# Kinetic energy and potential energy look very dissimilar

• burakumin
In summary, the conversation discusses the different natures of kinetic energy and potential energy and their sum, the total energy. The speaker questions the concept of total energy and its use in physics, particularly in regards to the frame dependence of kinetic energy and the lack of maximal or minimal values for potential energy. They also mention the differences in composition and behavior between kinetic and potential energy. The other participant suggests thinking of potential energy as proportional to height and kinetic energy as proportional to velocity. The speaker also discusses their disagreement with the idea that energy is just a tool invented by scientists and debates the epistemological view of science.
burakumin
The more I think about it the less clear the respective natures of kinetic energy and potential energy (and of their sum, the so-called total energy) become. The thing is I have the impression that once you try to go a bit further than the usual description of "scalar values assigned to systems and whose sum is conserved in isolation", the idea that kinetic energy and potential energy are different "shapes" for the same kind of "substance" starts to appear a bit ... sloppy (To be clear my reflections mainly concern Newtonian physics. Maybe Einsteinian relativity would shed a new light on this).

What makes me feel uncomfortable:
• As a scalar, kinetic energy is highly dependent on the frame of reference. Potential energy is not: it is only related on (relative) positions. (And if you start to consider some kind of space-time energy-momentum tensor for kinetic energy that is indeed frame-independent the equivalent for potential energy is not obvious).
• In any frame of reference kinetic energy has a natural minimum value: zero (immobility for that frame) whereas potential energy has neither a maximal nor a minimal value and remapping its zero has no physical impact.
• The behavior vis-a-vis composition of systems is very different. Kinetic energy is extensive (basically it's a measure). For potential energy it is far less clear: if you're composing two systems you will have to consider their respective internal potential energies plus any additional potential energy that may describe their mutual interaction. This difference means that in particular if you're given the kinetic energy of two disjoint systems (in the same frame) the global kinetic energy can be computed fairly directly and without any detail of their internal structure. On the contrary for potential energy you have no choice but understanding these internal details and what sort of interaction they may create. This makes kinetic energy very composable/decomposable and potential energy absolutely not.

So in the end I feel like the very concept of total energy is a sort of conceptual mess (as if we were adding apples and tables). I'm aware how this seems to be contradicted by the capital role of conservation of energy in every sub-domain of physics today. That's why I suspect you could imagine more sophisticated conceptual and mathematical frameworks (in particular frameworks that would not just consider scalar frame-dependent quantities) where these differences of behavior would be natural/obvious and that would explain how and why the concept of total energy makes sense. (If the answer is Lagrangian or Hamiltonian mechanics please explain how they can provide a better understanding of the composition issue above.) Is there anyone that can provide some hints?

pixel
burakumin said:
potential energy has neither a maximal nor a minimal value
It doesn't need to. It's the Change in Potential that counts and is what changes the Kinetic Energy in any particular frame. The Change in PE has a zero, when there is no change in co ordinates.

The energy is not a substance or any material object. It is a tool invented by scientist to help solve problems and help model the reality. Your complain is like saying that a hammer should not work because his head is made of metal and the handle from wood so it's a mess form a conceptual point of view. :)

russ_watters
Much of what you said is correct but you're making it sound more difficult than necessary.

Kinetic energy is totally frame dependent.

Potential energy is not frame dependent.

Total energy is conserved. (Don't forget that in the real world total energy can include heat, chemical, electrical, and nuclear energies in addition to kinetic and potential).

Can you more easily think of potential energy for a massive object in a gravity field as proportional to it's height above the ground, and it's kinetic energy as proportional to (the square) of its velocity?

A pendulum is a great example. At the top of its swing at each side, it has maximum potential energy but zero kinetic energy. At the bottom of the swing it has minimum potential energy and maximum kinetic energy. With two or more bodies, each can be at different heights. So at every moment during the pendulum swing, potential+kinetic=constant. In the long term, the pendulum heats the air and the axle, converts its potential+kinetic energy to heat energy and stops swinging.

sophiecentaur said:
It doesn't need to. It's the Change in Potential that counts and is what changes the Kinetic Energy in any particular frame. The Change in PE has a zero, when there is no change in co ordinates.

