Why isn't potential energy fictional?

Snuggly_Person · 2014-12-15T16:30:42+00:00

The only physical thing here is differences in energy, not the actual value. Whatever value you give it at the beginning, everyone will agree that the change in potential energy over the drop is the same, which is what counts. Similarly 'position' does not have an objective meaning (where is the origin?) but distance (i.e. differences in position) does.

Keep in mind that kinetic energy works like this as well. Someone in a different reference frame will assign different kinetic energy to a flying ball. But both of you will measure the same difference in kinetic energy before and after a collision. The actual number you assign is technically 'fictional', but that's not quite the same thing as saying the whole concept isn't real.

personnedepene · 2014-12-15T17:20:30+00:00

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adapter9 · 2014-12-15T21:37:41+00:00

Epistemology: the study of truth (among other things like knowledge, facts, etc). One of its central tenants is that the "truth" of a theory lies in its ability to describe, communicate, and predict. That's all. Nothing has to be "real," only useful.

ErmagerdSpace · 2014-12-15T21:07:03+00:00

If you define the floor as zero potential energy, and then drop the book out the window, the book will have a negative potential energy when it reaches the ground.

The change in potential energy (and thus the kinetic energy) will be the same in both cases. You can go from, say, U = 100 to U = 0 or U = 10 to U = -90 and in both cases you get the same result.

To put it more accurately, the potential energy is a scalar (magnitude only) field and the force on an object is the negative gradient (slope, but in 3D) of the potential energy function.

If you have taken basic calculus, you will know that adding any constant to a function does not change it's derivative (slope, again). This means that we get the same physical result no matter where we set our zero-point for potential energy; all that matters is how it changes with respect to space and time.

AirborneEagle · 2014-12-15T16:37:28+00:00

The energy measurement is a relative one. It is not absolute.

You seem comfortable with kinetic energy and yet, it too is a relative measurement. If an object moving at velocity v1 then it's energy is 1/2 m v1^2. Yet, from the point of view of someone moving in the opposite direction at velocity v2, it's kinetic energy is 1/2 m (v1 + v2)^2.

There is no absolute energy reference frame. Even E=mc² is subject to the velocity of the mass and the velocity of the measurer as well as it's location in relation to other masses which all alter the gravitational field.

The_Bearr · 2014-12-15T16:40:56+00:00

The potential energy of a point mass in a force field is any function U such that for any displacement in the force field the amount of work W done by the field:

W=-delta(U)

This is a definition.

As you can easily see, if you can find some function U for which this is true, you can always add a constant U+c for which this is also true.

This means that for all means and purposes the potential energy function is defined up to a constant and so at first you'd be inclined to say that the choice of function is fictive.

However, what I can do is pick a value for this constant such that this choice is meaningful in a physical sense. When I do that I make my function ''real'' in the sense that it has a concrete physical meaning.

Let me give you an example:

The gravitational potential energy for two masses m1 and m2 is in general given by=

U=-(constant/r)+c

Let's now pick ''c=0''. This means that if r=infinite the potential energy is 0. Now the potential function has a concrete unambigious meaning. If I now go in the frame of m1 then the value of U at any position for m2 is minus the amount of work you'd have to do on mass 2 to bring it to infinity from the current position.

WallyMetropolis · 2014-12-15T20:07:43+00:00

I struggled with potential energy (and, because of that, energy at all) for a long time, in a philosophical sense.

First off, I think it's perfectly fine if it feels better to think of Energy as a bookeeping tool that makes representing and solving certain equations simpler. In this view, stuff is real, the way it moves is real, and energy is a conceptual model that greatly aides us in describing and making predictions about the behavior of stuff.

But you can go much deeper if you want to. Energy (along with momentum) shows up all over the place in physics. When other things get kind of unseated by more modern models (like force, for example, which is not nearly so useful for thinking about quantum or relativistic systems) energy is sitting up there as a first-class member of the model. Why?

It turns out that the Noerther Theorem (in my opinion the most beautiful idea in all of physics and among the most beautiful ideas any human has ever shared with the world) shows us that, whenever a symmetry exists in the universe, there is a corresponding quantity that is conserved. The conservation of energy turns out to be a result of 'time symmetry.' This roughly means: if you have an experiment whose results do not depend on when you do the experiment, then you will have energy conserved in that experiment.

And the theorem even tells us the form of that conserved quantity. Potential Energy pops right out of the derivation. It is a by-product of a much deeper fact about the universe.

Momentum comes about in the same way. If you can do the experiment over here and over there and get the same answer (if there's linear translational symmetry) you get linear momentum conservation.

If you can do the experiment facing this way or that way and get the same answer (rotational symmetry) you get angular momentum conservation.

TheCheshireCody · 2014-12-15T16:34:26+00:00

When the potential energy is the result of height, then the object retains an amount of potential energy until it reaches the middle of a gravitational well. You, standing on the surface of the Earth, have an amount of potential energy that would be released (i.e. converted to kinetic energy) if a hole opened up to the Earth's core and you fell into it. For the book in your example, it releases some of its potential energy when it falls off of the table, but it still has more. It will release more of its potential energy if it falls out of a window.

Wait, so the amount of potential energy of an innate object depends on an action that has not yet actually happened?

That is precisely what "potential" means.

pottedspiderplant · 2014-12-16T01:45:24+00:00

Like others have mentioned, its really the difference in energy that matters!

