Inasmuch as physics equations are based in pure logic, it is illogical to suppose that they might change over time. There is also an aspect of these equations that is not determined purely by reason, but by observation. Let’s take the example of F=ma. It seems to be somewhere in between the two aspects: physics that’s determined by reason, and physics that’s discovered through observation. Without empiricism/observation, there would be nothing to apply the equation to, and it may be conceivable that there could be a universe where the equation is slightly different, although it seems it would be an absurd one that dynamically bends backward over satisfying the modified equation in every situation.
On the other hand, there’s a large degree to which, given the context of the universe as we know it, F=ma is merely a tautology. It’s merely consistent with the rest of the given rational framework. (Einstein said in ‘Geometry and Experience’, “… Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things? In my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.””)
This is because in a world with inertia, it only makes sense that increasing energy (and hence speed) linearly would require putting in more effort linearly, thus making force proportional to the first derivative of speed (so we have the F=a part), and of course doing this to twice as much stuff should of course require twice as much effort (so we have the F=m part). It wouldn’t make sense for force to act on increasing amounts of mass non-linearly.
Take Galileo’s experiments with dropping the differently sized cannonballs from the church tower, for example. The force of gravity has to pull them all down with equal acceleration, implying that the force of gravity is both multiplied by the amount of mass (as it acts on all mass equally) and divided by it (inasmuch as we consider the total force of gravity), because otherwise—if heavier cannonballs fell faster—then it would be a paradox if Galileo were to have tied a lighter cannonball to a heavier one and dropped them. The lighter one would have pulled the heavier one up while the heavier one pulls the lighter one down, thus resulting in some sort of average acceleration…but then how thick and dense would you mave to make the material connecting them before they’re considered one thing and hence add up their accelerations rather than averaging out: why an arbitrary value such as that, and what would happen right at the borderline?
(When it comes to F=ma, you’re performing the multiplying phase mentioned above and not the dividing one, because you’re reducing the force applied to every unit of mass to a single point of impact or other influence, which is made possible only via the nature of the solidity of solid matter, and thus you’re considering the total force being applied to every unit of mass, hence the multiplication by m.)
A more interesting consideration might be that, since the implications of a Newtonian universe versus a relativistic universe seem to differ only slightly (consider the fact that, in in the past, we had mistaken the universe for being Newtonian), the universe might evolve from one to the other, say, from a relativistic one to a Newtonian one. However, this doesn’t work for several reasons.
First, the implications of the equations go deeper than the slight differences observed in our everyday world. For one, space and time would have to evolve from being inseparable to fundamentally distinct. Since space and time in this universe are epiphenomenal, and also fundamental, this is no small step. The universe would have to completely change, the old universe becoming nothing but a memory before the new universe comes about—as opposed to smoothly slipping from one to the other. (Yes, an infinite speed of light would give results identical to Newtonian mechanics, and that’s possible under Maxwell’s equations, but you couldn’t actually make any sort of gradual transition between an infinite value and any finite value, per the nature of infinity.)
Second, it’s possible that reason alone can arrive at the conclusion that space and time are intrinsically connected, by virtue of their metaphysical co-dependence, and that Newtonian physics was therefore merely shortsighted/illogical to begin with.
Third, a shift from the Newtonian cosmic modus operandi to the relativistic would be more of a sudden, dramatic paradigm shift for all matter in the universe travelling at relativistic speeds and for any perspective that more elucidates relativistic effects in the universe, such as a perpsective that simply sees across a vast distance and thus highlights the vast separation of light cones in the relativistic version of the cosmos.
So, while large-scale change characteristically happens through analog continua, a change from Newtonian physics to relativistic or vice versa would be more of a gratuitous, massive binary shift since there are the only two possibilities in this arena of consideration, and they are discrete, because they are paragons of internal logical self-consistency, thus with no wiggle room, and no continuity between one paradigm and the other.
It is also noteworthy that it is the relatively high value of c that allowed us to think in Newtonian terms to begin with, thus that argument illustrates the essential illusion behind this “interesting consideration”: inasmuch as the universe could transmute to being Newtonian, it was already there, and vice versa, because it is the value of c that sponsors the apparent proximity between the two systems.
Traditionally, the laws of physics are considered to be immutable, and the states of affairs that they act upon are considered to be in flux. To me, this seems to be regarding the laws of physics in an almost religious way, although it’s understandable because reality does appear to be this way.