I don't see how this answers my questions. Furthermore you seem to miss that a zero kinetic energy in a given frame means immobility. So suggesting that only the change of Kinetic Energy is physically relevant seems incorrect to me. On the contrary it is indeed correct that only "the Change in Potential [...] counts". You do have the experimental possibility to check if the kinetic energy of a body is null or not in a given framework whereas having potential energy equal to zero is an pure convention. So again both forms of energy do not seem to work similarly.

nasu said:
The energy is not a substance or any material object.

I meant substance as a very broad concept with sense of "being", not necessarily material object.

nasu said:
It is a tool invented by scientist to help solve problems and help model the reality.

This is an epistemological position. I don't have to agree (and the fact is I don't). I do not subscribe to an empirical view where concept are only "invented pragmatic tools to describe reality". Now I also think this debate - while interesting - is off topic. Science provided successive or concurrent frameworks for very varied topics with different expressiveness and interpretative power. Whether these are just epistemological products of human societies or appropriate discourses on the reality itself is not my concern here.
anorlunda said:
Can you more easily think of potential energy for a massive object in a gravity field as proportional to it's height above the ground, and it's kinetic energy as proportional to (the square) of its velocity?

A pendulum is a great example. At the top of its swing at each side, it has maximum potential energy but zero kinetic energy. At the bottom of the swing it has minimum potential energy and maximum kinetic energy. With two or more bodies, each can be at different heights. So at every moment during the pendulum swing, potential+kinetic=constant. In the long term, the pendulum heats the air and the axle, converts its potential+kinetic energy to heat energy and stops swinging.

Example-based explanations are exactly not what I'm looking for. This kind of approach is painfully frustrating for me and hiding the kind of deeper understanding I'm looking for.

burakumin said:
Example-based explanations are exactly not what I'm looking for. This kind of approach is painfully frustrating for me and hiding the kind of deeper understanding I'm looking for.

What deeper? Do you mean quantum mechanics?

Energy is a property of objects and fields. It has no independent existence.

Edit: For something deeper, you may mean Noether's Theorum, where conservation of energy can be shown to be a consequence of time translation invariance. https://en.wikipedia.org/wiki/Noether's_theorem

nasu
burakumin said:
I meant substance as a very broad concept with sense of "being", not necessarily material object.

This is an epistemological position. I don't have to agree (and the fact is I don't). I do not subscribe to an empirical view where concept are only "invented pragmatic tools to describe reality".
Your agreement (or disagreement) does not change the nature of energy. You can redefine terms (like "substance") but all this has no effect on reality.
The status of energy is not different than that of other physical quantities even though people have tendency to confuse the objects with the physical quantities describing their properties.

russ_watters
nasu said:
The energy is not a substance or any material object. It is a tool invented by scientist to help solve problems and help model the reality. Your complain is like saying that a hammer should not work because his head is made of metal and the handle from wood so it's a mess form a conceptual point of view. :)
I would agree with this and point out that when you start looking at other types of energy (chemical, electromagnetic, nuclear), it gets even messier. That they are all related isn't a bug, it's a feature - and a cool one at that!

An more basic/self-evident: of course they are different - if they weren't, they wouldn't need different names!

nasu
burakumin said:
I don't see how this answers my questions.
What, exactly, are your questions? Your OP only asks if anyone can provide hints. Hints at what? If your real question is "can anyone relieve me of my discomfort?" then the answer is no.
This is an epistemological position. I don't have to agree (and the fact is I don't). I do not subscribe to an empirical view where concept are only "invented pragmatic tools to describe reality".
You do have to agree with the historical facts of how and why the concepts were invented. And you do have to accept that physicists aren't looking for a "deeper understanding" because they believe there is no point. You don't have to agree that there is no point -- but if you want to believe that, you should at least try to figure out what that point is, otherwise you are expending a lot of mental energy for an undefined reason.
Now I also think this debate - while interesting - is off topic.
Well, to the extent that the crux of your issue isn't necessarily what you think it is, it is on topic. We actually get this question/problem a whole lot. A lot of people have trouble accepting what energy is, as defined/used by physicists. If the topic here is about how physicists define and use it, that's been answered. If the topic is "assuage my discomfort", that doesn't have an answer.
Example-based explanations are exactly not what I'm looking for. This kind of approach is painfully frustrating for me and hiding the kind of deeper understanding I'm looking for.
What if there is nothing deeper? Why do you assume there must be? What are quarks made of? Nothing? Doesn't everything have to be made of something else?