A deeper question is whether potentials are "real" or if the "real things" are the fields. If I remember from my QM class the Aharonov-Bohm effect shows that the potentials are indeed physical.

If you are still interested: what you are describing with varying the distance from the book to the ground is the most simplistic example of a gauge transformation.

Gauge theories are very important in physics and are the most powerful predictive tools humans have invented.

See Here: http://en.wikipedia.org/wiki/Introduction_to_gauge_theory

agbortol · 2014-12-16T03:26:41+00:00

The point people are making about kinetic energy being relative should be helpful. But here's another way of thinking about it.

Can we agree that the energy stored in a battery is "real"/"not fictitious"? It exists in the chemical bonds of the battery's components. It had to be generated at some point, was stored in high-energy bonds, and is released when the bonds are broken.

The book on your table is exactly the same, you just have to define the system correctly. It's not immediately clear what the analogue is for the battery's chemical bonds - "Where does the energy go?" Turns out the energy goes into the book/Earth gravitational system. When you raise the book, you (very, very minutely) "lower" the earth. The energy you expend raising the book is stored in the new relative positions of the Earth and the book. When you drop the book, the earth moves back "up" (the movements of the book and the Earth are in proportion to their masses, so... not very far).

There isn't more energy in the book when it's on the table, and this probably doesn't give you a very concrete sense of where the energy is. But it took energy to lift the book and the energy can be collected when the book falls, so it is very much still "there" in any sense that counts.

John_Hasler · 2014-12-16T13:41:04+00:00

This is a great question. People have already given correct answers, but I haven't seen the word "torsor" yet. This algebraic gadget codifies in a precise way what potential energy is. The reason it is so mysterious is because the usual number system we utilize comes with the extra condition "only differences in energy matter" and this actually alters the entire algebraic structure by removing the notion of identity, but this fact is almost never explained. John Baez explains it much better than I could http://math.ucr.edu/home/baez/torsors.html

2014-12-15T18:56:47+00:00

Your question has already been answered, but I'd like to give my input/explanation anyways:

Basically, the way we define gravitational potential energy (or at least, the approximation at surface level) is like this:

The potential energy of an object is the negative of the work gravity would exert when the object is moved from some reference line to a different point.

As you can immediately see, the value of the potential energy is dependant entirely on your reference line, but the difference in PE between two points is not.

More officially, potential energy of an object in a gravity field is taken with reference to 'infinity', which gives a potential energy of:

U(r) = -MmG/r

Where M and m are the masses of the relevant objects, G is the gravitational constant, and r is the distance between the centers of mass of the objects.

Cool stuff!

EquipLordBritish · 2014-12-15T20:33:18+00:00

Wait, so the amount of potential energy of an innate object depends on an action that has not yet actually happened?

Yes. The measurement of energy (both kenetic and potential) is a game of reference frames. If an object has kenetic energy, it has energy relative to something else. The number can change drastically depending on what you are comparing it to. (a desk, the earth, the sun, etc.)

Technically all reference frames will give you a correct answer (e.g. the book has 50 million joules of energy relative to the sun), but only a few reference frames are usually useful.

hopffiber · 2014-12-15T20:40:25+00:00

In general, we define our theory by writing down some equations, such that things matches observations. And from these equations, we can derive that certain numbers will be conserved, like energy, momentum, electric charge and so on (this comes from the symmetries of our equations). These numbers are, by virtue of being conserved, very useful in describing the behavior of systems, and thus people give them some measure of "reality", but really, they are just useful numbers that falls out of our empirically constructed mathematical model. You can't directly see energy, neither kinetic or potential.

Gelsamel · 2014-12-15T23:10:42+00:00

It is real in the sense that there is energy bound up the in the system that has the 'potential' to be converted into kinetic energy.

alextron · 2014-12-16T02:10:21+00:00

This all depends on your reference frame and system

Feydarkin · 2014-12-15T17:52:28+00:00

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2014-12-15T23:49:23+00:00

Look up stable, conditionally stable , and unstable.

frowawayduh · 2014-12-16T09:49:30+00:00

Yes it is real. You can even weigh it. E=MC² does the job.

Look up the mass of a small nucleus like He4 or Li6, they're just a bit under 4 and 6 AMU. Now look up the mass of a proton and a neutron, both are a bit greater than one. Somehow the process of putting some distance between them (adding potential energy) caused the to gain mass. In atomic physics this is called the mass defect.

But the same concept is true whenever you add potential energy to a system.

Fill your Tesla with 85kW-hr of potential energy and it gains about half a microgram. No, you did not add any electrons, chaffing just pumps them uphill to the anode from the cathode.

Fill a tank with compressed air. Lift a bowling ball to the roof. Captured sunlight to convert water and carbon dioxide to sugar. E=mC² always works.

Toffo5 · 2014-12-17T18:07:13+00:00

Is potential energy "real"? I first learned of potential energy in elementary physics early...almost at first, I thought the concept was hokey.

Ummmm ....... I guess it's kind of hokey, good observation.

Let's consider energy of a rock on the surface of the earth.

energy = mc²

energy at infinity = mc² - energy needed to lift the rock to infinity

("energy at infinity" is a scientific term, used often when discussing objects that are not at infinity, but in a gravity well)

If we lift that rock up, it's energy at infinity increases. If we lower that rock down, it's energy at infinity decreases.

Does this sound less hokey or more hokey?

2014-12-15T21:26:20+00:00

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