New Theory of Gravity Does Away With Need for Dark Matter


Erik Verlinde explains his new view of gravity

Let’s be honest. Dark matter’s a pain in the butt. Astronomers have gone to great lengths to explain why is must exist and exist in huge quantities, yet it remains hidden. Unknown. Emitting no visible energy yet apparently strong enough to keep galaxies in clusters from busting free like wild horses, it’s everywhere in vast quantities. What is the stuff – axions, WIMPS, gravitinos, Kaluza Klein particles?

Estimated distribution of matter and energy in the universe. Credit: NASA
Estimated distribution of matter and energy in the universe. Credit: NASA

It’s estimated that 27% of all the matter in the universe is invisible, while everything from PB&J sandwiches to quasars accounts for just 4.9%.  But a new theory of gravity proposed by theoretical physicist Erik Verlinde of the University of Amsterdam found out a way to dispense with the pesky stuff.

formation of complex symmetrical and fractal patterns in snowflakes exemplifies emergence in a physical system.
Snowflakes exemplify the concept of emergence with their complex symmetrical and fractal patterns created when much simpler pieces join together. Credit: Bob King

Unlike the traditional view of gravity as a fundamental force of nature, Verlinde sees it as an emergent property of space.  Emergence is a process where nature builds something large using small, simple pieces such that the final creation exhibits properties that the smaller bits don’t. Take a snowflake. The complex symmetry of a snowflake begins when a water droplet freezes onto a tiny dust particle. As the growing flake falls, water vapor freezes onto this original crystal, naturally arranging itself into a hexagonal (six-sided) structure of great beauty. The sensation of temperature is another emergent phenomenon, arising from the motion of molecules and atoms.

So too with gravity, which according to Verlinde, emerges from entropy. We all know about entropy and messy bedrooms, but it’s a bit more subtle than that. Entropy is a measure of disorder in a system or put another way, the number of different microscopic states a system can be in. One of the coolest descriptions of entropy I’ve heard has to do with the heat our bodies radiate. As that energy dissipates in the air, it creates a more disordered state around us while at the same time decreasing our own personal entropy to ensure our survival. If we didn’t get rid of body heat, we would eventually become disorganized (overheat!) and die.

The more massive the object, the more it distorts spacetime. Credit: LIGO/T. Pyle
The more massive the object, the more it distorts space-time, shown here as the green mesh. Earth orbits the Sun by rolling around the dip created by the Sun’s mass in the fabric of space-time. It doesn’t fall into the Sun because it also possesses forward momentum. Credit: LIGO/T. Pyle

Emergent or entropic gravity, as the new theory is called, predicts the exact same deviation in the rotation rates of stars in galaxies currently attributed to dark matter. Gravity emerges in Verlinde’s view from changes in fundamental bits of information stored in the structure of space-time, that four-dimensional continuum revealed by Einstein’s general theory of relativity. In a word, gravity is a consequence of entropy and not a fundamental force.

Space-time, comprised of the three familiar dimensions in addition to time, is flexible. Mass warps the 4-D fabric into hills and valleys that direct the motion of smaller objects nearby. The Sun doesn’t so much “pull” on the Earth as envisaged by Isaac Newton but creates a great pucker in space-time that Earth rolls around in.

In a 2010 article, Verlinde showed how Newton’s law of gravity, which describes everything from how apples fall from trees to little galaxies orbiting big galaxies, derives from these underlying microscopic building blocks.

His latest paper, titled Emergent Gravity and the Dark Universe, delves into dark energy’s contribution to the mix.  The entropy associated with dark energy, a still-unknown form of energy responsible for the accelerating expansion of the universe, turns the geometry of spacetime into an elastic medium.

“We find that the elastic response of this ‘dark energy’ medium takes the form of an extra ‘dark’ gravitational force that appears to be due to ‘dark matter’,” writes Verlinde. “So the observed dark matter phenomena is a remnant, a memory effect, of the emergence of spacetime together with the ordinary matter in it.”

