Me in ’09: Physicists have long considered [thermodynamics] the physics area least likely to be overturned by future discoveries, in part because they understand it so well via “statistical mechanics.” Alas, not only are we far from understanding thermodynamics, the situation is much worse than most everyone admits! (
Actually, as it turns out, the universe didn't start with low entropy; in fact, it started with maximum entropy. The universe started out as a sphere of Planck dimensions (whether inflation happened or not), and then expanded. A sphere of Planck dimensions, however, is necessarily a black hole, and thus has maximum entropy. How, then, can the Second Law of Thermodynamics hold? Well, it's because the expanding universe increases the maximum entropy. Because of the 2nd LOT, entropy increases approximately polynomially with the radius of the universe, but the maximum entropy increases exponentially with radius. Since any exponential function increases faster than any polynomial function, there is an increasing room for order in the universe, despite the entropy constantly increasing.
Shannon entropy is only one particular definition of entropy (from information theory), which fails to take into account the actual *semantic* content of data, which is a product of the work that went into producing that data.
It's clear that fields (in physics) are closely analogous to a mind's representational system (since they carry information to mediate communciation exchanges), and they are also far in influence. This provides (weak) support for my claim that the universe is in fact a poorly optimized (broken, malfunctioning) RPOP.
If the universe is in fact a goal-directed system analogous to a mind, it's important we find out what 'priors' the universe is using. And that needs a more generalized definition of entropy.
Has it occurred to anyone that less complex things look more entropic to more complex things and that, therefore, the less complex elements of the universe look entropic to humans, while more complex elements look negentropic? But do we know how to recognize negetropy?
Thermodynamics only deals with equilibrium processes. Thermodynamics is the wrong tool to use to try and decide which paths a non-equilibrium process will take. By thermodynamics, everything should spontaneously convert to nickel-62 because Ni62 has the highest binding energy per nucleon. But that can only happen via a path, and there are not many paths that lead to Ni62 even though it is the most stable nucleus. Formation of Ni62 is kinetically unfavored (and so it is rare) even though it is thermodynamically the most favored.
The reason Ni62 is kinetically unfavored is because it takes a lot of energy to enter the transition state between other compounds and Ni62. The high energy of the transition state to Ni62 makes transitions to Ni62 unlikely.
The transitions states where paint particles spontaneously tunnel out into the air are extremely unlikely. A transition state where a molecules of solvent diffuse into the solid paint, cross linked molecules decompose and release O2, the paint softens and is then picked up by a brush wielded by a painter is much more likely than paint particles spontaneously tunneling from the canvas back into the paint tube.
At equilibrium, the rate of forward and reverse reactions is the same. The degree to which a system is out of equilibrium can be characterized by differences between the forward and reverse reactions. Reactions with a low activation energy are closer to equilibrium than reactions with a very high activation energy. The spontaneous formation of Ni62 is extremely low. The spontaneous decomposition of Ni62 would be even lower.
The deposition of paint on a canvas by a painter has a pretty low activation energy. The removal of paint from a canvas by a painter also has a pretty low activation energy and is of the same order of magnitude. The spontaneous tunneling of paint from a canvas to a tube has an extremely high activation energy as does the spontaneous tunneling of paint from a tube onto a canvas, so high that we should expect to never observe it on the time scale where we do observe removal of paint from a canvas by a painter.
> what reason is there to assume this is the most thermodynamically efficient way of reversing the entropy production that the painting involved? For instance, why not discard the painter entirely? —
This won't work, because Carroll is implicitly invoking a universe in which a painter remembers having squeezed paint out of the tubes and placed it on the canvas. That memory cannot simply be erased without temporarily increasing entropy in the surrounding environment and making the whole fluctuation even more implausible. Instead, the physical process which might have created that memory must be reversed; stated another way, causality must be preserved: tbe painter must actually have "painted" the canvas in her perceptual past, i.e. she will clear the canvas in our future.
You might ask why an entropy transition of this kind should involve painters and canvases at all, but that's a different matter.
> If high-entropy states can be simply specified, this is indicates a problem with current defintions of ‘complexity’.
