# Tag Archives: dark gravity

## Matter and Energy Tell Spacetime How to Be: Dark Gravity

Is gravity fundamental or emergent? Electromagnetism is one example of a fundamental force. Thermodynamics is an example of emergent, statistical behavior.

Newton saw gravity as a mysterious force acting at a distance between two objects, obeying the well-known inverse square law, and occurring in a spacetime that was inflexible, and had a single frame of reference.

Einstein looked into the nature of space and time and realized they are flexible. Yet general relativity is still a classical theory, without quantum behavior. And it presupposes a continuous fabric for space.

As John Wheeler said, “spacetime tells matter how to move; matter tells spacetime how to curve”. Now Wheeler full well knew that not just matter, but also energy, curves spacetime.

A modest suggestion: invert Wheeler’s sentence. And then generalize it. Matter, and energy, tells spacetime how to be.

Which is more fundamental? Matter or spacetime?

Quantum theories of gravity seek to couple the known quantum fields with gravity, and it is expected that at the extremely small Planck scales, time and space both lose their continuous nature.

In physics, space and time are typically assumed as continuous backdrops.

But what if space is not fundamental at all? What if time is not fundamental? It is not difficult to conceive of time as merely an ordering of events. But space and time are to some extent interchangeable, as Einstein showed with special relativity.

So what about space? Is it just us placing rulers between objects, between masses?

Particle physicists are increasingly coming to the view that space, and time, are emergent. Not fundamental.

If emergent, from what? The concept is that particles, and quantum fields, for that matter, are entangled with one another. Their microscopic quantum states are correlated. The phenomenon of quantum entanglement has been studied in the laboratory and is well proven.

Chinese scientists have even, just last year, demonstrated quantum entanglement of photons over a satellite uplink with a total path exceeding 1200 kilometers.

Quantum entanglement thus becomes the thread Nature uses to stitch together the fabric of space. And as the degree of quantum entanglement changes the local curvature of the fabric changes. As the curvature changes, matter follows different paths. And that is gravity in action.

Newton’s laws are an approximation of general relativity for the case of small accelerations. But if space is not a continuous fabric and results from quantum entanglement, then for very small accelerations (in a sub-Newtonian range) both Newton dynamics and general relativity may be incomplete.

The connection between gravity and thermodynamics has been around for four decades, through research on black holes, and from string theory. Jacob Bekenstein and Stephen Hawking determined that a black hole possesses entropy proportional to its area divided by the gravitational constant G. This area law entropy approach can be used to derive general relativity as Ted Jacobson did in 1995.

But it may be that the supposed area law component is insufficient; according to Erik Verlinde’s new emergent gravity hypothesis, there is also a volume law component for entropy, that must be considered due to dark energy and when accelerations are very low.

We have had hints about this incomplete description of gravity in the velocity measurements made at the outskirts of galaxies during the past eight decades. Higher velocities than expected are seen, reflecting higher acceleration of stars and gas than Newton (or Einstein) would predict. We can call this dark gravity.

Now this dark gravity could be due to dark matter. Or it could just be modified gravity, with extra gravity over what we expected.

It has been understood since the work of Mordehai Milgrom in the 1980s that the excess velocities that are observed are better correlated with extra acceleration than with distance from the galactic center.

Stacey McGaugh and collaborators have demonstrated a very tight correlation between the observed accelerations and the expected Newtonian acceleration, as I discussed in a prior blog here. The extra acceleration kicks in below a few times $10^{-10}$ meters per second per second (m/s²).

This is suspiciously close to the speed of light divided by the age of the universe! Which is about $7 \cdot 10^{-10}$ m/s².

Why should that be? The mass/energy density (both mass and energy contribute to gravity) of the universe is dominated today by dark energy.

The canonical cosmological model has 70% dark energy, 25% dark matter, and 5% ordinary matter. In fact if there is no dark matter, just dark gravity, or dark acceleration, then it could be more like a 95% and 5% split between dark energy and (ordinary) matter components.

A homogeneous universe composed only of dark energy in general relativity is known as a de  Sitter (dS) universe. Our universe is, at present, basically a dS universe ‘salted’ with matter.

