Potential Energy -- What's the Jist?

[Tsadi]

I know what potential energy is, i personally have a problem with the notion behind potential energy. I am not trying to speculate in this thread, just forward a few of my displeasures behind treating it a ''real thing.'' I hope for good discussion to come out of it.

 

Right, so where do i start?

 

Well, i always try to integrate relativistic framework into my thinking. In fact, i often believe, that if you integrate a relativistic framework into an idea, fitting quantum mechanics (usually), is easier, than fitting quantum mechanics into relativity.

 

You might think i am rambling, because surely, fitting one into the other, despite which way you do it, should yield the same difficulty. But i often believe, if it works well with relativity first, then any conclusions you draw forth on the idea, should be able to fit into a quantum framework relatively easy.

 

(I am sure people may disagree with that line of thought, but its how i have come to understand integrating theories together.)

 

Now, in relativity, a few weird situations arise when considering actions; those moments in time, which appear to us as linear representations of events unfolding around us as the hand on the clock passes us by. These events seem very real to us (the observer), but events in relativity that are seperated by a past cone and a future cone are stressed as being illusions -- or perhaps even better said yet, illusory of the mind.

 

Time does not seperate into a past, present and a future. Instead, we seem to accept in relativity that there is only a present time, and that ''all time''* is in fact one large river, that does not flow, but instead is frozen in its own framework. (Read Brain Greene's book, ''The Frozen River'', for some good insights.)

 

* I mean this ''all time'' to represent the notion of all events from the alpha point to the omega point.

 

So instead, we envision spacetime as a single frame of existence; or stops and starts, fleeting flashes of existence without a past and a future, but focused on the here and now. If that is true, then how can potential energy fit into this picture?

 

For something to have a potential energy, we consider the past work put into that system; but if a past does not exist, how can these two seemingly accepted notions of science ever work together in a sensical way?

 

Tsadi

[Mr Skeptic]

Potential energy is energy due to the positioning of your items. A rock on a mountain has potential energy. It has the same amount of potential energy regardless of its past. If it got there because someone carried it up, or because it is a meteor that fell there, or it was just sitting there minding its own business as plate techtonics created the mountain, it doesn't matter. It will have the same amount of energy regardless of how it got into that position.

[Tsadi]

On a wider scale of thought, every fleeting moment we call the present time, consists of the same ''constituents'' it had at any other time.

 

This is true, as i think you point out, but potential energy is written in respect to its past state, and potential energy of ''thing'' will continue without any past reference in a relativistic mainframe.

 

In order to overcome such a problem, i would have thought, is to say any potentiality, has already been made, and hence collapse in the wave function. If it didn't, i ask, how would such a system know how to propogate, without determination into the future?

 

It seems when Einstein said everything was predetermined, could not be so far from the truth, as to any potential is to actuality.

[foodchain]

It seems when Einstein said everything was predetermined, could not be so far from the truth, as to any potential is to actuality.

 

Does this have to do with quantum gravity at all, or why its so important to modern physics? I think I get the basics of this thread but in regards to determinism would that mean the present or whatever down to the smallest scale could have the information in it to see the future then? I know it sounds weird but in regards to the Copenhagen interpretation I think this falls short to describe quantum mechanics in regards to measurement or observation, simply put what on the quantum scale of things could support determinism? I think that would imply we can in experiment generate the physical universe with QM or it plus relativity?

[Mr Skeptic]

This is true, as i think you point out, but potential energy is written in respect to its past state,

 

This is wrong. Potential energy is defined only with respect to the present state. Where did you hear that the past had anything to do with it?

[Tsadi]

This is wrong. Potential energy is defined only with respect to the present state. Where did you hear that the past had anything to do with it?

 

Let's look at this from a thought-experiment.

 

Imagine we moved a rock to the top of a cliff. We know that from [math]PE=mgh[/math], we can deduct that the work put into the object (from moving a rock from a ground state to the top of a cliff) seriously determines the potential energy derived. We scale ourselves just how much potential energy a thing can have, due to the past variables no? This is the way i have always envisioned it.

 

I'm asking, how does one put a relativistic description of reality (one where the past is an illusion), into physics that kind of depends on some measure over time, relying on a past to exist?

 

Does anyone understand what i mean?

 

Moving the rock to the top of a cliff, seems straight forward, and relies on some past to exist to get that rock to the top of cliff. But in relativity, there is no past, so how can two theories like this ever work in a sensical way?