Not really. Think: PRNG. High thermodynamic entropy, low information-theoretic entropy. The answer is probably not Occam's razor - since high-thermodynamic entropy states can be made simply.
Anthropic explanation: entropy only increases, universe takes a long time to evolve intelligent agents, therefore, entropy started off being much smaller.
Thinking like a physicist can be misleading when dealing with complex (path dependent) processes, because the continuity you are demanding is so easily met. Granting all your points, without reservation, doesn't really get very close to the kind of 'time-reversal' Carroll is invoking, because the systems being examined are not in any strong sense historical. Consider the idea of paint spontaneously rehydrating and unmixing before being dipped off a canvas, deposited on a palette, and then (after more unmixing) sucked into a tube -- what reason is there to assume this is the most thermodynamically efficient way of reversing the entropy production that the painting involved? For instance, why not discard the painter entirely? -- it's probably less of a physical stretch to have the paint particles drift spontaneously across space and back into the tubes, which is to say, there are no sufficiently constraining causal factors to impose symmetry (time-reversal). It seems to me your point about quantum tunneling would tend to lead to exactly this conclusion -- numerous small increments of negative entropy production are vastly more probable than huge, bizarre -- even miraculous -- jumps in local order, of the kind that neat time-reversals of elaborate macro-systems inevitably require.
I don't think so. In the sense that I am using the term “continuous”, a time-reversed sequence that preserves local conservation of mass/energy exhibits continuity. A path where conservation of mass/energy is not locally conserved would be very much less likely, even than the very unlikely time-reversal case that does conserve it. Quantum tunneling over a Planck length is much more likely than quantum tunneling over macroscopic distances (meters).
The scanning tunneling microscope uses the change in the tunneling rate of electrons with distance to measure distances. The rate changes exponentially with distance with ~10x change per Angstrom. A meter being 10^10 Angstroms, an electron tunneling the distance of a meter is 10^(10^10) less likely than tunneling the distance of an Angstrom.
In other words, the paths where a single electron has to tunnel a meter are enormously less likely than paths where 10^100 electrons tunnel a few Angstroms. Paths where tunneling is confined to a few Planck lengths (and so mimics time reversal) will be common compared to paths where there is tunneling of meters.
Apologies for multiple posts, but one further point of clarification. IMHO Sean Carroll moves much too fast in suggesting that "the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium."A negentropic flux would still be statistically constrained by principles of thermodynamic economy / probability, in that it would tend to minimize negentropy production at each step, in contrast to the ordinary tendency to maximize entropy production. The two processes are NOT symmetrical. In complex systems, especially, there are FAR more probable paths to entropy reduction than simple time-reversal, which means that the production of plausible 'artificial memories' (fake consistent fossil records, for e.g.) are an extremely unlikely case, even in the flux universe of inherently improbable processes.
"Conservation laws [for] mass/energy, charge, momentum" exercise almost no constraint at all, at least relative to the constraints of ordinary, path-dependent (pro-entropic) causality.
This holds only if 'continuous' is defined so broadly that it sacrifices almost everything that is normally, and scientifically, associated with the term. Fluctuation out of chaos is no more causally constrained to proceed from dinosaur to dinosaur fossil than from dinosaur to Cthulhu fossil (or rather, and crucially in this case, from 'fossil' to 'fossilized') -- the mechanism that would ensure consistency with 'normal' (entropic) development simply does not exist. This is already granted as soon as it is conceded that recordings (e.g. memories) are causally dissociated from remembered facts, since there are far more economical paths to 'memory' formation in a contra-entropic flux than the process of remembering. Flux production of low-entropy states is already so contrary to conventional expectations that to assume it would neatly re-assemble ordinary causal sequences, just inversely, is nothing more than a huge leap of faith.
The universe is becoming more informationally complex by becoming more textured, with the information becoming densified in local regions. One has to take into consideration the relationship between information and entropy. I (I think) solve the problem in my book Diaphysics.
The past has to be "continuous" with the present. That imposes boundary conditions. The past of yesterday has to be continuous with today and with the day before yesterday.
The most likely paths that are continuous are the paths where there seems to be cause and effect.
