# Is Energy Fundamental or Derived?

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• LAP3141
So even if energy is not itself observable, we can still observe it indirectly by measuring its effects.Can we observe energy? It seems that energy is not observable but is always inferred from the action of some force.Energy is not directly observable, but we can observe its effects.f

#### LAP3141

In the beginning we had Newton's Laws which introduced force as the fundamental entity of nature. Energy was understood as a derived concept, i.e. Energy = force x distance.

Later, however, there arose the formulations of LaGrange and Hamilton where energy is the fundamental entity, i.e. Force = -dV/dx, etc., where V is energy.

But putting all the mathematics aside, what is the fundamental entity? Is it force or energy?

They are all just our models for predicting reality. Ultimately, if two models give the same result, then the only grounds to choose between them is if one is simpler or more elegant than the other. The only thing real is the universe itself.

Formulating physics in terms of equations of motion is a time-centric view. Both force and energy are concepts which are frame-dependent. On the other hand, the stress-energy tensor is frame independent and therefore somewhat more fundamental. It combines the information of the energy and force.

• Delta2
But putting all the mathematics aside, what is the fundamental entity? Is it force or energy?
You cannot put the math aside, which is fundamental depends on which mathematical approach you want to use.

• Shakir
I appreciate the answer about the frame dependence of force and energy and I also understand that mathematics is central to any description of reality.

But perhaps "fundamental" is the wrong term to use. A better term would be "observable." We do not require mathematics to observe and observation should be the basis to ascribe what is fundamental (at least within a given reference frame).

Can we observe energy? It seems that energy is not observable but is always inferred from the action of some force.

Can we observe energy?
There is a little box on the side of my house that claims to observe the electrical energy we use, and it is sufficiently believable that I have agreed to pay the power company based on the value displayed on that box.

I don't think that "fundamentalness" is a feature of the universe, just a feature of our models. If it were a feature of the universe then we could devise a fundamentalnessometer.

• Delta2, Vanadium 50, Asymptotic and 2 others
Many classical mechanics problems become a lot less unpleasant to solve when done with energy-based methods than with force-based ones. A simple example of that kind of a problem is in the image. From this it may be said that an Occam razor-type argument could be applied in the favor of the Lagrangian and Hamiltonian methods.

The theory of quantum mechanics would be really difficult to form using forces as the basic quantities instead of energies.

#### Attachments

• anorlunda and Dale
little box on the side of my house that claims to observe the electrical energy we use
Not really. That box is essentially measuring the current and voltage (separately) and integrating the product. So it is analogous to measuring the force and the distance, and calculating the energy, Quibble? maybe, but this is the essence of the OP question.

Not really. That box is essentially measuring the current and voltage (separately) and integrating the product. So it is analogous to measuring the force and the distance, and calculating the energy, Quibble? maybe, but this is the essence of the OP question.
Neither current nor voltage is force. So we are getting a measurement of energy without a measurement of force. If anything, voltage is more closely related to energy than it is to force, although it is not either.

I don't think that "fundamentalness" is a feature of the universe, just a feature of our models. If it were a feature of the universe then we could devise a fundamentalnessometer.

I don't want to become bogged down in a discussion on the philosophy of science which could lead anywhere without providing much benefit.

Your energy meter is actually measuring motion. The "internal" energy of a substance is again only a statistically averaged motion.

My original question was not so much about what is fundamental but more about what is not fundamental. I could be wrong, but I would tend to exclude energy.

Some would argue that energy is fundamental to quantum mechanics, but can we not also look upon QM energy as just an interpretation based on equations that only serendipitously work?

Maybe this topic should progress no further.

I appreciate the answer about the frame dependence of force and energy and I also understand that mathematics is central to any description of reality.

But perhaps "fundamental" is the wrong term to use. A better term would be "observable." We do not require mathematics to observe and observation should be the basis to ascribe what is fundamental (at least within a given reference frame).

Can we observe energy? It seems that energy is not observable but is always inferred from the action of some force.

Even that is the wrong question to ask.

Consider this: we believe that our universe and the properties of it depends on a set of symmetry principles. The fact that our universe (at least at the classical level) appears to have translational, rotational, temporal etc. symmetry is something that is the most "fundamental" property of our universe. You can't exactly "derive" those (we may add charge symmetry to that as well).

Via Noether theorem, each of those symmetry principle has a corresponding conserved quantity. The time symmetric principle results in the conserved energy laws (or mass+energy). So conservation of energy here is as "fundamental" as conservation of momentum, conservation of angular momentum, etc... because it came from a very fundamental symmetry principle.

Now, if this is what you mean by "fundamental" (and to many people, it is), then it is fundamental. If not, then you need to define what you consider ALREADY to be fundamental to illustrate your definition.

Zz.

• plasmon_shmasmon and Dale
Your energy meter is actually measuring motion.
I disagree, but regardless, motion is not force. You can have both force without motion and motion without force. So that doesn’t lend any particular privilege to force over energy.

can we not also look upon QM energy as just an interpretation based on equations that only serendipitously work?
If it works then it works. Science cannot really say more than that.

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I don't want to become bogged down in a discussion on the philosophy of science which could lead anywhere without providing much benefit.
Unfortunately, without a useful and consistent definition of "fundamental" (a word that isn't really very used/useful to scientists), that's exactly what your question is.

• The question seems to teeter ever closer to the reviled "... yes, yes, but what is really happening?" questions.

• anorlunda
Energy is a property of particles and fields. Force times distance is only one of many ways to calculate energy; it is not a definition. We have mechanical, heat, electrical, chemical, nuclear and other forms of energy. Much of engineering is dedicated to transforming one kind of energy to another or moving energy from one place to another.

If you are fond of the word fundamental in science, then consider three universal constants.
• c: the speed of light in a vacuum.
• h: Plank's constant
• G: Newton's constant of gravitation
They can be said to be fundamental because they apply to all things in all circumstances, not just sometime. But as others already said, fundamental is not a strictly defined, so you can choose any meaning you want.

In systems of measurement, sometimes fundamental quantities is another name for base quantities. Derived quantities are defined in terms of base quantities.

In my opinion in quantum mechanics the energy is not fundamental but the wave function. But as @Dale said, fundamentalness is a feature of our models and not of the universe. In the modelling according to Netwonian Mechanics force is fundamental, in Lagrangian mechanics the Lagrangian or the Energy are fundamental, in the quantum mechanical modeling, wave function is fundamental and according to the most widely accepted interpretation of wave function, it doesn't even exist, we can't measure it directly, it is just a mathematical object of our model that helps us calculate the probabilities for the various outcomes of a system's time evolution.