Can we have laws of physics without any laws of conservation?

Question

The famous physicist John Archibald Wheeler proposed that there were no fundamental laws and that eventually, at very high energies, they would be broken. He proposed this conjecture when it was proposed that the law of baryon number conservation does not hold at high energies. Therefore, he proposed that all conservation laws would be broken in such conditions and then he ultimately concluded that all laws of physics would also be broken and could potentially change 1, 2, 3.

There is also this question in Physics Stack Exchange 4, in which one of the answers points out that all laws of physics can be "rewritten" as some kind of conservation law. Therefore, following this logic, if there would be no conservation laws, then there would be no laws of physics at all.

And finally, in this Q&A site 5, someone asked what would the universe look like without conservation laws. We can read the following answer:

The key thing to know about conservation laws is Noether's theorem. Noether's theorem tells us that conservation laws are linked to symmetries. There is a one-to-one correspondence between conservation laws and symmetries. Conservation of energy is linked to time translational symmetry. Time translational symmetry means the laws of physics don't change over time. If you do the same experiment five minutes later you'll get the same result, just five minutes later. In any universe in which that is true, energy will be conserved. Conservation of momentum is linked to space translational symmetry. If I do the same experiment five metres to the left then I'll get the same result, just five metres to the left. Any universe where that is true will have conservation of momentum. You can do the same thing with, say, conservation of angular momentum and rotational symmetry. Once you get into quantum mechanics things get a little more complicated, but the same basic idea holds — conservation of electric charge, say, has a corresponding symmetry. So, in your universe where there are no conservation laws there are also no symmetries. That's going to be really problematic. The laws of physics will have to depend on your absolute location in space and time, so there is no relativity (even Galilean relativity doesn't hold). The results of an experiment will depend on which laboratory you do it in and on what day. If there were intelligent life in such a universe, trying to figure out the laws of physics would be an absolute nightmare for them. I don't think any complex processes could exist in such a universe, though. The laws of physics change as you move through space and time, so a process that worked in one time and place wouldn't work if you moved or just waited a few minutes. I think it is a non-starter.

If all of this is true, then, would this mean that in a hypothetical imaginary universe without conservation laws of any kind, there would be no fundamental laws of physics, but instead they would vary all the time? Or could we have laws of physics even without laws of conservation nevertheless?...

Answer 1

There are no fundamental laws of physics, but there are fundamental phenomena. Thus, while we've made major changes to the theory of gravity since Galileo, his experimental results remain valid.

Still, according to our present understanding, the phenomena do seem to demand conservation laws.

Answer 2

Symmetries prevent runaway effects which "destroy reality": In particular, an energy "gain" is coupled to an equivalent energy "loss" somewhere else. If that were not the case, things would just "explode" or "implode".

Such universes may be governed by laws -- but Lee Smolin would say that they are short-lived and barren.

Answer 3

I think this is a tautology. What we call "laws of physics" are essentially just descriptions of the symmetries that have been discovered in the universe. And as your quoted material explains, conservation is just the flip side of a symmetry.

So if there are no symmetries, then there's nothing to describe in laws.

And if there were no symmetries, everything would be just random chaos. Without any patterns, in nature, it's hard to imagine how anything concrete could be created. All the processes we see in the universe that create atoms, molecules, stars, planets, life, etc. come from material clumping and interacting according to regular, consistent principles that derive from symmetries and conservation.

Answer 4

It is possible, although we do not believe we have observed such a law yet.

Laws can be re-framed as symmetries in the system. Noether's theorem indicates that for every continuous symmetry, there is a conserved value (in time). However, it says nothing about whether there is a conserved value for any discrete symmetry. Thus there could be a law without a conserved value. And, of course, we may come up with a symmetry which cannot be phrased in the form of an action, and such a symmetry would not invoke Noether's theorem.

To date, we have not found any such symmetries which could not be re-written into a form which invokes Noether's law. But that does not mean one could not exist.