October 17, 2019
By Mark Campbell
“Intelligence cleaveth unto intelligence”
(D&C 88:40)
Emergence, a term en vogue within science circles today, is used to describe a concept that goes something like this: from the simple arises the complex. Emergence occurs when an entity (system) is observed to have properties its parts do not have on their own. The concept of emergence is applied to many scientific disciplines including biology and meteorology: Bee colonies exhibit behaviors that make it seem as if the colony was a single organism, demonstrating, as a whole, behaviors that are unseen when individual bees are considered. Hurricanes display structure and comportments that are fundamentally different than those found in the minute variances of atmospheric pressure and wind currents from which the massively destructive storms develop. An avalanche follows well-defined physical laws that are not at all applicable to the processes associated with snowfall or snowdrift. Emergence theory is also used within cosmology, in a number of ways, by a number of individuals, to provide an explanation of gravity.
In 1995, an American theoretical physicist, Ted Jacobson, introduced to modern physics the theory of Entropic (thermodynamic) Gravity. i The theory describes gravity as an entropic force—not a fundamental interaction mediated by a quantum field theory and a gauge particle (like photons for the electromagnetic force, and gluons for the strong nuclear force), but a consequence of physical systems' tendency to increase their entropy.
In our common, everyday world, experience, the maximum entropy (energy) in any given region is constrained by its volume (consider a closed box full of gas as Robert Boyle did). However, when the region is large enough and sufficiently dense for gravity to matter (as in a Black Hole), the actual entropy of a region, in its vacuum state, is constrained not by its volume but by the area of the region’s boundary. ii These two discordant strictures are understood to reflect the extreme differences in the conditions of the space they describe; it was ceded as fact that the punishing density associated with the region of a Black Hole requires a unique description for total entropy as it seems to do for every other fundamental law, force, or property.
Jacobson’s theory suggests, however, that gravity (or whatever fundamental principle gravity manifests) dictates that the entropy of every region of space is always proportional to the area of its boundary regardless of the regions density or size. Entropic gravity maintains that gravity emerges from the tension between the two constraints on total entropy, volume, and surface area, of a given region. Jacobsen’s calculations show that any increase in the entropy of a region will change the geometry of space itself, a change that includes the area of the boundary. In other words, Jacobson insists, general relativity ensures the area of every region is proportional to the total entropy inside the boundary (the geometry of spacetime always adjusts to make sure the area of the boundary is proportional to the amount of entropy inside, giving rise to its curvature).
i Ted Jacobson, "Thermodynamics of Spacetime: The Einstein Equation of State", Physical Review Letters, Vol. 75, Issue 7 (14 August 1995), pp. 1260-1263. Jacobsen argues that if (i) entanglement entropy density across any surface is a universal finite constant η, and (ii) local Lorentz symmetry holds, then the spacetime metric must satisfy the Einstein equation, with Newton’s constant equal to 1/(4 hbar η).
ii See: http://scholarpedia.org/article/Bekenstein-Hawking_entropy, Jacob D. Bekenstein, "Black Holes and Entropy," Physical Review D. 7: (April 1973), p.p. 2333–2346.
Figure 1. Entropic gravity understood in the simplest of terms (Verlinde interpretation) maps the information contained in three dimensional space onto the two dimensional surface of a sphere of equal volume (Holographic Principle or AdS/CFT correspondence). This results in the curvature of space that gives rise to gravity as described by the Einstein field equations. The curvature can be visualized as a realization of the warping of space needed to ensure cubed areas and spherical areas are representative of the same volume of space when, as can be seen here, spherical area for any given volume is less than the cubed area.
