Gravitational potential energy is easy to measure; it's just mass * height * force of gravity. So a 1kg ball 1m above the surface of the earth has 1kg * 1m * 9.8m/s^2 = 9.8J of potential energy. This is equal to the kinetic energy the ball will have right before it hits the ground.
You can calculate a number for it... but does it actually physically exist? Can you physically measure it with a device, if you eg don't know the altitude?
Also, isn't the potential energy always relative to something? An object has a potential energy X relative to the Earth, and a potential energy of Y relative to the Moon, and a potential energy of Z relative to the Sun. The calculation would always be in relation to one of them, or anything else, really. How much potential energy is there at a certain point in space?
It still just sounds to me like potential energy is an abstraction, not a physical entity that exists in physical space. Not unlike eg. speed. "Speed" is not something that somehow exists floating around there, but it's a notion we use to describe how an object behaves in relation to another object.
Thus, and kind of back to the original point: If "potential energy" really is just a notion, not a physical entity, then how can it be "converted to heat", given that heat is a form of energy that physically exists?
(On a meta-level: Why are things like "potential energy" taught as if they were conceptually simple, easy-to-grasp, self-evident things? They are far from easy to understand. They are so abstract, when you really think about them.)
Gravitational potential energy is easy to measure; it's just mass * height * force of gravity. So a 1kg ball 1m above the surface of the earth has 1kg * 1m * 9.8m/s^2 = 9.8J of potential energy. This is equal to the kinetic energy the ball will have right before it hits the ground.
You can calculate a number for it... but does it actually physically exist? Can you physically measure it with a device, if you eg don't know the altitude?
You can't speak about the energy of an object without talking in respect to the system the object is in. Even heat is, at a fundamental level, the motion of particles; if you isolate a particle from everything else then it has no heat. Energy is always the energy of a system. Thus if you want to speak of the gravitational potential energy of an object, you implicitly know the altitude of the object; it doesn't have any meaning otherwise.
(On a meta-level: Why are things like "potential energy" taught as if they were conceptually simple, easy-to-grasp, self-evident things? They are far from easy to understand. They are so abstract, when you really think about them.)
Potential energy is extremely helpful for calculating energy conversions, which is why it's taught. We teach plenty of highly abstract concepts to our students -- not just stuff like energy but also algebra, atoms, economics, basic game theory, justice, etc. We don't always expect them to fully understand these concepts, but we do expect them to be able to make use of them with a reasonable degree of proficiency.
Pyrel - an open-source rewrite of the Angband roguelike game in Python.
Energy in a physical sense is absolutely not the kind of energy we usually talk about. "There's energy coming out of that wall socket", "This light bulb uses 50 watts of energy".. nope.
Energy is a physical quantity defined in such a way that the sum of energy in a closed system cannot change. So you cannot "use" energy, and it's not quite like the thing your intuition tells you it is.
You can convert energy from one form into another. Ignite some black powder to convert it's chemical energy into kinetic energy in a bullet. The bullet disperses its kinetic energy into more kinetic energy (air turbulences) and heat as it flies along, slowing down.
Now shoot the bullet straight up in a vacuum. Its kinetic energy is reduced to zero by gravity. No new forms of energy (turbulences, heat) were created, but the total energy in the system cannot have changed. So where did it go?
The solution is to examine "potential energy". It is defined in such a way that regular energy can be converted into potential energy (raising the bullet into a higher position) and back (let it drop) without violating conservation of energy.
So no, it does not actually "exist". It is not a physical property of an object, there is no potential-energy-o-meter. Potential energy is a derived property of a system. Examine a closed system and you can calculate (but not "measure") the amount of potential energy in it.
Warp wrote:
Thus, and kind of back to the original point: If "potential energy" really is just a notion, not a physical entity, then how can it be "converted to heat", given that heat is a form of energy that physically exists?
Potential energy is created when you apply work against a constant force, like lifting a weight, or pulling apart two magnets.
Put some gas into a flexible container. Stretch the container, the gas expands and cools off. Let it go, the container shrinks back until pressures in- and outside the container have equalized, the gas gets hotter.
Derakon wrote:
So a 1kg ball 1m above the surface of the earth has 1kg * 1m * 9.8m/s^2 = 9.8J of potential energy. This is equal to the kinetic energy the ball will have right before it hits the ground.
It's not quite that simple.
Dig a hole in the floor below the ball. According to your formula, now the ball has more potential energy. Where'd that come from?
The ball has potential energy to get as far as the force he's resisting (gravity) can take him, straight to the center of the earth. Letting it drop to the floor only converts a part of its potential energy, but a lot of it remains.
If you're only interested in dropping it to the floor, your formula will yield a useful answer, but it's not the total potential energy the ball has.
First of all, I'd like to express that I have no idea what I'm talking about. Alright.
