# potential energy

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What basis is there for claiming that potential energy exists only relative to the arbitrarily chosen frame in which it is measured? Doesn't potential energy, just like kinetic energy, persist until it is converted into another form or dissipated? It may be possible to measure it differently according to what frame of motion/time you're interested in, but ultimately it exists as empirically observable potential insofar as it can be released and measured as such, correct? Just because something runs out of potential in a given frame doesn't make it absolutely devoid of potential energy in any possible frame.

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What basis is there for claiming that potential energy exists only relative to the arbitrarily chosen frame in which it is measured? Doesn't potential energy, just like kinetic energy, persist until it is converted into another form or dissipated? It may be possible to measure it differently according to what frame of motion/time you're interested in, but ultimately it exists as empirically observable potential insofar as it can be released and measured as such, correct? Just because something runs out of potential in a given frame doesn't make it absolutely devoid of potential energy in any possible frame.

Completely, totally, utterly wrong.

Potential energy is not only relative to a reference frame, it is relative to an arbitrary choice of ground state within any single reference frame.

The basis is called physics.

You are in desperate need of a physics book. Try The Feynman Lectures on Physics.

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What basis is there for claiming that potential energy exists only relative to the arbitrarily chosen frame in which it is measured? Doesn't potential energy, just like kinetic energy, persist until it is converted into another form or dissipated? It may be possible to measure it differently according to what frame of motion/time you're interested in, but ultimately it exists as empirically observable potential insofar as it can be released and measured as such, correct? Just because something runs out of potential in a given frame doesn't make it absolutely devoid of potential energy in any possible frame.

Lemur, we're dealing with definitions here. Potential energy is defined by arbitrarily chosen (but *consistent*) relative points.

That is, if I stand on a 1 meter chair on top of a 10 story building and jump off the chair, it is my choice how to define my "potential energy" comparison point, but this point MUST be consistent later. I can choose that my "zero" is the ground (at the bottom of the building), in which case I started with potential energy of mg(10stories+1meter) and ended with potential energy of mg(10 stories), and the difference is just mg(1 meter).

Or I can decide that my "zero" is on the floor relative to me, that is on the floor of the 10th floor -- in which case I started with potential energy mg(1 meter) and ended with mg(0), which makes the difference again mg(1 meter).

The only time a potential energy is not really arbitrary is in the case of potential elastic energy, where the "zero" point is considered the equilibrium resting point of the spring.

That's the way we define potential energy. It is, therefore, dependent on a location in the same frame it's being measured. By definition.

I am stating a bit of simplistic stuff here, but you should really pick up a physics book for the more elaborate concept; this "pick up a book" deal isn't to condescend you. It's to help you understand.

Before you try to revolutionize physics I think you probably would do best to learn what it actually says on the matter...

~mooey

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The only time a potential energy is not really arbitrary is in the case of potential elastic energy, where the "zero" point is considered the equilibrium resting point of the spring.

There's gravity, too, when r changes enough that g is not constant; we choose infinite separation to be zero PE. Those choices are technically arbitrary as well, but it is much more convenient to choose a particular location, because then you have a nice equation describing the potential energy, namely 1/2 kx^2 and GMm/r

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There's gravity, too, when r changes enough that g is not constant; we choose infinite separation to be zero PE. Those choices are technically arbitrary as well, but it is much more convenient to choose a particular location, because then you have a nice equation describing the potential energy, namely 1/2 kx^2 and GMm/r

Oh, good point, didn't think about that. Thanks!

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There's gravity, too, when r changes enough that g is not constant; we choose infinite separation to be zero PE. Those choices are technically arbitrary as well, but it is much more convenient to choose a particular location, because then you have a nice equation describing the potential energy, namely 1/2 kx^2 and GMm/r

When you choose infinite separation as the ground state, gravitational potential energy is negative and you need a minus sign in your expressions: -GMm/r .

Edited by DrRocket
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Lemur, we're dealing with definitions here. Potential energy is defined by arbitrarily chosen (but *consistent*) relative points.

That is, if I stand on a 1 meter chair on top of a 10 story building and jump off the chair, it is my choice how to define my "potential energy" comparison point, but this point MUST be consistent later. I can choose that my "zero" is the ground (at the bottom of the building), in which case I started with potential energy of mg(10stories+1meter) and ended with potential energy of mg(10 stories), and the difference is just mg(1 meter).

