Is this the alternative definition of Entropy? 
Gravity never zero
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Machta asserts that, starting with algorithmic entropy (or complexity) you can derive forms of Shannon and Gibbs entropy.Robbitybob1 said:
Usually in physics you start with thermodynamic entropy of a 'Gibbs ensemble'. Shannon entropy has the same formula, so they seem to be isomorphic, and so "heat is information".
So you might understand entropy better than all of us. In what way does entropy play in the expansion of space?
The expansion of space reflects an increase in entropy. If you wish to talk in terms of entropy equals complexity an expanding universe increases the complexity of all energy signals; red shift. The entropy within the expansion is needed by the second law. If we take away the red shift and the changes in space and time the entropy is too low.
I think it's important to first of all understand what entropy is. It does seem to be defined in quite different ways depending on the context.
Shannon entropy is a measure of the probability of receiving a message from a set of messages. So this somehow is related to the probability of detecting a black hole somewhere with a given mass (??).
Another way to think about it is "difference", things (like messages) that are different have mutual information entropy.
Messages containing different characters have more entropy of information than messages with identical characters (i.e. the algorithm that produces the first kind is more complex).
Different sized black holes are an expression of gravitational entropy--the "message" is encoded in a way that we can't decode, except as I mentioned, we do know the sizes of these messages (all of which contain identical "characters").
Entropy is really quite a general concept. You can understand it informationally, or thermodynamically, or both.
Shannon entropy is a measure of the probability of receiving a message from a set of messages. So this somehow is related to the probability of detecting a black hole somewhere with a given mass (??).
Another way to think about it is "difference", things (like messages) that are different have mutual information entropy.
Messages containing different characters have more entropy of information than messages with identical characters (i.e. the algorithm that produces the first kind is more complex).
Different sized black holes are an expression of gravitational entropy--the "message" is encoded in a way that we can't decode, except as I mentioned, we do know the sizes of these messages (all of which contain identical "characters").
Entropy is really quite a general concept. You can understand it informationally, or thermodynamically, or both.
Another point of view: how much randomness is there in the way proteins are folded up?
What can we conclude from this result? That the process of folding a sequence of amino acids into a protein is very efficient: it uses a shortest program length which this result says has the same complexity as the sequence it acts on. Protein folding is known to be mediated by enzymes, which are also proteins. A case of information "acting on itself".
http://pre.aps.org/abstract/PRE/v54/i1/pR39_1
What can we conclude from this result? That the process of folding a sequence of amino acids into a protein is very efficient: it uses a shortest program length which this result says has the same complexity as the sequence it acts on. Protein folding is known to be mediated by enzymes, which are also proteins. A case of information "acting on itself".
There is another definition of entropy which comes into play, associated with work cycles. This applies to both gravitational work and enzymatic work. Entropy is also defined as inefficiency within the work cycles. If a process is 80% efficient, only 20% of the available energy goes into entropy. This is compared to 100% going into entropy if efficient was not important. Many assumptions and definition of entropy are not concerned with efficiency.
A common definition of entropy is connected to complexity. However, complexity and efficiency do not always go in the same direction, since higher efficiency means less entropy=complexity.
Let me give an example, the US government is a very complex organization. However, it is not very efficient. The low efficiency means it is based on higher entropy=complexity. If we wanted the government to become more efficient, we need to simplify departments such as consolidate and less redundancy. The complexity=entropy falls allowing more efficiency. The final result is still complex, but now we have less complexity=entropy.
If you look at an enzyme, the substrate fits into the active site like lock and key. The enzyme does it catalytic activity (increases its own complexity). But after it is done it returns to step 1 (lowers that complexity back to step 1). The result of this entropy loss is its high efficiency. This is why it is called a catalysts.
I think in terms of work cycles like gravitational work and efficiency. Things can still become complex, but less than expected if we assume a fully random system that is totally inefficient. Humans are evolving but this is subtle, Two obvious changes are the loss of wisdom teeth and tonsils. The loss is implicit of lowered complexity compared to retaining these with all else being equal. This is based on increasing efficiency so entropy=complexity drops.