For those paths to not be continuous requires violation of conservation laws, mass/energy, charge, momentum.
Actually, as it turns out, the universe didn't start with low entropy; in fact, it started with maximum entropy. The universe started out as a sphere of Planck dimensions (whether inflation happened or not), and then expanded. A sphere of Planck dimensions, however, is necessarily a black hole, and thus has maximum entropy. How, then, can the Second Law of Thermodynamics hold? Well, it's because the expanding universe increases the maximum entropy. Because of the 2nd LOT, entropy increases approximately polynomially with the radius of the universe, but the maximum entropy increases exponentially with radius. Since any exponential function increases faster than any polynomial function, there is an increasing room for order in the universe, despite the entropy constantly increasing.
I blame Greenspan amd Bernanke.
I'm sorry, okay. I had to. Its a compulsion.
Shannon entropy is only one particular definition of entropy (from information theory), which fails to take into account the actual *semantic* content of data, which is a product of the work that went into producing that data.
It's clear that fields (in physics) are closely analogous to a mind's representational system (since they carry information to mediate communciation exchanges), and they are also far in influence. This provides (weak) support for my claim that the universe is in fact a poorly optimized (broken, malfunctioning) RPOP.
If the universe is in fact a goal-directed system analogous to a mind, it's important we find out what 'priors' the universe is using. And that needs a more generalized definition of entropy.
Has it occurred to anyone that less complex things look more entropic to more complex things and that, therefore, the less complex elements of the universe look entropic to humans, while more complex elements look negentropic? But do we know how to recognize negetropy?
Thermodynamics only deals with equilibrium processes. Thermodynamics is the wrong tool to use to try and decide which paths a non-equilibrium process will take. By thermodynamics, everything should spontaneously convert to nickel-62 because Ni62 has the highest binding energy per nucleon. But that can only happen via a path, and there are not many paths that lead to Ni62 even though it is the most stable nucleus. Formation of Ni62 is kinetically unfavored (and so it is rare) even though it is thermodynamically the most favored.
The reason Ni62 is kinetically unfavored is because it takes a lot of energy to enter the transition state between other compounds and Ni62. The high energy of the transition state to Ni62 makes transitions to Ni62 unlikely.
The transitions states where paint particles spontaneously tunnel out into the air are extremely unlikely. A transition state where a molecules of solvent diffuse into the solid paint, cross linked molecules decompose and release O2, the paint softens and is then picked up by a brush wielded by a painter is much more likely than paint particles spontaneously tunneling from the canvas back into the paint tube.
At equilibrium, the rate of forward and reverse reactions is the same. The degree to which a system is out of equilibrium can be characterized by differences between the forward and reverse reactions. Reactions with a low activation energy are closer to equilibrium than reactions with a very high activation energy. The spontaneous formation of Ni62 is extremely low. The spontaneous decomposition of Ni62 would be even lower.
The deposition of paint on a canvas by a painter has a pretty low activation energy. The removal of paint from a canvas by a painter also has a pretty low activation energy and is of the same order of magnitude. The spontaneous tunneling of paint from a canvas to a tube has an extremely high activation energy as does the spontaneous tunneling of paint from a tube onto a canvas, so high that we should expect to never observe it on the time scale where we do observe removal of paint from a canvas by a painter.
> what reason is there to assume this is the most thermodynamically efficient way of reversing the entropy production that the painting involved? For instance, why not discard the painter entirely? —
This won't work, because Carroll is implicitly invoking a universe in which a painter remembers having squeezed paint out of the tubes and placed it on the canvas. That memory cannot simply be erased without temporarily increasing entropy in the surrounding environment and making the whole fluctuation even more implausible. Instead, the physical process which might have created that memory must be reversed; stated another way, causality must be preserved: tbe painter must actually have "painted" the canvas in her perceptual past, i.e. she will clear the canvas in our future.
You might ask why an entropy transition of this kind should involve painters and canvases at all, but that's a different matter.
> If high-entropy states can be simply specified, this is indicates a problem with current defintions of ‘complexity’.
Not really. Think: PRNG. High thermodynamic entropy, low information-theoretic entropy. The answer is probably not Occam's razor - since high-thermodynamic entropy states can be made simply.
