It From Bit - Entropic Gravity For Pedestrians
    By Johannes Koelman | March 25th 2010 08:00 PM | 79 comments | Print | E-mail | Track Comments
    About Johannes

    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune


    View Johannes's Profile
    Two and a half months since Erik Verlinde submitted his entropic gravity paper, and all of physics and cosmology has turned into entropy. Well, I am exaggerating a bit, and perhaps more than just a bit. Yet, fact is that within two weeks of Erik's publication a steady stream of 'entropic everything' papers has developed at a rate of close to one paper per day. Gravity, Einstein's equations, cosmic expansion, dark energy, primordial inflation, dark mass: it's all entropic. Chaos rules. Entropy is king!

    Or is it?

    Could it be that an 'entropic bandwagon' has started rolling? Is this all not just a fad appealing to scientist tired of string theory? What is this elusive entropic force anyway? Do these folks really believe bits of information attract each other?

    Of cause not. Bits don't attract, and entropy doesn't pull. The term 'entropic force' seems to wrong-foot large groups of readers (and some physics bloggers alike). Entropic interactions are not mediated by forces acting at micro scales. Entropic forces exist even in systems that at a microscopic level poses no energies other than kinetic energy. Yet, at a macroscopic level such systems are subject to configurational accelerations. These accelerations result simply from certain configurations corresponding to a larger number of micro states than others. This, combined with the tendency of physical systems to sample the microscopic states in an unbiased way, yields a macroscopic dynamics that prefers configurations that are denser in terms of micro-states.

    Puzzled? Let's look at some simple, yet progressively more realistic examples.

    Tetrahedron Hole Dynamics

    We start with a seemingly trivial toy model. A model that strips entropic attraction to its barest essentials. You might feel this Mickey Mouse model can impossibly have any bearing on the problem of entropic gravity.

    Be patient, I promise you all will become clear in a minute!

    Our toy universe consists of six 'ray paths' that form the edges of a tetrahedron. Each ray path can be in two distinct states: occupied or empty. This accounts for a total of 26 = 64 states. Three ray paths meet at each vertex. If all three are empty, the vertex represents 'a hole' that gets filled with at least one particle. If any of the three ray paths is occupied, the vertex is 'full' and can not contain any particle.

    We investigate configurations with two particles, and therefore limit the tetrahedron configurations to those containing one or two holes. The dynamics is straightforward. We label the ray paths '1'..'6', construct a suitable starting configuration, and grab a die.

    Throw the die, note down the number of spots, and check the corresponding ray path in the tetrahedron:

    A) If the ray path is occupied, make it empty, unless doing so would create more than two vertices containing particles.

    B) If the ray path is empty, occupy it, unless this would result in zero particle vertices.

    Again throw the die and repeat ad infinitum.

    This simple process creates a sequence of configurations, each of which contains two particles occupying either two different vertices (two particles in two distinct holes), or the same vertex (two particles in the same hole). Below animation clarifies the process.

    Tetrahedron universe

    The tetrahedron 'universe'. The edges change from 'empty' (grey), into 'occupied' (red) such that there are always one or two 'holes': vertices where three empty edges meet. This edge dynamics dictates the movements of two particles that hop from vertex to vertex such that any hole contains at least one particle.

    In this model there is no explicit force acting between the two particles. So one might naively postulate that both particles will jump randomly from vertex to vertex, and will be as often at the same vertex as at different vertices. This is not the case. The reason is simply that there are 16 states with one hole, against only 6 states with two holes (by allowing only for one and two-hole configurations, 42 of the 64 total number of microstates are forbidden).

    Another way of looking at this is that for a given vertex to contain a particle, the three ray paths meeting at that vertex need to be empty. This reduces the entropy (the number of bits needed to describe the tetrahedron universe) by three. For two given vertices to contain a particle, both vertices need to have three empty ray paths. One would therefore expect an entropy reduction of 3 + 3 = 6 bits. However, both vertices necessarily have one ray path in common, and an entropy reduction of 6 – 1 = 5 bits results. However, if both particles are accomodated at the same vertex, both particles dictate the same three ray paths to be empty. In other words: there is 3 common ray paths and an entropy reduction of 6 – 3 = 3 bits results. So, the two particles being together at the same vertex creates a smaller entropy reduction compared to the case of the two particles being seperate. In other words, two particles together at one vertex corresponds to significantly more states than two particles at separate vertices. This is all that is needed for a tendency for both particles to stick together. 

    The Mikado Universe

    Now we are ready for the next step. The mikado universe. Still a toy model, but I promise you we are getting closer to 'the real thing'.

    Imagine a two-dimensional space spanned by a large number of ray paths. Think of each ray path as extending indefinitely, and the whole network of ray paths forming a discrete Planck-scale configuration from which the planar space emerges. Like in the tetrahedron universe, each ray path represents an elementary degree of freedom of the system: it can be occupied or empty. We will interpret a ray path being occupied, as a causal influence being transmitted via the ray path. (More about that later.)

    We need particles in our model, and therefore restrict the allowable mikado universe configurations to those containing enough empty ray paths such that we have available two 'holes'. In this model holes are defined as regions not crossed by any occupied ray paths, and large enough to contain a circle of given radius. Below figure clarifies the concept.

    The mikado universe. The straight lines represent the ray paths. The ray paths shown in gray are 'empty' and do not contribute to the entropy. As a result two 'holes' exist: regions void of causal influences large enough to contain circles of specified radius (indicated in red).

    Now imagine a dynamics similar to that in the previous example. We label the ray paths '1', '2' ... 'N', construct a starting configuration with two holes, and grab an N-sided die.

    Throw the die, note down the number of spots, and check the corresponding ray path in your mikado universe:

    A) If the ray path is occupied, make it empty.

    B) If the ray path is empty, occupy it, unless this would cause one or both of the holes no longer capable of fitting the circle of given size.

    Again throw the die and repeat ad infinitum.

    What will you see happening would you be patient enough to go through many of these steps? If you have understood the tetrahedron model, the answer is simple. You will see both holes moving towards each other.

    Why is that?

    Like in the tetrahedron model, there are more micro-configurations available when the holes are closer together. To see why this is the case, first consider two holes far apart. Each hole requires a certain number of ray paths to be empty. Each hole thereby reduces the overall entropy by a corresponding number.

    Now place the holes close together. Again, each hole rules out a certain number of ray paths from becoming occupied. However, as both holes are in each other's vicinity, the set of ray paths prevented by hole 1 from becoming occupied will have an overlap with the set of ray paths prevented by hole 2 from getting occupied. Like in the tetrahedron model, the two holes being closer together creates a smaller entropy reduction compared to the case of the two holes being far apart. And the result, as we know by now, is an entropic attraction.

    Now, for this model we can even deduce how the entropy drop reduces when the holes move together. And knowing this entropy drop, we can derive the distance dependency of the entropic force.

    All we have to calculate is the scaling of the number of ray paths crossing both holes. For a uniform and isotropic distribution of ray paths, this number S is proportional to the radii (r1 and r2) of both holes and inversely proportional to the distance (R) between both hole centers:

    S ~ r1 r2 / R

    The entropic force is proportional to the gradient of this number:

    F ~ dS/dR = -r1 r2 / R2

    Here, the minus sign indicates the force to be attractive.

    Finally, we ask ourselves what really are these holes of given radius? You might have noticed that no occupied ray paths leave these holes. With occupied ray paths interpreted as paths along which causal influences propagate, this means that no causal influence leave these holes. Sounds familiar, right? Indeed, the holes in the mikado model can be thought of as black holes. And black holes have a radius r proportional to their mass M. So, we finally have:

    F ~ - M1 M2 / R2

    OK, let's call in Sir Isaac...

    The Real Thing

    Are you ready for the real model of the universe?


    Well, maybe you are ready, but I am afraid I have to disappoint you. I have no 'real' model. No one has.

    What about the above mikado universe?” you might ask. “That did lead to the right equation for Newtonian gravity, right?” Well, yes. But I did cheat by more than a bit. Firstly, I presented a two-dimensional universe. Would I have constructed the same mikado model in three-dimensions, things would not have worked out so nicely. In order to make things work in three dimensions, the number of ray paths need to be diluted with distance in such a way that a two-dimension behavior results. In other words, a holographic description needs to be introduced. (You are not surprised by that, are you?)

    Secondly, for a model like this to make physical sense, it needs to be properly embedded not in space, but in spacetime. So we even need to go one dimension higher (and retain the holographic description).

    Thirdly, the fixed ray path network violates various physical symmetries. And also the model is not quantum mechanical in nature. And there are several more problems with this model, some more subtle than others.

    But we need not go into all of these. In physics it is entirely valid to construct models with shortcomings, provided these models do provide certain insights. And such is the case here. We have seen how a force-free and almost trivial microscopic dynamics can lead to an attractive force at macroscopic scales. But there is more. The model also elucidate other important aspects of entropic gravity.

    One such aspect has to do with the question of the reversibility of entropic gravity forces. Some have claimed that entropic forces are necessarily irreversible. In other words, in a system with entropic gravity it would in general not be possible to cause the system to trace back its history.

    Reversible Entropic Forces

    The claim that entropic forces are necessarily irreversible is a misconception. Verlinde has tried to argue against this wrong concept, but he failed to note a key point. Key is that if the underlying microscopic (Planck scale) dynamics is reversibility, so will be the emerging entropic force.

    Using the above models, it should be immediately clear that entropic forces can also be observed in reversible systems. The careful reader will have noticed that in both models I stated “Throw the die, and note down the number of spots”. Assuming you did so, the evolution in both models can be reversed. Simply start with the last configuration, and instead of throwing the die, read out the written numbers in reverse order, starting with the last one. That's all. The system will reverse its whole history, and when you arrive at the first number, it will be back in its original state.

    This is not a unique behavior of the above models. Any system with an underlying reversible micro-dynamics, when generating a macro-scale entropic interaction will do so in a reversible way. This is nothing shocking. Entropic attraction can be observed in molecular dynamics simulations as simple as mixtures of hard spheres of different sizes. Such molecular dynamics simulations are nothing more than ways to solve Newton's equations of motions for large numbers of interacting particles. And as we all know, Newton's equations of motion can be reversed in time simply by reversing all individual velocities.

    What next?

