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> considering all the exceptions that exist for every other set of physical laws, thermodynamics has exactly zero exceptions Actually, conservation of energy d

> considering all the exceptions that exist for every other set of physical laws, thermodynamics has exactly zero exceptions Actually, conservation of energy doesn't hold on cosmological scales, at least with the usually accepted meaning of conservation of energy. [0] That's not relevant to the author's argument, but I think it's dangerous to perpetuate the idea that thermodynamics is somehow an inviolate theory that doesn't break down under certain conditions just like every other physical theory. [0]: http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ http://www.preposterousuniverse.com/blog/2010/02/22/energy-i...

TeMPOraL 11y ago
It's interesting that the only theory that seems to be treated as inviolatable is the one that has big parts built on statistical, aggregate behaviour which doesn't hold on the small scale.
- KMag 11y ago
  The author of the linked article points out there are competing interpretations under which mass-energy is still conserved on the small scale. It's just that if you introduce the variable of local gravitational energy you wind up with a system of more variables than equations. We don't presently know of any laws that further constrain the system of equations to a unique solution unless we take local conservation of energy as an axiom... which of course prevents us from proving local conservation of energy. However, we don't have any observations that are inconsistent with local conservation of energy if gravitational energy is taken into account.
KMag 11y ago
That's a bit misleading. As the author of your linked article points out, the ere interpretations of all observed phenomena that are still consistent with conservation of energy. I think the least-confusing way to state it is "to the best of our knowledge, the mass-energy of the Universe is constant, but due to ambiguities in accounting for gravitational energy, we cannot presently prove that this holds true for sub-divisions of the Universe". The author states that he prefers to ignore the energy of the gravitational field because there isn't a unique solution to apportioning the energy of the gravitational field to some subdivision of the Universe unless one takes local conservation of energy as an axiom. So, conservation of energy of the whole Universe is still believed to hold if one takes gravitational energy into account. We can take conservation of energy of a block of space (accounting for gravitational energy) as an axiom and get consistent equations. It's just that we don't (at least as of yet) have other equations that prevent us from apportioning the gravitational energy in a way that violates conservation of energy for a given block of space. Maybe we'll later discover other laws that force us to apportion the gravitational energy in a way that proves conservation of energy for sub-divisions of the Universe, or maybe we'll discover other laws that force us to apportion gravitational energy in a way that's inconsistent with local conservation of energy. Maybe we'll never discover any additional laws that force us either way. EDIT: bringing it back to the original context: to the best of our knowledge, locally violating conservation of energy to charge a phone ultrasonically at a rate higher than the energy is being put into the sound waves would involve manipulating the gravitational field, and many people would consider the local violation of conservation of energy to just be an accounting trick.

TeMPOraL 11y ago

It's interesting that the only theory that seems to be treated as inviolatable is the one that has big parts built on statistical, aggregate behaviour which doesn't hold on the small scale.

KMag 11y ago
The author of the linked article points out there are competing interpretations under which mass-energy is still conserved on the small scale. It's just that if you introduce the variable of local gravitational energy you wind up with a system of more variables than equations. We don't presently know of any laws that further constrain the system of equations to a unique solution unless we take local conservation of energy as an axiom... which of course prevents us from proving local conservation of energy. However, we don't have any observations that are inconsistent with local conservation of energy if gravitational energy is taken into account.

KMag 11y ago

That's a bit misleading. As the author of your linked article points out, the ere interpretations of all observed phenomena that are still consistent with conservation of energy. I think the least-confusing way to state it is "to the best of our knowledge, the mass-energy of the Universe is constant, but due to ambiguities in accounting for gravitational energy, we cannot presently prove that this holds true for sub-divisions of the Universe". The author states that he prefers to ignore the energy of the gravitational field because there isn't a unique solution to apportioning the energy of the gravitational field to some subdivision of the Universe unless one takes local conservation of energy as an axiom. So, conservation of energy of the whole Universe is still believed to hold if one takes gravitational energy into account. We can take conservation of energy of a block of space (accounting for gravitational energy) as an axiom and get consistent equations. It's just that we don't (at least as of yet) have other equations that prevent us from apportioning the gravitational energy in a way that violates conservation of energy for a given block of space. Maybe we'll later discover other laws that force us to apportion the gravitational energy in a way that proves conservation of energy for sub-divisions of the Universe, or maybe we'll discover other laws that force us to apportion gravitational energy in a way that's inconsistent with local conservation of energy. Maybe we'll never discover any additional laws that force us either way. EDIT: bringing it back to the original context: to the best of our knowledge, locally violating conservation of energy to charge a phone ultrasonically at a rate higher than the energy is being put into the sound waves would involve manipulating the gravitational field, and many people would consider the local violation of conservation of energy to just be an accounting trick.