In the world of science that is based on chaos and random, there is a bias which can see complexity=entropy but cannot fully see efficiency at play, since efficient is not exactly random like entropy suggests. Evolution is due to genetic changes which increase complexity and diversity. But natural selection is about efficiency and skinnies this wide range of genetic complexity down to the best of the best.
Gravity does work, which is force over a distance. This work is not 100 percent inefficient. The level of efficiency places a limit on complexity=entropy. The pressure on earth due to gravity will not allow the same diffusion rates into space we get on the moon. This is a restriction in entropy=complexity. The second law requires additional sources of complexity=entropy such as the expansion.
A common definition of entropy is connected to complexity. However, complexity and efficiency do not always go in the same direction, since higher efficiency means less entropy=complexity.
Let me give an example, the US government is a very complex organization. However, it is not very efficient. The low efficiency means it is based on higher entropy=complexity. If we wanted the government to become more efficient, we need to simplify departments such as consolidate and less redundancy. The complexity=entropy falls allowing more efficiency. The final result is still complex, but now we have less complexity=entropy.
If you look at an enzyme, the substrate fits into the active site like lock and key. The enzyme does it catalytic activity (increases its own complexity). But after it is done it returns to step 1 (lowers that complexity back to step 1). The result of this entropy loss is its high efficiency. This is why it is called a catalysts.
I think in terms of work cycles like gravitational work and efficiency. Things can still become complex, but less than expected if we assume a fully random system that is totally inefficient. Humans are evolving but this is subtle, Two obvious changes are the loss of wisdom teeth and tonsils. The loss is implicit of lowered complexity compared to retaining these with all else being equal. This is based on increasing efficiency so entropy=complexity drops.
In the world of science that is based on chaos and random, there is a bias which can see complexity=entropy but cannot fully see efficiency at play, since efficient is not exactly random like entropy suggests. Evolution is due to genetic changes which increase complexity and diversity. But natural selection is about efficiency and skinnies this wide range of genetic complexity down to the best of the best.
Gravity does work, which is force over a distance. This work is not 100 percent inefficient. The level of efficiency places a limit on complexity=entropy. The pressure on earth due to gravity will not allow the same diffusion rates into space we get on the moon. This is a restriction in entropy=complexity. The second law requires additional sources of complexity=entropy such as the expansion.
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I'm wondering if this discussion can get past entropy? Which ultimately wins in the long run.
Can gravity ever be zero?
Can gravity ever be zero?
The discussion of entropy is important to the discussion of zero gravity. At zero gravity there is zero work due to gravity. This means there is no entropy deficit (100% ineffiency) and the universe acts as though the formation of entropy is 100% random. There would be no need for the expansion of the universe to maintain the second law when we have perfect inefficiency.
Let me show this with an example. I will start with two tanks of compressed gas. The first I will open up into room 1. The expansion of the gas, as it lowers pressure, will increase entropy as it flow into the room. The energy for the entropy is contained within the pressure.
In the next room, or room 2, I connect a similar air tank to a work cycle. This work cycle is 80% efficient, with only 20% energy loss into entropy. We essentially steal 80% of the energy the other room had, which went into entropy. At the exhaust end of our work device, the gas trickles out in a wimpy way (20% entropy) since I took away a lot of its energy could have used for entropy.
The two rooms will act differently, using the similar gas cylinders exhausted to the air. The work cycle took energy away from room 2 entropy. If I open the door between the two rooms, since there is an entropy potential between the two rooms, I can direct the flow of the entropy. It will go from room 1 to room 2. The pressure will push it that way.
Zero gravity is analogous to room 1 where the expansion of the gas goes into 100% into entropy, unobstructed by a work cycle, scavenging energy. Higher gravity is connected to room 2 where work occurs. The flow of entropy goes from zero gravity to higher gravity due to the entropy potential between 100% inefficiency and the efficiency of the work cycle.
The gravitational work is slick because it creates entropy potential and therefore increases the odds for things to happen in a directed way. The zero gravity loses its 100% inefficiency since it lose entropy toward the work cycles of gravity. To maintain the second law we need a way to increase entropy; expansion.
Let me show this with an example. I will start with two tanks of compressed gas. The first I will open up into room 1. The expansion of the gas, as it lowers pressure, will increase entropy as it flow into the room. The energy for the entropy is contained within the pressure.
