Do the laws of physics evolve? Hubble's constant $a(t)$ appears to be changing over time. The fine stucture constant $\alpha$, like many others in QFT, is a running constant that varies, proportional to energy being used to measure it. Therefore, it could be agued that all running constants have 'evolved' over time as the Universe has expanded and cooled. Both the local and global curvature of the Universe changes over time implying that so too does the numerical value of $\pi$. All these things are however constants (well, let's say parameters since they are not really 'constant'.) 
In a discussion with astronomer Sir Fred Hoyle, Feynman said "what today, do we not consider to be part of physics, that may ultimately become part of physics?" He then goes on to say "..it's interesting that in many other sciences there's a historical question, like in geology - the question how did the Earth evolve into the present condition? In biology - how did the various species evolve to get to be the way they are? But the one field that hasn't admitted any evolutionary question - is physics."
So have the laws of physics remained form-invariant over the liftetime of the Universe? Does the recent understanding of the aforementioned not-so-constant constants somehow filter into the actual form of the equations being used? Has advances in astronomical observations, enabling us to peer back in time as far back as the CMB, given us any evidence to suggest that the laws of nature have evolved? If Feynman thinks that "It might turn out that they're not the same all the time and that there is a historical, evolutionary question." then this is surely a question worth asking.
NB/ To be clear: this is a question concerning purely physics, whether the equations therein change as the Universe ages, and whether there is any observational evidence for this. It is not intended as an oportunity for a philosophical discussion.
 A: If the laws of physics "evolved", then the law governing this evolution would be your new law of physics, provided it is positivistically meaningful (i.e. it isn't last-Thursdayism) and we have enough evidence to say it is probable. 
Note regarding your claim about biology and geology -- the laws of biology and geology do not evolve, much like the laws of physics (including those of biology and geology) don't evolve. Biological and geological structures evolve, much like physical structures (including biological and geological ones) evolve. I don't know how you conflate the two.
There are some hypotheses which claim an evolving set of values for certain physical constants -- (they're probably wrong, but fun to think about)
Dirac's large numbers hypothesis
Some numerological coincidences like $\frac{r_H}{r_e} \approx 10^{42} \approx \frac {R_U}{r_e}$, $r_e =  \frac {e^2}{4 \pi \epsilon_0 m_e c^2}$, $r_H = \frac {e^2}{4 \pi \epsilon_0 m_H c^2}$, $m_H c^2 = \frac {Gm_e^2}{r_e}$ are used to claim that "values of constants changing over time", as some of these constants (like $R_U$, the radius of the universe, and anything with a subscript $H$, a hypothetical particle with the radius of the universe) clearly vary. Dirac also hypothesised that these coincidences could be explained with a varying gravitational constant, $G = \left(\frac{c^3}{M_U}\right)t$ (which is odd, because you expect a symmetry between space and time).
Brans-Dicke theory
This modifies GR by replacing $1/G$ with a scalar field $\phi$ picked via the field equation $\frac{\partial ^ 2}{\partial a^2}\phi^a_a= \frac{8\pi}{3+2\omega}T$ for some coupling constant $\omega$.
A: For many (most? all?) physicists, it's something like an axiom (or an article of faith, if you prefer) that the true laws don't change over time. If we find out that one of our laws does change, we start looking for a deeper law that subsumes the original and that can be taken to be universal in time and space.
A good example is Coulomb's Law, or more generally the laws of electromagnetism. In a sense, you could say that Coulomb's Law changed form over time: in the early Universe, when the energy density was high enough that electroweak symmetry was unbroken, Coulomb's Law wasn't true in any meaningful or measurable sense. If you thought that Coulomb's Law today was a fundamental law of nature, then you'd say that that law changed form over time: it didn't use to be true, but now it is. But of course that's not the way we usually think of it. Instead, we say that Coulomb's Law was never a truly correct fundamental law of nature; it was always just a special case of a more general law, valid in certain circumstances.
A more interesting example, along the same lines: Lots of theories of the early Universe involve the idea that the Universe in the past was in a "false vacuum" state, but then our patch of the Universe decayed to the "true vacuum" (or maybe just another false vacuum!). If you were around then, you'd definitely perceive that as a complete change in the laws of physics: the particles that existed, and the ways those particles interacted, were completely different before and after the decay. But we tend not to think of that as a change in the laws of physics, just as a change in the circumstances within which we apply the laws.
The point is just that when you try to ask a question about whether the fundamental laws change over time, you have to be careful to distinguish between actual physics questions and merely semantic questions. Whether the Universe went through one of these false vacuum decays is (to me, anyway) a very interesting physics question. I care much less whether we describe such a decay as a change in the laws of physics.
A: It is not the laws of Physics that evolve, it is our understanding of them which does. Well, I cannot prove that there exist constant a priori laws that the Universe obeys, but I sure have elevated this practically to an axiomatic state within my worldview. But what we call 'constants' obviously need not be fundamental constants - the only reason they were called like that in the first place is that the quantities appeared to be constant when they were first discovered. Hubble's constant is an excellent example: he observed that the Universe seems to be expanding with a constant velocity in all directions - an amazing discovery for a time when we didn't even have the Big Bang model, mind you! I can imagine how it might have felt at the time that this is a constant in-grained in the fabric of our Universe. Better understanding, and more precise measurements, however, show that in fact the expansion of the universe is accelerating, hence the constant increases in time. But it's obviously not the laws of Physics that changed, it's our understanding of them. 
A: Very simplistically, the fact that we detect hydrogen emission lines from stars many light years away at the same wavelengths we detect hydrogen emission lines here on Earth suggests not!
A: Not exactly in line with your question, but you might wanna have a look at the theory of Cosmological Natural Selection, which says that a new universe is spawned within each black hole with parameters inherited from its parent universe, only slightly mutated. In this sesne the laws of physics would be evolving as parameters change. Also, I just asked a question about it here :)
A: (This answer is mostly copy-pasted from Do the laws of physics work everywhere in the universe? since the same essence applies.)
Noether's theorem states that if there is a symmetry in the system, there is also a conserved quantity, and vice versa.
Some examples of the theorem in action:


*

*Rotational symmetry $\leftrightarrow$ angular momentum. If you set up an experiment, its behavior doesn't change depending on the direction you observe the experiment from. This symmetry is rotational symmetry, and its existence implies angular momentum is conserved.

*Time symmetry $\leftrightarrow$ energy. The results of experiments don't depend on when it is performed. This is time symmetry, and implies energy is conserved.

*Translational symmetry $\leftrightarrow$ linear momentum. If the laws of physics don't depend on where the experiment is performed, then linear momentum is conserved.


All these things can be tested. If we measure conservation of angular momentum, then we know that rotational symmetry exists. Similarly, if we measure conservation of energy - and we do - then the laws of physics do not depend on time. In other words, they don't evolve (or if they do they evolve very slowly indeed, below our threshold of detection).
A: Lee Smolin is one physicist that has posited that the laws of nature evolve.
Personally, I would suggest that if this is the case, then that simply means that we do not have the true laws of physics. After all, if the laws of physics change, then they change in some law like way, and we would need to understand what this over-arching law is
This argument shows, that att bottom, the laws of physics are timeless, that is outside of time altogether.
A: One example of such theory is MET. It says that every new moment is a result of evolution by necessity arising from information-related (entropy-related) criteria. It depends on recent work. More information is available here: metatemporal evolution theory.
