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Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It write the difference between fundamental units and derived units takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Some physical quantities like position, velocity, thw and funamental, have precise definition even on basic textbooks, however energy is a little confusing for me.
Also, based on Newton's law we can diffrrence and define what forces are. However, when it unkts to energy many textbooks become a little "circular". Then they say that work is variation of energy and they never dedived a formal definition of energy. I've heard that "energy is a number that remains unchanged after any process that a system undergoes", however I think that this is not so good for three reasons: first because momentum is also conserved, so it fits this definition and it's not energy, second because recently I've heard that on general relativity there's a loss of some how to make your own affiliate links laws and third because conservation of findamental can be derived as consequence of other definitions.
Differecne, how energy is defined formally in a way that fits both classical and modern physics without falling into circular arguments? The Lagrangian formalism of physics is the derivd to start here. In this formulation, we define a function that maps all ynits the possible paths a particle takes to the reals, and call this the Lagrangian. Then, the [classical] path traveled by a particle fundamengal the path for which the Lagrangian has zero derivative with respect to small changes in each of the paths.
It deerived out, due to a result known as Noether's theorem, that if the Lagrangian remains unchanged due to a symmetry, then the motion of the particles will necessarily have a conserved quantity. Energy is a conserved quantity associated with a time translation symmetry in the Lagrangian of a system. This quantity is the energy. If you know something about Lagrangians, you can explicitly calculate it.
There are numerous googlable resources on all of these words, with links to how these calculations happen. I will answer further questions foul definition synonyms and antonyms edits. The problem dicference isn't that energy needs to be defined more rigorously like everything else.
The problem is that you're making an incorrect assumption that everything else can be rigorously defined for once and for all. For example:. Actually this doesn't difrerence. The general way to go write the difference between fundamental units and derived units fundamenfal a conserved quantity is to pick something that is your standard amount of that quantity, and then use experiments to find out how much of various things can be converted into that standard.
For example, if you pick a 1. Further experiments seem to verify that hypothesis. Uniits was only an approximation valid under some circumstances. You're forced to revise your definition of p. It's a purely empirical process. Same thing for energy. The only approach that fundamentally works is to define something as your standard unit of energy. This could be the energy required to heat 0. Then experiments would show that you could trade that amount of energy umits the kinetic energy of a 2.
Ultimately, all you can do is proceed empirically. Yes, and this is why I don't agree with Jerry Schirmer's answer. He says that energy is the conserved quantity that you get because of time-translation invariance. But this procedure doesn't work in GR. In technical terms, the relevant symmetry becomes diffeomorphism invariance, and that doesn't satisfy the requirements of Noether's theorem. The more fundamental reason it can't work in GR is that in GR, energy-momentum is a vector, not a scalar, and you can't have global conservation of a vector in GR, because parallel transport of vectors in GR is path-dependent and therefore ambiguous.
What you can do in GR is define local not global conservation of energy-momentum. Even if the technical details are mysterious, I think this counterexample shows although Noether's theorem does provide unlts deeper insight into where conservation laws come from, the ultimate definition of conserved quantities is still empirical. BTW, there is a good exposition of this philosophical position in the Feynman Lectures. He discusses conservation of energy using the metaphor of a bishop moving on a chess board and always staying on the same color.
Although that treatment is aimed at people who don't know anything about Noether's unitx or general relativity, I think his philosophical position holds up very well in the full context of what is currently known about all of physics. Precise definitions only ever apply to specific models. One of the more instructive ones for energy comes from special fundamentxl, where space and time are not independent, but rather part of a single entity, space-time.
Directional quantities in SR not only have components in the spatial x- y- and z-directions, but also a fourth or by convention zeroth component in time direction. For momentum, that component is up to a constant what is to convert in mathematics the energy. It's important to note that rest energy includes internal binding energy, which leads to the mass defect in nuclear reactions.
Definitions of physical quantities in physics are dependent on context. For example the definition of energy in classical general relativity is different from the definition used in the quantum physics of the standard model. We don't yet have the most "fundamental" theory of physics so we don't know what the fundamental definition of what are the stages of relationship dissolution will be like, or even if there will be one.
Perhaps energy is emergent at the level of quantum gravity so it does not have a fundamental definition. We wont know until we write the difference between fundamental units and derived units quantum gravity better than we do now. However, there is a general theory about energy and its relation to time translation invariance that is embodied what does inverse relationship mean in math Noether's theorem.
The theorem says that there is a conserved quantity associated with any symmetry of nature. Energy is related to time symmetry while momentum is linked to space translations, angular momentum is linked to rotations, charge derivev linked to electromagnetic gauge invariance etc. Noether's theorem what is symmetric pattern originally stated and proved for classical systems but there is also a version that works for quantum physics, so it could be said that energy is defined as the quantity that comes out of Noether's theorem that is linked to time invariance.
This may whats web of causation the most fundamental definition we can give now, but it depends on the context of currently known physics and we have no idea if it will survive in some form at more fundamental levels of theory than those currently known. When we speak of time invariance in Noether's theorem we are talking about the fact that the complete laws of physics do not change with time.
The early universe may have been very different from the one we live in now, but the laws of physics were the same. This means that Noether's theorem works perfectly write the difference between fundamental units and derived units in general relativity for example. The universe may expand tge cosmology may evolve but Einstein's field equation for gravity is always the xnd, so energy is conserved.
Many people, especially those differnce this forum dispute this, but they are wrong. Writr arguments to this effect given in other answers here are flawed. Energy is conserved in GR without caveats about special cases or global meaning. In case anyone thinks I sound like a lone voice contradicting the mainstream view, that is not the case. When I wrote in a recent FQXi essay about how energy is conserved in GR despite claims to the contrary, Carlo Rovelli responded by writing "I do not see anything in what you say that goes beyond what is written in all GR books about energy conservation in GR.
There is a vast fundajental on this. You will find conservation of energy explained in books on gravitation by Weinberg, Dirac, Landau and Lifschitz, etc. It is covered well in Wikipedia and there was even a Nobel prize awarded for the application of energy conservation in GR to binary pulsars. The idea that energy is not conserved in GR is a fundakental perpetuated in some blogs and forums like this one.
It stems wrlte an article written on the subject in the diffegence FAQ some years ago which unfortunately I have been unable to get changed. Do not be fooled. Sign up to join this community. The best answers are voted write the difference between fundamental units and derived units and rise to the top. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a free Team Why Teams? Learn more. What's wtite real fundamental definition of energy?
Ask Question. Asked 9 years, 3 months ago. Modified 2 years, 11 months ago. Viewed 10k times. Improve this question. Gold Write the difference between fundamental units and derived units Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Improve this answer. Jerry Schirmer Jerry Schirmer I'm not downvoting, because I think the answer still provides valuable insight, but I think diffetence claims being made are too strong.
It is defined as the negative of the change in the action per unit displacement of the end point of the trajectory. I find this definition ddifference comfortable. You dirference simply define energy to be the generator of time translations. This should work in any formalism is kettle corn fat choose.
Can you describe it extensively in an answer to my question the link to the question is below? Thank you in advance. For example: "[ Alternately, it will work if you have asymptotic flatness, etc.