In the next room, or room 2, I connect a similar air tank to a work cycle. This work cycle is 80% efficient, with only 20% energy loss into entropy. We essentially steal 80% of the energy the other room had, which went into entropy. At the exhaust end of our work device, the gas trickles out in a wimpy way (20% entropy) since I took away a lot of its energy could have used for entropy.
The two rooms will act differently, using the similar gas cylinders exhausted to the air. The work cycle took energy away from room 2 entropy. If I open the door between the two rooms, since there is an entropy potential between the two rooms, I can direct the flow of the entropy. It will go from room 1 to room 2. The pressure will push it that way.
Zero gravity is analogous to room 1 where the expansion of the gas goes into 100% into entropy, unobstructed by a work cycle, scavenging energy. Higher gravity is connected to room 2 where work occurs. The flow of entropy goes from zero gravity to higher gravity due to the entropy potential between 100% inefficiency and the efficiency of the work cycle.
The gravitational work is slick because it creates entropy potential and therefore increases the odds for things to happen in a directed way. The zero gravity loses its 100% inefficiency since it lose entropy toward the work cycles of gravity. To maintain the second law we need a way to increase entropy; expansion.
Admit the hyperbolic black hole galactic gravitational field (HBHF) as a postulate th
I have shown that it is expedient and practical to admit the hyperbolic black hole galactic gravitational field (HBHF) as a postulate – that is, as a mere tentative logical premise. There are several ways in which it could be confirmed as a contender for a place in the cosmological pantheon of physical “law”. If it could be seen as a real cosmic rule, every single one of the phenomena that are now ascribed to “Dark Matter” can be more parsimoniously charged to the HBHF. This is also because, by extension, the HBHF can be used to characterize the hyper-excited “inflaton particle” in the false vacuum of the ultra-high energy “inflaton field” that is supposed to have sprung into existence as a probabilistic quantum fluctuation. It offers a new way to forge another link between quantum dynamics and relativity theory.
When enough such links are made, we shall obtain a quantum theory of relativity without having to tolerate the putative overbearing “grand unified theories” or “theories of everything” like superstring theory or quantum loop gravity. These seem to offer no advantage other than the grandeur of hyper-complexity and the safe haven of unfalsifiability. In other words, the HBHF might allow theorists to “get real”. So, it is practical and expedient to admit the HBHF as just such a postulate.
The HBHF, if it can be allowed, would further reinforce Inflation Theory by providing a mechanism for the transition of the excited inflaton HBHF particle/field to a “ground state” inverse square gravitational field. It implies how potential energy in the inflaton field might have powered inflation and how it may now be powering “reinflation”, the accelerating Hubble expansion of the universe in the current epoch. It would seem to require endorsement of the “Many Worlds” interpretation of quantum mechanics/dynamics because the HBHF must have pre-existed inflation in a sort of “metatime” in a “multiverse”. But, this is implied by Alan Guth’s inflation hypothesis anyway. And then, if the universe was once a quantum entity, then it still is – with profound implications and more opportunities to forge links with GR.
Incidentally, the HBHF can certainly be admitted according to common interpretations of some theorems of general relativity if spacetime, in the moments before inflation, was indeed regarded as “flat”. That is, the HBHF can certainly be allowed by GR if the HBHF inflaton field is restricted to two dimensions. This gives a new twist to inflation. It may mean that inflation involved “unpacking” our spatially 3-D universe from a more compactified 2-D version.
And then, the deep interior of black holes at their singularities (as physical realities) might be viewed as recompactifications of spacetime – reconvolutions to a strictly 2-D format wherein the HBHF can persist with no contradiction to conventional interpretations of GR. Then, in our multiverse, the galactic 2-D HBHF sibling set might define orbital planes for each and every entity in its purview.
That this galactic field must be defined as a disk shaped oblate spheroid means that its tidal influence on the central super-massive Black Hole (SMBH) must be concentrated in the plane of the galaxy. The mass of the disk may be thousands of times the mass of the SMBH so, its (mutual) effects on the SMBH are very substantial. Thus, Einstein’s theory of the relativistic non-symmetric gravitational field must be used to characterize it and that of the SMBH. Nobody has ever done this. And Birkhoff’s Theorem or its congeners simply do not exactly apply to any real BHs.
