Is energy a fundamental physical quantity or a derived one?

[Mayan Fung]

I recall my memory when I was a high school student. I first learned about energy from Newton Mechanics. The only forms of energy involved are kinetic energy and potential energy. At that time, energy is more like a mathematical shortcut derived from F = ma rather than a concrete physical quantity. Conservation of (mechanical) energy is equivalent to Newton's Law of Motion. Intuitively, Newton's Law of Motion looks more "fundamental".

However, when I learned more about physics, it seems that energy is taking over the role. For example, the quantized picture of light, photon, is sometimes described as light carrying a packet of energy. Under the framework of general relativity, mass and energy can cause gravity. In different physical systems, we know that there is a tendency to transit into the lowest energy state.

I feel like that the concept of energy and some fundamental physical laws may be mathematically equivalent. The discussion on whether energy is a fundamental quantity may sound philosophical. But the concept of energy seems to behave homogeneously over different fields and frameworks, even more than the laws themselves (e.g. the well-known conflicts between GR and QM).

It would be great if some friends with a more comprehensive understanding of physics can give me some insights on my question!

 

[weirdoguy]

concept of energy and some fundamental physical laws may be mathematically equivalent

Physical laws usually involve several physical quantities and show connection between them within the domain of their applicability. Energy is only one quantity and, well, that's all. The only law that can be built using only energy is energy conservation. So I don't see how laws can be "mathematically equivalent to energy". Besides, energy is not the only observable that is sometimes quantized. I really don't understand why people tend to treat energy as being something super-special. Momentum feels depressed all the time, keep that in mind when you glorify energy!

 

[PeroK]

To say anything meaningful about physics you generally have to be precise. Although you can say some general things about energy, it's the more specific statements that are important.

Conservation of energy is a fundamental idea that applies across all physics (except cosmologically in an expanding universe)

Perhaps the most important equation in Special Relativity relates the energy, momentum and mass of a system:
$$E^2 = p^2c^2 + m^2c^4$$
And in QM the Hamiltonian, which is related to the energy of a system, is the generator of time evolution of the system, through the Schroedinger equation.

 

[A.T.]

But the concept of energy seems to behave homogeneously over different fields and frameworks

If by "more fundamental" you mean more generally applicable or having a wider range of application, then yes, energy is more general than force. Although the momentum conservation expressed in Newton's 3rd is also quite general.

 

[vanhees71]

The question is, what does a possible answer to this question help? The question, what's fundamental in physics, is very vague. You can answer it in an arbitrary way, and it's more an opinion of each physicist answering it than a scientific one.

My personal answer, given the historical development of physics until today, the most fundamental principles are symmetry principles. They provide the most simple way to organize the huge amount of knowledge physics has collected since it was discovered by Kepler, Galileo, and Newton about 400 years ago.

 

[Dale]

I feel like that the concept of energy and some fundamental physical laws may be mathematically equivalent.

What does fundamental mean in this context?

In the context of particles a fundamental particle is one which does not have interior structure. This can be tested experimentally using scattering experiments. Energy isn’t a particle so scattering doesn’t apply. So what does?

If it is a scientific concept then there should be an experiment which would answer the question of energy’s “fundamentalness”. Even if it is a philosophical question there should be some definition that we can apply to check.

So, what do you mean by “fundamental” in this question? What test or definition can be used to decide?

 

[russ_watters]

Gravitational potential energy can be converted to kinetic energy can be converted to electrical energy can be converted to heat energy, and all of these quantities are equivalent. Does that make energy "fundamental"? What do we gain by applying that label?

 

[sophiecentaur]

The thing about 'quantities' is that they are involved in the relationships between other quantities. Whilst we tend to talk of mass and length etc. as being fundamental, it's more because they are easy to define and measure using other quantities.

I feel that, whilst the so called basic quantities used in Dimensional Analysis make it a useful tool, are only there for convenience.

This is even trickier when you consider that the (probably) only quantity in the Universe that's really fundamental ( the speed of light), is described as ratios between other 'fundamental quantities' - e.g. distance and time or Energy and Mass. So which way round is it? (Those danged labels again.)

 

[Mayan Fung]

Thank you all for the inspiring discussion.

Some question about the meaning of "fundamental". To be honest, I also can't give a precise answer. I guess it may like what @sophiecentaur said, something that is easy to define and measure using other quantities. This is also why I said this question may sound philosophical which may not really add anything to the science.

What I mean by mathematically equivalent can be illustrated by some examples in classical mechanics. An equation of motion relating velocities, acceleration and displacement:
$$v^2 = v_0^2 + 2as$$
can be rewritten as:
$$\frac{1}{2}mv^2 - \frac{1}{2}mv_0^2 = mas = Fs$$

All in all, I agree that this discussion may not be very meaningful in the sense that it didn't add new things to physics. I remember, if correctly, when I learned EM with Griffiths' book, in the chapter about electric field, he mentioned that electric field was first treated as a mathematical tool. But later on, electric field became a fundamental physical quantity. This piece of memory suddenly came to my mind a few days ago so I revisited the question again.

I am glad to learn about more ideas on how to comprehension these physical concepts. Thank you all!

 

[Dale]

Some question about the meaning of "fundamental". To be honest, I also can't give a precise answer. I guess it may like what @sophiecentaur said, something that is easy to define and measure using other quantities. This is also why I said this question may sound philosophical which may not really add anything to the science

If you cannot clearly explain what you mean by fundamental then the discussion is not even philosophical. Philosophers go to great lengths to be clear in what they mean by a word.

Please spend some time thinking in detail about what you mean by “fundamental” in the context of physical quantities like energy. Once you can express your meaning clearly, send me a PM and I can reopen the thread.