Then one needs to ask how does gravity behave in dark energy influenced domains? Now unlike ordinary matter, dark energy is highly uniformly distributed on the largest scales. It is driving an accelerated expansion of the universe (the fabric of spacetime!) and dragging the ordinary matter along with it.

But where the density of ordinary matter is high, dark energy is evacuated. An ironic thought, since dark energy is considered to be vacuum energy. But where there is lots of matter, the vacuum is pushed aside.

That general concept was what Erik Verlinde used to derive an extra acceleration formula in 2016. He modeled an emergent, entropic gravity due to ordinary matter and also due to the interplay between dark energy and ordinary matter.  He modeled the dark energy as responding like an elastic medium when it is displaced within the vicinity of matter. Using this analogy with elasticity, he derived an extra acceleration as proportional to the square root of the product of the usual Newtonian acceleration and a term related to the speed of light divided by the universe’s age. This leads to a 1/r force law for the extra component since Newtonian acceleration goes as 1/r².

## $g _D = sqrt {(a_0 \cdot g_B / 6 )}$

Verlinde’s dark gravity depends on the square root of the product of a characteristic acceleration a0 and ordinary Newtonian (baryonic) gravity, gB

The idea is that the elastic, dark energy medium, relaxes over a cosmological timescales. Matter displaces energy and entropy from this medium, and there is a back reaction of the dark energy on matter that is expressed as a volume law entropy. Verlinde is able to show that this interplay between the matter and dark energy leads precisely to the characteristic acceleration is $a_0 / 6 = c \cdot H / 6$, where H is the Hubble expansion parameter and is equal to one over the age of the universe for a dS universe. This turns out be the right value of just over $10^{-10}$ m/s² that matches observations.

In our solar system, and indeed in the central regions of galaxies, we see gravity as the interplay of ordinary matter and other ordinary matter. We are not used to this other dance.

Domains of gravity

 Acceleration Domain Gravity vis-a-vis Newtonian formula Examples High (GM/R ~ c²) Einstein, general relativity Higher Black holes, neutron stars Normal Newtonian dynamics 1/r² Solar system, Sun orbit in Milky Way Very low (< c/ age of U.) Dark Gravity Higher, additional 1/r term Outer edges of galaxies, dwarf galaxies, clusters of galaxies

The table above summarizes three domains for gravity: general relativity, Newtonian, and dark gravity, the latter arising at very low accelerations. We are always calculating gravity incorrectly! Usually, such as in our solar system, it matters not at all. For example at the Earth’s surface gravity is 11 orders of magnitude greater than the very low acceleration domain where the extra term kicks in.

Recently, Alexander Peach, a Teaching Fellow in physics at Durham University, has taken a different angle based on Verlinde’s original, and much simpler, exposition of his emergent gravity theory in his 2010 paper. He derives an equivalent result to Verlinde’s in a way which I believe is easier to understand. He assumes that holography (the assumption that all of the entropy can be calculated as area law entropy on a spherical screen surrounding the mass) breaks down at a certain length scale. To mimic the effect of dark energy in Verlinde’s new hypothesis, Peach adds a volume law contribution to entropy which competes with the holographic area law at this certain length scale. And he ends up with the same result, an extra 1/r entropic force that should be added for correctness in very low acceleration domains.

In figure 2 (above) from Peach’s paper he discusses a test particle located beyond a critical radius $r_c$ for which volume law entropy must also be considered. Well within $r_c$  (shown in b) the dark energy is fully displaced by the attracting mass located at the origin and the area law entropy calculation is accurate (indicated by the shaded surface). Beyond $r_c$ the dark energy effect is important, the holographic screen approximation breaks down, and the volume entropy must be included in the contribution to the emergent gravitational force (shown in c). It is this volume entropy that provides an additional 1/r term for the gravitational force.

Peach makes the assumption that the bulk and boundary systems are in thermal equilibrium. The bulk is the source of volume entropy. In his thought experiment he models a single bit of information corresponding to the test particle being one Compton wavelength away from the screen, just as Verlinde initially did in his description of emergent Newtonian gravity in 2010. The Compton wavelength is equal to the wavelength a photon would have if its energy were equal to the rest mass energy of the test particle. It quantifies the limitation in measuring the position of a particle.