Or I can decide that my "zero" is on the floor relative to me, that is on the floor of the 10th floor -- in which case I started with potential energy mg(1 meter) and ended with mg(0), which makes the difference again mg(1 meter).

The only time a potential energy is not really arbitrary is in the case of potential elastic energy, where the "zero" point is considered the equilibrium resting point of the spring.

That's the way we define potential energy. It is, therefore, dependent on a location in the same frame it's being measured. By definition.

I am stating a bit of simplistic stuff here, but you should really pick up a physics book for the more elaborate concept; this "pick up a book" deal isn't to condescend you. It's to help you understand.

Before you try to revolutionize physics I think you probably would do best to learn what it actually says on the matter...

~mooey

I'm well aware of this frame-relative approach to quantifying potential energy, which mooeypoo describes so thoroughly. My point is that while I see how this emphasis on the framing allows the analysis to be defined according to the problem at hand, it doesn't eliminate the fact that empirically more potential energy may be available that is excluded from analysis arbitrarily because it is outside the selected frame. E.g. so in terms of the example of going from 10 stories + 1 meter to the ground +1 meter, the object treated as being at an arbitrary frame-relative ground state at +1 meter may be empirically observed to have more potential energy by triggering the release of that energy. So while it makes sense to use frame-relative parameters for measurement, you can't claim that all potential energy has been exhausted simply because an object has reached the limits of its potential in terms of the applied frame.

Can anyone acknowledge that potential energy is an empirically observable form of energy and that it may exist regardless of how it is framed by physicists?

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So while it makes sense to use frame-relative parameters for measurement, you can't claim that all potential energy has been exhausted simply because an object has reached the limits of its potential in terms of the applied frame.

Potential energy is just that, potential energy. It's the energy the object potentially could have with respect to where it is. Hence our insistence on it being dependent on "arbitrary relative position". Any object at any time has multiple options for its potential energy, that's what I was trying to convey with my example. My phone, for instance, is sitting on my table right now. It can be said that it has no potential energy because it's at rest relative to "zero" position (the table). But it also DOES have potential energy if I think of my chair as the "zero" - and I could use conservation of energies to figure out what velocity it would have in case it fell off and hit the chair. But then, I'm also at the fourth floor right now. My phone, theoretically speaking, has the entire height of the four floors AND the height of my desk as its potential energy height at any given time, if I take the ground floor as my "zero".

It's relative and chosen arbitrarily because it's not really usable energy until you actually drop it. It's energy that is only usable when it's converted, really. If an object remains at rest somewhere, it can have all sorts of "potential energies" that are meaningless until you find one you want to use when it actually moves somewhere lower or higher.

Therefore this statement:

Can anyone acknowledge that potential energy is an empirically observable form of energy and that it may exist regardless of how it is framed by physicists?

-- is meaningless. Potential energy exists out of definition of it. On one hand everything has potential energy relative to some arbitrary point that is not their own position, and on the other everything that doesn't move is at zero potential energy relative to their own position.

The only place where you have use of this energy is when an object moves. The problem with Relativistic movement is, among other things, that the mass changes and the velocity is relative (.. hence 'relativity'). Also, General Relativity deals with different gravitational issues and that affects the "gravitational potential energy", obviously. I must admit that General Relativity is NOT my strong side, so I will have to rely on one of the other physicists to assist in explaining this further, but the general idea is that 'potential energy' is, quite empirically proven and working, depended on arbitrary position that are absolutely relative to the object and MUST be in the same frame.

If they're not in the same frame, then the relative position is moving with relation to the object, and you lose your whole definition. The entire point is that "potential energy" is, by definition, whether you like it or not, exactly what it is defined to be. By the way, you should read a bit about the derivation of the formulas. It might help you understand why it's defined the way it is, and why we insist it's dependent on the frame.

Also, lemur, you speak about empirical things but you don't give empirical data. See, empirically, there's no meaning to what you're saying, really, and in order for it to have empirical meaning, you need to supply empirical evidence.

Say, a calculation that works the way YOU describe the problem. The calculations in special relativity aren't difficult at all, so this should be relatively easy to check if it *actually works*. can you give us an example of where potential energy exists regardless of the definition of it?

~mooey

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It's relative and chosen arbitrarily because it's not really usable energy until you actually drop it. It's energy that is only usable when it's converted, really. If an object remains at rest somewhere, it can have all sorts of "potential energies" that are meaningless until you find one you want to use when it actually moves somewhere lower or higher.