I would like to point out, first, that the entirety of the “states of affairs” is in flux. Matter is a process. Atoms “bounce off of” each other constantly, electrons travel around the nucleus (or their probability fields oscillate, or whatever), the quarks in the nucleus are moving around, etc. Every time we see stasis we are merely objectifying repeating patterns of motion that are too small to be seen. The atom appears to be a constant object because its internal processes remain within certain parameters. This doesn’t mean that the parameters themselves are “states of affairs” that are not in flux. The parameters are merely limits that derive from the logic of physical law. For example, the earth has a certain abstract delineation in space because it is held together by gravity, but its breadth on a smaller scale is constantly in flux, as its matter is in motion.
To focus on the “energy” side of things, light, or an EM field, is of course a propagating wave, and is thus in motion. The staticity of a force field like gravity or electrostatic charge is not really a state of affairs because the force field only exists insofar as it produces an effect. It is not a thing-in-itself. It is an aspect of the way material interacts with other material across distance, which is a manifestation of the laws of physics themselves. It would be superfluous to posit the existence of a force field in-itself when (a) its state is completely supervenient (in the philosophical sense) upon the state of the matter that engenders it, and (b) it can only be known/detected or influenced through its effect on matter. So, the posited phylically existing force field woul be functionally isomorphic to the mere equations describing the force field. Secondly, since the mass that manifests a gravitational or electrostatic force field is constantly in motion, and is itself a process, the gravitational or electrostatic force field actually consists of uncountable tiny waves of force propagating outward at the speed of light and averaging out to a practically static field; so, there is no such thing as a static force field.
Universal flux is given rise to by the causal interconnectedness of everything. Unpredictability is given rise to by two things: 1. Causal, chaotic systems, and 2. quantum indeterminacy/”absolute randomness”. You can predict some things better than others, but certainty and precision can never be 100%, and thus stasis can never be 100%. (This is why there is no such thing as a temperature of absolute zero in the universe, temperature being a measure of the motion of molecules.)
Another point I want to make is that physical laws do not “control” or “act upon” matter and energy to “make” them do what they do. If a law acted upon matter, there would have to be an active agent, and that active agent would have to have further laws that control its own animation. Or, for law X that says matter must behave in a certain way, there would have to be a law Y that says that matter must behave in accordance to law X, and a law Z that says matter must behave in accordance to law Y, etc. At the bottom of this pile of turtles, there would have to be a set of rules that maintain themselves just because, and it’s equally (actually, more) likely that matter maintains its behavior just because (as opposed to being dictated by abstract “laws”).
Furthermore, if time is sponsored by laws “controlling” matter and energy, there must be a meta-time that makes it possible for these laws to commit the process of exercising this control.
Also, control and action as we know them require an expenditure of energy. “Control” is a very humanistic concept that essentially requires intended result and active manipulation to narrow down the possibilities in the flow of energy/matter from many to a selected few. This requires energy expenditure in nearly the same way that Maxwell’s demon does, so if physical laws “controlled” matter then it would grossly violate conservation of energy.
So, how does physical “law” “work,” or limit what we think is possible, or act as the selector of possibilities, such that the selected is not forced and thus doesn’t require energy expenditure to actualize, or actively select, the selection? The answer is that the process of behaving in accordance to physical law is the process of being logically self-consistent. For the universe to violate a law of physics would be illogical, and one would recognize the specific absurdity if one were able to apprehend the entire situation on all levels. In other words, anything one imagines to be a possibility that physics won’t allow is no more logical than a square circle. (Notice that physical laws are described in the form of mathematical equations, and math itself is nothing but a big tautology of pure logic.)
Therefore, the only immutable aspect of the laws of physics is what is derived from pure logic. Everything else is subject to the states of affairs/the flow of time/change. Of course, some things change more slowly than others. (See the “the entirety of the ‘states of affairs’ is in flux” argument above.)
If you were to do something that a naive philosopher might call “violating a law of physics,” such as by figuring out a way to travel faster than the speed of light, or by inventing an anti-gravity machine, what you are really doing is utilizing a higher order of physics that supersedes the “law” in question. If you thought that Newtonian mechanics was the true law of the universe, you could violate it by flying two atomic clocks around the earth in opposite directions in fast airplanes.