    The above description makes it clear what is the main task ahead of us: working out what are the right microscopic degrees of freedom that results in the correct entropic gravity. Verlinde's work gives the hope that as soon as we know the correct holographic degrees of freedom, a gravity-free holographic quantum field theory can be constructed that describes gravity in four-dimensional space-time along with electromagnetism and the weak and strong nuclear forces.

    I am not too optimistic that we will soon have such a theory. Yet, even in the absence of such a full description, we can still make progress and clarify further consequences of an entropic gravity theory.

    In a previous blog post I have made it clear that such a theory unavoidably (and almost trivially) lead to an accelerated universe. Whilst it might not be immediately obvious that clogging together of mass leads to an increase in the number of degrees of freedom, the fact that cosmic expansion leads to increased degrees of freedom should not surprise anyone. A quick calculation shows that the corresponding entropic acceleration is of the right magnitude to describe the cosmic acceleration: d2R/dt2 = 2c2/N dN/dR = 4c2/R, where N represents the number of degrees of freedom of the observable universe (assumed to be proportional to 4R2, the area of the cosmic horizon). Subsequent work by Li and Wang and Gao, as well as more recent work by a group around Nobel laureate Smoot has corroborated these results. Smoot et al recently also demonstrated entropic effects also hold the potential to explain the postulated primordial cosmic inflation.

    Inflatons, dark energy: will all of it disappear? Surely, holographic entropy holds the promise of taking up the role of a well-polished Occam's razor!


    More Hammock Physicist articles: The largest distance between two points. What you didn't know about E=mc2. Time's arrow. Quantum telepathy. Booting up the universe. Fibonacci chaos. Powers of six-billion. Quantum virus. The grand arena of physical reality. Game theory and the art of acting rational. Holographic hot horizons. Holographic horizons get hotter. How to get rid of dark energy.


    Great article! I recall from the early days of cellular automata that even the simplest of feedback mechanisms collapsed the number of possible states by a far larger amount than seemed intuitively possible. So much for intuition!
    Johannes Koelman
    Thanks Rycharde. It is interesting that you mention cellular automata (CA). CA researchers like Stephen Wolfram have been criticized for presenting their CA work as 'new physics'. I think the criticism of 'overselling' is in itself correct, but this does not take away the fact that CA models have helped enormously in elucidating many fundamental concepts in the statistical physics of systems with many degrees of freedom, and in chaos theory in particular.
    You are right: the above two discrete ray models can indeed be seen as CA models. And yes, although not introducing 'new physics', they serve the same purpose that makes CA models so useful: reducing the physics to its barest essentials.
    Thanks Johannes, this helps me to better understand the entropic gravity concept. It seems you are hinting at an underlying twistor model for entropic gravity?

    Gravity, Einstein's equations, cosmic expansion, dark energy, primordial inflation, dark mass: it's all entropic. Chaos rules. Entropy is king! Or is it?

    What is your view on these claims? Will all of this likely prove to be correct?

    Johannes Koelman
    You're welcome, Henk.

    1) The microscopic model need not be a twistor model perse, but it is definitely a possibility. Key, I think, is that it is a model that captures the degrees of freedom solely in terms of holographic causal influences.

    2) It should not surprise you (see text at bottom of the above blog post) that I am a strong believer in entropic acceleration (or entropic dark matter if you like). I proposed it two months back, and since (also thanks to further work by Smoot and others) I have only seen further support of the concept.

    I also believe the idea of entropic inflation holds promise. (Although I must stress here that I don't know enough about inflationary theory to have a strong opinion.)

    I do not believe (yet) the claims that dark matter has an entropic explanation. And I feel even less in support of entropic Coulomb interactions (which also have been proposed).
    This is the best 'laymans' explanation of the Verlinde / entropic gravity theory I have found. Being mathematically challenged I really appreciated the clarity and approachability of this article. Thanks.


    Johannes Koelman
    Wow, I consider that the best compliment I could get. Thanks.
    Thanks for the article. There is something that is nagging me about the emergence of a force, I was wondering if you could perhaps clarify.

    In both of your examples, you say there is no intrinsic force pushing or pulling the elements together, but that they end up clumped together. You then state that there is an emergent force at play.

    What I don't get is why you describe this emergent clumping of things as being an attractive force between those particles. Yes, in the purely physical sense, acceleration towards each other implies force, but really, the "force" particle in those examples is the dice which, as is more intuitively seen in the mikado example, lights up ray-paths that "nudge" the voids in a certain direction. So wouldn't this mean that while being an emergent force, really, there *is* a "force particle" that creates it (those ray paths)?

    In other words, while air pressure is an emergent force that arises from the existence of EM repulsion between charged molecular shells, gravity is an emergent force that would arise from the interaction of a fundamental force between particles with any charge (even neutrons). Isn't this begging the question? Gravity is already assumed to be an force interaction between particles of mass over long distances. What are those Mikado rays in the unified theory?

    This may not have any impact on the answer to The Lay man's question, but a correction I want to point out is that the force of air pressure does not arise from repulsion of like charges. Rather, it comes from the Pauli exclusion principle. When two atoms collide, they do not pass through one another because the shell electron energy states are already filled up. It's not because of any like-charge repulsion. I believe that a gas of neutral fermions, such as neutrons, would exhibit 'air' pressure just as well as atoms.

    Is this significant in some deeper way? The Pauli principle has always seemed odd to me, where the concepts of being 'identical' and 'indistinguishable' merge together with strange quantum consequences. Maybe there is something entropic hidden in that relationship as well?

    Johannes Koelman
    Indeed, the Pauli exclusion principle plays a role. However, this role is manifest as an effective interaction (repulsion) between the atoms. 
    Johannes Koelman
    Good questions, Lay man.

    It is important to realize that the mikado universe consists of just a fixed large number of ray paths that we can think of as being fixed in space. There is nothing else really. Yes, there are particles (or voids as you call them), but these are simply a manifestation of a group of ray paths being in a particular state.

    Each ray path can be 'lit' or 'dark'. We now start playing with the states of the ray paths and switch these between 'lit' and 'dark'. It doesn't matter really how we do this (with a die or some other chaotic mechanism), as long as we don't light up ray paths that would cause a particle to disappear. So if the die tells us to light up a ray path straight through a particle (an area covered by dark ray paths only), the die throw is ignored and we throw again.

    Note that we have not introduced any force between ray paths. The lighting pattern of the ray paths doesn't cause any repulsion or attraction. As the particles are defined in terms of the lighting pattern of the ray path there is also no explicit force between the particles. The lighting up of ray paths does not cause them to "nudge" the particles.

    Yet, the particles will move together... 

    You also ask what these 'mikado rays' would correspond to in a 'mikado-type theory' describing the real universe. It is best to think about the mikado rays as a discretisation of the light cones in four-dimensional spacetime. A discretisation that is holographic in nature. That means that the number of light rays in a certain region should not scale with its spatial volume, but rather with its area.

    I see. So these mikado lines aren't actual paths of photons or anything actually manifest, but rather something more abstract like quantum states. Is that the idea? It makes sense that way, indeed.

    Johannes Koelman
    Well, the 'mikado lines' are the actual paths of photons. The complication (or simplification?) is that in a quantum spacetime the paths photons can take (the directions in space) are discrete. 
    Cue my proclaiming with indignations: it's turtles all the way down!

    thanks a lot , Johannes!
    came here from reddit and this blog post was the most rewarding thing I read in ages on this kind of stuff.

    not a physicist, nor mathematician, far from it, but I think I did manage to get what you're saying.
    the basic idea, and please correct me if I'm way off, would be that... hm... I'll put it in the most mundane words I can... well... is that... stuff clogs together just to 'make room' for the universe to 'express' itself in a more entropic way :)
    was that too mundane? :))) or maybe I'm completely wrong?

    Johannes Koelman
    "stuff clogs together just to 'make room' for the universe to 'express' itself in a more entropic way"

    I like that!  Could turn out to be a surprisingly accurate description of emergent gravity. With a small modification it can also incorporate the cosmic accelerated expansion:

    Mass clogs together and distant horizons recede to give the universe more freedom to express itself.

    Thanks Corcodell.
    Amateur Astronomer
    To get a force F from Entropy S requires a gradient involving temperature T and distance x. Otherwise the units would not add up to a force.

    (35.7) .......... Fs = S dT/dx ..... or

    (35.8) .......... F = T dS/dx ...... or some combination of the two.

    (35.9) ....... dE = TdS - Fdx ....... for internal energy E.

    (35.10) ........ Fdx = PdV ....... showing that E really is the classical internal energy of thermodynamics.

    Verlinde used a combination something like (35.8) with partial differentials in his published paper and (35.9) in his Logic of the Paper. In the Logic he made it clear that it is the differences of Entropy from one place to another that leads to the concept of a generalized force.

    Entropy has the units of Boltzmann’s constant k on the microscopic scale and the gas constant R on the macroscopic scale.

    That means Entropy is a type of specialized Heat Capacity that determines how much energy of a certain type is required to raise the temperature of a system.

    Entropy relates to ordinary Heat Capacity at constant pressure.

    (35.11) ..... dS/dT = Cp/T ...... or with partial differentials when pressure is not constant.

    I think of the difference between Entropy and Heat Capacity in terms of degrees of freedom compared to energy states where Heat Capacity by definition has all states randomly occupied with energy that is equally partitioned in a thermal equilibrium condition. By contrast Entropy is a similar type of variable, but allows for a system where some states can be biased by construction such that they are not randomly occupied, energy might be partitioned equally or unequally or some combination of both types, and the system might or might not be in thermal equilibrium. This is how Entropy acts as a measure of orderly arrangement in a physical system.

    In other words Heat Capacity occurs when the number of possible states is equal to the degrees of freedom, but Entropy is able to keep track of additional information about how the number of possible states differs from the degrees of freedom. This is the important point in the Third Law of Thermodynamics where entropy can decrease if some of the possible states are not randomly occupied with energy.

    With these thoughts in mind, the examples in Johannes’ article are easier to understand, as a trade off between orderly construction and random operation. Then the force arises from the difference of Entropy between two states at a certain temperature and the physical distance between the two states.

    My concern with the direction that work on Entropic force is taking is that the examples some other writers are giving look more like Heat Capacity than Entropy, while the discussion always tries to call it Entropy. If Entropy really is intended in the examples then the papers must encompass realistic combinations of random and non random distributions, partitions that are not always equal, and thermal states that are not always in equilibrium. If these things are not allowed then the force is arising from ordinary thermodynamics and heat capacity.