Then the change in boundary (screen) entropy can be related to the small displacement of the particle. Assuming thermal equilibrium and equipartition within each system and adopting the first law of thermodynamics, the extra entropic force can be determined as equal to the Newtonian formula, but replacing one of the r terms in the denominator by $r_c$ .

To understand $r_c$ , for a given system, it is the radius at which the extra gravity is equal to the Newtonian calculation, in other words, gravity is just twice as strong as would be expected at that location. In turn, this traces back to the fact that, by definition, it is the length scale beyond which the volume law term overwhelms the holographic area law.

It is thus the distance at which the Newtonian gravity alone drops to about $1.2 \cdot 10^{-10}$ m/s², i.e. $c \cdot H / 6$, for a given system.

So Peach and Verlinde use two different methods but with consistent assumptions to model a dark gravity term which follows a 1/r force law. And this kicks in at around $10^{-10}$ m/s².

The ingredients introduced by Peach’s setup may be sufficient to derive a covariant theory, which would entail a modified version of general relativity that introduces new fields, which could have novel interactions with ordinary matter. This could add more detail to the story of covariant emergent gravity already considered by Hossenfelder (2017), and allow for further phenomenological testing of emergent dark gravity. Currently, it is not clear what the extra degrees of freedom in the covariant version of Peach’s model should look like. It may be that Verlinde’s introduction of elastic variables is the only sensible option, or it could be one of several consistent choices.

With Peach’s work, physicists have taken another step in understanding and modeling dark gravity in a fashion that obviates the need for dark matter to explain our universe

We close with another of John Wheeler’s sayings:

“The only thing harder to understand than a law of statistical origin would be a law that is not of statistical origin, for then there would be no way for it—or its progenitor principles—to come into being. On the other hand, when we view each of the laws of physics—and no laws are more magnificent in scope or better tested—as at bottom statistical in character, then we are at last able to forego the idea of a law that endures from everlasting to everlasting. “

It is a pleasure to thank Alexander Peach for his comments on, and contributions to, this article.

References:

https://darkmatterdarkenergy.com/2018/08/02/dark-acceleration-the-acceleration-discrepancy/ blog “Dark Acceleration: The Acceleration Discrepancy”

https://arxiv.org/abs/gr-qc/9504004 “Thermodynamics of Spacetime: The Einstein Equation of State” 1995, Ted Jacobson

https://darkmatterdarkenergy.com/2017/07/13/dark-energy-and-the-comological-constant/ blog “Dark Energy and the Cosmological Constant”

https://darkmatterdarkenergy.com/2016/12/30/emergent-gravity-verlindes-proposal/ blog “Emergent Gravity: Verlinde’s Proposal”

https://arxiv.org/pdf/1806.10195.pdf “Emergent Dark Gravity from (Non) Holographic Screens” 2018, Alexander Peach

https://arxiv.org/pdf/1703.01415.pdf “A Covariant Version of Verlinde’s Emergent Gravity” Sabine Hossenfelder

## Dark Gravity: Is Gravity Thermodynamic?

This is the first in a series of articles on ‘dark gravity’ that look at emergent gravity and modifications to general relativity. In my book Dark Matter, Dark Energy, Dark Gravity I explained that I had picked Dark Gravity to be part of the title because of the serious limitations in our understanding of gravity. It is not like the other 3 forces; we have no well accepted quantum description of gravity. And it is some 33 orders of magnitude weaker than those other forces.
I noted that:

The big question here is ~ why is gravity so relatively weak, as compared to the other 3 forces of nature? These 3 forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force. Gravity is different ~ it has a dark or hidden side. It may very well operate in extra dimensions… http://amzn.to/2gKwErb

My major regret with the book is that I was not aware of, and did not include a summary of, Erik Verlinde’s work on emergent gravity. In emergent gravity, gravity is not one of the fundamental forces at all.

Erik Verlinde is a leading string theorist in the Netherlands who in 2009 proposed that gravity is an emergent phenomenon, resulting from the thermodynamic entropy of the microstates of quantum fields.

In 2009, Verlinde showed that the laws of gravity may be derived by assuming a form of the holographic principle and the laws of thermodynamics. This may imply that gravity is not a true fundamental force of nature (like e.g. electromagnetism), but instead is a consequence of the universe striving to maximize entropy. – Wikipedia article “Erik Verlinde”

This year, Verlinde extended this work from an unrealistic anti-de Sitter model of the universe to a more realistic de Sitter model. Our runaway universe is approaching a dark energy dominated deSitter solution.

