121–130 of 144 posts
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I don't think that's true. An object would be attracted to the inner surface of the sphere because that's where the mass actually is. The shape you're describing doesn't have a center of mass the way we traditionally think of it.
At the center of a uniform hollow sphere the force will be precisely 0.
From the publication itself: > Note that in the discussed example the reservoir acts as some quantum analogue of the classical Maxwell demon. Namely, having been prepared in a special state, the reservoir is able to decrease the entropy of the system without the energy exchange with it, and can be referred to as a ‘quantum Maxwell demon’ […] In what was discussed above, an electron interaction with the quantum spin d…
I don't think so. There is no energy transmission involved at all. I suspect that there is some entropy transmission, but I didn't see an analysis of that, and the amount is negligible compared to what is already in the quantum mechanical system. Of much greater surprise to me was the claim that an isolated quantum mechanical system neither gains nor loses entropy. I'm almost as astonished at this as I am at the fact…
Why is this surprising? It's a simple consequence of unitarity.
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aren't people (and all living organisms) the quintessential example of a local decrease in entropy that results in greater overall entropy? we are highly ordered groupings of matter but we're really great at churning about the matter and energy around us and we eventually decompose too.
> aren't people (and all living organisms) the quintessential example of a local decrease in entropy that results in greater overall entropy Complexity is orthogonal to entropy. The aforementioned barrier-separated box is high in entropy but simple. Upon lifting the barrier, a description of the gas front moving into the vacuum is enormously complex. It is also lower in entropy than the previous, barrier-separated st…
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This argument that the Second Law is a simple logical consequence of basic probability always seems glib to me. Why would probability demand entropy increase as one extrapolates forward in time, but probability not similarly demand entropy increase as one extrapolates backwards in time? In other words, what of Loschmidt's paradox ( https://en.wikipedia.org/wiki/Loschmidt%27s_paradox )?
There fact that is not a consequence of statistics is that we observe the universe to not be in the state of maximal entropy. That is sufficient to explain asymmetry of time, I think. The mystery is -- why wasn't the universe in a state of maximal entropy at time 0?
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An object inside the hollow sphere would in fact be attracted to each individual mass-ful particle on the surface of the hollow sphere. But (assuming uniform density on the sphere) the net effect is 0 (it feels no gravitational attraction whatsoever). The best way to prove this is to compute the gravitational force between your object and any arbitrary particle on the surface, then do the integration over all the par…
The best way is to use symmetry. Ask yourself, which way would the net force be directed?
Earlier quoted context omitted.
> aren't people (and all living organisms) the quintessential example of a local decrease in entropy that results in greater overall entropy Complexity is orthogonal to entropy. The aforementioned barrier-separated box is high in entropy but simple. Upon lifting the barrier, a description of the gas front moving into the vacuum is enormously complex. It is also lower in entropy than the previous, barrier-separated st…
Is there a way to quantify complexity in that sense?
> The aforementioned barrier-separated box is high in entropy but simple.
This isn't true in any meaningful objective sense; representing the exact state of the system in some basis (e.g. the position or momentum states of all particles in the system) requires a huge amount of information, corresponding to the entropy. The GP only said it's a "simple" system because we (for arbitrary reasons) don't really care very much about the position of each gas molecule. We as humans are satisfied with describing the system in terms of bulk statistical characteristics like temperature and pressure. However, we would be unsatisfied doing the same thing with a similarly information-rich system such as a microprocessor, because now the bulk characteristics of the system aren't sufficient information to describe the characteristics that humans care about.
"Simplicity" or "complexity" as described by the GP is not a physical quantity; it's a reflection of which precise dynamical behavior we happen to care about. You could probably find all sorts of heuristics that generally match with human intuition, but in the end it's up to opinion.
The second law of thermodynamics isn't really a fundamental physical law, but rather a promise based on statistics that says "disorder will increase or stay constant in a closed physical system". That said, it's entirely possible for entropy to spontaneously decrease in a closed system, the probability of this happening is just astronomically small for typical macroscopic systems. Example: If you have a system consis…
The second law of thermodynamics is as fundamental as the uncertainty principle: The former is a result from markov chains and information theory, the latter is a result from fourier analysis of conjugate variables. What would you consider a "fundamental physical law"?
The probability of either theory producing an incorrect prediction external to the theory is much higher, and will be about the same for each theory. That is, it's more likely we're wrong about all of physics than that the second law makes a bad prediction in a bulk system.
Explanation of "internal" vs "external" probability: http://lesswrong.com/lw/3be/confidence_levels_inside_and_out...
Earlier quoted context omitted.
aren't people (and all living organisms) the quintessential example of a local decrease in entropy that results in greater overall entropy? we are highly ordered groupings of matter but we're really great at churning about the matter and energy around us and we eventually decompose too.
A living organism is of course a noble endeavor standing against the tide of entropy. But it can do so only with significant influx of energy extracted from its external environment. The cost of constructing such an elaborate order of matter is paid by disorder elsewhere. As we know, the living stance can be maintained for only a relatively short time, after which it rapidly decomposes to background entropy. Interest…
A living organism also increases the entropy of the environment.
The second law of thermodynamics isn't really a fundamental physical law, but rather a promise based on statistics that says "disorder will increase or stay constant in a closed physical system". That said, it's entirely possible for entropy to spontaneously decrease in a closed system, the probability of this happening is just astronomically small for typical macroscopic systems. Example: If you have a system consis…
The second law of thermodynamics is as fundamental as the uncertainty principle: The former is a result from markov chains and information theory, the latter is a result from fourier analysis of conjugate variables. What would you consider a "fundamental physical law"?