    (35.12) ..... Fc = Cp dT/dx ..... compared to (35.7)

    Verlinde is the only published writer I’ve seen so far who deliberately makes the important distinction between Entropy and Heat Capacity. The concept is also implied in the two examples Johannes gave above. As usual Verlinde was very clever in the way he inserted the most important concept with the least possible explanation.

    The implication is that vacuum space has a structure represented by Planck units on a hologram that support a variety of situations very much different than the unstructured kinetics of a gas.
    Johannes Koelman
    Wow, Jerry. Equations numbered up to 35.12. It seems you are busy writing a book on the entropic universe!
    "Equations numbered up to 35.12. It seems you are busy writing a book on the entropic universe!"

    Chapter 35, and he only just arrived at variations of F dx = T dS

    That is going to be one massive tome.

    So take this a step further. If entropy is increasing, then light in transit will eventually be presented with an ever-decreasing difference between available quantum levels for each E/M and M/E transition. And of course since energy is conserved it can never jump to a higher level. If there are any transitions they must be towards lower levels. Levels of energy translate to frequency and wavelength. Ergo, redshift over time.

    Dear Johannes,

    many thanks for your terrific article !

    Entropy is actually not a king - and even not a queen: Entropy is nothing but an exact measure of our sheer ignorance about the system.

    I was very glad to learn that young people start to recognize this. This brings me hopes that there will be some important paradigm change in the foreseeable future ...

    In physical chemistry we know since more than 80 years about the enthalpy-entropy compensation which is still hotly debated, because there are many colleagues who are adepts of Her Majesty Entropy. But in fact, if we read into the Clausius' classical work and carefully re-think it over, we'll readily see that entropy is simply dual to energy - and this is why all this "garbage" like "entropic forces" etc. has its full right for existence ...

    Recently, Grisha Perelman has also shown where the true place of the entropy concept is. Everybody is happy about his proof of the Poincaré conjecture, but nobody (and this is astonishing !) was not capable of recognizing this important and far-reaching aspect of his brilliant work.

    A propos, we are also humbly trying to understand the nature of entropy, already during several years:

    1. Starikov, E. B.; Nordén, Bengt: Enthalpy-entropy compensation: A phantom or something useful?. Journal of Physical Chemistry B, 2007, 111 (51) pp. 14431-14435.

    2. Evgeni B. Starikov, Itai Panas and Bengt Nordén, "Chemical-to-Mechanical
    Energy Conversion in Biomacromolecular Machines: A Plasmon and Optimum
    Control Theory for Directional Work. 1. General Considerations
    ", J. Phys. Chem. B, 2008, 112 (28), pp 8319–8329.

    3. Starikov, E. B.; Hennig, D.; Nordén, Bengt: Protein folding as a result of 'self-regulated stochastic resonance': A new paradigm?. Biophysical Reviews and Letters, 2008, 3 (3) pp. 343-363.

    4. Starikov, E. B.; Norden, B.: Physical Rationale Behind the Nonlinear Enthalpy-Entropy Compensation in DNA Duplex Stability. Journal of Physical Chemistry B, 2009, 113 (14) pp. 4698-4707.

    5. Starikov, E. B.; Nordén, Bengt: DNA Duplex Length and Salt Concentration Dependence of Enthalpy-Entropy Compensation Parameters for DNA Melting. Journal of Physical Chemistry B, 2009, 113 (33) pp. 11375-11377.

    I would be pleased to send you the PDF copies of all those papers somehow, if you are interested.

    Respectfully yours,

    Evgeni B Starikov

    PS After looking at your profile, I see that we are colleagues - I have also quit the official academic science and am continuing my work in the industrial R&D sector.
    Johannes Koelman
    Thanks Evgeni.

    I fully agree. Perhaps we could still refer to entropy as 'king', albeit a king who suffers from amnesia... ;)

    I am interested in your first paper (from 2007). You should have access to my e-mail via my profile page.

    Many thanks in advance!
    Dear Johannes,

    have just sent you a private message to reveal my physical E-mail address.

    How to consider entropy is rather a philosophical question, I guess. Who should be crowned king: a Knowledge (that is, something we are able to reliably measure with the devices at hand) or Ignorance (which defies any reproducible measurement) ?

    Each of the above two cannot be useful without its counterpart, thus it's a kind of duumvirate. But, hopefully, without any sign of pathologies like amnesia etc :-))

    Respectfully yours,

    Evgeni Starikov

    Thanks Evgeni.

    There are a few things that puzzle me about the Verlinde paper: 1. it seems to hop between logical and thermodynamic entropy; 2. in assuming that a high entropy state for large scale gravitational objects (clumped together) is the inverse of that for smaller scale objects such as gas particles (randomly distributed) it implies an attractive gravitational force rather than a repulsive one.

    When the entropy gradient is described as energy difference it seems a lot less startling, there is an energy difference between two things, so they clump together at a large scale - hence gravity.

    Surely I am missing something in thinking this is circular i.e. you need to define gravity (or at least define the absence of the repulsive forces which make things like particles bump off each other and not clump together at the larger scales that gravity applies) to see gravity emerge?

    Ha Ha I agree with Evgeni, however it is a shame that his 'Young People' link didn't work - I'm not so young but I see this as all going PLOP! IMO Jerry gives a good insight I think, in hinting that some people are confusing entropy states with heat capacity It's going to take much better modelling than this to include all the known variables synchronistically, though, isn't it? Aitch
    Johannes Koelman
    It's going to take much better modelling than this to include all the known variables synchronistically, though, isn't it?

    Aitch -- absolutely. Let me stress here once more: one should not read too much into the above 'mikado model'. This is just a toy model introduced for didactical purposes.

    Maybe it gives some clues about how to work towards a real model, but it certainly doesn't represent such a model. The real model needs to be relativistically covariant (I guess that is what you mean by 'synchronistically'?). And that is just one requirement violated by the mikado model.
    Sorry, Aitch - I have corrected my typo, so now it should work for you and everybody ...

    Respectfully yours,
    Evgeni Starikov
    many thanks,........ and the included post by Robert Olley is also very enlightening ;-)

    Amateur Astronomer
    Reply to Scott.

    "since energy is conserved it can never jump to a higher level"

    There is one exception to the rule you quoted. If there were no exceptions then our universe could not exist. When radiant energy fields like heat or microwaves are focused to a hot spot, like in a parabolic reflector, energy does jump to a higher level, with no work being done on it, and no waste energy being rejected to a lower temperature reservoir. Most people have done something like this with a curved mirror or a magnifying glass. So it isn't a hard concept or something strange. It is a familiar concept in life that is usually ignored in science, and left out of physical theories.

    The third law of thermodynamics governs the radiant focusing. It is well understood and documented, but not taught in college. Your quote is from the second law of thermodynamics, that does not apply to radiant focusing.

    I believe you are correct that the universe is tending to degenerate at present, but to do so it had to be generated at some previous time. The third law describes how the universe became orderly in its earlier years by a predominance of non random events out numbering random events.

    While the natural world tends to randomness at present, it is possible to construct devices that are biased against random actions.

    It means that the human race has a future that is not imprisoned in a hopelessly degenerating system.
    Amateur Astronomer
    Reply to Henry.
    Thanks for your comments.

    The difference between entropy states and heat capacity is the key concept that leads to progress in physical science.

    In fact both functions operate exactly the same way on a large scale system with one very important exception. Entropy carries with it a database of information that exactly describes how the system differs locally from random action, equal partition, and the equivalence of degrees of freedom with the number of possible states. It means that Entropy accounts for exceptions in the Planck scale structure of the space time continuum as departures from the kinetic theory.

    This is exactly what was lacking from the first kinetic theory of gravity dating from the 16th century.

    With entropy replacing heat capacity in the kinetic theory of gravity, the old objections are removed about conservation of energy, by reference to the catalog of exceptions carried by the entropy function.

    In this way the holographic representation with emergent gravity is a continuation of work that began in the year 1590, but got side tracked by a lack of understanding about entropy.
    Damsterdiep At Wirdumerdraai

    The path forward I referred to is a movement to describe the space time continuum and general relativity in terms of how the multiple states of Planck scale Zero Point differ from thermal equilibrium, random filling, and equal partition under stress of gravitational curvature, force fields, condensed mass, and propagation of particles or wave energy.

    It is called quantum field theory and is very active now in science.

    An example is given in the photo of the Damsterdiep At Wirdumerdraai where a variety of random and non random systems are operating. Certainly the entropic function here contains far more information than can be expressed in a heat capacity. This part of the canal was dug more than a thousand years ago following a convenient natural feature, so the entropic function is actually more complicated than it looks.

    I guess my vote is with the people who say Entropic Gravity is important for advancement of science, and not just a fad that disappears later. Combined with 420 years of Kinetic Theory, the Entropic Gravity takes on a fairly substantial appearance.

    I can't help but think that Biologists/systems analysts seem to refer to Entropy as what I would refer to as reverse entropy; skewed so far, it goes back on itself [antilog function?]
    Surely, if two observers use different sets of macroscopic variables, then they
    will observe different entropies? - the illustration of the Dutch canal bridge is a fine example where the remaining information about the initial conditions appears to maximise entropy due to the apparent system stability. No human can put back the original information in the bridge or the canal, as some of it is lost over time, yet, as a structure it obviously is being maintained despite the entropy at work over the centuries. It seems as though entropy in physical systems modeling is different to the entropy in information systems modeling

    This part of the canal was dug more than a thousand years ago following a
    convenient natural feature, so the entropic function is actually more
    complicated than it looks.

    ....bit of an understatement....?

    Combined with 420 years of Kinetic Theory, the Entropic Gravity takes on
    a fairly substantial appearance.

    and an even greater catalogue of exceptions, one assumes...?

    Just as metal, rusts, does the rust retain memory of the catalogue of exceptions to the former metal's state? *

    [*Acknowledgments to Patrick for discussion of ideas on this, prior to posting, as I find the whole conceptual model somewhat dependent on the individual, in a way as yet not included in the theories - caveat; Patrick may have a slightly different take on this if he blogs it!]

