# What is energy

Fine, if you don't like the book-keeping definition then energy is the capacity to do work =)

I think the main problem of trying to define energy is that energy is not quantized, and so we can't imagine a chewy nugget of energy. Personally, I could care less about the "real" definition of energy; problem sets are hard enough without dealing with philosophy.

mcah5 said:
I think the main problem of trying to define energy is that energy is not quantized,
Are you sure?

I'm pretty sure. You could argue that E=hf means energy is quantized, but f can be any value. And I'm pretty sure there is no lower bound on the frequency of light.

mcah5 said:
I'm pretty sure. You could argue that E=hf means energy is quantized, but f can be any value. And I'm pretty sure there is no lower bound on the frequency of light.
The assertion that energy is quantized is not meaningful. Before one can state that energy is quantized one must first specify what you're speaking of, i.e. energy of what??

If E = hf refers to the energy of a photon then it can't be assumed that E only comes in certain values. But if E refers to the energy state of an atom then E is quantized. In quantum mechanics there are systems which have a continuos energy spectrum and those which have a descrete energy spectrum. For example, the energy of a free particle is not quantized. The energy of a particle in a box is quantized.

Pete

mcah5 said:
Fine, if you don't like the book-keeping definition then energy is the capacity to do work =)
That holds true for potential energy and kinetic energy. So that can be taken as a definition of either. But that does not give you a definition of energy, only instances of energy. What am I talking about you ask? Suppose you ask what the definition of life is. If you give examples of life then you've not actually defined life. E.g. a human being is a life form. An ant is a life form. Yet with that knowledge I still don't know what a life form is.

Pete

Once again we don't seem to have found a satisfactory answer.

Remarkably, we seem to have come to the conclusion that energy isn't real. It only exists in our models and not in reality. How strange that the entirety of physics would depend on something that isn't real? Or am I mistaken?

It exist and it doesn't. That's the simplest one can put it. It exist because it takes up space. It doesn't exist because it's value is zero.

That's what I think anyway.

Telos said:
Remarkably, we seem to have come to the conclusion that energy isn't real.
WHAT??? Where did you get that impression???

Is the number 4 real? Is height real? Is life real? Don't hold that something is not real because you've been unable to define it.

Pete

Enos, that almost sounds like energy "is" space. After all, space tautologically takes up space and has an unwarpped equilibrium value we might as well call zero.

energy....something that seems to squeeze everyone's mind.....for to tell all the truth...man doesnt know too much abt out energy....we have defined energy as "energy is the ability to do work", this would be Force dotted wit distance. such that we get change in energy and if you notice its not energy itself that we are finding out...similarly in thermodynamics too...we try and calculate the change in internal energy but never rather find the total internal energy of the system.....it is thru such theards and sharing of knowledge will we be able to get in depth understanding of the world....

to add to this discusion could be the fact that energy is a relative quantity.....yes...the energy possed by a system is relative to the observer.....on close thought this idea will make itself pretty clear.....wit this idea in mind...jus hypothetically thinking.....can we define as the measure of diffrence between two systems......its jus an opinion...not based on any concerte theory....nevertheless worth a thought

Mk
coburg said:
energy....something that seems to squeeze everyone's mind.....for to tell all the truth...man doesnt know too much abt out energy
I think we do, it seems the mentors and advisors and moderators think they know what they are talking about, its just that not all who read the thread do.

i think energy is fancy world ,we use it apply what we have and what we use

What is energy? Easy. Maybe I have an oversimplified view as a physics undergraduate, but here is what I think.

First of all, it is important to treat each model of reality differently, since they are, well, different.

Classical mechanics:
$$E=\frac{1}{2}m\dot{x}^2$$

Relativistic classical mechanics:
First I define the energy-momentum 4-vector:
$$p=m\frac{dx}{d\tau}$$
and define energy as the zeroth component of that vector.

Non-relativistic quantum mechanics:
$$\hat{H}|\Psi\rangle=E|\Psi\rangle$$
where $|\Psi\rangle$ is an eigenvalue of the $\hat{H}$ operator.

energy is local time

Telos said:
Once again we don't seem to have found a satisfactory answer.

Remarkably, we seem to have come to the conclusion that energy isn't real. It only exists in our models and not in reality. How strange that the entirety of physics would depend on something that isn't real? Or am I mistaken?
Yes:!!) I agree with you in many sense
For example, in classical Mechanics we have the definitions
$$K.E.={1\over 2}mv^2$$
and $$P.E.= mgx$$ for energy

while $$p=mv$$ for momentum

We can simply think of the [Energy,Momentum] pair $$(E,p)$$ as a transformation rule of the [Displacement,velocity] pair $$(x,v)$$

That happens again in special relativity
[Energy,Momentum] pair is just another way of describing the universe by the [Displacement,Velocity] pair.

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I like to think of energy as the "stuff" that all matter is made of, ultimately. And this is not quite right.

I like to think of energy as the "stuff" that fields are made of. And this is not quite right.

But it helps me wrap my little brain around some concepts.

Energy is just a human concept devised to help with our analysis of the physical world.

Galileo
Homework Helper
I don't think the following has been suggested yet.

Every symmetry in physics leads to a conservation law. Energy is that conserved quantity of any closed physical system that results from the time-independence of physical laws.

I would suggest an analysis based on Torricelli equation, which has only to do with the way acceleration causes changes in the square of velocities. Since the concept of force is deeply related to the concept of acceleration, energy emerges.

Best Regards

DaTario

DaTario said:
I would suggest an analysis based on Torricelli equation, which has only to do with the way acceleration causes changes in the square of velocities. Since the concept of force is deeply related to the concept of acceleration, energy emerges.

Best Regards

DaTario