the myth of potential energy

Factual Questions
1

This had bugged me for a long, long time. Since junior high, actually.

See, I think “potential energy” is a myth, a fiction, and therefore, at the very least, so is the law of the conservation of energy.

Instead of describing how I come to this unique conclusion, I’ll give you a thought experiment to illustrate my point.

Imagine that there are two rooms. These rooms are completely identical as far as human science can determine. They look the same, they smell the same, and there is no way to tell them apart.

In each of these rooms lies a large, heavy boulder. These boulders are also completely identical in all ways.

The only difference between these two rooms, in short, is that one is on the top of a hill, and the other is at the bottom of the hill.

The experiment, then, is to determine which of the two boulders is which. Describe, in detail, how you detect this “potential energy” that the boulder on the hill must have. After all, if the boulder rolled down the hill, it could smash a house to pieces. Where is that energy right now? How do you find it?

We say that the energy “must” be there. Yet we can’t prove it. We say "Well it must be there, because that boulder could smash a house. " But isn’t that circular reasoning? Isn’t that, in a sense, faith?

You can’t see it or smell it or find it in any way, but trust us, that potential energy is there, and the proof is that the boulder has a lot of energy after rolling down the hill. That’s basically saying “It’s true because it explains it”, a type of explanation along the lines of “storks bring babies”, or “lightning comes from angels fencing”, or “a wizard did it”.

Now, I’ve put this question to many groups of people over the years since I first frustrated the hell out of a teacher with it in grade 8 science class.

I’ve gotten reactions like frustrated anger without any actual answer, blank incomprehension, mumbled changes of subject, and simple shrugs.

What I’ve never gotten is a clear, concise, convincing argument of why I am wrong. I feel I must be. It does not seem likely that a very important plank in basic physics is just a myth we created and keep believing in because it seems to work out. I’m probably just missing something basic. In fact, I’ve probably made the sort of simple error of reasoning that a Real Actual Science would find so basic as to be almost cute.

But I have just enough pig iron in this head of mine that I reguse to take a basic law of physics on faith.

Surely, help Teems out there somewhere?

2

MichaelJohnBertrand writes:

> Now, I’ve put this question to many groups of people over the years since I first
> frustrated the hell out of a teacher with it in grade 8 science class.

Have any of these people been scientists? Why would you expect a non-scientist to be able to answer such a question?

3

In your example, both your boulders have equal potential energy, but not the rolling down a hill kind. That’s gravity, and that’s contained most in the planet underfoot. The boulders contain a bit of radioactivity and heat, like everything else around us does.

4

I cut a hole in the wall and shove the boulder out. If it gains speed, it had potential energy, if it doesn’t, then it didn’t.

5

Why is this harder for you to understand than speed or kinetic energy, all of which (like potential energy) depend crucially on “with respect to what reference point?”

If I am standing alongside you on a flatbed railcar travelling at 20 mph, and we both start walking at 3 mph., we will tie in reaching the opposite end of the car, but I will badly beat a guy alongside the track who starts walking at 3 mph. at the same time. If while we are standing still on the moving rail car, I stick my fist right in front of your nose, nothing will happen to you – my fist has no (relative) kinetic energy within the moving-railcar frame of reference. If I stick my fist outside the railcar and it hits the guy on the side of the track, it’s going to mess him up because in the off-the-train frame of reference, my fist has scads of kinetic energy to impart to his face.

6

You could weigh the two boulders with suitably sensitive scales. Since the boulder at the top of hill is farther from the Earth’s center of mass, it will weigh ever-so-slightly less.

7

you’re statement of the problem is wrong: the two rooms are not identical. One of them is on top of a hill. Take it a little farther–Imagine one of your rooms is on the moon.

The rooms look the same and smell the same, but they do not weigh the same. If you perform
an experiment to measure gravity in each room, you will see that the rock, the furniture in the room, and your own butt all weigh a little more in the room closer to the center of the
earth

8

Take two identical boulders, lift one up against gravity. That boulder will now have a slightly greater mass. A guy named Einstein came up with an equation that explains that.

9

Others have touched on it, but just to be clear: potential energy isn’t some innate measurable property of the boulder only in this scenario. What we describe as potential “energy” here is simply the potential for the boulder’s situation in a gravitational field to be harnessed into kinetic energy, through motion to a lower point in the gravitational field.

10

The thing is, potential energy is only defined up to an additive constant, which means effectively that its absolute value is arbitrary – you can perfectly well say that both of your boulders, in their respective systems, have potential energy 0.
However, once you put both of them in the same system – say, magically transporting the boulder on the hill to the same height directly above the other boulder’s house --, then you’ll have to set a zero somewhere, for instance (and convenience) at ground level. Thus, your as-of-now still magically hovering boulder does a Wile E. Coyote, realized that he’s suddenly got a lot of potential energy and promptly gets busy converting it into kinetic energy, by falling (and then crushing the other boulder’s house).
In other words, when talking about potential energy, only differences are important, absolute values are arbitrary.

11

Simple. Measure the difference in elevation.

12

All of science is actually just a model. It’s a useful model that explains and predicts our observations very well indeed. But it’s all just a human-made explanation for what we percieve and measure. There might be a better one. Aliens might have completely different, but equally valid models.

So yep, it’s “true” because that explains it.

