"energy"：ἐνέργεια,4。
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Take kinetic energy, it''s the movement of something - now does that actually exist as a ''substance'' for lack of a word, or is it just when objects move, so we''re describing what they''re doing?
Same with potential energy - does it exist or is it just a description of what could happen to an object?
Could anyone tell me what energy really is? I searched for it, and some people said that energy doesn''t exist physically and it is not fundamental, but it is a relationship between other fundamental things, and there is not energy by itself, so it should be related to something else.
"What energy is" is a philosophical question. It turns out its impossible for science to talk about what "reality" is like, other than to say that science forms models which have an "energy" term in them and they seem to be pretty good predictors. If you''re interested in that line of reasoning, I highly recommend looking into the philosophy of science.
However, we can find energy as a meaningful thing in our models. One of the foremost ways of modeling our reality for scientific purposes is in the idea of "action." The idea of action is formed from this question:
This is a very abstract concept, and it''s okay if it doesn''t make 100% sense when you first work with it. But what makes it important was that we came to this concept of Action without invoking forces or energy, or any of those other terms. We just pointed out that the paths objects take tend to be the one which minimizes action across the entire path. Or, more generally, we determined that you could find a Lagrangian for which the "correct" path is always found by solving this optimization problem that minimizes the action. Actually figuring out a Lagrangian function which does this is another matter, what matters is that one exists!
Now should you accept this declaration that there always exists a Lagrangian function such that the correct path of objects is always found by minimizing the action? Perhaps not. Don''t take my word for it. Science is an empirical art, not a purely mathematical art. It''s the observation of scientists over the centuries that say "We can always describe the motion of particles this way!"
Now once you have this, we then can invoke one of the most powerful mathematical formalisms in all of physics: Nother''s Theorem. This theorem shows that if you have a system which is described by this optimization problem, this minimization of action, and it has a continuous symmetry, then there is some conserved value. This is neat because it takes some very abstract mathematical concepts, like continuous symmetries and action, and ties it directly to the idea of conserved values.
This continuous time symmetry must have an associated conserved value, by Nother''s theorem. We call that conserved value "energy." And if you actually go through all the fancy Calculus of Variations, you find that the thing that we conserve when we conserve energy is precisely what we told you was "energy" all along.
Well, maybe it''s not important to know what energy is, as much as it is to know what energy can do. The typical definition of energy is that energy is the capacity to do work. If something has energy, it has the capacity to move things, lift things, heat things, and so forth. The other thing that is important to know is that energy can never be "created" or "destroyed". In other words, total energy is always conserved. It simply morphs into different forms as it is transferred between things in the form of either heat or work.
I think term energy has slightly different meanings in different branches of physics. I prefer to think of it as the quantity that is conserved due to time-invariance of the equations of motion, i.e. my notion of energy is related to the Largangian mechanics (https://en.wikipedia /wiki/Lagrangian_mechanics), and energy is basically the Hamiltonian.
Energy doesn''t exist itself, it''s just a mathematical representation to make a relationship between the capacity of several objects to develop work. I can make an analogy. Energy is like money, doesn''t have value itself, it only represents the value of things (work, savings, estates,)
The simplistic undergrad explanation aside, I''ve never really understood what energy really is. I''ve been told that it''s something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?
Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I''ve learned from thermodynamics where it goes, but where does it come from?
I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can''t grasp what it is. Maybe it is because I lack the mathematical understanding that I can''t grasp the subtle things the universe is doing. Still, I want to understand what it is doing. How do I get to the point of understanding what it''s doing?
(Note: What prompted me to ask this was this answer. I''m afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.)
Energy is any quantity - a number with the appropriate units (in the SI system, Joules) - that is conserved as the result of the fact that the laws of physics don''t depend on the time when phenomena occur, i.e. as a consequence of the time-translational symmetry. This definition, linked to Emmy Noether''s fundamental theorem, is the most universal among the accurate definitions of the concept of energy.
What is the "something"? One can say that it is a number with units, a dimensionful quantity. I can''t tell you that energy is a potato or another material object because it is not (although, when stored in the gasoline or any "fixed" material, the amount of energy is proportional to the amount of the material). However, when I define something as a number, it is actually a much more accurate and rigorous definition than any definition that would include potatoes. Numbers are much more well-defined and rigorous than potatoes which is why all of physics is based on mathematics and not on cooking of potatoes.
Centuries ago, before people appreciated the fundamental role of maths in physics, they believed e.g. that the heat - a form of energy - was a material called the phlogiston. But, a long long time ago experiments were done to prove that such a picture was invalid. Einstein''s $E=mc^2$ partly revived the idea - energy is equivalent to mass - but even the mass in this formula has to be viewed as a number rather than something that is made out of pieces that can be "touched".
Energy has many forms - terms contributing to the total energy - that are more "concrete" than the concept of energy itself. But the very strength of the concept of energy is that it is universal and not concrete: one may convert energy from one form to another. This multiplicity of forms doesn''t make the concept of energy ill-defined in any sense.
Because of energy''s relationship with time above, the abstract definition of energy - the Hamiltonian - is a concept that knows all about the evolution of the physical system in time (any physical system). This fact is particularly obvious in the case of quantum mechanics where the Hamiltonian enters the Schrödinger or Heisenberg equations of motion, being put equal to a time-derivative of the state (or operators).
The total energy is conserved but it is useful because despite the conservation of the total number, the energy can have many forms, depending on the context. Energy is useful and allows us to say something about the final state from the initial state even without solving the exact problem how the system looks at any moment in between.
Work is just a process in which energy is transformed from one form (e.g. energy stored in sugars and fats in muscles) to another form (furniture''s potential energy when it''s being brought to the 8th floor on the staircase). That''s when "work" is meant as a qualitative concept. When it''s a quantitative concept, it''s the amount of energy that was transformed from one form to another; in practical applications, we usually mean that it was transformed from muscles or the electrical grid or a battery or another "storage" to a form of energy that is "useful" - but of course, these labels of being "useful" are not a part of physics, they are a part of the engineering or applications (our subjective appraisals).
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