Therefore this statement:

-- is meaningless. Potential energy exists out of definition of it. On one hand everything has potential energy relative to some arbitrary point that is not their own position, and on the other everything that doesn't move is at zero potential energy relative to their own position.

My argument is that if you take your phone example or any other empirical example of an object framed with some amount of potential energy, there may be a method of further releasing more kinetic energy, in which case that energy must have been potential in the object/system prior to it being released.

Certain things/systems don't have any more potential energy to give. A dead battery or any thermodynamic system in equilibrium has exhausted its potential, correct? Matter at the center of the Earth lacks gravitational potential, correct, except for relative to other gravity-wells, such as the sun? I contend that even if you define the center of the Earth as an absolute ground position for that frame, you could still cite an empirical method of further releasing any potential energy present. Actually, I don't think there is any further potential energy present for the Earth to fall into the sun since it is already free-falling at a stable-altitude. Could this be empirically contradicted if I was wrong? I think it could, and that's my point.

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A dead battery or any thermodynamic system in equilibrium has exhausted its potential, correct?

incorrect

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incorrect

I hate to be rude, but making assertions like this with no grounds or explanation is only helpful to someone willing to take you at your word. Do you want to discuss/debate these things or just make absolute claims and expect to have them taken as indisputable fact?

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I hate to be rude, but making assertions like this with no grounds or explanation is only helpful to someone willing to take you at your word. Do you want to discuss/debate these things or just make absolute claims and expect to have them taken as indisputable fact?

Go read a physics book. There is nothing to debate.

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I'm well aware of this frame-relative approach to quantifying potential energy, which mooeypoo describes so thoroughly. My point is that while I see how this emphasis on the framing allows the analysis to be defined according to the problem at hand, it doesn't eliminate the fact that empirically more potential energy may be available that is excluded from analysis arbitrarily because it is outside the selected frame.

There is no potential energy which is "excluded from analysis."

Consider a 1kg object which falls from a 10m height to the ground. Its potential energy [imath]mgh[/imath] at 10m is [imath]10g[/imath], and at the ground is 0. When it falls, all that potential energy is converted to kinetic energy, and so it has [imath]10g[/imath] of kinetic energy when it strikes the ground. (Conservation of energy requires it to, since it starts with [imath]10g[/imath] energy, and must end with [imath]10g + 0 = 10g[/imath] total energy as well.)

Now suppose I redefine the zero point to be at exactly 10m height above the ground. Its potential energy [imath]mgh[/imath] at 10m is 0, and at the ground is [imath]-10g[/imath]. When it falls, its potential energy is converted to kinetic energy, and so it has [imath]10g[/imath] of kinetic energy when it strikes the ground. (Conservation of energy requires it to, since it starts with 0 energy, and must end with [imath]10g + -10g = 0[/imath] energy as well.)

So no energy has been excluded because of my choice of zero point or framing.

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Go read a physics book. There is nothing to debate.

I might not have enough potential energy to read the book if it's beyond my chosen frame of analysis.

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A much shorter summary:

Since potential energy can be arbitrarily defined, what matters is the potential energy difference between two states. If I start with 0 potential and proceed to -10, that's 10 units of energy freed up to do something else. The fact that I had 0 at the beginning is irrelevant, since negative potential isn't a problem.

So if something has a potential energy of 0 in some chosen system, that doesn't mean it cannot move. Perhaps other states have negative potential energies.

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A dead battery or any thermodynamic system in equilibrium has exhausted its potential, correct?

If you believe that a dead battery has no potential energy, just take it out of your car and drop it on your foot.

Thermodynamics texts are filled with engines that operate by taking gas in one state of thermodynamic equilibrium and extracting work, resulting in another state of thermodynamic equilibrium.

Go read the book.

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A much shorter summary:

Since potential energy can be arbitrarily defined, what matters is the potential energy difference between two states. If I start with 0 potential and proceed to -10, that's 10 units of energy freed up to do something else. The fact that I had 0 at the beginning is irrelevant, since negative potential isn't a problem.

So if something has a potential energy of 0 in some chosen system, that doesn't mean it cannot move. Perhaps other states have negative potential energies.

If you believe that a dead battery has no potential energy, just take it out of your car and drop it on your foot.

Thermodynamics texts are filled with engines that operate by taking gas in one state of thermodynamic equilibrium and extracting work, resulting in another state of thermodynamic equilibrium.

Go read the book.

