Is Energy conservation among sectors (EM,GR,QM) a principle?

[Roberto Pavani]

TL;DR

Energy conservation (exchange) among EM,GR,QM

Considering QM,EM,GR "sectors" we know that the energy conservation apply but this is a principle.

Noether theorem provides a justification of it for each sector but for the combined (intra-sector conservation) it seem a circular loop:
Energy is conserved through sectors -> I can write a combined action -> Noether proof the conservation -> then the Energy is conserved through sectors.

I'd like to have more comments if the Energy conservation when exchanged between sectors is just a principle or if it is a Theorem on modern physics.

Roberto Pavani
[Link to Orcid preprints redacted by the Mentors]

 

[Dale]

I'd like to have more comments if the Energy conservation when exchanged between sectors is just a principle or if it is a Theorem on modern physics

What is assumed and what is derived is something that individual authors can decide according to their own personal preferences.

 

[Roberto Pavani]

What is assumed and what is derived is something that individual authors can decide according to their own personal preferences.

true, but there is a big difference between:
I assume the Dirac Equation for my Theory
I derive the Dirac Equation from my Theory

 

[martinbn]

What do you mean by energy conservation when exchanged between sectors?

 

[Dale]

true, but there is a big difference between:
I assume the Dirac Equation for my Theory
I derive the Dirac Equation from my Theory

Right. But because different authors make different choices, there is no one single answer to the question.

 

[Roberto Pavani]

What do you mean by energy conservation when exchanged between sectors?

The conservation of energy between gravity and Electromagnetism and Quantum Mechanics (e.g annichilation of electron and positron)
We all know that the Energy is conserved, what I'm asking if for modern physics it is just a principle or a theorem.

 

[renormalize]

We all know that the Energy is conserved, what I'm asking if for modern physics it is just a principle or a theorem.

Can you define what what you mean by the word "principle"?
Or are you asking:
"We all know that the Energy is conserved, what I'm asking if for modern physics it is just a postulate or a theorem."
If that's your actual question, then the answer is: the conservation-of-energy is a theorem.

 

[javisot]

https://en.wikipedia.org/wiki/Noether's_theorem

 

[Dale]

I'm asking if for modern physics it is just a principle or a theorem.

Again, there is no single answer. Any author can choose whether they take it as an assumed principle or a theorem proven from other principles.

Explicitly, Noether’s theorem goes both ways. So either you can assume the symmetries and derive the conserved quantities or you can assume the conserved quantities and derive the symmetries.

 

[Roberto Pavani]

Noether’s theorem is ok, but can be used because we assume to write a combined lagrangian that is justified by the energy conservation among sectors, so it seems circular.
Was asking if there are any non-cicular explanation or if it is just an accepted principle.

 

[Roberto Pavani]

https://en.wikipedia.org/wiki/Noether's_theorem

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law.

But it means that you can write a combined action of the physical system, then the energy is conserved.

But the reason you can write the combined action mus be different than "because the total energy is conserved", otherwise we are using the ouput of Noether's theorem as input on what we want to demonstrate.

We all know and agree to the principle of energy conservation.

So Noether as explanation is ok as long as there is a theorem that can write a combined action.

 

[renormalize]

We all know and agree to the principle of energy conservation.
So Noether as explanation is ok as long as there is a theorem that can write a combined action.

Our best current model of fundamental physics is the Standard Model of particle physics combined with General Relativity for gravitation. Both of those theories are based on Lagrangians. So the existence of a "combined action" is an empirical observation about nature.

 

[Roberto Pavani]

Our best current model of fundamental physics is the Standard Model of particle physics combined with General Relativity for gravitation. Both of those theories are based on Lagrangians. So the existence of a "combined action" is an empirical observation about nature.

Each sector separately has time-translation symmetry and its own conserved energy.
The fact that energy can flow between sectors while the *total* is conserved is what we use as a guiding principle to write the combined action.
Noether then formalizes it, but we have already used the conservation across sectors as input to write the combined action.
So the conservation is the input, not the output.
That's why I'd call it a principle.

 

[Dale]

Noether’s theorem is ok, but can be used because we assume to write a combined lagrangian that is justified by the energy conservation among sectors, so it seems circular.

This is incorrect. Not all Lagrangians have a conserved energy. That is kind of the point of Noether's theorem. It lets you understand which Lagrangians will have which conserved quantities.

Was asking if there are any non-cicular explanation or if it is just an accepted principle.

As I have said now three times, every author can choose what they want to have as principles (postulates/axioms) and what they want as theorems.

That's why I'd call it a principle.

You are certainly free to make that choice.

 

[renormalize]

Each sector separately has time-translation symmetry and its own conserved energy.
The fact that energy can flow between sectors while the *total* is conserved is what we use as a guiding principle to write the combined action.
Noether then formalizes it, but we have already used the conservation across sectors as input to write the combined action.
So the conservation is the input, not the output.
That's why I'd call it a principle.

I think that's an eccentric view. What I would say instead is that, for each particle/field we observe in nature, we discover that the behavior of each individually derives from a Lagrangian and the concomitant principle of least action. We can add those individual Lagrangians, along with interaction terms coupling all those particles/fields with one another, to arrive at the overall Lagrangian that describes the experimentally-verified SM/GR model. To me, that means the "input" is: "Nature obeys the Principle of Least Action". From that single principle flows all the standard conservation laws (energy, linear-momentum, angular-momentum, charge, etc.) via Noether's theorem.