My extremely naive notion of what potential energy is is that it's energy that had to have been put into a thing for it to exist in its present form. At any point in time, the whole object/body could disintegrate (usually by interacting with much more disorderly things) releasing all of that energy again (usually as warmth, which I naively think of as just "random" chaotic movement of particles). So within my naive logic, potential energy is visible by order: a fixed position relative to something, a fixed shape, a mass; rather than chaos: constant change, only measurable by its impact on things that aren't in chaos.
Pretty sure that's at least partially wrong though, if not completely, but I'll state it as naively as that. I feel like almost any interpretation of physical equations should be at least partially wrong anyway.
How to measure it then, it depends. By converting it all into warmth maybe, splitting every atom if you want to go to extremes. As you are familiar with quantum physics, the idea that measuring something might have a radical impact on the thing you are measuring might not be foreign. According to my naive logic, to measure the potential energy, you'd have to convert it all into other forms of energy.
Why can potential energy exist at all, I think of it as a system being temporarily stuck in a local minimum of energy efficiency. To move it into a truly more efficient state, it has to be forced out of that minimum first.
Feel free to tell me why I'm completely wrong, and why I shouldn't think of potential energy as that. I honestly think that even concepts such as "mass" are just necessary (for us) analogies and abstractions and don't truly exist either, so all our interpretations of the world would have to be fundamentally flawed at some level anyway.
As long as you talk about concepts within a certain framework, they all make perfect sense, what they truly mean is often beyond our grasp. I don't even know what 1+1=2 truly means outside of mathematics. It seems to presuppose that something can be quantified. Can anything be truly quantified, or is it just a way of thinking about things, a helpful abstraction? I don't know. Gödel's incompleteness theorems are why I see science as a tool rather than as truth.
Potential Energy is not an abstract concept. It's the energy that can be released by entropy. A basketball that's 1m above the Earth has less entropy than a basketball sitting on the Earth that has released the rest of the energy in the form of heat and sound. The measurement of the difference of this entropy is the potential energy of the system.
Other things that have potential energy: a compressed gas cylinder, a radioactive sample, a loaded spring, etc. They all represent low entropy states.
This is a simplification, of course. But I just wanted to fight the notion that potential energy only makes sense when you relate it to something else, and that it's only an abstract concept.
Build a man a fire, warm him for a day,
Set a man on fire, warm him for the rest of his life.
Potential Energy is not an abstract concept.
...
This is a simplification, of course. But I just wanted to fight the notion that potential energy only makes sense when you relate it to something else, and that it's only an abstract concept.
It isn't just an abstract concept? How can that be shown? Any theorem must be based on axioms, which can't be proven from within the system. How can any knowledge at all ever be anything more than an abstraction? You are saying that it truly exists, right? Not that it truly exists within the framework of physics. I wonder how that can be done.
Potential Energy is not an abstract concept.
...
This is a simplification, of course. But I just wanted to fight the notion that potential energy only makes sense when you relate it to something else, and that it's only an abstract concept.
It isn't just an abstract concept? How can that be shown? Any theorem must be based on axioms, which can't be proven from within the system. How can any knowledge at all ever be anything more than an abstraction? You are saying that it truly exists, right? Not that it truly exists within the framework of physics. I wonder how that can be done.
Oh wow, really? A pedantic absurdist?
Build a man a fire, warm him for a day,
Set a man on fire, warm him for the rest of his life.
Now shoot the bullet straight up in a vacuum. Its kinetic energy is reduced to zero by gravity. No new forms of energy (turbulences, heat) were created, but the total energy in the system cannot have changed. So where did it go?
The solution is to examine "potential energy". It is defined in such a way that regular energy can be converted into potential energy (raising the bullet into a higher position) and back (let it drop) without violating conservation of energy.
Do I understand correctly that, while that's how it's modeled in classical physics, in the context of general relativity there's only inertial motion happening to the bullet all the way through, ie. no forces and therefore no acceleration anywhere, and therefore it's just likewise kinetic energy all the way through?
(But if that's so, then it raises the question that if at the height of its apparent parabola it lands on a surface, where did the kinetic energy disappear?)
Energy in a physical sense is absolutely not the kind of energy we usually talk about. "There's energy coming out of that wall socket", "This light bulb uses 50 watts of energy".. nope.
Energy is a physical quantity defined in such a way that the sum of energy in a closed system cannot change. So you cannot "use" energy, and it's not quite like the thing your intuition tells you it is.
Your reasoning is flawed. A building on Earth, or an electrical cord, is not a closed system, and it's perfectly possible to use up a concentration of energy existing within that system. When you turn on your light bulb there is real energy coming out of your wall socket, through the cord and into the light bulb, which then disperses out into the room and eventually into the surrounding air and soil. As long as the 50 W light bulb is on, the amount of (useful) energy contained within your house increases by 50 J each second, minus any leakage through walls and windows.