Simple geometry is used to define radiant flux and other quantities that are posited to emanate from a point source. An imaginary sphere is constructed around the source. An infinitesimally small area is defined on the surface of this sphere. Then the flux, quantity of lines of force or light lines, through this fractional area must be proportional to 1/r^2 because the total area of a sphere is proportional to 1/r^2 and the spherical enclosure envelopes all the flux. Using this definition to prove that gravity must be an inverse square (1/r^2) phenomenon uses circular reasoning because it assumes as a premise that which is to be proven (it begs the question).
What if the source, even though it is a point, is assumed to be enclosed by an infinitesimally small space that is a very oblate spheroid by virtue of its extremely rapid rotation? What if this is the ultimate source, in fact. Then, what if this flux emission pattern is also very strongly oblately spheroidal? In addition, what if this flux was influenced by relativistic “frame dragging” and “thirring”? Also, what if the gravitational tidal influence of a galactic disk would also influence this spheroid to be even more oblate? The gravitational field of the disk must be perfectly coaxial and concurrent with the field of the SMBH. Its field must perfectly superpose. Then, the combined field must be treated in order to determine if there could be a hyperbolic field component. But, this combined field is even more “non-symmetric” and even more difficult to handle with GR, except by Einstein’s non-symmetric field theory, which has never been done. So, it is really impossible to prove by appeal to any theory or principle whatever whether the hyperbolic gravitational field is impossible. But, it is possible to appeal to strong geometric principles to argue that, indeed, it is possible.
I need a collaborator ! ! !
See more details at www.NeoCosmology.blogspot.com .
See the latest replies by Gary A on this forum under the titles:
Looking for a cosmology collaborator
No Trouble with Tribbles
[SIZE=+1]Admit the hyperbolic black hole galactic gravitational field (HBHF) as a postulate that explains Dark Matter[/SIZE]
I have shown that it is expedient and practical to admit the hyperbolic black hole galactic gravitational field (HBHF) as a postulate – that is, as a mere tentative logical premise. There are several ways in which it could be confirmed as a contender for a place in the cosmological pantheon of physical “law”. If it could be seen as a real cosmic rule, every single one of the phenomena that are now ascribed to “Dark Matter” can be more parsimoniously charged to the HBHF. This is also because, by extension, the HBHF can be used to characterize the hyper-excited “inflaton particle” in the false vacuum of the ultra-high energy “inflaton field” that is supposed to have sprung into existence as a probabilistic quantum fluctuation. It offers a new way to forge another link between quantum dynamics and relativity theory.
When enough such links are made, we shall obtain a quantum theory of relativity without having to tolerate the putative overbearing “grand unified theories” or “theories of everything” like superstring theory or quantum loop gravity. These seem to offer no advantage other than the grandeur of hyper-complexity and the safe haven of unfalsifiability. In other words, the HBHF might allow theorists to “get real”. So, it is practical and expedient to admit the HBHF as just such a postulate.
The HBHF, if it can be allowed, would further reinforce Inflation Theory by providing a mechanism for the transition of the excited inflaton HBHF particle/field to a “ground state” inverse square gravitational field. It implies how potential energy in the inflaton field might have powered inflation and how it may now be powering “reinflation”, the accelerating Hubble expansion of the universe in the current epoch. It would seem to require endorsement of the “Many Worlds” interpretation of quantum mechanics/dynamics because the HBHF must have pre-existed inflation in a sort of “metatime” in a “multiverse”. But, this is implied by Alan Guth’s inflation hypothesis anyway. And then, if the universe was once a quantum entity, then it still is – with profound implications and more opportunities to forge links with GR.
Incidentally, the HBHF can certainly be admitted according to common interpretations of some theorems of general relativity if spacetime, in the moments before inflation, was indeed regarded as “flat”. That is, the HBHF can certainly be allowed by GR if the HBHF inflaton field is restricted to two dimensions. This gives a new twist to inflation. It may mean that inflation involved “unpacking” our spatially 3-D universe from a more compactified 2-D version.
And then, the deep interior of black holes at their singularities (as physical realities) might be viewed as recompactifications of spacetime – reconvolutions to a strictly 2-D format wherein the HBHF can persist with no contradiction to conventional interpretations of GR. Then, in our multiverse, the galactic 2-D HBHF sibling set might define orbital planes for each and every entity in its purview.
