. That is, ensembles of causally independent systems act together in the maximum likelihood ("most plasuible") way simply as a result of the laws of large numbers to beget consistent macroscopic behaviors. I say more about this notion in my answer here. Note the likeness here to notions of testing for statistical significance through confidence testing.