Rotation curve of the typical spiral galaxy M 33 (yellow and blue points with errorbars) and the predicted one from distribution of the visible matter (white line). The discrepancy between the two curves is accounted for by adding a dark matter halo surrounding the galaxy. Credit: Public domain / Wikipedia
This diagram shows rotation curves of stars in M33, a typical spiral galaxy. The vertical scale is speed and the horizontal is distance from the galaxy’s nucleus. Normally, we expect stars to slow down the farther they are from galactic center (bottom curve), but in fact they revolve much faster (top curve). The discrepancy between the two curves is accounted for by adding a dark matter halo surrounding the galaxy. Credit: Public domain / Wikipedia

I’ll be the first one to say how complex Verlinde’s concept is, wrapped in arcane entanglement entropy, tensor fields and the holographic principal, but the basic idea, that gravity is not a fundamental force, makes for a fascinating new way to look at an old face.

Physicists have tried for decades to reconcile gravity with quantum physics with little success. And while Verlinde’s theory should be rightly be taken with a grain of salt, he may offer a way to combine the two disciplines into a single narrative that describes how everything from falling apples to black holes are connected in one coherent theory.

Astronomy Cast Ep. 391: Entropy

Have you ever been doing thermodynamics in a closed system and noticed that there’s a finite number of ways that things can be arranged, and they tend towards disorder? Of course you have, we all have. That’s entropy. And here in our Universe, entropy is on the rise. Let’s learn about entropy in its specific, thermodynamic ways, and then figure out what this means for the future of the Universe.
Continue reading “Astronomy Cast Ep. 391: Entropy”

Will the Universe Run Out Of Energy?

It seems like the good times will go on forever, so feel free to keep on wasting energy. But entropy is patient, and eventually, it’ll make sure there’s no usable energy left in the Universe.

Thanks to the donations of generations of dinosaurs and their plant buddies, we’ve got fossils to burn. If we ever get off our dependence on those kinds of fuels, we’ll take advantage of renewable resources, like solar, wind, tidal, smug and geothermal. And if the physicists really deliver the goods, we’ll harness the power of the Sun and generate a nigh unlimited amount of fusion energy using the abundant hydrogen in all the oceans of the world. Fire up that replicator, the raktajino is on the house. Also, everything is now made of diamonds.

We’ll never run out of H+. Heck that stuff is already cluttering up our daily experience. 75% of the baryonic mass of the Universe is our little one-protoned friend. Closely followed up by helium and lithium, which we’ll gladly burn in our futuristic fusion reactors. Make no mistake, it’s all goin’ in.

It looks like the good times will never end. If we’ve energy to burn, we’ll never be able to contain our urges. Escalating off into more bizarre uses. Kilimajaro-sized ocean cruise liners catering to our most indulgent fantasies, colossal megastructure orbital laser casinos where life is cheap in the arena of sport. We’ll build bigger boards and bigger nails.or something absolutely ridiculous and decadent like artificial ski-hills in Dubai. Sadly, it’s naive to think it’s forever. Someday, quietly, those good times will end. Not soon, but in the distant distant future, all energy in the Universe will have been spent, and there won’t a spare electron to power a single LED.

Astronomers have thought long and hard about the distant future of the Universe. Once the main sequence stars have used up their hydrogen and become cold white dwarfs and even the dimmest red dwarfs have burned off their hydrogen. When the galaxies themselves can no longer make stars. After all the matter in the Universe is absorbed by black holes, or has cooled to the background temperature of the Universe.

Combining observations done with ESO's Very Large Telescope and NASA's Chandra X-ray telescope, astronomers have uncovered the most powerful pair of jets ever seen from a stellar black hole. The black hole blows a huge bubble of hot gas, 1,000 light-years across or twice as large and tens of times more powerful than the other such microquasars. The stellar black hole belongs to a binary system as pictured in this artist's impression. Credit: ESO/L. Calçada
Artist’s impression of a Star feeding a black hole. Credit: ESO/L. Calçada

Black holes themselves will evaporate, disappearing slowly over the eons until they all become pure energy. Even the last proton of matter will decay into energy and dissipate. Well, maybe. Actually, physicists aren’t really sure about that yet. Free Nobel prize if you can prove it. Just saying.

And all this time, the Universe has been expanding, spreading matter and energy apart. The mysterious dark energy has been causing the expansion of the Universe to accelerate, pushing material apart until single photons will stretch across light years of distance. This is entropy, the tendency for energy to be evenly distributed. Once everything, and I do mean all things, are the same temperature you’ve hit maximum entropy, where no further work can be done.