    I'm just a chemist, and to be honest not a very good one, but when I think of entropy I think of it as the driving force behind molecular bonding/PE curves. I guess that's a missapropriation of terms though. I guess the molecules aren't actually drawn together until it enters the morse PE well. Before then it's just a matter of chance that the particles will enter that PE well, which is facilitated by just moving around a lot. I guess that really isn't a force any more than being a good player at Hungry Hungry Hippos forces the balls into your hippos mouth, its more that every state/hippo get's a chance, but your state/hippo is the lowest energy/best hippo.

    Just thinking out loud on your page.

    Dear Jerry, Dear Aitsch,

    ... absolutely: The entropy is throughout subjective and ought therefore to be considered within the Bayesian statistical framework.

    Respectfully yours,
    Evgeni Starikov


    Really enjoyed the article.

    As an interested layperson and not a mathertician or physicist can you perhaps explain how this concept relates to that of the 'Principle of Least Action'? - Your mikardo model seems intuitively similar to Feynmanns Path Integrals approach. Does the principle give insights into the degrees of freedom problem?

    Maximum Entropy Change and Least Action Principle for Nonequilibrium Systems - QA Wang 2006, Astrophysics and Space Science
    Reformulation of a stochastic action principle for irregular dynamics QA Wang et al 2007

    Johannes Koelman
    Absolutely, Andrew. The quantization of mikado-type models would be rather straightforward provided the holographic nature prunes the degrees of freedom such that the Feynman sums behave well (no infinities).

    I am now traveling. Haven't read the articles you link to, but will do later.
    I have been thinking this same thing. Seems like "Entropy", long a fascinating concept, is getting over-applied semantically in this case. What I am reading through all of this breakthrough is that it is possible to [derive formulas describing gravitational effects] by simply saying that THE physical system (the universe) seeks the lowest energy state, ie, the lowest disorder (entropy), as objectively measured by for example in the toy model the mathematical permutations possible vs the observed permutations.

    What is incredible is that, rather than some Feynmann-esque "we don't know why the universe is this way, it just is" explanation for physical laws, this is based on a simple concept which is the same in all realities. A mathematical measure comparing one permutation of information compared to another shows that one is closer to a pure random distribution and the other is less so (more "orderly"). Incredibly, magically, Nature has a preference for the order in this case which causes the effect known as gravity. No dimensions, no physical units, no scales or forces, just a confirmation that the CA approach is for the first time quite plausible in that the universe might simply be a space governed by an abstract "low entropy" principle.

    The main question that surfaces for me is that in the toy models, there is a "higher probability" of a low-energy (low random / low disorder / low entropy) configuration, but by no means a guarantee. If each die rolled is one unit time, it could be a million rolls before the two spheres approach each other, if at all. I understand that there is a greater likelihood of this occurring, but overall what we really see is that two massive objects immediately approach each other and do not retrogress.

    Which further makes me state simply: there must therefore be *a force* which is causing objects to seek a low-entropy state in response to this pressure. This is gravity. I am - humbly - in the same camp as others who have said "we're explaining gravity by introducing gravity".

    Hammock Physicist, comment please?

    SG, you're mixing up several facts.

    First of all, you cannot derive the laws of gravitation (wether they be'd Newton's or Einstein's) by simply asserting that "the universe" seeks the lowest possible energy state. More input than that is needed.

    Second, entropy most definately is not the same thing as energy, as you seem to be implying, and these two concepts should be strictly separated. The correct view is given by statistical mechanics, which holds that loosely said, the entropy for a system is the aggregate number of states available to the system. Energy comes in it because the more energy, the more states that become available.

    Third, entropy is not a fundamental force, or some deep organizational principle shrewdly invented by nature to Keep Order. Its simply the evolution of a system that tends to smooth out any macroscopic un-evenness in some distribution (like temperature or density) due to microscopic interactions.

    Fourth. The issue of gravity. For decades physicists have been utterly baffled by it. It's been known that black holes, because of the nature of the event horizon, has some interesting thermodynamic properties. This has (mis-)led some, out of sheer desperation, to simply proclaim gravity to be an emergent (entropic) phenomena, most recently Verlinde. In his article he simply combines some phenomena from black holes (Unruh acceleration, holography) and combines them with the formula for (macroscopic, themodynamic) entropy, and then churning out Newton's law - which is simply an inverse square relation with a coupling constant.

    At first this might appear as very deep, but you'll soon realize the problem with this is many-fold. Entropy, by its very nature, deals with configurations of many, many particles that have some direct interaction with each other (in "classical" thermodynamics this is the electrostatic repulsion between atmos/molecules as they bounce off each other). There has been no substitute interaction been offered thus far.

    If gravity is just emergent/entropic, then just what is the underlying microscopic/fundamental force that keeps two masses far apart circling around each other without any possible physical coupling (weak, strong, electromagnetic)?

    Even if we were to just accept the emergent formalism as a working hypothesis there are severe problems too. Just how is a microscopic statistical averaging going to give rise to a curved bulk?

    Even at the microscopic level it doesn't work out. Emergent gravity makes some predictions about the the motion of ultra-cold neutrons in the presence of a gravitational field. These experiments have been carried out, and found, of course, that the motion of neutrons is perfectly described by ordinary quantum mechanics and a non-entropic, fundamental gravity.

    Amateur Astronomer
    Reply to Aitch and Evgeni.

    Your comments deserve a better reply than I am able to give at this time. We use entropy for a variety of different purposes, and tend to define it differently depending on how it is used. The mathematical functions in all of these situations are exactly the same, suggesting there is really only one variety of entropy, but it has many applications, and our understanding of it is not complete.

    For Entropic Gravity on the Planck scale the entropy is arising from fundamental quantum mechanical functions. This agrees with the mathematical statement of the third law of thermodynamics where the natural logarithm is taken over the sum of quantum mechanical states. I always try to express the Planck scale actions in terms of the Zero Point oscillators because they have properties that are important for advancement of science. One apparent property of the Zero Point oscillators is that they have an 8 pole structure, with capacity to store a four bit binary code based on electric charge, polarity, frequency, and partition of energy between gravity potential and electromagnetic potential. Another property is that the oscillators have to work together in clusters to meet the strict requirements of geometric symmetry, giving rise to the classical laws by averaging the quantum effects at a fairly small scale in a Bayesian statistical framework.

    The information carried by entropy resides in the binary code of the Zero Point oscillators. Where else could it possibly be found? Information has to be stored somewhere. Entropic Gravity is an important concept in the understanding of entropy. The Zero Point field contains the information about mass quantity and location. There is more than enough storage capacity for information that is necessary to define a local condition of curvature, energy, and momentum, but the storage capacity is limited and some far away bits of information are not propagated when they are not necessary to define the local state.

    Wave entanglement is a property that applies to the Zero Point. With entanglement there are topics of coherence and decoherence, showing that old information can be lost if it is not essential enough to be refreshed occasionally in the binary code.

    Questions arise about how the entropy can be relativistically invariant. I refer to Richard Tolman RELATIVITY THERMODYNAMICS AND COSMOLOGY, Oxford 1958. Interpreted in terms of the Zero Point, for information expressed in a binary code, entropy can be relativistically invariant, while some of the other thermodynamic functions it operates on like temperature might not be invariant in a particular case.

    The picture is not complete. A question arises about what the Zero Point oscillators are made of and in what medium they reside. These questions might be more appropriate for a separate topic, but for now it can be said that the Zero Point wavelengths are thought to be the strings of string theory residing on the intersections of two hidden dimensions. The virtual particles of the Zero Point are thought to be the nodes of string theory residing at the intersections of three hidden dimensions. This work is in the early stages, but provides a path forward for scientific advancements.

    At present there is a lot of work being done on quantum field theory. I guess the entire body of physical laws including general relativity will be expressed in terms of quantum mechanics in the Zero Point field extending to the macro scale through the Bayesian statistical framework.

    In closing I would like to apologize for the rather primitive explanations I have given together with the absence of advanced mathematics, and invite other writers to give a more appropriate description of entropy.

    Sorry, mate, not wishing to sound unappreciative, but I'm not convinced by the concepts of string theory, and the fact that people, yourself included, seem to rely on the strings to tie everything together - kinda neat, but to my mind flawed
     - There's this impossible to go beyond the 'we can say only that the universe came into existence when it already had an age of 10-43 seconds' point, which seems to contradict the big bang theory on which it all rests, since there's no causality for the heat from an initial entropic state - unless the string has explosive qualities.....?

    Or is there something more that can be described as hidden?

    Once a theory starts needing too many new words to define a needed device to make the ailing model buoyant, part of me starts yawning - yet I sense that there IS something;
    ..... as yet untapped and unexplained in the zero point radiation field which makes my soul tingle.....and it seems to me to be key to our concept of synchronicity - nowness.....and nowness just IS, not
    10-43 seconds past or future.....and something happens to my consciousness when I've touched tasted and sensed it - I just can't dang well lock into it!!

    ....and no amount of math would help, I know

    And it's this - whatever - which has caused me to have writer's block on my Oak of Science blog part 3, which was very clear in my mind when I started.....but it I wait, and meditate.....maybe it's internal wave entanglement coming into and out of, conscious focus?

    Hope that makes sense?

    Amateur Astronomer
    Thanks Aitch.

    String theory is not the central part of my thinking about the next steps in physics. It is just a convenient and familiar warehouse of parts that can be adapted to a variety of purposes. Nice and neat is not the way I would describe the present situation.

    My main interest is in describing the Vacuum Energy or Zero Point field in sufficient detail to remove the abstract notions of space curvature and replace them with gradients and partitions of space and time. The field of Quantum Field Theory applies to this topic. The main obstacle in QFT is the people who work on it have failed to correctly partition the vacuum to get a small cosmological constant and most of their colleges in general relativity have failed to use a complete stress energy tensor, of the Reissner-Nordström type.

    Making reference to String theory is a way to bypass the arguments that block QFT from completion, just as Holographic Theory is a way to make progress and avoid the battle about Dirac Sea of Energy. In fact the battles have been won and remedies have been found, but it is still risky to ignore the opponents who remain.

    Space and time have properties that have been measured, light speed c, gravity G, Planck's constant h, and constants of static electricity epsilon and magnetism mu. It is on these measured things that I build my opinions. Theories based on other things are useful to give examples, and express opinions in familiar words that avoid disputed concepts.

    I guess the best answer at this time is that the Big Bang Theory will be greatly changed by a complete QFT, so if you don’t like it as it is then you get a chance to change it later. The missing part is that light of high intensity counter acts gravity and bends space backward.