 

Does this have to do with quantum gravity at all, or why its so important to modern physics? I think I get the basics of this thread but in regards to determinism would that mean the present or whatever down to the smallest scale could have the information in it to see the future then? I know it sounds weird but in regards to the Copenhagen interpretation I think this falls short to describe quantum mechanics in regards to measurement or observation, simply put what on the quantum scale of things could support determinism? I think that would imply we can in experiment generate the physical universe with QM or it plus relativity?

 

 

Well gravity so far has failed as fundamental theory, but predeterminism is something else.

 

But i do believe that the future is a history that we simply can't remember, not in the sense we can remember the history we call ''past''. I believe, as many scientists do, that somehow every event is written into spacetime. Everything i do, come to do, say or write, is somehow stored into the vacuum itself.

 

We are taught in physics that quantum actions are never lost. The process of a bit of energy being shared between two atoms, is in fact stored in the vacuum itself, in a form of memory. So actions moving from [math]t_0[/math] to [math]t_1[/math] is ''memorized'' by the vacuum.

 

If this is true, and if relativity is correct in its conclusions, then everything in the future has already happened, and somehow the future effects us in a statistical way, as to say, the probable future can be determined in principle whilst still living in the present. But how much knowledge we can gain, is probably more complicated.

Edited October 9, 2008 by Tsadi
multiple post merged

[Mr Skeptic]

Let's look at this from a thought-experiment.

 

Imagine we moved a rock to the top of a cliff. We know that from [math]PE=mgh[/math], we can deduct that the work put into the object (from moving a rock from a ground state to the top of a cliff) seriously determines the potential energy derived. We scale ourselves just how much potential energy a thing can have, due to the past variables no? This is the way i have always envisioned it.

 

No, that is not how it is. The potential energy difference between two points is [math]PE=mgh[/math] (approximately). In classical physics it doesn't ever say what the potential energy is, just the difference. And the past has nothing to do with it. If you have a rock 10 m above the ground, can you tell me how you could get there two different ways so that the potential energy is different? If not, why do you keep insisting that the past has anything to do with it?

[Baby Astronaut]

Potential energy is energy due to the positioning of your items. A rock on a mountain has potential energy. It has the same amount of potential energy regardless of its past. If it got there because someone carried it up, or because it is a meteor that fell there, or it was just sitting there minding its own business as plate techtonics created the mountain, it doesn't matter. It will have the same amount of energy regardless of how it got into that position.

Does this mean that potential energy is dependent on gravity? Because with a higher gravity, the rock would crash harder into the ground below. And with a lower gravity, less impact = less energy.

[Royston]

Does this mean that potential energy is dependent on gravity? Because with a higher gravity, the rock would crash harder into the ground below. And with a lower gravity, less impact = less energy.

 

In this instance yes, providing you don't go too high, if you read the equation an increase in h, will mean the rock will have a greater potential energy. Mr Skeptic is quite right that potential energy is merely a difference. The past is irrelevant to the situation. Remember potential energy isn't solely confined to situations involving gravity, think about the potential difference across a battery terminal (voltage), or the energy values of an electron bound to a nucleus (these values are potential energy.)

 

I'd go further that potential energy is possibly one of the most important principles to understand in physics, especially when you move into QM specifically the Schrodinger equations which are as fundamental as Newtons Laws.

[npts2020]

What about chemical potential energy? Unexploded ordinance for example.

[D H]

Does this mean that potential energy is dependent on gravity? Because with a higher gravity, the rock would crash harder into the ground below. And with a lower gravity, less impact = less energy.[/quote']In this instance yes, providing you don't go too high, if you read the equation an increase in h, will mean the rock will have a greater potential energy.

You're answer is correct, but I don't think that what question BA asked.

 

To elaborate, for objects near the surface of the Earth, the potential energy of some object with mass m due to gravity is approximately [math]mgh[/math], where h is the height above the surface of the Earth. More generally, the potential energy of some object with mass m due to the gravity resulting from a point mass with mass M (or any spherical distribution of mass with mass M) is [math]U = U_0 -\,GMm/r[/math], where r is the distance from the point mass and U₀ is an arbitrary constant. The same expression applies in the case of a spherical mass rather than point mass (in which case r is the distance to the center of the sphere), but it is only valid for points outside the mass.