That this galactic field must be defined as a disk shaped oblate spheroid means that its tidal influence on the central super-massive Black Hole (SMBH) must be concentrated in the plane of the galaxy. The mass of the disk may be thousands of times the mass of the SMBH so, its (mutual) effects on the SMBH are very substantial. Thus, Einstein’s theory of the relativistic non-symmetric gravitational field must be used to characterize it and that of the SMBH. Nobody has ever done this. And Birkhoff’s Theorem or its congeners simply do not exactly apply to any real BHs.
Simple geometry is used to define radiant flux and other quantities that are posited to emanate from a point source. An imaginary sphere is constructed around the source. An infinitesimally small area is defined on the surface of this sphere. Then the flux, quantity of lines of force or light lines, through this fractional area must be proportional to 1/r^2 because the total area of a sphere is proportional to 1/r^2 and the spherical enclosure envelopes all the flux. Using this definition to prove that gravity must be an inverse square (1/r^2) phenomenon uses circular reasoning because it assumes as a premise that which is to be proven (it begs the question).
What if the source, even though it is a point, is assumed to be enclosed by an infinitesimally small space that is a very oblate spheroid by virtue of its extremely rapid rotation? What if this is the ultimate source, in fact. Then, what if this flux emission pattern is also very strongly oblately spheroidal? In addition, what if this flux was influenced by relativistic “frame dragging” and “thirring”? Also, what if the gravitational tidal influence of a galactic disk would also influence this spheroid to be even more oblate? The gravitational field of the disk must be perfectly coaxial and concurrent with the field of the SMBH. Its field must perfectly superpose. Then, the combined field must be treated in order to determine if there could be a hyperbolic field component. But, this combined field is even more “non-symmetric” and even more difficult to handle with GR, except by Einstein’s non-symmetric field theory, which has never been done. So, it is really impossible to prove by appeal to any theory or principle whatever whether the hyperbolic gravitational field is impossible. But, it is possible to appeal to strong geometric principles to argue that, indeed, it is possible.
I need a collaborator ! ! !
See more details at www.NeoCosmology.blogspot.com .
See the latest replies by Gary A on this forum under the titles:
Looking for a cosmology collaborator
No Trouble with Tribbles
Actually, it has been shown to you why this is incorrect. Carefully read the responses to your earlier threads.
"Cosmologists are always wrong, but never in doubt." - Lev Landau
"Cosmologists are always wrong, but never in doubt." - Lev Landau
Absolutely.
They overlook what is happening literally right in front of their very eyes. There is a supermassive black hole (SMBH) in the center of our galaxy. It contains at least 4 million solar masses and is still growing. Virtually all the galaxies in the universe (U) contain SMBHs. So, as the U expands cosmologists say entropy (S) is increasing and so, it is not conserved. Redshift is a symptom, not a cause. It is a sign of Hubble expansion. But the consolidation of matter into black holes all over the universe means that entropy is being sucked up by them (and is stored on the quasi-surface of the "event horizon") so that S is reduced in the whole rest of the universe by an amount that may be just equal to the S increase implied by Hubble expansion.
You might say, then, that S is still increasing if the entropy in black holes is counted in the audit. But, prophets say that the universe is proceeding toward a state wherein all the matter and energy in it will eventually reside in these black holes. They will all be SMBHs too, so they will become indistinguishable to even an observer who might see such a universe from a perspective in the multiverse in metatime.
This means that the whole universe will eventually collapse into just one representative SMBH and the U will effectively become a single particle once more. Especially, as the universe will eventually reach a state wherein galaxies and their embedded SMBHs will expand beyond "causal contact", the entropy of "the universe", as it must then be defined, must decline by at least as much as may have been gained by expansion.
So, entropy may be conserved after all and such conservation may be of crucial importance in discerning the details of the process of accelerating Hubble expansion according to the Friedmann equations under the FLRW relativistic metric. Friedmann uses an analog to the ideal gas equation with a work function, w and with the potential of defining and manipulating thermodynamic quantities like S, "delta S".
No cosmologists are working on this as though gravitational lensing has induced a sort of intellectual myopia.
"Cosmologists are always wrong, but never in doubt." - Lev Landau
Absolutely.