    I don’t have a remedy for your concern about Planck time in the creation. There might be something smaller than a plank unit, we just don’t have a way to measure it. That will change when we travel at light speed. The Lorentz contraction works in reverse and makes small things large. So you get another chance on that one too.

    About the energy of creation I rely on the third law of thermodynamics for a scientific basis and description of entropy decreasing in non random processes.

    Any serious physics or astrophysicists should have a theory to describe the vacuum or be working on such a theory before going off on a tangent with theories that rest on things that cannot be measured.

    So it isn’t nice and neat, or fully defined, but there is a path forward A lot of questions have been answered that get neglected in college studies.

    As for your references to mystical concepts, I tend to be more mystical than most scientific people, but deliberately express opinions in a rational frame on a scientific web site.


    Isn't a stress energy tensor merely a mass equivalence, though? A link between Einstein and Newton?

    Although if you mean it in the theoretical black hole concept, then it is likely the theory will come to nothing, as I don't believe such a non rotational device with internal event horizons have or will ever exist

    You say, "The missing part is that light of high intensity counter acts gravity and bends space backward." - are you saying that that light was the big bang or the source of it or what, as I find it hard not to see some sort of conjuring going on?
    The missing part to me, as I said, is the very consciousness within the universe - nowhere can I see an explanation of it or where it came from or why it manifested, yet we know of it, but always seem to confuse it with our physical modeling in space time

    I also am perplexed by the question as to whether it, consciousness, could also shift dimensions such as is included in the abstract or randomness requirement, at a collective level
    The whole idea of the inexplicability of the zero time to 10-43 seconds, could to me contain as much as we know, or think we know of our universe, and which can only be reached via a dimensional shift in consciousness - I am reminded of the idea that our whole Universe exists inside a bubble on top of a glass of Guinness!
    I have had experiences, which I know Gerhard probably writes off as unscientific mumbo jumbo, but that is only because as scientists you agree on the terms of reference. Some experiences take a person consciously through a shift which I can only describe as 'a tort in time'. - In a zero time moment a lot 'happens'  - even though the conventional meaning of the word 'happen' suggests an event between point a in time and point b in time.

    My experience suggests, and I can do no more than suggest, since there is no scientific proof of such things, and yet - I had them as experiences - like being conscious of a change occurring at a molecular energy level, which I think of as connected to the zero field theory stuff, as it's about the closest to it, that it is possible to see the very 'reality of the physical world in which you believe you live' become an identical 'appearance' as the same physical world, even though what consciousness is showing you, as a soul, is that the energy field of everything in that 2nd reality is so different, that it would be like crossing the  10-43 seconds boundary, and seeing the whole universe in it
    Now, I don't know how that squares with your belief, knowledge or theories, but it may be of little consequence, as I cannot undo my life experiences, any more than I can accurately or scientifically explain them, to myself as a rational process, let alone to anyone else, but I feel an urge to try.....

    Hope that helps, as its the closest I can get, and I'm at the limits of my knowledge of a field which is your speciality as a theory......maybe there really is a connection?

    Do you have a place for an helix of time, in your model, whereby the zero point energy relates to the observer, as the observer [as an energy consciously affected] is related to by the event? If so, then maybe a black hole occurs only in consciousness, yet manifests outside the observer as a manifestation of some unknown inner consciousness shift?
    There HAS to be an inclusion of consciousness for me, or all the equations evaporate....and my universe with it, if that makes sense to you? There is a reason, ......the question remains, - what else is consciousness for? we use it just like we use gravity, and yet we include gravity in the equations, because it is accepted scientific 'fact' that gravity exists due to its effects, yet science denies the same right of inclusion to consciousness, whilst utilising its effects for all science experimentation....
    That's my puzzle!

    So, if you are to continue to deny it from the model, why use it on the model?
    Isn't that a logical proof of concept, worthy of examination?

    BTW, it's not a personal attack on you, just in case I sound a bit harsh, it's just years of not knowing how to communicate something I feel so passionately about, and I suppose I need to know if rationality CAN be applied to it....?

    Amateur Astronomer

    I not offended or even greatly surprised to hear a different opinion or an unanswered question. It is disappointing if no one responds.

    Many people over the centuries have had the type of experiences you described. Sometimes they are called Metaphysics, although that is not one of my favorite words.

    From ancient times people have been telling the technical community that something important is missing from the prevailing science and technology. To some extent they were always right in the past, so there is no reason to expect that there isn't something important missing now.

    You asked for some affirmation of consciousness on a universal time scale. Certainly that is possible within the wide boundaries of a Rational Mystic. In science today it is an open ended question, but one that could conceivably be answered at some future time. I write about such topics, but for a different (small) audience, and not on a scientific web site. Science should pursue the truth where ever it leads, and not be tampered with to support any particular belief. That's a lot to ask for, and it seldom happens.

    In January I published a book that relates to your comments , and that book has now been read by about 10 people, COMMENTARY ON EZEKIEL AND RELATED TOPICS OF MODERN SCIENCE. This type of writing does not have a wide appeal. I don't have a final scientific answer to your questions, but I can show that the possibility of consciousness is included within a scientific frame work. It has to do with the origin of the Universe and the Cosmos that proceeded it.

    The Dirac Sea Of Energy was proven to exist last year beyond a reasonable doubt when Dirac's supporters derived the vacuum energy from General Relativity and the solutions of Einstein's Field Equations for the special cases of black holes. The vacuum energy density was set equal to the potential energy density of curved space time at the edge of a black hole, giving essentially the same results Dirac got from quantum mechanics. That argument is over. The Dirac Sea is enormously more powerful than all of the other energy in the universe. So your question about energy in creation is answered by the Vacuum Energy, sometimes called the Zero Point field. The Vacuum Energy predated the Universe and provided the energy for creation.

    The Vacuum is governed by Heisenberg's uncertainty principle. Energy is loaned for a time, then collected again by the vacuum. The usual means of collection can be prevented by construction of non random mechanisms, causing the Vacuum to collect the loan by unusual methods, most likely a displacement in time and space.

    Non random processes tend to decrease entropy according to the third law of thermo dynamics. So your question about creation is connected to non random events and an undiscovered science of how it happened and what the non randomness represents physically. That is an open question that could possibly include some of your experiences in the answer.

    Although the Vacuum is older than the Universe, it's immense Sea Of Energy must have an origin. The only science we have that can create energy in empty space is the focusing of radiant energy. It is a well known science of parabolic reflectors and magnifying glasses. The output is small, about 360 watts per square meter of surface at room temperature. If Radiant Focusing created the Vacuum Energy, it took a long time and we can calculate the time it would take.

    A calculation says the Vacuum Energy could be created by Radiant Focusing if the Cosmos is older than the Universe by a factor of 10^123 power. I tend to believe that something like that happened, because there is no competing science, or a theory, or even a good guess to explain the energy in a World where theories proliferate freely about almost everything.

    If you accept the possibility that the Cosmos is tremendously older than the Universe, then your thinking about consciousness sounds very reasonable. Your opponents are left with no science, no theories, and no data.

    " bubble on top of a glass of Guinness"

    I'm at a loss for words to reply about the Guinness suggestion. Maybe if it was Guinness Stout...

    Best Wishes Aitch. If you continue looking for an answer, you have a chance of finding one. Answers came to me in old age after a life time of searching everywhere. I read everything, listened to everyone, and considered every opinion. When the answers were found my reaction was something like the experiences you described. The answers had been sitting on my bookshelf for 20 years, in old books from famous pioneers in science.


    Yes, it WAS a Guinness stout!

    and as for your, 'and answers came to me in old age' quip, I smile, as I think you are younger than me, [I'm 62] and I have experienced  such as you describe, only to later experience what I call 'a great reversal' - where the model of the cosmos inside me opened a door and I stepped into an abyss, and nothing made any sense any more and I had to re-construct it all, as there's no going back at that point in consciousness
    Where I am now is about where I was at 17, but with less baggage

    Amateur Astronomer
    Again to Aitch,

    "Isn't a stress energy tensor merely a mass equivalence, though? A link between Einstein and Newton?"Reissner–Nordström metric

    The stress energy tensor is supposed to be all of the energy in space that acts to modify the curvature. It can be a mass equivalent if mass is the only modifier present. Dating from 1918 the Reissner–Nordström metric (equation) is a special case solution to Einstein's General Relativity for the presence of an electromagnetic field. The results clearly show the electromagnetic term (red) counteracting the gravity term (green) in the link.

    Peter Bergmann republished the Reissner–Nordström metric in his text book of 1942, but excluded it from his popular book on gravity in 1968. 

    I expect that black holes tend to rotate which adds a centrifugal term which also counteracts gravity. A number of black holes have been found by astronomers. Galaxies tend to have them near the center.

    ......The results clearly show the electromagnetic term (red) counteracting  the gravity term (green) in the link.
    Counteracting...That's a curious way to put it -  I had a look at the Reissner–Nordström metric, and see that removing the terms causes .....
    'The classical Newtonian theory of gravity may then be recovered in the limit as the ratio rs/r goes to zero. To do this, you just remove term in \,\color{OliveGreen}\text{green}.
    In that limit, the metric returns to the Minkowski metric for special relativity'
    In practice, the ratio rs/r is almost always extremely small. For example, the Schwarzschild radius rs of the Earth is roughly 9mm (3⁄8inch), whereas a satellite in a geosynchronous orbit has a radius r of the that is roughly four billion times larger, at 42,164km (26,200miles) .....The ratio only becomes large close to a Black hole and other ultra-dense objects such as Neutron stars
    So, this raises the question to me as to how you apply this rs/r term to all of the energy in space that acts to modify the curvature - depending on whether you set it approximating to zero, close to earth, or a similar body, or close to a black hole, presumably approaching infinity?

    Maybe a mind-bender, that one

    Amateur Astronomer

    No conjuring

    The reference to light was to demonstrate the mechanism of creation and a modification of the standard model, not the cause of creation or the timing of creation, or a reason for having the Planck time limit 10^(-43) seconds. It takes at least 10^(-9) seconds for a thought to form in your mind, so I really think you should give this one to us. Your concept of right now is an eternity of Planck times.

    Classical Greece had problems with irrational numbers for the same reasons. The constant Pi gave them fits.

