# Do all impossible processes disobey certain conservation laws?

I was reading from this book on Lagrangian Mechanics where the author wrote the following-

As an example from the field of elementary particle physics, it is observed that some reactions never occur. There is no apparent reason why a reaction such as $$\pi_− + p → π^o + \Lambda$$ does not take place. It must violate some conservation law. However, it does not violate any of the everyday conservation laws such as charge, mass-energy, parity, etc. But since the reaction does not occur, using the principle that “what is not forbidden is required,” physicists concluded that there must be a conservation principle at work. They called it conservation of strangeness. Then they assigned strangeness quantum numbers to elementary particles.

And hence my question, does every impossible physical process disobey certain conservation laws?

• Yes, that's how conservation laws get discovered empirically. What does your text say? Jun 3 at 15:41
• @Cosmas Zachos it goes on to explain Noether's theorem. Jun 3 at 16:33
• Facts cannot explain Noether's theorem. It is the other way round! One posits a symmetric lagrangian and then one sees it implies a conservation law, which nature may or may not comport with. Jun 3 at 16:36
• This is really a philosophical question, since you're asking about "every impossible physical process," so do not be surprised when the answers below are philosophical! Also, how does one define "Impossible process" in a general sense? It's deceptively difficult. Sometimes the logic in the textbook works, as for the strangeness example, but I think one can conceive of examples where it hasn't worked. That is, a lack of reasons for some process to be possible does not necessarily imply that there is some reason why it does not occur - it could be true, but we don't know a priori. Jun 3 at 16:36
• By every impossible process I mean processes which have a probability of 0; not even possible statistically. Jun 4 at 8:03

Yes. Formulated differently, every physical process that is allowed will happen, but the context may influence how simple the answer is. @rob pointed out the corresponding Wikipedia article on the Totalitarian Principle which has some info too.

In particle physics, any interaction that is not forbidden will happen, i.e. every Feynman graph that is allowed will have an associated cross-section. Processes that are can not happen can not happen because they violate some conservation law.

The statement is also correct in the context of statistical physics, but time may be of the essence. As @gandalf61 points out in his answer, allowed processes may become exceedingly rare. Various examples when explaining entropy come to mind, like, having every air molecule in a room suddenly condense in a puddle in the floor. But again, that's then exactly where the concepts from statistical physics take the place of conservation laws. So "yes" remains the correct answer to your question even in those cases.

• en.wikipedia.org/wiki/Totalitarian_principle
– rob
Jun 3 at 16:05
• That wiki paragraph is actually a better answer than my sentence :)
– rfl
Jun 3 at 18:23
• @rfl please update it so that I can mark it right Jun 4 at 15:52

Every physical process that is allowed will happen ... eventually. But you may have to wait a very, very long time. For example, it is physically possible for ripples to converge on a point and eject a stone from a pond - this breaks no conservation laws and similar phenomena have been demonstrated in wave tanks under highly controlled conditions. But it is extremely unlikely to occur naturally.

• But are humans not naturally occurring and thus our measurements are also? Jun 3 at 16:34
• @DaddyKropotkin "naturally" in this post means "spontaneously". Jun 5 at 10:45
• So physical processes that are not "spontaneous" are somehow not natural? Jun 5 at 12:57
• @DaddyKropotkin My point was that you can create time-reversed converging ripples under very artificial conditions in a water tank (and even this is only an approximation since it does not reverse sound waves or heat conduction) but if you sit by a pond waiting for this to happen of its own accord then you will wait for a very, very long time. Jun 5 at 16:51

The point is: every physical law can be rearranged and reinterpreted into a conservation law.

Take $$F=ma$$, at a first glance it does not appeare as a conservation law at all, but you can manipulate it into one: $$F=ma \ \Rightarrow \ F=\frac{dp}{dt}$$ and this is a conservation law! It tells us that if our system is isolated: $$\frac{dp}{dt}=0$$ the momentum is conserved. Keep in mind that every conservation law comes with some string attached: momentum is conserved in an isolated system, as well as energy. You can say for some systems that mechanical energy is conserved, but only under some conditions, etc.

It's important to understand that the fact that every law can be reinterpreted as a conservation law is not a physical property of our universe, it's instead a quite simple mathematical property: to express laws we use equations $$F(x)=G(x)$$ but every equation can be rewritten as $$\frac{d}{dx}K(x)=0$$ for some appropriate K(x). This is in fact quite trivial to do. In the case of multivariable functions we can simply impose arbitrary conditions and collapse variables until we obtain the desired form.

Of course in some cases makes sense to view a physical law as a conservation law but in others it's just a silly way to rewrite our law under some unpractical conditions.

But since, if you want, you can always view a law as a conservation law we can now understand that your question, as you written it, is equivalent to:

Does every impossible physical process disobey certain physical laws?

And the answer to this one must be yes, by definition of the term: "physical law".

Keep in mind of course that this is a really abstract argument. In practice, empirically, if you see only processes that conserve a certain quantity $$Q$$ then makes a lot of sense to hypothesize that $$Q$$ is conserved. This is exactly how physical laws are "discovered" in most cases (or better: how they are postulated).