Furthermore, potential energy is as real as other forms of energy and could in theory be measured with very high precision instruments. Gravitational energy is always negative. At the center of the earth, it is at a local minimum, and approaches zero in outer space. Usually, the absolute value of a system's energy does not matter, and one is primarily concerned about energy gradients, which are much more easily observed. Therefore, on the surface, it looks like an abstract mathematical tool where in reality that is far from the case.
Pedantic, I'll take. I was pedantic about it because your post came directly after mine and contradicted it. I am sorry about that.
I wonder what's absurd about what I've said though. Newtonian physics are an abstraction that works very well, testable, makes thousands of predictions. Some people take that to mean that anything it claims is truly true, not just within the system. It's suddenly self-evident, right? That way of thinking is what's absurd to me. To me, it just means Newtonian physics is a very powerful tool, an abstraction that works. In case it ever doesn't work for something, no problem, we'll work out something that does. (And we did.)
Do closed systems truly exist? Besides the point, we can just assume they do, and create a powerful tool. Make assumptions, create a system within which we can make predictions. How, if it made those assumptions, is it then absurd to question whether it's truly true? Shouldn't that be the default stance? Of course, it's annoying if somebody brings that up in discussions all the time, but I feel like it was directly relevant to Warp's question.
Not to offend you, but I really sometimes feel like science is some people's religion. Saying the number 1 truly exists outside of mathematics is as absurd to me as saying potential energy truly exists outside of physics, which I took was what you meant to say. You really said it wasn't just an abstract concept. Anyway, I'm starting to derail. I'll stop posting again. Sorry if there have been any misunderstandings.
A basketball that's 1m above the Earth has less entropy than a basketball sitting on the Earth that has released the rest of the energy in the form of heat and sound. The measurement of the difference of this entropy is the potential energy of the system.
No, entropy is something entirely different. It is a logarithmic measure of the number of microstates available for a thermodynamic system. Entropy is measured in joules per kelvin. It has nothing to do with potential energy, which is strictly defined by the fields and valid even at microscopic scales.
For reference, HHS is absolutely correct -- potential energy is as real as kinetic energy, or chemical energy, or whatever other form of energy you want. Except for New Age bullshit "energy", but that is not relevant here.
But gist of the issue is that "potential energy" is a highly misleading name: there is a load of things that are very real that get assigned that name, such as electromagnetic potential energy, gravitational potential energy, and so on. These are only "potential" because we misleadingly call them that -- they are very real interactions of the objects we are studying with well defined and measurable fields. Where does the "kinetic energy" go when you climb up a gravitational field? Into the gravitational field. Where does the kinetic energy come from when you fall back? From the field. Where is the elastic potential energy stored in a spring? In the electromagnetic interaction between the atoms of the spring. And so on. The energy is real, and it is all there; it is so real, in fact, that general relativity says right out of the box that it generates gravitational fields. I can elaborate on that, if so desired, but I won't do it now.
For reference, HHS is absolutely correct -- potential energy is as real as kinetic energy, or chemical energy, or whatever other form of energy you want. Except for New Age bullshit "energy", but that is not relevant here.
But gist of the issue is that "potential energy" is a highly misleading name: there is a load of things that are very real that get assigned that name, such as electromagnetic potential energy, gravitational potential energy, and so on. These are only "potential" because we misleadingly call them that -- they are very real interactions of the objects we are studying with well defined and measurable fields. Where does the "kinetic energy" go when you climb up a gravitational field? Into the gravitational field. Where does the kinetic energy come from when you fall back? From the field. Where is the elastic potential energy stored in a spring? In the electromagnetic interaction between the atoms of the spring. And so on. The energy is real, and it is all there; it is so real, in fact, that general relativity says right out of the box that it generates gravitational fields. I can elaborate on that, if so desired, but I won't do it now.
I agree with marzojr, and he certainly has proven himself many times in this thread to be quite the physicist.
But maybe it isn't necessary to invoke gravitational fields or electromagnetic interactions...
I once asked my research advisor if virtual photons are "real". By that I meant that since they are a perturbative expansion on the action integral, can we truly imagine little unseen packets of light shooting back and forth between two particles? (Don't worry if you don't know what a virtual photon is. It's not central to my argument.) His response (after much badgering) was, "Is force real?" I realized that technically it isn't real because there is no quantum mechanical analogue to force. He said, "Yes, but does that stop you from using it?"
He then quoted a famous physicist (probably Steven Weinberg) as saying, "It's real if it's useful."
So that's my answer to this question. Potential energy is a useful concept, therefore it is real.
Gravity isn't a force, as far as we know.
Light passing through a transparent solid causes it to change direction. This is caused by a really complex quantum-mechanical effect (it has something to do with the light taking all possible paths and interacting with the particles of the object, or something along those lines), but I don't know if it could be said to be caused by a force since I know next to nothing about QM. (I suppose interaction with other particles could be considered a force?)