    Pi probably is a rational fraction in the physical world (not in mathematics) but the denominator has more than 35 digits in it.

    You are struggling with the difference between mathematical abstractions where infinities occur, and the physical world where infinities are prevented by quantum mechanics.
    You are struggling with the difference between mathematical
    abstractions where infinities occur, and the physical world where
    infinities are prevented by quantum mechanics.
    No,  that occurred when I joined the advanced math class at 14 and was introduced to Calculus, and my model universe in my head collapsed the first time!

    "Fool me once, shame on you. Fool me twice shame on me"  ;-)

    It takes at least 10^(-9) seconds for a thought to form in your mind, so
    I really think you should give this one to us. Your concept of right
    now is an eternity of Planck times.

    No way....That's merely your estimate of my concept
    Let me illustrate by a story. In 1988 I went to India on a spiritual quest. One day, after a fairly intense cathartic meditation session, I was sat on a smooth rock by a river, and could hear the bubbling of the water as it flowed over the boulderous coastline just behind the boulder I was sat on, near the edge. I was feeling very relaxed and my mind had been in turmoil an hour or so earlier, just about the time it had taken me, meandering down the road, until I was drawn mysteriously to this spot
    Some part of me was talking to all of creation at that point in time, as I queried existence as to my purpose for being there, and the meaning of 'nowness' which my guru had talked to us about that morning

    Then I had a satori experience*
    I experienced, not heard, thought, or saw, the answer!

    'I' ceased to be aware of a distinction between the me, sitting, and the rock, - I WAS the rock, but not just the rock I sat upon, but the rocks in the river, and the water was bubbling inside me and the sound was intensely loud, and I sensed water flowing over me, and the warmth of the sun roasting me as if I'd been in it for too long, against the coolness of the water above me

    That did not occur in plank time, nor any time - time stood still, yet everything was 'happening' the whole cosmos was 'happening' all at was very intense, and I can never forget such a thing, because it showed me that thinking is not what consciousness is, nor can thinking know the cosmos - only its shadow in time, left as a reminder, for those who were not conscious of it

    Science seems to me to be exploring those shadows, thinking,  and confusing them with eternity and all the cosmos


    Amateur Astronomer

    Consider again the Reissner–Nordström metric for a case in deep space where the (green) gravity term (rs/r) is very nearly zero but the (red) electromagnetic term (r^2Q/r^2) is reinforced by microwaves from the background radiation. For that case the metric describes space that is curved backward where masses repel each other and clusters of galaxies accelerate.

    It is the science of 1918 and doesn’t need any help from the dark side of the force.

    Next consider a creation event with the same equation but with no gravity term and a powerful burst of light adding to the electromagnetic term. Then creation doesn’t have to be a huge explosion with a messy entropy function. Creation can be a more orderly process of low entropy where the universe expands slowly at first but accelerates because of the negative curvature.

    The physical science of 1920, is still on the leading edge of technology, 90 years later.

    Best wishes in your search.
    The physical science of 1920, is still on the leading edge of
    technology, 90 years later.

    Oh, good, maybe I'll get born before you figure it all out..... ;-)

    Does that mean that the 'Big Bang' theory has a competitor as the 'Slowly baking into existence' theory

    I'd still like to know where the Light came from, and come to that the vacuum

    Then again, odds on I'll die before then, too

    Best wishes in YOUR search, Jerry

    and thanks to Johannes Koelman for an interesting article

    Johannes always writes the most thought-provoking articles, Henry. He's not only a first-rate physicist but a damn good writer as well! ;-)
    Amateur Astronomer
    Surprise Aitch, I'm older than you. My photo is as far out of date as yours.

    I have a great variety of experiences and thoughts, with some similar to ones you described, but not the abysmal one. Some experiences contribute to a path forward in science, but others are more for personal development.

    With Guinness Stout, we have some common ground.

    The point of no return is a serious event, especially when it sets you back 45 years. Maybe an average person wouldn't need to go through such a dramatic reversal to reach a higher consciousness, if there were fewer barriers to advancement along the way, and a greater expectation of break throughs in understanding. I tend to put more importance on understanding than on consciousness.

    Consciousness can be taught, but understanding is a gift. Not everyone gets the same gifts.
    Ah, you're a sly fox to be sure.....

    It's funny I'm having a consciousness talk with Gerhard here

    I didn't say that the point of no return wasn't a serious event, or that it was a a sense it WAS my chosen path, as I had previously gotten in trouble too many times through 'always being right', or 'being in the right place at the right time' and a precursor to it was a strong religious experience, bigger even than the satori I describe

    I don't think consciousness can be taught, and if you read my posts to Gerhard you'll see why

    I think you use words to mean different things to me, but I sense we are quite similar in understanding of the spiritual

    To me knowledge is taught, but wisdom is the gift

    Understanding is the knowing of the difference

    and I agree, not everyone gets the same gifts

    Where can I find a copy of 'COMMENTARY ON EZEKIEL AND RELATED TOPICS OF MODERN SCIENCE'?.... as I'm interested,  and since you've whetted my appetite, I could be number 11!

    Jerry, I don't know what's going on with the chatbox, I tried to reply, but apparently you couldn't see it, so I tried to repeat what I's said and the box closed, - when I re-opened it, there was no message - I must have guessed something was going on, or something, as I copied your email before it dissolved
    Amateur Astronomer
    To get Minkowski space from Reissner–Nordström metric you have to delete both the red term (electromagnetics) and the green term (gravity). Wikipedia can be a bit confusing at times. In the example you gave the red term (electromagnetic) had already been deleted to get the Schwarzschild metric, but the text was not clear about that.

    “In practice, the ratio rs/r is almost always extremely small”

    That is the gravity term and it is small. Earth gravity differs by only about 3 parts per billion from flat space, but still gives us a substantial gravity field. The collapsed stars you mentioned are really extreme gravity fields that humans can barely imagine.

    “So, this raises the question to me as to how you apply this rs/r term to all of the energy in space that acts to modify the curvature - depending on whether you set it approximating to zero, close to earth, or a similar body, or close to a black hole, presumably approaching infinity“

    The gravity term (rs/r) approaches one (1) not infinity near a black hole and it only represents gravity caused by mass, not necessarily all of the energy that modifies curvature. Other terms are added when there are other types of energy that modify curvature like the red term (r^2Q.r^2) for electromagnetic energy. Counteracting means that (rs/r ) always has a negative sign tending to increase the gravitational curvature, and (r^2Q.r^2) always has a positive sign tending to decrease the gravitational curvature. The difference governs space curvature.

    To put (rs/r) equal to zero means that there is no gravity field caused by mass. That could be a big mistake, for example in rock climbing. Even if the term (rs/r) is close to zero it is still important.
    Amateur Astronomer
    Aitch, about 10^(-9) seconds you are claiming to process mental images faster than light speed crosses your brain. There are some theories about tachyons faster than light, but no experimental data independently measured. The other theory about faster than light processes comes from quantum mechanics of entangled wave functions where some researchers claim to have data for faster than light processes. I have other opinions about variable light speed in strong gravity fields, but they don’t apply to your head.

    Best guess would put your thoughts into the entangled category where coherence and decoherence describe the possible states.

    Our brains have the ability to think very fast in dynamic situations, at which times our field of view decreases to free up band width. If it continues too long or occurs too often we run the risk of becoming narrow minded.
    Amateur Astronomer
    Big bang has a competitor. Slowly Baking doesn’t sound quiet right.

    I call it Radiant Glory. That’s a different book, with a lot of the same information, but expressed mostly in mathematics of high school level (differential calculus).

    I don’t know why creation occurred at just that time, in that intensity, for that duration.

    Just a guess, it might be that the Cosmic Vacuum can only contain a certain amount of energy, and when Radiant Focusing over fills the energy reservoir, the Cosmos gives back the excess in the form of a Universe. With the Cosmos thought to be vastly older than the universe there are a lot of possibilities, and the chance of a different filling mechanism and triggering event.

    In either case there is the indication of nonrandom processes to make entropy low and give order to the universe. So there is the unanswered question about what type of nonrandom process occurred. There is no direct evidence for an older universe some where outside our universe, but with a very old Cosmos, Vacuum Energy, and Radiant Focusing, there very well could have been other universes and other technical societies more advanced than ours. Then you get all sorts of chances for consciousness.

    Aitch, about the Commentary on Ezekiel, somehow we became friends, (maybe over Guinness Stout) so if you find my photo at the bottom of the page and click on my forehead area, a text box opens and you can send me an email address. So far I’ve never sold a book, but only given copies as gifts.
    Amateur Astronomer
    Aitch, I sent you an email address over the friend text box.
    Yes, sorry, anti-gravity took hold of my reply and threw it up the page..... ;-)

    What are your thoughts on what the ‘Entropic Gravity’ arguments are implying about the origin of intertia? That to me is the most fascinating aspect of recent thoughts. Broadly, part from the ‘shut up intertia just is’ approach there appears to be a continuum of ideas about the origins of intertia - from
    -The ‘Pure machian’ - the cosmos creates inertia. Such as in Sciama’s approach - The universe obeys mach’s principle. At each point in space local force (F=MA) minus negative equal inertial force applied at that point and generated by the total cosmos.
    -The electrodynamic – inertia is an entirely local phenomenon – unless the inertia of electrons was precisely what it is atoms would fly apart or collapse in on each other – Fermi, Pearle
    Hmm interesting that arguments at such totally different scales can produce the same result? Perhaps we are missing something fundamental and underlying? As Jaume Gine has pointed out this is too good a relationship to be purely a coincidence.
    One objection to Mach’s principle is, as put for example by Ashfar, that accelerating towards an object would cause it to heat up and that is silly. But that is precisely what the Unruh Effect shows. Haisch, Puthoff and Rueda inertia arises as a drag force on accelerating particles, Unruh disproved their formulation Http://
    Verlinde concept appears to be more rigorous reversing Unruhs argument and utilising (as clarified in his futher notes) Prigonines concept that ‘dynamics of the system will adapt itself so that entropy production is minimized. Yes, really minimized. This may appear counterintuitive, but I like to look at it as that it seeks the path of least resistance’
    He states ‘very general random microscopic processes cause inertia and motion.’ But also ‘the mass of an object and therefore its energy can change due to the displacement of matter far away from it. There is action at a distance hidden in gravity, even relativistically.’
    The cosmological and quantum scales are tied together but does he pull it off?? Im not sure.
    If space itself is perceived as a quantised metric that emerges from the actions of an entropic force but as time advances provides the context for the actions of that force. Thermodynamics is a topological rather than a geometrical concept. Concepts of ‘pressure’, ‘temperature’ etc. apply whatever the geometry. The combination of a metricated spacetime +thermodynamic topology is all that is necessary to create ‘space’ whatever the size or form of the universe. Does Mach’s principle doesn’t require the distant stars it simply requires the minimum information in any topology to describe order and disorder.
    Why do we describe intertia as a ‘fictitious force’ and therefore gravity – using Einsteins concept of a man in a falling lift – as a fictitious force also. Rather than being ‘fictiticous’ is it better simply to describe it as a ‘real’ machian force.
    Kavassalis on her blog criticises the entropic ‘force’ concept as it is not a ‘force’ simply the consequence of a curved spacetime
    To me that is begging the question and leaving the origins of inertial mass unexplained. It seems an Aristotelian argument which the founders of classical dynamics derided, real forces were not curved they said, they act in straight lines and curved motions are the product of forces. Is it better to think of inertial mass creating an antisotropic tensor spacetime.
    Coming from a cartography background I know that a ‘mountain’ for example can be ‘described’ mathematically as a manifold, or can be ‘described’ as a field’ – (isoline contours) but a mountain is not ‘caused’ by either, it is the product of differential forces over time.

