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 August 24Aug 24 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

17 hours ago, MigL said:

Isn't every equation a mathematical definition ?
One variable is defined in terms, or changes of, other variables.

An identity simply defines itself, and so is the simplest type.

Mmmm. I don't think so. P=NkT/V is definitely not a definition.

People loosely (IMO) use the words "equation" and "equality" as equivalent. I demand from an honest-to-goodness equation to ve solvable.

sin²x + cos²x = 1 is not solvable. sin²x + cos²x is but a fancy way to write the number one. Any x (even complex ones) satisfies this. It's just one, for Euler's sake!

30 minutes ago, joigus said:

Mmmm. I don't think so. P=NkT/V is definitely not a definition.

Mmmm. I have a different opinion 🙂 .
What we call pressure is defined as the number of particles, of a given kinetic energy, in a specified volume.
Sure sounds like a definition,

I suppose, given @studiot lack of a specific definition of 'simple', we are all free to voice ( and back up ) our disparate opinions.

One more thought ...

The equation P=NkT/V can be simplified, by substitution, to yield P=P, the identity equation.
So which is 'simpler' ?

Edited August 24Aug 24 by MigL

11 minutes ago, MigL said:

Mmmm. I have a different opinion 🙂 .
What we call pressure is defined as the number of particles, of a given kinetic energy, in a specified volume.
Sure sounds like a definition,

I suppose, given @studiot lack of a specific definition of 'simple', we are all free to voice ( and back up ) our disparate opinions.

I respectfully --but most emphatically-- disagree. For a more realistic gas, P does not obey the same equation, but the Van der Waals eq., or more generally a so-called virial expansion. It depends on what range of systems you want to describe or what kind of subtle effects are within your scope of interest.

Gases with molecular attraction coded by a certain coefficient a and a molecular volume coded by a parameter b satisfy (P+a/V²)(V-b)=NkT

PV=NkT does not account for, eg, phase changes, while the Van der Waals eq. explains the triple point of water, for example.

So P in P=NkT/V is hardly a simple definition of pressure.

20 minutes ago, joigus said:

I respectfully --but most emphatically-- disagree.

But the equation presented was not the Van der Waals equation.
It was for an ideal gas; and that is what I addressed.

If I had addressed the Van der Waals gas equation, I would have included the volume correction ( since gas molecules occupy physical space ), and the pressure correction ( since gas molecules affect each other with residual electromagnetic forces ) in the definition.

2 minutes ago, MigL said:

But the equation presented was not the Van der Waals equation.
It was for an ideal gas; and that is what I addressed.

If I had addressed the Van der Waals gas equation, I would have included the volume correction ( since gas molecules occupy physical space ), and the pressure correction ( since gas molecules affect each other with residual electromagnetic forces ) in the definition.

But the fundamental definition stands: pressure = Force/Area.

Or perhaps our concept of what a definition is differs, and for you it can be carried over to different contexts?

Ahhh.
But then you need to define what accounts for the force ( and the various effects that add/subtract due to differences between idealized particles and real gases ).

It's mathematical definitions all the way down ...

1 hour ago, joigus said:

But the fundamental definition stands: pressure = Force/Area.

Or perhaps our concept of what a definition is differs, and for you it can be carried over to different contexts?

2 hours ago, MigL said:

Mmmm. I have a different opinion 🙂 .
What we call pressure is defined as the number of particles, of a given kinetic energy, in a specified volume.
Sure sounds like a definition,

I suppose, given @studiot lack of a specific definition of 'simple', we are all free to voice ( and back up ) our disparate opinions.

One more thought ...

The equation P=NkT/V can be simplified, by substitution, to yield P=P, the identity equation.
So which is 'simpler' ?

Interesting discussion gentlemen.

But that is what this thread is all about.

For my part I chose to use an equation expressed as a multiplication not a division to avoid the issue of division by zero.

I would also consider that equations that require boundary conditions to be complete are less simple than those that do not.

Edited August 24Aug 24 by studiot

3 hours ago, studiot said:

Interesting discussion gentlemen.
But that is what this thread is all about.

Keep introducing interesting topics, and we will keep participating in the discussion ...

20 hours ago, geordief said:

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

20 hours ago, KJW said:

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

Apologies, I’m only now realising that I never explicitly named the principle in question - it is indeed the principle of least action, so S represents the action.

13 hours ago, studiot said:

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

In that case my suggestion doesn’t qualify, as you need to know a good few concepts in order to solve the equation for anything at all…

On 8/24/2026 at 12:43 AM, studiot said:

I was thinking that since frequency is the inverse of time then in a way they really are just one single variable in the equation

Frequency x time = 1

I find it interesting.

it's funny how in science and math we end up coming back to the simplest things...there was a time I got a lot of difficulties explaining the above esp when you couple it with

On 8/24/2026 at 8:15 AM, Markus Hanke said:

I’d offer up

δS=0