Ok, you're both giving reasons why framing is useful and how potential energy is empirically demonstrable beyond whatever framing is applied. I never disagreed with anything except the implication that potential energy ONLY exists insofar as it is frame-defined. I never said that it COULDN'T be defined according to different framings in ways that would render a particular system as having a specific amount of energy between specified points of reference.

No thanks dropping the dead battery on my foot. I'll try it with the physics books you keep recommending though.

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No thanks dropping the dead battery on my foot. I'll try it with the physics books you keep recommending though.

The Feynman Lectures on Physics comes in a nice, boxed, three-volume set. That should illustrate the principle quite clearly.

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Ok, you're both giving reasons why framing is useful and how potential energy is empirically demonstrable beyond whatever framing is applied. I never disagreed with anything except the implication that potential energy ONLY exists insofar as it is frame-defined.

There is nothing to disagree with. Nobody has made this claim. DrRocket told you that this was utterly wrong at the outset of the thread.

You are misusing "frame" here. A frame of reference is a coordinate system. Other frames of reference move at some speed with respect to it. The amount of potential energy is defined in terms of location; you have X amount of potential energy with respect to some position. If you choose another position, you have a different amount of potential energy. It is not an absolute. The existence of potential energy does not depend on the choice of the reference point.

It can vary between frames because, as I explained before, invariant and conserved do not mean the same thing.

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There is nothing to disagree with. Nobody has made this claim. DrRocket told you that this was utterly wrong at the outset of the thread.

You are misusing "frame" here. A frame of reference is a coordinate system. Other frames of reference move at some speed with respect to it. The amount of potential energy is defined in terms of location; you have X amount of potential energy with respect to some position. If you choose another position, you have a different amount of potential energy. It is not an absolute. The existence of potential energy does not depend on the choice of the reference point.

It can vary between frames because, as I explained before, invariant and conserved do not mean the same thing.

Maybe "utterly wrong" was just insufficiently specific and I ended up interpreting it to mean that things were wrong that weren't actually wrong. Suffice to say there was miscommunication, though it was not entirely my fault because the things I was saying were not wrong.

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Maybe "utterly wrong" was just insufficiently specific and I ended up interpreting it to mean that things were wrong that weren't actually wrong. Suffice to say there was miscommunication, though it was not entirely my fault because the things I was saying were not wrong.

Lemur, sometimes you're plainly wrong. I understand that you're searching for answers, but you seem to insist on being so defensive about your own point of view, it tends to make the argument completely moot.

Either you want to know what mainstream (workable, testable, empirically proven) physics say on the matter, or you wish to stick to your guns and play allknowing. There's nothing wrong with being wrong. There's a lot wrong with insisting you're right when the evidence is against you.

This wordplay games and defensive redefinitions are really unhelpful here. Getting things wrong is how we learn.

~mooey

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Lemur, sometimes you're plainly wrong. I understand that you're searching for answers, but you seem to insist on being so defensive about your own point of view, it tends to make the argument completely moot.

Either you want to know what mainstream (workable, testable, empirically proven) physics say on the matter, or you wish to stick to your guns and play allknowing. There's nothing wrong with being wrong. There's a lot wrong with insisting you're right when the evidence is against you.

This wordplay games and defensive redefinitions are really unhelpful here. Getting things wrong is how we learn.

If I was somehow strawmanning the frame-relative definitions of potential energy given, than I apologize. There is a difference between the existence of potential energy in physical systems and the framing of it for analysis and measurement. My concern was that potential energy was being explained as something more abstract than kinetic energy, i.e. because it is latent instead of manifest. I agree that potential energy can't be directly observed except in terms of how much kinetic energy is released or how much force it exerts, but I still think it is correct to acknowledge that it exists regardless of how it is framed. Swansont resolved that conflict in a recent post. I don't think you should be pushing me to abandon my point of view and adopt some other "mainstream" point of view instead. There are different ways to express things and by allowing differences to interact, critical rigor subjects knowledge to scrutiny and stimulates it to check and defend itself. That is not a bad thing. You claiming that it's unhelpful ignores the fact that the OP in the PE thread may well have understood the insistence on frame-relativity the same way I was, i.e. as an absolute relativism of energy, which Swansont clarified it is not. Whether or not you recognize it, that ambiguity was present in the thread that this all emerged from. Denying that just buries the problem in order to assert that orthodoxy is always right and never misunderstood; and that's overzealous, imo.

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