    Amateur Astronomer

    Verlinde deliberately chose a small part of physics to describe as holographic, and was careful to say so several times in his follow up logic. A lot of things were left out that will presumably get a representation some other time and place.

    Description of inertial mass is from my own opinions about the properties of the Zero Point or Vacuum Energy field.

    The key point is that everything moves at light speed no matter how feeble or how powerful it is, unless it has a rest mass. Then the vacuum apparently has a large dynamic massless energy field moving at light speed in all directions at the same time, propagated by induction among the Zero Point oscillators. Massless particles always have momentum related to their energy, such that the Vacuum propagates and conserves both energy and momentum at the same time, until some event occurs to alter the situation.

    Mass is the exception that does not travel a light speed. Then mass must be regarded as a form of energy that has geometrical symmetry with respect to its interactions with the Vacuum. Mass interacts with the vacuum, to modify some property of space, like vibration frequency, charge and polarity of virtual particles, or partition of the vacuum energy between different forms like gravitational potential or electromagnetic potential. For a mass the modification is the same in every direction. That is the gravitational field representation of mass. When science speaks about curvature of space, the physical representation is a modification that mass makes on the Zero Point field propagating the same in all directions.

    Inertial mass in your question arises from conservation of energy in the Zero Point field. When a mass is moving or just starting to move, the modification its gravity causes in the Vacuum moves with it such that for a total extended region around the mass, the net change of energy is zero, but there are local differences and changes in the energy density or the types of energy caused by the gravitating mass as it moves. The momentum of a mass resides in the gravity modification it causes to propagate or not propagate in the Vacuum field around it. To change the movement speed or direction requires that energy be added to the extended region of the Vacuum or subtracted from it.

    Inertial mass is equal to gravitational mass because the magnitude of the inertia depends on the magnitude of the gravitational modifications in the Zero Point field.

    Holographic representation of inertia is possible, because the Planck units of the Vacuum carry the momentum and energy as well as the entropic information that describes it, such that the energy, momentum, and entropic information propagate from place to place by induction among the Zero Point oscillators.
    Amateur Astronomer
    Where did the Vacuum come from?

    Wow Aitch. I guess you stumped me on this one.

    Now we are talking about what might have happened 10^135 years ago. I'm running short of ideas. Here is my best guess.

    Verlinde constructed his paper from the assumption of time existing before space, and in some way that is probably true. Remember that I am routinely working in 6 or more dimensions with 3 or more varieties of time, and when pressed for an answer can easily reach for 26 dimensions, which stretch the consciousness every time.

    In my models space and time are always defined by the energy fields they contain.

    One variety of time for the Cosmic age might be called Cosmic Time. It dates from the first bit of energy flowing in the first bit of space of a very small Cosmos. One bit does not create a statistical distribution, even if it happened by chance. A single bit always has some form of non randomness. Non randomness is the key to creation of the Universe, and now I am suggesting that non randomness was also the key to creation of the Cosmos, but in a small space with a small energy that accumulated slowly over time by the nonrandom process of radiant focusing, and by other non random processes at the very beginning.

    To avoid conjuring at this point requires an assumption about positive and negative energy, like Dirac predicated in his first work on antimatter.

    Then the Cosmos could be created with space and energy by the Heisenberg uncertainty principle, if an Anti Cosmos was created at the same Cosmic Moment with negative energy carried by antiparticles. Richard Feynman showed that antimatter is the same as matter except that antimatter goes backward in time. So the Anti Cosmos drifted away from the Cosmos by separation in time. There is a version of this story that is sometimes applied to the creation of the Universe, but for now we are discussing the Cosmos origin.

    Now we are speaking of two bits of time, two bits of power, and two bits of space. It still is too small to form a statistical distribution, so the original non random process continued to operate for a while. It seems likely that a process of focusing radiant energy developed rather early out of the original non random process of small numbers, and continued to fill space with energy, causing space to expand. At first there wasn't enough energy to create a mass, so the energy was electromagnetic, and space was curved backward.

    It's only a guess as to how all of this happened and survived long enough to create a Universe. At the beginning of the Cosmos all of the physical constants were different than they are now. They changed as the vacuum energy increased.

    Most likely gravity G increased at the same rate c^2 did. Planck's constant probably increased also, but is still a very small number. So the properties of space and time were very much different than what our common sense says they should be. Then you get a rational chance that the whole thing could have happened differently than my guess.

    This representation predicts the existence of an Anti Cosmos receding into in the distant past, that could conceivably be eventually confirmed of disproved.

    "10^135 years ago......"

    Not wishing to throw any more spanners in the works, .....but have you ever tried looking at the known cosmos, from a non-solar time perspective?

    We have only really had a 'unified' Gregorian time system for such a few  [2 hundred or so] years, and here you are saying that Verlinde bases his construct on time existing before space
     - so it just got me wondering if there is even commonality in our exchanges about time itself.....?

    I'm thinking in terms of consciousness time

    Have a quick watch of the videos by Ian Xel Lungold, and you may get an idea of the perspective I'm referring to

    It's the first of a series of videos, done a few years ago,  but he gets into it pretty quickly as he's done these talks before, but by all means check out the following parts, I recommend trying to see at least the first 5 videos, if you have the time

    Also, how do you feel about the idea of all of us, shaping the universe we live in, as a consciousness perceptual creation of our collective thoughts?

    How much we influence where and how we live, shaped by our perception and consciousness of it.....It requires a big paradigm shift for many many people, but I'm sure you know about the need for that, just on what you perceive to be our cosmos, already

    Here's a video which comes close to what I'm referring to....

    I'd be interested in how that 'grabs you' or not.....

    I know this question wasn't aimed at me, but since temporal mechanics is my fundamental area of research, I'll express a few thoughts.

    1. The Gregorian system, or any other calendar system, is only a method of measuring the passage of time based on a certain cyclical series of events. It is not time itself.

    2." Consciousness time" is subjective. Regardless of how the perception of time is measured, it has nothing to do with the actual physical construct of time, unless, due to being in an extreme, accelerated reference frame or gravitational well, time is slowed down. The phenomena of duration dilation is a good example of "consciousness time" but is the result of the brain speeding up the processing of information so that it appears that things around the observer are slowing down. 

    And just in case anyone is thinking about the David Eagleman experiment, that was alleged to have proved that duration dilation is not real but a function of elongated memory, I already proved conclusively that that studied was so flawed that it's one of the worst scientific experiments on record. I currently do lectures where I have the audience analyze it themselves and they are always shocked when the data they get, from looking at his actual work, comes back with the opposite conclusion than what he has promoted...

    Amateur Astronomer

    The writings, speeches, and videos of and Ian Xel Lungold are creative and artistic, but lack a technical or scientific foundation, placing him at a great disadvantage among the forward thinking people. Mayan astrology is not a substitute for rational thinking.

    My reaction to all of the different claims about the mysterious powers, wisdom, and consciousness of ancient civilizations is that their societies collapsed under the stress of competition for living space and resources. Whatever abilities they might have had were not sufficient to preserve their institutions, except in a state of ruin for tourist destinations and university studies. It encourages a different type of enlightenment than the one Ian Xel Lungold is promoting.

    I don’t get too excited about the Mayan calendar ending in 2012 or even in 2010. My personal calendar ends every year. Then I get a new calendar. My interest in the Mayans is more related to their comprehension of large numbers, which is the first occurrence in mathematics, and just as important as the discovery of zero in India.

    About time, higher dimensions, consciousness, and the ancient civilizations, I believe there is a lot more to the story than our science is telling us, but probably very much different than the New Age writers are suggesting.

    From modern science we have entangled wave functions that connect a lot of things together in astonishing ways. It gets more interesting when we realize that the physical parts of our brains, the particles were created in pairs with antiparticles, with the antiparticle side of the pairs going backward in time, transporting our entangled wave functions with them. This is a widely accepted science that is necessary to explain experimental data from particle colliers. The entanglements have some limits which result in the attachments diminishing over time and distance or by interference, but they never completely disappear. According to modern science, our thoughts are physically connected to events that preceded the creation, and in ways that can alter or be altered now by the ancient events.

    So I believe you have something substantial in your thoughts about time and consciousness, but Ian Xel Lungold does not have the enlightened pathway forward to the next level of human development.
    First came the underpinnings of time as well as of electromagnetism. A 'natural medium' having nothing to do with space, but from which space itself including matter and energy emerge and consist. Time itself gives rise to space and matter and energy therein; time is not just passive ticks of the clock nor an independant variable, but in fact that which gives rise to all else. However for thermodymics to be obeyed, space cannot be continually fed with matter and energy through continued causal changes, so gravity becomes the mechanism for excess to be absorbed back into the time medium. Matter and energy are not being created nor destroyed, but transferred, as time gives rise to and changes space and particularly all else therein. There is not a space-time, because space itself emerges out of time, as time gives rise to space. This is also why events perceived from within space, appear to "move forward in time", wheras time itself does not have spacial dimensions, but causal dimensions and mechanism by which space both exists and is transformed, including provision and alteration of matter and energy.