Figure 2. Three dimensional space is mapped to the two dimensional surface area of a spherical boundary that surrounds any given region of space. The surface coordinate on the sphere is indicated by a latitudinal and longitudinal value at the point where a line drawn through both the measured object (within) and the center point of the region passes through the boundary layer. The point on the surface records all states of the particle/object no matter how complex. The constraint placed upon the total entropy allowed in the region is determined by the surface area’s ability to contain the information. The granularity (Planck length, Planck time) of the information on the surface ensures that only one object /particle is in line with any point of the surface and the center of the region at any given time.
So, we have an emerging idea that gravity is not fundamental but is itself emergent from another fundamental, entropy. This is where the story takes a turn. What is entropy? How do we describe it?
Entropy is an increase in the number of states of degrees of freedom in any given volume of space. A state is the sum of all parameters that are used to define an object or particle at any given time: up, down, at motion, or at rest, temperature, spin, etc. A state can be complex (many parameters must be used to describe the object) or simple, (the object is completely still, as in not accelerating). Degrees of freedom are associated with states but only loosely, in fact, loose is a good word for it. In a region with a boatload of degrees of freedom, objects and particles are free to move around and change their states often. When the degrees of freedom in any given region of space are confined and restricted, the objects and particles within are limited in their ability to change states. Think of a team of soccer players running freely on a soccer field; now picture that same team all stuffed into a tiny elevator or an old-fashioned phone booth. In general, states are the properties of objects or particles, and degrees of freedom (at least how many are allowable in any given volume) is a property of spacetime. There are other significant factors at play here as well: The very nature of certain objects and particles may restrict the number of states they can hold or attain. And even the most voluminous space and expanse of time can only allow as much freedom as there are objects within to exercise it; freedom, it turns out, isn’t really free, but requires action to be counted (degrees of freedom are measured in the currency of rate-of-change-of-state).
An emerging realization amongst physicists today is that the number of states of degrees of freedom (entropy = number of objects/particles x states x rate of change) in any given volume of space is information itself. The states of objects and particles, their ups and downs, spins, momenta, temperature, their ability to freely change (degrees of freedom), even the numbers of such particles and objects in any region are all countable, describable in some way, it is all information. In 2009, the Dutch born theoretical physicist, Erik Verlinde, followed up on Jacobsen’s entropic gravity idea when he proposed a conceptual model that describes gravity as emergent from the “information associated with the positions of material bodies.” iii Entropy is information, the very presence of it.
Nothing moves or changes state, degrees of freedom cannot be realized or expressed, without energy. Take any region of space, with any number of particles or objects in it; add energy and things will happen. States will change, temperatures will rise, and the amount of information required to describe the space and its contents will increase. There is a relationship between energy and information; they are directly proportional; in the broadest sense, they are equivalent.
According to Jacobson’s entropic gravity theory, there is a relationship between the geometry of space and the amount of information it can hold. This relationship is expressed in terms of the boundary itself. Boundaries, regions dividing an area within, one that is tracked and known (states identified and degrees of freedom observed and understood); from an area without, that is untracked and unknown, are the locations (regions) of maximum entropy. Entropy, in Jacobsen’s model, is defined by the surface area of the region, curved to ensure that the area where the information is to be found is representative and maps the volume of space where the particles and objects described by that information are located. From entropy and area, we can derive all of gravity. An extension of this idea is that not just the geometry of spacetime, but all of spacetime itself can emerge from entropy and different degrees of freedom.iv It is not important that you fully understand this challenging concept, just that you know entropy causes spacetime to curve and curved spacetime gives rise to what manifests as the attractive force of gravity.
How is all of this important to our theology? It is in the information, how it is understood, and the power that understanding provides that the link can be found. Information utilized is purpose, when applied it is knowledge, even intelligence. By linking entropy to gravity, Ted Jacobsen revealed a profound truth. So did Eric Verlinde when he proposed that gravity is emergent from entropic information. We have already illuminated the fact that energy and information are equivalent; as a result, we can express the following equation:
entropy=information=intelligence=energy=gravity
The terms in the equation are not manifestly equivalent; so much as they are intimately entangled. Quantum entanglement is what gives birth to physical reality from the ethereal uncertainty the lies within the probability fields of the quantum wave function.