In regard to higher orders of physics, how high does it go? Perhaps it goes all the way up to pure logic. (Or maybe, metaphysically, there simply layers and layers of what I’ll call “world texture” that results in what we perceive as immutable laws, or some combination of the pure logic and word texture; and if that’s the case, the “world texture” part of it could easily be mutable over time.) If you can use a higher order of physics to violate or affect a lower one, then in between the higher order and the lower order is the input of a state of affairs—meaning that the lower order of physics is an implication of the higher order given a specific current or typical state of affairs, which is what you are controlling if you are “violating a law of physics.”
So, again, the only immutable aspect of physics is pure logic.
The issue that I’ve been driving at here all along is the decision to include “constants,” such as the speed of light and the gravitational constant, in with the supposed immutability of the laws of physics. You use a constant by plugging it into an equation. The constant comes from observation of the states of affairs, ultimately. It is arbitrary to consider the constant a part of the actual “law” and all other inputs to the equation merely parts of the states of affairs that the law acts upon. (This is also quasi-religious thinking: “We don’t know why c is the value it is, but we know that it will never change and has never changed.” It might as well be God-given.)
It would be easy to say that it could go either way—maybe it’s changeable, maybe it’s not—if it weren’t for all of my above arguments. Everything is in flux but the laws of physics, and those are only constant inasmuch as they are manifestations of logic.
It follows from everything I’ve said that including “constants” in with the supposed immutability of the laws themselves is simply incorrect, unless the values of c, G, Planck’s constant, or whatever can be derived from pure logic. The best I can imagine is that it would be derived from pure logic given another “constant” to base it on, thus making it supervenient upon that other “constant” (with the possibility of that constant being derived from another constant, etc.), in part because these constants are necessarily in arbitrary units of measurement.
Perhaps c can be derived from G, or vice versa, or both, or they can both be derived from some other constant(s) (but I think this would imply you could derive one from the other as well), thus if they changed they would have to change together. Perhaps not. If they can’t, we can only assume that they are independent, and if they are independent there is nothing to keep them in constancy with relationship to each other, except “inertia” (e.g., of the “metaphysical world texture”). (If they are not derived via logic, they are somehow handed down from the states of affairs, and if they are not logically dependent on each other, they are handed down from independently variable states of affairs.)
c and G change so little that we don’t consider them variables, and they may change so little that no significant change in them has happened in the life of the universe. But for them to be exactly the same would require an immutable reason that they are what they are, and the only reason that fits that bill is logical necessity, and we (probably) can’t derive c or G from logic alone. It’s unlikely that they can be derived from logic alone because they are such seemingly arbitrary and large/finely specific numbers.
I suppose it only makes sense to say that they are intrinsically large (or finely specific?) numbers with respect to some kind of fundamental quantization to afford an objective unit of measurement (i.e., because 1 unit of something would have some absolute meaning, being the smallest possible value), and this quantization would have to be incorporated into the axioms of the logic at hand. This would, of course, make it much easier to derive their values through logic. However, without some kind of intrinsic quantization, perhaps they’re still baseless with respect to any logical axioms.
Now I will attempt to go more in-depth in regard to the speed of light being a state of affairs.
Imagine the universe as a completely dynamic cascade of change, some aspects changing faster and some changing slower. We have no choice, personally and evolutionarily, but to wrap our minds around the more slower changing aspects as a reference point for the faster changing aspects, lest we be lost in confusion. We thus perceive the more slowly changing aspects as the structure of the universe.
The more consistent patterns of behavior in the universe—i.e., the ones that repeat themselves—i.e., “laws”—are slower-changing aspects to the degree that they’re exactly the same behavior repeated, which is a limited degree because every situation/event has its specific, unique combinations of properties.
Well, they say that all electrons are identical, so maybe this “folding” consistency into deeper structure applies not only across time but across space, too, when entities are considered to be identical to each other. In other words, maybe there is only one electron, for example, and it is part of the deep/slowly changing structure of the universe.
So, what we have is basically a cascade of change, with the fastest/most chaotic changes at the figurative top, and the slowest/most uniform changes at the figurative bottom. The speed of light can probably only be at the bottom.
I wrote a more brief version of the same basic concept expressed here, and another one here.