13

Bolder on top hill. Begins to roll down the hill and gains speed. Now I think you will agree that bolder has kinetic energy. Where did the kinetic energy come from? Other than converting mass to energy, energy can not be created.

The amount of potential energy the rock at the top of the hill has depends on many factors. Is it only rolling because of gravity, or was it push started. How high is the hill? How steep is the hill? What is the coeficient of friction? How strait is the downward slope of the hill. What is the gravity? What is the mass of the rock?

Potential energy is the amount of energy yeilded when the state of an object is changed.

14

Both boulders have potential energy, since I assume the bottom of the hill is not at the centre of the earth.

How do we detect the difference in their ‘potential’? Well, if we could detect gravity waves, then we could tell that they were at different heights, but there’s a much simpler way: weigh the boulders.
The difference between the boulders’ heights and the earth’s radius is slight, so the difference in weights will be small, but it’s there.

Imagine that the high boulder rolls down the hill, and then you roll it back up again. One description is to say that the boulder had potential energy; some of that potential energy was converted to kinetic energy. The kinetic energy is converted to other forms, let’s say to heat via friction. Then you used chemical energy in your muscles, converted to kinetic energy, to ultimately give the boulder the amount of potential energy that it started with.

It’s useful, and we can actually crunch numbers (e.g. calculate a (very) rough estimate of how many calories you’ll burn pushing the boulder).

Alternatively, we could just say the boulder’s kinetic energy came from nowhere, which isn’t very useful.

If the conservation of energy law is wrong, then could we fashion a machine that could gain energy?

15

Snnipe I think your last sentence answers the OP’s question exactly.

16

Assuming your question is sincere, yes, you are misunderstanding the fundamentals of the problem and your “exactly the same” premise in your gedanken experiment is a false statement. As others have noted the elevations are different within their shared physical frame of reference, which puts the objects in very different states relative to each other. The “potential” energy of one object is potential (in this case) only as it exists RELATIVE to the other objects frame of reference.

Your primary mistake is that you are de-linking the relationship of the two objects in your example and treating them as discrete entities. They are not, and this relates to your empirical question of “how do you measure it”. You measure it as the difference between the two linked states. In this case a straightforward mass/acceleration, friction, slope etc. equation.

17

MichaelJohnBertrand, may I be the first to say that your question is very insightful.

A few posts above have dismissed the question by noting that the strength of Earth’s gravity varies with distance from the Earth. This issue can be eliminated from the thought experiment by making the gravitational field uniform (or at least sufficiently so that you can’t measure its non-uniformity.) An infinite sheet of mass should do nicely.

I suspect part of your worry stems from the following important fact: The total energy in a closed system can be set to any number you wish. However, that total won’t change.

If we are to treat your rooms as two closed systems, then they are indeed equivalent. (Your approach to this equivalence – namely, noting that there is no experiment you can perform to distinguish them – is a good one.) You can choose to set your energy “zero point” anywhere you like, so it doesn’t make any sense to say that one boulder has more or less potential energy than the other – they have whatever potential energy you assign them.

Changing configurations takes work, though. If in one of your rooms there is a table, and you lift the boulder onto the table, you had to use energy. We can calculate, based on knowledge of the forces at play, the amount of energy that is required to change the configuration from A (boulder on floor) to B (boulder on table). This calculation should match the amount of energy we actually spent.

Notice importantly that I didn’t say we could calculate the potential energy of configuration B. What we can do is calculate the potential energy different between configurations A and B. We can thus say things like “configuration B has more potential energy than configuration A,” but we can’t say “configuration B has 92 joules of potential energy.” If we want to say something like the latter, we must define what “zero joules of potential energy” means first. (This latter step is what is often left out in high school physics. Misleading teachers will happily calculate the potential energy of a rock in orbit, not noting that some zero point has been secretly chosen. In orbital dynamics, this zero point is often set such that the satellite has zero potential energy when it’s infinitely far from its host, but that’s arbitrary.)

Now, we can remove your rooms and have a boulder that is free to move down a hill. Again, based on the forces acting on the boulder, I can calculate how much energy will become available to me in bringing the boulder to the bottom of hill. If that is E joules, then I can say that the new configuration has E joules less potential energy. (Some other aspect of the system must have gained E joules of energy in the process: the motion of the boulder, or perhaps a battery if I used the decent to power a generator+battery.)

18

I don’t think that the “E” term in Einstein’s famous equation has anything to do with an object’s gravitational potential. My impression is that Einstein’s “E” term is about the inherent energy that mass possesses, and that energy can only be liberated by converting mass to energy. For purposes of the OP’s question, I think we can safely ignore that term and stick with E(g) = mg(h2 - h1) (gravitational potential) and E(k) = 1/2 mv^2 (kinetic energy).

19

Indeed. Especially since the potential energy thus stored doesn’t belong to the object itself (in this case, the boulder,) but rather to the Earth-boulder system as a whole.

20

And? What is your point? Sure, you put some energy into lifting the boulder. Some goes into the boulder, some goes into the Earth. But as far as comparing the two original boulders go, one of them has a greater mass.

The energy used in lifting the boulder goes somewhere. Law of Conservation of Energy. It is stored as mass in the lifted boulder (and the Earth, which we assume the OP is not interested in measuring the mass of).

This is not a subtle issue folks. Very, very simple.