    Amateur Astronomer
    AN EVENT HORIZON HAS NO PHYSICAL EXISTENCE EXCEPT AS A LOCATION IN SPACE AND TIME. It can be described as one of the holograms for a super massive collapsed star. The definition of the event horizon means that light can not escape from it to an infinite distance. That doesn't mean that light cannot escape from the event horizon to some other less distant palace.

    For each observer there will be a different radius of the apparent event horizon, depending on the distance from the observer to the black hole. As a traveler approaches a black hole the apparent event horizon will retreat to smaller and smaller radius, until the apparent density of the black hole reaches the Planck unit density, about 1096 kg/m3.

    Singularities don't exist in the physical world. That is just a mathematical abstraction that says the physical calculation was done wrong. Quantum mechanics prevents singularities from occurring. General relativity ignores quantum mechanics, leading to a wrong conclusion about black holes.

    A lot of scientific work has been published that tries to say the event horizon has mass, entropy, and temperature. To some extent these are the descriptions of a hologram. That is to say that the mass dos not reside on the surface of the event horizon, and move around as a traveler advances toward the black hole or retreats from it. The hologram simply describes the physical contents enclosed by it's surface in terms of local gravity and spin.

    Some super massive black holes can have rather mild conditions of gravity and radiation at the conventional event horizon distance. For example a black hole with mass of about 6 x 1012 solar masses would have local gravity about the same as earth at the location of a conventional event horizon. A complicated group of physical, properties cannot be assigned to such a place in space.

    Crossing an event horizon has no physical possibility, because the event horizon retreats from the traveler until it is too small to cross, and the Planck density it encloses is too dense to penetrate. Under those conditions the largest black hole becomes the size of a grain of sand or a speck of dust, but it isn't a singularity.
    Amateur Astronomer

    In reply to you comment about creation of the universe by the slowly baking method instead of the big bang, a further explanation of the Hubble parameter and how it changes with time is given here.

    A big bang does not lend it's self to an orderly universe of low entropy at the beginning.

    Low entropy and an orderly beginning fit much better into the radiant power model as shown in the graphs about the change of Hubble parameter.

    General relativity does not require a big bang, as long as there is enough radiant energy to bend space backward and cause masses to repel each other.
    Something seems to be missing in the toy model. I don't see how a periodic (or approximately periodic) motion can be realized in the mikado universe or anything like that.

    Dear Johannes,

    there is yet another standpoint as concerns entropy and thermodynamics as a whole.

    I hope, you'd be interested in this:

    Respectfully yours,

    Evgeni B Starikov
    A very good and well written blog article. Ironically, I found it from a reference in the bitter man blog The Reference Frame, where Lubos Motl make big efforts to debunk Verlinde's hypothese and describe you and Verlinde as more ignorant than undergraduate students. But obviously he dont even understand the hypothese. All this is a little funny, I think ;)

    Amateur Astronomer
    Erik Verlinde gave a presentation on Gravity at ICHEP. It develops emergent gravity from entropy in the residual of the third law of thermodynamics. That links gravity to quantum mechanics in an elegant way through the microscopic degrees of freedom. One of Verlinde’s main points is that the microstates are locally modified by the presence of macroscopic objects like mass. The presentation is a very good one directed toward the general practitioner with an extension of the holographic concept and how it relates to work by other people. The theory is constructed on Non De Sitter space bounded by De Sitter space. Many useful definitions are included together with enough of the intermediate level math to show how the theory is constructed.
    Inertia and gravity I like to elucidate on a remark of Andrew Lainton. He mentioned the work of Denis Sciama who in his article “On the origin of inertia” ( has put a very interesting view not only on the origin of inertia, but also on the origin of gravity. His approach is only very very indirectly related with entropy. However, his approach includes the influence of the whole of the universe. He starts by simplifying the problem to its bones. He assumes, quite properly, that the most distant items in universe together constitute the largest influence on a chosen subject. Every variance in this background averages out. So this background acts as a uniform solid body. He uses this in the computation of the Newton potential at the location of the subject. The uniformity is used in the form of a constant “charge” density. Then he gives the subject a uniform speed and interprets this as a current. Again he takes the volume integral over the whole universe. This time it delivers a vector potential. Sciama does not say this in his article, but the two volume integrals are in fact the two components of a vector field that play their role in the Helmholtz decomposition theorem. This puts Sciama’s approach in an interesting light. It is well known that Helmholtz decomposition divides the vector field in a rotation free component and a component that is rotational. What makes the situation special is what we get when we reverse Sciama’s interpretation. The current in the field correspond to the movement of physical items! Helmholtz decomposition only treats the stationary condition of the fields. It is related to the fact that the Fourier transform of a vector field can be split in a longitudinal and a transversal part. On its turn, this relates to the fact that the multidimensional Dirac function can be split in a longitudinal and a transversal part. As long as the whole situation stays stationary the two field parts stay independent. However, as soon as a dynamic change happens, then the two fields get coupled. Maxwell’s equations show these facts. Sciama uses one of Maxwell’s equations in order to show that the coupling of the fields goes together with an acceleration of the considered physical subject. This is his explanation of the origin of inertia. In the same article he relates it to the interaction between two physical items, which to my opinion is gravity rather than inertia. Helmholtz decomposition only treats the stationary situation. In a curved space the Helmholtz theorem must be replaced by the Hodge decomposition theorem. However, the main relations stay the same. There exits another set of laws that control the stationary relations between physical items. This is the set of axioms of the traditional quantum logic. This logic has the structure of an atomic orthomodular lattice, which is the same as the lattice structure of the closed subspaces of an infinite dimensional separable Hilbert space. It means that a proposition about a physical item can be represented by a closed Hilbert subspace. When a physical item moves, then the atomic propositions that describe its properties change. It means that the enveloping proposition that says everything about that item that can be said, is redefined. If this is interpreted in the light of what is stated above, then it means that there must exist something in quantum logic that represents the fields that accelerated the physical item. With other words, the propositions in the lattice of quantum logic influence each other when the propositions get redefined. This influence depends on the distance between actor and subject. So, there must exist a notion of distance in quantum logic. This can be similar to the notion of distance that exist in Hilbert space. These insights can guide the way to transform the current stationary traditional quantum logic into a more dynamic version of logic. The movement treated here, is a movement of subspaces in Hilbert space. It is not yet an observed movement. Our coordinate time does not yet play a role there. The spaces that we talked about do not yet have a Minkowski signature. However, the distribution of items in the neighborhood of the considered subject is no longer uniform. As a consequence the fields are curved. We have to find a thing that couples the stationary fields and the Hilbert subspaces such that the fields change and the subspace moves. Elsewhere I have indicated that unitary transforms are not sophisticated enough to perform that job. However, it is possible to build a construct consisting of a trail of infinitesimal unitary transforms where each trail element gets a new set of eigenfunctions, that can do the job. I have called this thing a redefiner. It is a stepper. Its steps define a progression parameter. It is wrong to interpret that parameter as “time”. Somewhere the transfer to an observed space with a Minkowski signature must be made. To my opinion the vehicle that does this is the number waltz. (c=ab/a). Its effect is only noticeable in Hilbert spaces where the number field is non-commutative.
    If you think, think twice
    Interesting article.

    One point that bugs me is this; entropy is used in sense of statistical mechanics. The microscopic force in thermodynamics that is the direct cause for the rise of entropy are the electrostatic interactions of orbital electrons.

    By virtue of statistical mechanics, entropy is generalized, and this fact is trivialized. Eric makes use of this in his paper by simply declaring the microscopic dynamics irrelevant.
    It does raise an interesting question.

    If indeed gravity is emergent as described, just *what* are the fundamental forces that give rise to these interactions? How do 2 point masses "attract" each other over large distances entropically if is solely due to microscopic dynamics?

    Kind regards,


    One can look at relativity, and say that its action is consistent with thermodynamics; or turn that around 160 degrees and say that of course entropy is consistent with gravity. Verlinde's work should not be so startling; perhaps relativists have claimed precedence for too long. But thermodynamics, and its alter ego information science, will of course devour all in the end.

    Spectacular article. I'm saving it to PDF now - to join Verlinde's article in my archived articles folder!

    I did a 2D computer simulation of the "mikado universe" described above. It calculates the gravitational constant for the model, based on the assertion in this article: S ~ G * r1 * r2 / R. My system had millions of random lines passing through (though this article says they must be "uniform"). If they're not random then any particular set (such as horizontal & vertical lines) will cause "distortions" in the gravitational field.

    As for the results, I have two comments. One is that the variation in G was larger than I would have liked. The other is that the gravitational constant seems dependent on the density of the lines. This would make sense in light of [Easson 2010 - Entropic Accelerating Universe], for eg.

    The variation may be large because of my methodology, which is too involved to discuss here. I'll continue looking at this, and reading articles and papers etc. Thanks!

    Johannes Koelman
    Hi AGreenhill -- I couldn't spend much time on blogging recently, and very seldomly look at comments to 'old' articles, but happened to stumble upon your postings (albeit with a delay). Great to see someone taking the effort to put this in a simulation. A straightforward means to reduce the noise in the simulations would be to average the observed effects over multiple realisations (different random patterns at he same density). Curious to see what outcomes you have obtained!
    Yes, my simulation was over only 20 random masses & locations using just the one "realisation" (background lines). With only 20 it was clear the results were fixing on a single value ~ with some noise (no further correlations between mass or distance between the two masses). Using more masses/locations and switching out the background would likely yield some cleaner looking data... but I'm too busy to even read & respond to this (I'm being naughty) - so maybe in a few weeks if I find some time I'll poke around further.

    Wahhh, very impressed by the quality of the article, even if I understood half of it !
    It reminded me the Bolzmann equation for gas, back when I did my electrical engioneering degree ...
    Johannes, you make me think of Richard Feynman, whose quality was to make to most secret side of physicts available to the masses. You should teach quantum physics, cosmology etc to kids in elementary school, not kidding !
    Thanks a lot, I will continue to follow your blog.
    Francis, Belgium

    Im trying develop a simulation of the mikado universe and i need to ask, how would you calcule at the point you try occupe a ray if it reduces an area to a invalid small size (hypotetical circle dont fit in it) ?

    Of course calculing all posible areas of occupied rays doesnt looks like an option i have just a small pc nto a cray computer...