He proposes that general relativity is modified at large scales in a way that mimics the phenomena that have generally been attributed to dark matter. This is in line with MOND, or Modified Newtonian Dynamics. MOND is a long standing proposal from Mordehai Milgrom, who argues that there is no dark matter, rather that gravity is stronger at large distances than predicted by general relativity and Newton’s laws.

In a recent article on cosmology and the nature of gravity Dr.Thanu Padmanabhan lays out 6 issues with the canonical Lambda-CDM cosmology based on general relativity and a homogeneous, isotropic, expanding universe. Observations are highly supportive of such a canonical model, with a very early inflation phase and with 1/3 of the mass-energy content in dark energy and 2/3 in matter, mostly dark matter.

And yet,

1. The equation of state (pressure vs. density) of the early universe is indeterminate in principle, as well as in practice.

2. The history of the universe can be modeled based on just 3 energy density parameters: i) density during inflation, ii) density at radiation – matter equilibrium, and iii) dark energy density at late epochs. Both the first and last are dark energy driven inflationary de Sitter solutions, apparently unconnected, and one very rapid, and one very long lived. (No mention of dark matter density here).

3. One can construct a formula for the information content at the cosmic horizon from these 3 densities, and the value works out to be 4π to high accuracy.

4. There is an absolute reference frame, for which the cosmic microwave background is isotropic. There is an absolute reference scale for time, given by the temperature of the cosmic microwave background.

5. There is an arrow of time, indicated by the expansion of the universe and by the cooling of the cosmic microwave background.

6. The universe has, rather uniquely for physical systems, made a transition from quantum behavior to classical behavior.

“The evolution of spacetime itself can be described in a purely thermodynamic language in terms of suitably defined degrees of freedom in the bulk and boundary of a 3-volume.”

Now in fluid mechanics one observes:

“First, if we probe the fluid at scales comparable to the mean free path, you need to take into account the discreteness of molecules etc., and the fluid description breaks down. Second, a fluid simply might not have reached local thermodynamic equilibrium at the scales (which can be large compared to the mean free path) we are interested in.”

Now it is well known that general relativity as a classical theory must break down at very small scales (very high energies). But also with such a thermodynamic view of spacetime and gravity, one must consider the possibility that the universe has not reached a statistical equilibrium at the largest scales.

One could have reached equilibrium at macroscopic scales much less than the Hubble distance scale c/H (14 billion light-years, H is the Hubble parameter) but not yet reached it at the Hubble scale. In such a case the standard equations of gravity (general relativity) would apply only for the equilibrium region and for accelerations greater than the characteristic Hubble acceleration scale of  $c \cdot H$ (2 centimeters per second / year).

This lack of statistical equilibrium implies the universe could behave similarly to non-equilibrium thermodynamics behavior observed in the laboratory.

The information content of the expanding universe reflects that of the quantum state before inflation, and this result is 4π in natural units by information theoretic arguments similar to those used to derive the entropy of a black hole.

The black hole entropy is  $S = A / (4 \cdot Lp^2)$ where A is the area of the black hole using the Schwarzschild radius formula and Lp is the Planck length, $G \hbar / c^3$ , where G is the gravitational constant, $\hbar$ is Planck’s constant.

This beautiful Bekenstein-Hawking entropy formula connects thermodynamics, the quantum world  and gravity.

This same value of the universe’s entropy can also be used to determine the number of e-foldings during inflation to be 6 π² or 59, consistent with the minimum value to enforce a sufficiently homogeneous universe at the epoch of the cosmic microwave background.

If inflation occurs at a reasonable ~ $10^{15}$ GeV, one can derive the observed value of the cosmological constant (dark energy) from the information content value as well, argues Dr. Padmanhaban.

This provides a connection between the two dark energy driven de Sitter phases, inflation and the present day runaway universe.

The table below summarizes the 4 major phases of the universe’s history, including the matter dominated phase, which may or may not have included dark matter. Erik Verlinde in his new work, and Milgrom for over 3 decades, question the need for dark matter.