Gravity isn't a force, as far as we know.
Light passing through a transparent solid causes it to change direction. This is caused by a really complex quantum-mechanical effect (it has something to do with the light taking all possible paths and interacting with the particles of the object, or something along those lines), but I don't know if it could be said to be caused by a force since I know next to nothing about QM. (I suppose interaction with other particles could be considered a force?)
Warp is close to the crux of the issue. Applying classical notions like force to quantum mechanical and relativistic (decidedly non-classical) entities like photons is a stretch at best.
Do photons interact with "stuff"? Yes, they definitely do. So forces act on photons? Maybe. Photons can be deflected in many different ways. If your definition of a force is something that causes a change in an object's velocity, then sure, forces act on photons. But photons fail to follow Newton's second law, F=ma, which is the most useful thing we can do with forces. Calling a force something that changes an object's velocity is a weaker notion than F=ma (or F=dp/dt, the more powerful version of the second law). The whole question is kind of built on a fallacious notion of forces.
It reminds me of a chapter from Surely You're Joking, Mr. Feynman, in which an acquaintance asked him, "Is electricity fire?" Of course, Feynman immediately knew that the answer is "no", but simply couldn't convey it to this man. The man had a notion that fire something that burns. "Logically", he scaled this down to something that burns just a little bit in a small area, which seems to be what happens when you rub your socks on a carpet and then touch a doorknob. All he was doing, however, was extrapolating something intuitive and familiar to him into a field in which it isn't applicable.
I think the same thing is going on with the question at hand. A lot of us (especially those in introductory physics classes) are familiar with forces, how you can feel and measure them, and how they affect objects. However, we struggle with notions of photons, which travel at a constant speed and appear to have wave-like properties. But wouldn't it be neat if we could connect these two ideas? Forces on photons?
Nope. Can't be done.
Aren't photons the force-carrying particles of the electromagnetic force anyway, and thus a force themselves?
I've never understood hawkins when he talked about "virtual" photons (that are supposed to carry the force) and "real" photons (that somehow don't?).
Aren't photons the force-carrying particles of the electromagnetic force anyway, and thus a force themselves?
I've never understood hawkins when he talked about "virtual" photons (that are supposed to carry the force) and "real" photons (that somehow don't?).
Photons do mediate the electromagnetic force. It's an abuse of language, however, to say that photons are the electromagnetic force. As for real versus virtual photons, both can exert a "force" (better put, both can deliver an impulse). There is no definite distinction between real and virtual photons, although we can make a few arbitrary distinctions:
• "Real" photons are observable, virtual ones are not. This criterion is the closest we can come to a definite distinction between the two, since it's what we mean (in practical terms) when we say a photon is real/virtual. If you observed its effects directly, it's real. If neither you nor anyone else observed it directly, it was virtual.
• Real photons last a (relatively) long time, virtual ones pop in and out of existence quickly. That's why we are able to observe them-- they last long enough to reach our eyes.
• Real photons travel (relatively) long distances, virtual photons travel short distances before disappearing. This can be deduced by using the speed of light and the previous point.
• Real photons travel at speed c=3*10^8 m/s, virtual photons have a nonzero amplitude to travel faster or slower than that. Over long distances/times, the amplitudes for traveling faster or slower start to "cancel out", blurring the distinction between the virtual and real photons. (Don't think of this as the photon traveling "sometimes faster, sometimes slower". The cancellation is more fundamental than that.)
• Real photons satisfy E=pc, where E is the energy, p is the momentum (magnitude), and c is the speed of light. Virtual particles can have more or less energy than this.
I'm sure there are other ways to distinguish between the two, but that's all I know.
Fun fact: Albert Einstein is best known for the theory of relativity. Much less known is that the concept of photons was also first invented by him. In fact, it was Einstein who first introduced the whole concept of quanta (and his Nobel prize was related to that. For some reason he was never awarded a Nobel for his theory of relativity, even though it's one of the most fundamental theories of physics today.)
Fun fact: Albert Einstein is best known for the theory of relativity. Much less known is that the concept of photons was also first invented by him. In fact, it was Einstein who first introduced the whole concept of quanta (and his Nobel prize was related to that. For some reason he was never awarded a Nobel for his theory of relativity, even though it's one of the most fundamental theories of physics today.)
To continue the story, for much of the rest of his life, he campaigned against quantum mechanics. This is where the apocryphal (but accurate in spirit) quote, "God does not play dice with the universe," came from. What I think is even funnier is that every effort he made to poke holes in quantum mechanics just illuminated new facets of the theory. He may be second only to Niels Bohr in importance to quantum mechanics' formulation, despite his distaste (or outright disgust) with the theory.
