Is Potential Energy Just an Accounting Trick to Describe Energy Conservation?

[Nano-Passion]

Potential energy has always bothered me. Is it just an accounting trick to describe that energy is always conserved ( E = K + U)? Because if so, there are probably other ways we can describe this.

 

[russ_watters]

There is another thread here somewhere on the same topic you should look for. But anyway: Yes, PE is as real as KE.

 

[Nano-Passion]

There is another thread here somewhere on the same topic you should look for. But anyway: Yes, PE is as real as KE.

So far from reading the thread, the general consensus seems to point that it is fictitious. But I'll carry the conversation on the other thread.

 

[russ_watters]

Hmm...must be the wrong thread then.

 

[Nano-Passion]

Hmm...must be the wrong thread then.

This is it https://www.physicsforums.com/showthread.php?t=613384&highlight=is+potential+energy+real

 

[Dickfore]

Potential energy has always bothered me. Is it just an accounting trick to describe that energy is always conserved ( E = K + U)? Because if so, there are probably other ways we can describe this.

In some sense, you're right. Potential energy looses its meaning in Relativity. In Relativity, the interaction between the particles is carried through a field. But, the field itself becomes a physical system with its own (innumerably infinitely many) degrees of freedom.

Then, the potential energy is the energy carried by the field due to its disturbance by the presence of the particles within it.

But, this way of looking at things is so hard to imagine, that, especially when the speeds of the particles are much smaller than the speed of light in vacuum, it is still beneficial to introduce a potential energy.

One relativistic consequence of the difference between the two ways of looking at things is that, classically, the orbit of an electron around a proton is inherently unstable. Namely, as the electron revolves, it is accelerated. Accelerated charges emit electromagnetic waves. Thus, some of the energy of the proton-electron system gets radiated away in a form of electromagnetic waves (which are disturbances of the electromagnetic field). A similar thing should occur in a gravitationally bound system, although the energy emitted through gravitational waves is very much lower.

 

[Dickfore]

For what I mean, see Darwin Lagrangian.

 

[Nano-Passion]

For what I mean, see Darwin Lagrangian.

That's funny, I've stumbled onto that page earlier today. The math formalism is a bit over my head but the concept is a bit more familiar.

One thing that made me really want to question potential energy is that I derived a formula that is almost exactly analogous to it. I'm a bit hesitant to share it at this point though.

 

[PhanthomJay]

Whether potential energy..or any form of energy...is real, is debatable. What really is real, are changes in energy...ΔK, ΔU, ΔE, etc...(definition of reality not withstanding).

 

[Dickfore]

What is the potential energy of a charged particle moving in an electromagnetic field?

 

[Nano-Passion]

What is the potential energy of a charged particle moving in an electromagnetic field?

Hmm..

In an electric field:

$$k \frac{q_1 q_2}{r}$$

In a uniform magnetic field, with the particle perpendicular to it:

F=qvB

For potential energy, we take the integral of that with respect to ? In a uniform field, velocity & B will not change. So this approach is limited.

Note, I've only completed Calc based Physics II.

Whether potential energy..or any form of energy...is real, is debatable. What really is real, are changes in energy...ΔK, ΔU, ΔE, etc...(definition of reality not withstanding).

Fair enough.