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nasu
anorlunda said:
What deeper? Do you mean quantum mechanics?

Energy is a property of objects and fields. It has no independent existence.

Edit: For something deeper, you may mean Noether's Theorum, where conservation of energy can be shown to be a consequence of time translation invariance. https://en.wikipedia.org/wiki/Noether's_theorem

Noether's Theorem is indeed something I only have a superficial understanding (basically the vague idea that geometrical spacio-temporal invariances of a system imply the conservation of some related physical quantities) and I had already promised myself to investigate. I don't know if that can clarify the dissymetry i'd like to explain but that may be a interesting suggestion.

nasu said:
Your agreement (or disagreement) does not change the nature of energy. You can redefine terms (like "substance") but all this has no effect on reality.

I didn't redefine substance. This term "substance" comes from philosophy and I'm sorry if it caused some misunderstanding. I promise not to reuse it here but I think quibbling on its polysemy would be again offtopic.

russ_watters said:
What, exactly, are your questions? Your OP only asks if anyone can provide hints. Hints at what? If your real question is "can anyone relieve me of my discomfort?" then the answer is no.

My question is about the possible existence of different perspective (understand mathematical framework if you need something more concrete) that treat potential and kinetic energy as two different kind of object. For example analytical mechanics is a framework where the potential energy of a system is some scalar field on the manifold representing its configuration space whereas the kinetic energy is a a scalar field on the cotangent bundle: the phase space. This makes both concept structurally different. As the cotangent bundle contain special points (null vectors on each fiber) this could for example a hint about the dissymetry concerning a zero value whereas the configuration space has no priviledged point. But this framework as far as I understand it cannot provide but limited clarification on the other points I mentioned (almost nothing on how potential energy work for composition of system, and it's also frame dependent). This is the kind of conceptual clarification I'm looking for.

russ_watters said:
You do have to agree with the historical facts of how and why the concepts were invented. And you do have to accept that physicists aren't looking for a "deeper understanding" because they believe there is no point.

I don't want to discuss "what physicists beleive" because I consider this very sentence as quite reductive. As far as I know physics is not a cult, physicist are not a homogenous mass of people with a single perspective on every subject (including and in particular on their domain).

russ_watters said:
Well, to the extent that the crux of your issue isn't necessarily what you think it is, it is on topic.

Why looking down on me by pretending "we know better than yourself what is your issue ?"

Does that mean that now that I've made explicit that what I'm looking is in the end some mathematical structures/framework (that would account for the differences between potential and kinetic energy) nobody has a clue?

## 1. What is the difference between kinetic energy and potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state.

## 2. How do kinetic and potential energy relate to each other?

Kinetic energy can be converted into potential energy and vice versa. For example, when a ball is thrown in the air, it has kinetic energy due to its motion. As it reaches the highest point, its kinetic energy is converted into potential energy. As it falls back to the ground, the potential energy is converted back into kinetic energy.

## 3. How can we calculate kinetic and potential energy?

The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. The formula for potential energy depends on the type of potential energy, such as gravitational potential energy (PE = m * g * h) or elastic potential energy (PE = 1/2 * k * x^2), where g is the acceleration due to gravity, h is the height, k is the spring constant, and x is the displacement.

## 4. Why do kinetic and potential energy look dissimilar?

Kinetic energy and potential energy have different physical manifestations. Kinetic energy is associated with motion, while potential energy is associated with position. This is why they may look dissimilar, but they are both forms of energy and are interrelated.

## 5. Can kinetic energy and potential energy be converted into other forms of energy?

Yes, both kinetic and potential energy can be converted into other forms of energy. For example, kinetic energy can be converted into electrical energy in a generator, and potential energy can be converted into heat energy when an object falls to the ground. Energy can neither be created nor destroyed, but it can be transformed from one form to another.

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