Is potential energy real?

Question

Or is it just a useful construct that does not satisfy E = mc², and in fact doesn't fit into any real equation?

And what early physics teachers tell you, that potential energy "turns" into kinetic energy and so forth, is just another confusing and inappropriately informal misrepresentation?

Where's the rigor in potential energy? Does it have a differential equation? Can it even really be measured, or just deduced?

The object being above the ground is a concept with no rigor. How do you define that? How is it different from the object being on the ground?

I took those courses too, been taking them the last 3 years.

Oh, and also! Additional question. Voltage has been called electric potential or something like that. Is there a connection to potential energy? Does anyone have any useful analogies to help me understand voltage?

Answer 1

"Energy" is usually defined as "the ability to do work." (And, as you may know, "work" has a rigorous definition as ∫F·ds).

Systems which are said to "store potential energy" are clearly capable of doing work (take a compressed spring or a weight on a pulley as examples); so it seems reasonable to say that that is "real" energy.

> ...that potential energy "turns" into kinetic energy and so forth, is just another confusing and inappropriately informal misrepresentation?...

It's informal; but I don't think it's misleading. It fits with the notion of conservation of energy, and that's an important point: If we don't consider PE to be "real" energy, then the principle of conservation of energy falls down. We'd have to replace it with something like:

"Energy is conserved, except in circumstances X [such as lifting a weight], when the energy 'goes away'--and in reciprocal circumstances Y [such as a falling weight], when energy suddenly 'appears'; but _always_ it appears from the same place that it previously 'disappeared into' by some previous process."

To me, that kind of description seems really awkward. Considering the fact that the energy that "comes out" of a PE system is _always_ the same as the amount that "went into" it, it seems parsimonious to include PE in the overall conservation law and allow it to be classified as genuine "energy."

> Where's the rigor in potential energy? Does it have a differential equation?

Absolutely. A particle's PE is defined by its location within a so-called conservative force field (of which "gravity" is an example, but "friction" is not).

> The object being above the ground is a concept with no rigor. How do you define that? How is it different from the object being on the ground?

That's a good observation. In truth, the association of a _particular_ amount of energy with the particle's position in the force field is arbitrary. In other words, you need to arbitrarily define some locus of points within the field as representing "zero" energy. However, this doesn't diminish its rigor, because the _difference_ in PE between position "A" and position "B" within the field is independent of your choice of the "zero-energy" position (this can be shown by looking at the properties of a vector field). And in fact, in all discussions of "converting" PE to KE and vice versa, we are always talking about "ΔPE", not "absolute PE". The "absolute" amount of PE "in" a system is arbitrary and is chosen for mathematical convenience; but the _change_ in PE (which is what concerns us in conservation and work questions) has an unambiguous value.

> ...Is there a connection [between voltage and] potential energy?

Yes. In fact, "voltage" is exactly a measure of the electrical potential energy stored in a given amount of charge (e.g., a given number of electrons). Specifically, "1 volt" means that each coulomb of charge contains 1 Joule of electrical potential energy.

As with all PE systems, the "zero point" is arbitrary; and the part of a circuit that you call "zero volts" is an arbitrary choice (for convenience, "zero volts" is often equated with "ground"; i.e. the voltage level of the surrounding earth). The thing that really determines how the electrons will travel through the circuit is the _difference_ in voltage between various points in the circuit.

Answer 2

Potential energy is quite "real". Take a hammer and drop it from three feet on your big toe. Then try to explain to the doctor at the ER that you were going to disprove the concept of "potential energy".

Your question implies that there is only one correct explanation for a natural phenomenon. That just isn't so.

Physics as all sciences can offer many different explanations for the same thing. Potential energy is the classical mechanics explanation for how conservative forces behave. Schroedinger QM would be another one way to treat the same thing. Relativistic quantum field theory is another one. And so is general relativity for gravitation. Not all of them describe exactly the same aspects of nature. Not all of them even overlap. But often they do and in this case you could use each and every one to treat the potential energy problem for slowly moving masses in weak gravitational fields with exquisite precision.

You could, but you wouldn't.

For where potential energy takes a one liner, a quantum field theoretical calculation about a macroscopic mass falling in a gravitational (or any other potential field) would take a dissertation, if it can be done at all. And it would be nothing but the Rube Goldberg solution to a problem that is perfectly well understood in a single equation.

You see, good physics is ALWAYS a matter of knowing a good enough approximation rather than doing it "right".

There is no "rigor" on the level you are looking for. There never was and there never will be. And if you demand that there should be, physics is not for you. You will never advance beyond the most trivial problems because you will always be looking for the "ultimate correctness", something that was never planned into the system.

Physics is not math. And can not be. And does not strive to be.

If you need formal proof, you need to be a mathematician. There you will get formal proof for all kinds of things that don't exist. Like integers. There is no real world representation for integers because the world is finite. Integers are not. But you can prove all kinds of useful stuff about the properties of arbitrary sized integers. Like that there is always a bigger prime number. Except... there are prime numbers that nobody could write on a piece of paper because there ain't enough matter in the universe to make a piece of paper that large. Or enough time to print them. So how "real" is that?

Potential energy, on the other hand, is quite real, even though it is only an approximation of what is happening in the "real" world. But when that hammer drops on your toe, the quantum corrections and the relativistic effects will matter zip. Your toe will be broken. And this is true for almost all phenomena in physics. There is always a model or theory good enough that is not even close to being rigorous.

That's a handful to think about. Isn't it?

Have fun!

PS: To make it clear: the average science teacher does not understand what science is. They will explain the next to trivial stuff to you but unless they are very good, they won't have the slightest clue about what science does and how it does it. My physics teacher happened to be very good. But that was one out of a dozen that I happen to know and only he could have explained this to you. All the other guys would have been completely blown out of the water by such a question.

Answer 3

I feel like I'm not fully qualified to answer that but as someone who's studied physics at University-level I'll try to do my best and answer the question. Potential energy vs. kinetic energy is a model which describes reality. It's a useful way of making fairly accurate predictions. Potential energy cannot be real energy stored in the object in question, otherwise the object's mass would increase with its potential energy as per Einstein's E=mc^2. And that would make no sense since the object's mass would be a function of what point of space we are comparing it to. Each object would have all masses and none of them, a clearly impossible scenario and one which would also make everything we see around us impossible. Kinetic energy on the other hand *is* stored in the object in question, objects traveling at a speed have an increased mass by just as much as predicted by E=mc^2. Potential energy is just a useful model with which you can make predictions, it does not point to any non-physical realities.

Answer 4

What is called potential energy is often energy that is stored in a field. For example when you stretch a spring, energy is actually being stored in the spring, and ultimately that energy is the energy stored in the electric fields created between the atoms that would not usually be there.
The being said, you can define an object to have zero potential energy at any point or position you want. Think of it as energy that depends on position and you can define it to have zero potential energy at any position you choose.

Answer 5

i think its real. Idk the equations for it but i know it real. Its when an object isnt above ground.we learned about it last year in science.