Epoch  /  Dominated  /   Ends at  /   a-t scaling  /   Size at end

Inflation /  Inflaton (dark energy) / $10^{-32}$ seconds / $e^{Ht}$ (de Sitter) / 10 cm

Radiation / Radiation / 40,000 years / $\sqrt t$ /  10 million light-years

Matter / Matter (baryons) Dark matter? /  9 billion light-years / $t^{2/3}$ /  > 100 billion light-years

Runaway /  Dark energy (Cosmological constant) /  “Infinity” /  $e^{Ht}$ (de Sitter) / “Infinite”

In the next article I will review the status of MOND – Modified Newtonian Dynamics, from the phenomenology and observational evidence.

References

E. Verlinde. “On the Origin of Gravity and the Laws of Newton”. JHEP. 2011 (04): 29 http://arXiv.org/abs/1001.0785

T. Padmanabhan, 2016. “Do We Really Understand the Cosmos?” http://arxiv.org/abs/1611.03505v1

S. Perrenod, 2011. Dark Matter, Dark Energy, Dark Gravity 2011  http://amzn.to/2gKwErb

S. Carroll and G. Remmen, 2016, http://www.preposterousuniverse.com/blog/2016/02/08/guest-post-grant-remmen-on-entropic-gravity/

## Gravitational Waves and Dark Matter, Dark Energy

What does the discovery of gravitational waves imply about dark matter and dark energy?

The first detection of gravitational waves results from a pair of merging black holes, and is yet another magnificent confirmation of the theory of general relativity. Einstein’s theory of general relativity has passed every test thrown at it during the last 100 years.

While the existence of gravitational waves was fully expected to be confirmed, the discovery took several decades and represents a technological tour de force. Detected at the two LIGO sites, one in Louisiana and one in Washington State, the main event lasted only 0.2 seconds, and was seen as a change of length in the “arms” of the detector (laser interferometers) of only one part in a thousand billion billion.

The LIGO detection of gravitational waves. The blue curve is from the Louisiana site and the red curve from the Washington state site. The two curves are shifted by 7 milliseconds to account for the speed-of-light delay between the two sites. Note that most of the power in the signal occurs within less than 0.2 seconds. The strain is a measure of proportional change in length of the detector arm and is less than 1 part in 10²¹.

Nevertheless, this is the most energetic event ever seen by mankind. The merger of two large black holes totaling over 60 times the Sun’s mass resulted in the conversion of 3 solar masses of material into gravitational wave energy. Imagine, there were 3 Suns worth of matter obliterated in the blink of an eye. During this brief period, the generated power was greater than that from the light of all of the stars of all of the galaxies in our known universe.

What the discovery of gravitational waves has to say about dark matter and dark energy is essentially that it further confirms their existence.

Although there is as of now no direct detection of dark matter, we infer the existence of dark matter by using the equations of general relativity (GR), in a number of cases, including:

1. Gravitational lensing – Typically, a foreground cluster of galaxies distorts and magnifies the image of a background galaxy. GR is used to calculate the bending and magnification, primarily caused by the dark matter in the foreground cluster.
2. Cosmic microwave background radiation (CMBR) – The CMBR has spatial fluctuation peaks (harmonics) and the first peak tells us about ordinary matter and the third peak about the density of dark matter. A GR-based cosmological model is used to determine the dark matter average density.

Dark matter is also inferred from the way in which galaxies rotate and from the velocities of galaxies within galaxy clusters, but general relativity is not needed to calculate the dark matter densities in such cases. However, results from these methods are consistent with results from the methods listed above.

In the case of dark energy, it turns out to be a parameter in the equations of general relativity as first formulated by Einstein. The parameter, lambda, (Λ) is known as the cosmological constant, and represents the minimum energy of the vacuum. For many years astronomers and cosmologists thought it might take the value of zero. However in 1998 multiple teams confirmed that the value is positive and not zero, and it turns out that dark energy has more than twice the energy content of dark matter. Its non-zero value is actually another stunning success for general relativity.

Thus the detection of gravitational waves indirectly provides further support for the canonical cosmological model ΛCDM, with both dark matter and dark energy, and fully consistent with general relativity.

References

B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 – Published 11 February 2016 – http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102

NEW BOOK just released:

S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)

## 2013 in review

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