They overlook what is happening literally right in front of their very eyes. There is a supermassive black hole (SMBH) in the center of our galaxy. It contains at least 4 million solar masses and is still growing. Virtually all the galaxies in the universe (U) contain SMBHs. So, as the U expands cosmologists say entropy (S) is increasing and so, it is not conserved. Redshift is a symptom, not a cause. It is a sign of Hubble expansion. But the consolidation of matter into black holes all over the universe means that entropy is being sucked up by them (and is stored on the quasi-surface of the "event horizon") so that S is reduced in the whole rest of the universe by an amount that may be just equal to the S increase implied by Hubble expansion.
You might say, then, that S is still increasing if the entropy in black holes is counted in the audit. But, prophets say that the universe is proceeding toward a state wherein all the matter and energy in it will eventually reside in these black holes. They will all be SMBHs too, so they will become indistinguishable to even an observer who might see such a universe from a perspective in the multiverse in metatime.
This means that the whole universe will eventually collapse into just one representative SMBH and the U will effectively become a single particle once more. Especially, as the universe will eventually reach a state wherein galaxies and their embedded SMBHs will expand beyond "causal contact", the entropy of "the universe", as it must then be defined, must decline by at least as much as may have been gained by expansion.
So, entropy may be conserved after all and such conservation may be of crucial importance in discerning the details of the process of accelerating Hubble expansion according to the Friedmann equations under the FLRW relativistic metric. Friedmann uses an analog to the ideal gas equation with a work function, w and with the potential of defining and manipulating thermodynamic quantities like S, "delta S".
No cosmologists are working on this as though gravitational lensing has induced a sort of intellectual myopia.
Yours is not proof.
Yours is not proof.
Carefully read my stuff and you will see why.
It is irrelevant anyway. A tentative postulate needs no proof. Otherwise, Galileo, Kepler and Copernicus should have been burned at the stake for heresy. The Pope should have been proud. All attempts to induce a paradigm shift should have failed and we should all be still living on a flat Earth.
Yours is not proof.
Carefully read my stuff and you will see why.
It is irrelevant anyway. A tentative postulate needs no proof. Otherwise, Galileo, Kepler and Copernicus should have been burned at the stake for heresy. The Pope should have been proud. All attempts to induce a paradigm shift should have failed and we should all be still living on a flat Earth.
Yes. It is just very difficult to measure.
Frame-dragging and the curvature of space or spacetime are not entirely the same thing. At least to the extent that the curvature of space is associated with gravitation.
The curvature of space is more like a description of the shape of space, defined by the presence of mass.
Frame-dragging is more like a motion of space associated with the motion of mass through it. While frame-dragging can affect the motion of objects in space it does not add to the gravitational attraction between objects.
There is also a bit of a trap in this description, in that frame-dragging is not space moving with matter. It is a very weak interaction. Any analogy we make can only suggest the relationship. Keeping that in mind, you might think of frame-dragging as the way a stick stirring a pot of honey, very slowly.., pulls the honey in the direction of the stick's motion without making the honey swirl.
If your above statement is true , then Newton's First Law of Motion on inertia is no longer true ; because motion of objects will be affected at any speed without any gravitational force .
Correct!
But not measureablely. For locally flat space and time, where Newtonian Mechanics can still be applied, any affect on the motion of an object is trivial and insignificant.
Though there is little said about how special and general relativity affect the first law, Newton's second law of motion, F = ma, from the perspective of special relativity, becomes $$F = ma\gamma$$ where $$\gamma = \frac{1}{\sqrt{v^2/c^2}$$, the Lorentz factor, which acts as a modifier for the influence of relatavistic velocities, in this relationship.
It is more difficult to explain how the Lorentz factor figures into Newton's formula for momentum, p = mv, but it plays a similar role, limiting velocities to less than the speed of light, c.
There is also little discussion as to how all of this affects Newton's third law of motion, "For every action, there is an equal and opposite reaction." If the motion of an object drags on space, then space must resist in some way. Some of the more recent attempts to explain inertia, as an interaction between a moving object and the zero-point field or vacuum energy of QM, begins to touch on this, at least indirectly... However, again this interaction remains insignificant at the classical velocities we are able to achieve at present.
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