Insights Is Energy Only What We Think It Is?

[bhobba]

And how does Noether define energy ? I couldn't figure it out reading those links.

Its the conserved Noether charge from time symmetry.

If that's gooblygook you have to know the theorem:
http://phys.columbia.edu/~nicolis/NewFiles/Noether_theorem.pdf

The situation is this. The theorem states given any symmetry then there exists a conserved quantity. For time symmetry, ie the laws of physics do not change with time, that is defined as energy, so from its very definition is conserved. Its beauty is not only does it define what it is, it explains why it's conserved.
'if the Lagrangian is invariant under time translations, that is if it does not depend explicitly on time, then the Hamiltonian of the system is conserved In most physically relevant cases the value of the Hamiltonian is the total energy. We thus discovered that the conservation of energy is a direct consequence of the invariance of the Lagrangian under time translations. Under stable conditions, if you perform a lab experiment today or tomorrow you expect to get the same results. This fact alone implies that energy is conserved.'

The other advantage is it works in mechanics or field theory. It explains why you can't define energy in GR in a straightforward way - because in GR you have space-time curvature:
http://motls.blogspot.com.au/2010/08/why-and-how-energy-is-not-conserved-in.html

Its usually only encountered in advanced treatments, but most when they first see it are simply dumbfounded - its implications are very deep. As Shyan pointed out when Einstein found out about it he was just as amazed.

The other interesting thing about it, is I have found most philosophy types are blissfully unaware of it.

Thanks
Bill

 

[Jimster41]

I was blissfully aware of it. It 's the way Susskind presents the Lagrangian, and Hamiltonian in his first (excellent) "Theoretical Minimum".
I agree. It is as elegant as observation gets...

The reference for time, as we have it. The asymmetry of energy density?

Wow, I actually enjoyed that Motl essay.

 

[DirkMan]

Thanks
Bill

So I have read that blog, and also the comments. If I understand it at the simple most basic level, energy is conserved because of time, that is if we have X energy in a system at time t0 , and we have energy increasing towards Y at time t1 , we can have that conserved because we can imagine rewinding back the time evolution of the energy in the system as decreasing from Y to X , and if we add up the increase and decrease we get the same X. Is it nonsense what I'm thinking ?

 

[bhobba]

Is it nonsense what I'm thinking ?

Nonsense isn't quite the way I would put it - its simply a bit complex and not easy to grasp without math.

As simply as I can put it, there is this theorem, called Noethers Theorem, that says if the laws governing a system do not change with time, then a quantity exists that also does not change in time ie is conserved. It, by definition, is called energy.

Thanks
Bill

 

[anorlunda]

Dalespam,

Can nuclear energy or chemical energy be expressed as capacity to do work, without converting to mechanics first?

 

[afcsimoes]

If time is defined as "the way to order events from past to present to future", then no events implies no time

Please explain. Time is measured by clocks. A clock is something where periodic changes occurs. When there are no changes there are no time? But if I MUST have a clock to measure the time...

 

[Neandethal00]

DaleSpam submitted a new PF Insights post

What is Energy?

Continue reading the Original PF Insights Post.

I do not want to start a new thread, I think this Energy thread is the right place to ask a new question.

Is Potential Energy Real Energy?

In my opinion the answer is NO. A stationary object has no energy.

 

[bhobba]

Is Potential Energy Real Energy? In my opinion the answer is NO. A stationary object has no energy.

That's one reason why the definition I gave based on Noethers theorem IMHO is the best - it avoids all this stuff.

Yes its real energy, just as real as kinetic, or any other kind of energy.

Energy is simply a quantity required because the laws of physics do not change with time, or to be even more exact, required by an inertial frame - but detailing that will take us too far from the purpose of this thread. Start a new thread about the laws of physics and inertial frames if it interests you.

Thanks
Bill

 

[Neandethal00]

That's one reason why the definition I gave based on Noethers theorem IMHO is the best - it avoids all this stuff.

Yes its real energy, just as real as kinetic, or any other kind of energy.

Energy is simply a quantity required because the laws of physics do not change with time, or to be even more exact, required by an inertial frame - but detailing that will take us too far from the purpose of this thread. Start a new thread about the laws of physics and inertial frames if it interests you.

Thanks
Bill

Thanks Bill for all the links you posted above on Noethers Theorem. Isn't it sad so many brilliant minds like Emmy Noethers go unknown in history of science. Even though I have to read them a few more times to understand her theorem, but its conclusion has touched the area from which I made the statement about Potential Energy.
In uncertainty principle I noticed there is a relation between energy and time.

 

[anorlunda]

Please explain. Time is measured by clocks. A clock is something where periodic changes occurs. When there are no changes there are no time? But if I MUST have a clock to measure the time...

Think of causality, cause before effect. Before and after express concepts of time. We only need clocks to measure the quantity if time.

 

[Mark Harder]

If we ignore the different classical classifications of energy (heat energy, sound energy, etc) and take a fundamental view, can we say that all energy at the fundamental level is ultimately one of these four categories:

• Kinetic;
• Static, ie deriving from an object/particle's position in a physical force field;
• Energy incarnated in mass; and
• Dark energy, which we know little about.

IH

Shouldn't we extend that list? There are thermodynamic potentials and associated generalized forces related to generalized gradients of the thermodynamic potentials. Thermodynamic potentials include internal energy, enthalpy, free energy and others.

Of course, thermodynamic energies are a bit more complicated than the mechanical energies that generate mechanical forces, in that they include the mysterious, vaguely defined energy called 'heat'. Heat is not a true potential. Nor is it something that 'flows', an outdated usage left over from the phlogiston theory of heat, which held that the stuff that raised temperatures was this massless invisible fluid that flowed from hot bodies to cool ones. Nor is it a single, differentiated form of energy like the mechanical potentials. In fact, it can be in the form of any of them. Perhaps it's best defined as the sum of all the energies that increase as the temperature of a system is increased. Maybe heat is thermo's equivalent of mechanical kinetic energy, an energy that exchanges one PE for another. Heat an iron bar, for example, and it will radiate light, so the heat given to the bar must have been transmuted into quantum jumps in the electronic energy of the iron atoms, which then is lost as electromagnetic energy in the form of photons.

 

[HomogenousCow]

I feel like calling something a "defined quantity" might make it sound like a useless or ad hoc measure to laymen.

 

[Dale]

Several speculative posts and responses have been deleted and this thread is now closed.