 

About that arbitrary constant U₀: The potential energy corresponding to some conservative force field is some scalar function whose gradient yields the force field. Suppose you have some function [math]\phi(\boldsymbol {x})[/math] such that [math]\nabla \phi(\boldsymbol {x}) = \boldsymbol F[/math]. Add an arbitrary constant to the function phi and you get another function whose gradient is also the same force field. Potential energy is indeterminate with respect to an arbitrary constant. There is no problem here, as it is only the difference between two values of the potential that is of interest. Physicists are free to choose any value for that arbitrary constant. For a point not necessarily close to a spherical mass distribution, one obvious choice is U₀=0.

 

So, how does one go from [math]U_0-\,GMm/r[/math] to [math]mgh[/math]? They certainly don't look at all like one another. Suppose that [math]r=r_0 + h[/math], where r₀ is the radius of a spherical mass and h is the height of some object above the sphere. Then [math]U=U_0-\,GMm/(r_0+h)[/math]. Rewriting the denominator [math]r_0(1+h/r_0)[/math] and approximating [math]1/(1+h/r_0)[/math] as [math]1-h/r_0[/math], valid for [math]h \lll r_0[/math], the potential energy for an object of mass m near the surface of a spherical mass is approximately

 

[math]U \approx U_0 -\frac{GMm}{r_0} + \frac{GM}{r_0^2}mh[/math]

 

Choosing [math]U_0 = \frac{GMm}{r_0}[/math] (it's an arbitrary constant; I can choose whatever value I want so long as I stick with it),

 

[math]U \approx \frac{GM}{r_0^2}mh[/math]

 

That first factor, [math]GM/r_0^2[/math], is the acceleration due to gravity at the surface of the object, which in the case of the Earth is g. Thus [math]U \approx mgh[/math] for objects near the surface of the Earth.

[Gilded]

What about chemical potential energy? Unexploded ordinance for example.

 

What about it? In that case the potential is electric rather than gravitational. Energy differences in electron configurations and so forth.

[npts2020]

What about it? In that case the potential is electric rather than gravitational. Energy differences in electron configurations and so forth.

 

Well, from the discussion above one could be led into believing gravity was the only force involved in potential energy. It is not true.

[insane_alien]

yes, but that was the OP was talking specifically about gravitational potential energy. y'know keeping the thread on topic and all that.

[swansont]

We are taught in physics that quantum actions are never lost. The process of a bit of energy being shared between two atoms, is in fact stored in the vacuum itself, in a form of memory. So actions moving from [math]t_0[/math] to [math]t_1[/math] is ''memorized'' by the vacuum.

 

We are? I was never taught that, and if it were true, it would have huge implications on using quantum systems as a basis for metrology, since these systems would no longer be identical.

[Tsadi]

We are? I was never taught that, and if it were true, it would have huge implications on using quantum systems as a basis for metrology, since these systems would no longer be identical.

 

I stand by it like stone. The actions, such as quantum actions are memorized by the vacuum. They are never lost.

 

Depends on the type of your training perhaps, but you will learn it eventually; the fact you haven't i cannot comment on. But quantum actions are not forgotten in the vacuum, as everything is recorded.

 

Now the implications are huge. It means to some extent, nothing is ever lost, even simple actions themselves. I do believe the first physicist i heard mention this was Frank J. Tipler. (back in the day).

[Klaynos]

I stand by it like stone. The actions, such as quantum actions are memorized by the vacuum. They are never lost.

 

Depends on the type of your training perhaps, but you will learn it eventually; the fact you haven't i cannot comment on. But quantum actions are not forgotten in the vacuum, as everything is recorded.

 

Now the implications are huge. It means to some extent, nothing is ever lost, even simple actions themselves. I do believe the first physicist i heard mention this was Frank J. Tipler. (back in the day).

 

I think you're going to have to reference this. It's not something I've ever heard of.

[Tsadi]

I think you're going to have to reference this. It's not something I've ever heard of.

 

I've seen this statement a few times... my memory does NOT serve me well, but i do believe there is a mention of this quantum fact in The Anthropic Principle, by Tipler and John Barrow.

 

It's been a while, i might be wrong.

[Klaynos]

A pop science book is NOT a reference...

 

Do you know what it might have been called or anything? Something I can do a journal search on... Or even just look in the QM text I've now got next to me....

[Tsadi]

All due respect, i've read it in other places as well. I based the last part on something i remember, but still not well, as i said.

[Klaynos]

All due respect, i've read it in other places as well. I based the last part on something i remember, but still not well, as i said.

 

I'm sure, I'm genuinely interested in reading about it.

[Mr Skeptic]

Just find any credible reference. This is something I have not heard of, but it would be interesting.

 

In classical physics you should be able to deduce previous situations from the current ones, but I've never heard of that with quantum.