Anthropic explanation: entropy only increases, universe takes a long time to evolve intelligent agents, therefore, entropy started off being much smaller.
Thinking like a physicist can be misleading when dealing with complex (path dependent) processes, because the continuity you are demanding is so easily met. Granting all your points, without reservation, doesn't really get very close to the kind of 'time-reversal' Carroll is invoking, because the systems being examined are not in any strong sense historical. Consider the idea of paint spontaneously rehydrating and unmixing before being dipped off a canvas, deposited on a palette, and then (after more unmixing) sucked into a tube -- what reason is there to assume this is the most thermodynamically efficient way of reversing the entropy production that the painting involved? For instance, why not discard the painter entirely? -- it's probably less of a physical stretch to have the paint particles drift spontaneously across space and back into the tubes, which is to say, there are no sufficiently constraining causal factors to impose symmetry (time-reversal). It seems to me your point about quantum tunneling would tend to lead to exactly this conclusion -- numerous small increments of negative entropy production are vastly more probable than huge, bizarre -- even miraculous -- jumps in local order, of the kind that neat time-reversals of elaborate macro-systems inevitably require.
I don't think so. In the sense that I am using the term “continuous”, a time-reversed sequence that preserves local conservation of mass/energy exhibits continuity. A path where conservation of mass/energy is not locally conserved would be very much less likely, even than the very unlikely time-reversal case that does conserve it. Quantum tunneling over a Planck length is much more likely than quantum tunneling over macroscopic distances (meters).
The scanning tunneling microscope uses the change in the tunneling rate of electrons with distance to measure distances. The rate changes exponentially with distance with ~10x change per Angstrom. A meter being 10^10 Angstroms, an electron tunneling the distance of a meter is 10^(10^10) less likely than tunneling the distance of an Angstrom.
In other words, the paths where a single electron has to tunnel a meter are enormously less likely than paths where 10^100 electrons tunnel a few Angstroms. Paths where tunneling is confined to a few Planck lengths (and so mimics time reversal) will be common compared to paths where there is tunneling of meters.
Apologies for multiple posts, but one further point of clarification. IMHO Sean Carroll moves much too fast in suggesting that "the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium."A negentropic flux would still be statistically constrained by principles of thermodynamic economy / probability, in that it would tend to minimize negentropy production at each step, in contrast to the ordinary tendency to maximize entropy production. The two processes are NOT symmetrical. In complex systems, especially, there are FAR more probable paths to entropy reduction than simple time-reversal, which means that the production of plausible 'artificial memories' (fake consistent fossil records, for e.g.) are an extremely unlikely case, even in the flux universe of inherently improbable processes.
"Conservation laws [for] mass/energy, charge, momentum" exercise almost no constraint at all, at least relative to the constraints of ordinary, path-dependent (pro-entropic) causality.
This holds only if 'continuous' is defined so broadly that it sacrifices almost everything that is normally, and scientifically, associated with the term. Fluctuation out of chaos is no more causally constrained to proceed from dinosaur to dinosaur fossil than from dinosaur to Cthulhu fossil (or rather, and crucially in this case, from 'fossil' to 'fossilized') -- the mechanism that would ensure consistency with 'normal' (entropic) development simply does not exist. This is already granted as soon as it is conceded that recordings (e.g. memories) are causally dissociated from remembered facts, since there are far more economical paths to 'memory' formation in a contra-entropic flux than the process of remembering. Flux production of low-entropy states is already so contrary to conventional expectations that to assume it would neatly re-assemble ordinary causal sequences, just inversely, is nothing more than a huge leap of faith.
The universe is becoming more informationally complex by becoming more textured, with the information becoming densified in local regions. One has to take into consideration the relationship between information and entropy. I (I think) solve the problem in my book Diaphysics.
I see. Thanks for explaining Robin.
The past has to be "continuous" with the present. That imposes boundary conditions. The past of yesterday has to be continuous with today and with the day before yesterday.
The most likely paths that are continuous are the paths where there seems to be cause and effect.
For those paths to not be continuous requires violation of conservation laws, mass/energy, charge, momentum.