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Are there really non-conservative forces in actuality ?

Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close enough ( microscopic level ). The reasoning is that we can't allow non-conservative forces in order for Conservation of Energy to follow.

But at the same time, physicists who seem to really know the subject in an advanced-level, assert that most forces refuse to be conservative.

For instance, see acepted answer of Locally every force admits a potential?.

So, are all forces conservative forces and conservation of energy is not violated, or are there non-conservative forces and conservation of energ is violated , or finally, Law of Conservation of energy can cohexist with non-conservative forces ?

Community
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nerdy
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  • An example of non-conservative force, friction. – Sofia Feb 13 '15 at 18:21
  • That's the problem. Feyman argues that friction is actually conservative, if we look close enough, because afterall heat ( and maybe sound ) is being generated in the physical system. See the point ? – nerdy Feb 13 '15 at 18:24
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    The non-conservative force transforms for example the kinetic energy into heat. Thus, in a process that transforms potential energy into kinetic, and vice-versa, after part of the kinetic energy is lost into heat, won't return to potential, s.t. the total mechanic energy isn't conserved. – Sofia Feb 13 '15 at 18:27

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There are macroscopic forces that admit no description in terms of a potential, for example, any friction force proportional to the velocity of a moving object as path-dependent integral, and is hence non-conservative.

But we know the macroscopic description is not the fundamental description. In terms of the interaction of the constituents of matter, all fundamental forces known - gravity, electromagnetism, the strong and the weak force - are conservative forces in the sense that they are descended from a (gauge) potential. It is highly non-trivial (and indeed, not done for the general case as far as I know) to derive the appearance of superficially non-conservative forces from this fundamental Lagrangian description.

Nevertheless, in the spirit of reductionism, Feynman and most other physicists believe the description in terms of the fundamental forces is more or less complete - all other forces emerge in some sense from them, and so, since the underlying microscopic description conserves energy, so must the emergent macroscopic description.

ACuriousMind
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  • isn't there a contradiction in your statement above:"But we know the macroscopic description is not the fundamental description...." and then "...It is highly non-trivial (and indeed, not done for the general case as far as I know) to derive ..."? I, for one, am skeptical about that general case. – hyportnex Feb 13 '15 at 18:45
  • @user31748: You may well believe that the world is not reductionist, i.e. that there are additional phenomena appearing at higher scales that are not emergent from a microscopic decsription. It is just the case that the contrary assumption has hitherto worked perfectly fine. – ACuriousMind Feb 13 '15 at 18:47
  • Ty for the answer.Can you help me with related doubt? Most people say that potential energy is not a property of an object above surface of earth,but rather a property of the Earth-object system.

    But this is a bit wierd, because in fact what is causing the gravitational motion of the object is the curvature of the space-time. So, it would make sense to talk about Potential energy of the object alone (and not the earth-object system ) whenever in a certain position of the curved space-time,and it becomes wierd now to talk about potential energy of the object-earth system. Don't you agree ?

     – nerdy Feb 13 '15 at 19:20
  • @nerdy: You are mixing different descriptions. The Earth-Object description is Newtonian, and in it, the presence of the gravitational potential is dependent on both the Earth and the Object. When you talk about curved spacetime, you have to first provide a notion of energy that works within the formalism of General Relativity, which is not trivial, and leads you to the idea of an energy-momentum tensor generalising the idea of conservation of energy. The energy-momentum tensor is again a property of all matter jointly, and not of any particular piece of matter. – ACuriousMind Feb 13 '15 at 19:26
  • This is really interesting ! Thank you very very much for the help :) – nerdy Feb 13 '15 at 19:45
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All the known forces conserve energy, but they don't necessarily conserve energy in macroscopic modes.

For instance friction takes some of the energy of macroscopic motion and coverts it into an increase in temperature (i.e. energy in microscopic modes). Total energy is conserved but energy that is useful at the human scale is not.

Feynman is talking about all energy and introductory textbooks (and those that concern themselves with thermodynamics) use a more restrictive definition.

Just make sure you know which definition you care about.

dmckee --- ex-moderator kitten
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