Gravity attracts. That it does, is not at all questionable. How it attracts, why it attracts, that it can attract instantaneously over distance, is a complete mystery. Gravity has eluded unification with the other three forces of nature (Strong Nuclear force, Weak Nuclear force and Electromagnetic force) for decades, with no hope in sight. To solve these problematic questions, Jacobsen and Verlinde have developed convincing arguments that gravity is not a fundamental force at all, but it is emergent from another fundamental, entropy. If they are right, gravity (though not fundamental) is, in fact, something far more - it is foundational.
Is what we are seeing actually there, or is it an artifact of the numbers. Does this emerging understanding really exist in the expanse, or does the intervening space, the numbers and our math, just make it appear to be so, like a mirage on the horizon, inviting us forward, but never allowing us to draw near? Perhaps an answer can be found by looking at the developing image from another direction.
In December of 1832, before Jacobsen and Verlinde were born, The Lord revealed to Joseph Smith a revelation called the Olive Leaf. About a third of the way through the long revelation, the Lord told Joseph, “Intelligence cleaveth unto intelligence” (D&C 88:40). In the primary context of the revelation, this concept (of intelligence drawing to itself) alludes to the basis for love; the bonding of one Intelligence to another is a foundational attribute of the Universe, a primary law of God, the law of intelligence.
From the beginning, the Lord has made it his work to bind our intelligences to his. In opposition, the adversary, Lucifer, seeks to bind independent intelligences to him by severing the bonds we have with others. It is intelligence that causes a righteous man to “cleave unto his wife,” truly clinging and sticking to her until “they shall be one flesh” (Gen. 2:24). Intelligence is Glory;v as such, the Glory of God draws us to Him, and that same Glory is love itself. Intelligence, in the form of an individual entity (Latter-day Saint understanding), or as an exchangeable, acquirable attribute, attracts, drawing one thing to another. However, the truth revealed in the Olive Leaf has a broader meaning as well, one that pertains directly to our discussion here.
Jacobsen’s and Verlinde’s proposals infer that this law of intelligence is manifest in the laws of physics as well. Their equations suggest that gravity is an emergent property of intelligence. Intelligence as an equivalent of information, energy or entropy, creates matter and shapes spacetime; it attracts (cleaves) all that there is to all that there is. What is the source of the force of Gravity? It is intelligence. Though the young prophet Joseph Smith probably never understood it in this broader context, this truth (the source of gravity is intelligence), that we are only now beginning to appreciate in its fullness, was nonetheless revealed to him long ago.
Will this important intersection of faith and science continue to play out? Are these two distinct human endeavors of exploration pointing to the same foundational truth? I think so, but perhaps only another foundational principle, time, will tell. For now, we can continue to be amazed by what seems to be revealed and contentedly sit back waiting to see what else will emerge.
iii In Verlinde’s theory, gravity exists because of a difference in concentration of information in the empty space between two masses and its surroundings. Dr. Verlinde first proposed his theory at a symposium at the Dutch Spinoza-institute on 8 December 2009. He subsequently followed up with refinements published in multiple iterations, among them: E.P. Verlinde, "On the Origin of Gravity and the Laws of Newton", Journal of High Energy Physics, (7 April 2011).
iv This intricate concept, that all things material are a realization of free agency and thought, will be the focus of a future blog post, I promise.
v Doctrine and Covenants 93:36, The glory of God is intelligence, or, in other words, light and truth.
Mark Campbell
7:30 am PST October 17, 2019
TAGS: Entropic Gravity, Black Holes, D&C 88, D&C 93, Ted Jacobsen, Erik Verlinde, In The Beginning, Holographic Principle
Mark Campbell,
Mark Campbell is an author, speaker and Sunday school teacher. For over 40 years he has brought his understanding of the gospel, cosmology, physics,