3 hours ago, Markus Hanke said:

I’d offer up

δS=0

because the expression has the simplest form while still capturing the widest phenomenology in physics. After all, this principle underlies most things from QFT all the way up to GR; it is, in a sense, the closest thing we have to a “theory of everything”.

So I’m relating “simplicity” to the form of the equation; other choices will lead to other candidates.

Can I ask what does the "s" in "delta s" quantify?

Not the spacetime interval,I think.

I think I saw it described as "entropy" but maybe also as to do with the path of least action which is supposed to explain gravity and geodesics.

Edited 8 hours ago8 hr by geordief

15 minutes ago, geordief said:

I think I saw it described as "entropy" but maybe also as to do with the path of least action which is supposed to explain gravity and geodesics.

Thank you. When I first saw it, I thought S referred to entropy, but now I'm almost certain it refers to action.

5 hours ago, TheVat said:

My first stab at it was identity, x=x, but then I wondered if it was too much a tautology. An equation should "say something" if we're speaking in the domain of science. The simple ones do seem to be definitions. V=IR. The complexity comes when we unpack the deeper physical meaning of volt and amp and ohm as those exist in a circuit. (Or that volts are also joules per coulomb, or watts per amp, or electronvolts per elementary charge, etc.) Then we get into complex relationships that are teased out empirically and can't always be handily compared to water flow in some ideal Hagen–Poiseuille setup. For me, a really simple equation would say something that doesn't get you into all that unpacking. It's late here, so I'll have to think on that later.

Wait, okay, I guess water flow in a pipe at its most basic might be one of the simplest, the rate is Q = A × V (Flow Rate equals Area times Velocity).

Yes, I don't think V=iR is just a definition. While it is true that ohms can be defined as volts per amp and so on, the relation also means something physical: that there is a thing called resistance in a circuit, which impedes current flow in a way that follows an algebraic rule, and that if you double the voltage you will double the current, and so on. So a number of important concepts are embedded in that equation.

7 hours ago, Markus Hanke said:

I’d offer up

δS=0

because the expression has the simplest form while still capturing the widest phenomenology in physics. After all, this principle underlies most things from QFT all the way up to GR; it is, in a sense, the closest thing we have to a “theory of everything”.

So I’m relating “simplicity” to the form of the equation; other choices will lead to other candidates.

I had considered the principle of stationary action, but, other than the mathematical expression, nothing about it is 'simple', as it underlies most of modern Physics.
And, at least in my mind, is still defining the trajectory where the time integral of the Lagrangian has a 1st order variation of zero ( stationary ).
Its implications are far from 'simple', as are those of the identity.

Perhaps @studiot might be so kind as to clarify what he means by 'simple'

2 hours ago, MigL said:

I had considered the principle of stationary action, but, other than the mathematical expression, nothing about it is 'simple', as it underlies most of modern Physics.
And, at least in my mind, is still defining the trajectory where the time integral of the Lagrangian has a 1st order variation of zero ( stationary ).
Its implications are far from 'simple', as are those of the identity.

Perhaps @studiot might be so kind as to clarify what he means by 'simple'

As far as I know there is no right answer.

But this is a recovering science discussion site and this question is already well into its second page.

I suppose by simple I was thinking "how many things do you have to know to solve the equation"

As I said if you know either time period or frequency you also know the other one.

With more general equations of proportionality you also need to know the constant of proportionality.

I am not convinced that x is a valid quantity in any science it normally is used in mathematics to stand for a general unknown quantity.

For instance if we wish to know distance we do not write x = speed times time, we write d = speed times time