This is known as the heat death of the Universe. The temperature of the entire Universe will be an infinitesimal fraction of a degree above Absolute Zero. Right above the place where no further energy can be extracted from an atom and no work can be done. Terrifyingly, our Universe will be out of usable energy.

The white dwarf G29-38 (NASA)
The white dwarf G29-38 (NASA)

Interestingly, there’ll still be the same amount it started with, but it’ll be evenly distributed across all places, everywhere. This won’t happen any time soon. It’ll take trillions of years before the last stars die, and an incomprehensible amount of time before black holes evaporate. We also don’t even know if protons will actually decay at all. But heat death is our inevitable future.

There’s a glimmer of good news. The entire Universe might drop down to a new energy state. If we wait long enough, the Universe might spontaneously generate a new version of itself through quantum fluctuations. So with an infinite amount of time, who knows what might happen?

Burn up those dirty dinosaurs while you can! Enjoy the light from the Sun, and the sweet whirring power from your counter-top Mr. Fusion reactor. Your distant descendants will be jealous of your wasteful use of energy, non-smothering climate and access to coffee and chocolate, as they huddle around the fading heat from the last black holes, hoping for a new universe to appear.

What’s the most extreme use of energy you can imagine? Tell us in the comments below.

Astronomy Without A Telescope – Holographic Dark Information Energy

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Holographic Dark Information Energy gets my vote for the best mix of arcane theoretical concepts expressed in the shortest number of words – and just to keep it interesting, it’s mostly about entropy.

The second law of thermodynamics requires that the entropy of a closed system cannot decrease. So drop a chunk of ice in a hot bath and the second law requires that the ice melts and the bath water cools – moving the system from a state of thermal disequilibrium (low entropy) towards a state of thermal equilibrium (high entropy). In an isolated system (or an isolated bath) this process can only move in one direction and is irreversible.

A similar idea exists within information theory. Landauer’s principle has it that any logically irreversible manipulation of information, such as erasing one bit of information, equates to an increase in entropy.

So for example, if you keep photocopying the photocopy you just made of an image, the information in that image degrades and is eventually lost. But Landauer’s principle has it that the information is not so much lost, as converted into energy that is dissipated away by the irreversible act of copying a copy.

Translating this thinking into a cosmology, Gough proposes that as the universe expands and density declines, information-rich processes like star formation also decline. Or to put it in more conventional terms – as the universe expands, entropy increases since the energy density of the universe is being steadily dissipated across a greater volume. Also, there are less opportunities for gravity to generate low entropy processes like star formation.

The link between entropy and information - more interesting and information-rich things occur in low entropy states than in high entropy states.

So in an expanding universe there is a loss of information – and by Landauer’s principle this loss of information should release dissipated energy – and Gough claims that this dissipated energy accounts for the dark energy component of the current standard model of universe.

There are rational objections to this proposal. Landauer’s principle is really an expression of entropy in information systems – which can be mathematically modeled as though they were thermodynamic systems. It’s a bold claim to say this has a physical reality and a loss of information actually does release energy – and since Landauer’s principle expresses this as heat energy, wouldn’t it then be detectable (i.e. not dark)?

There is some experimental evidence of information loss releasing energy, but arguably it is just conversion of one form of energy to another – the information loss aspect of it just representing the transition from low to high entropy, as required by the second law of thermodynamics. Gough’s proposal requires that ‘new’ energy is introduced into the universe out of nowhere – although to be fair, that is pretty much what the current mainstream dark energy hypothesis requires as well.

Nonetheless, Gough alleges that the math of information energy does a much better job of accounting for dark energy than the traditional quantum vacuum energy hypothesis which predicts that there should be 120 orders of magnitude more dark energy in the universe than there apparently is.

Gough calculates that the information energy in the current era of the universe should be about 3 times its current mass-energy contents – which closely aligns with the current standard model of 74% dark energy + 26% everything else.

Invoking the holographic principle doesn’t add a lot to the physics of Gough’s argument – presumably it’s in there to make the math easier to manage by removing one dimension. The holographic principle has it that all the information about physical phenomena taking place within a 3D region of space can be contained on a 2D surface bounding that region of space. This, like information theory and entropy, is something that string theorists spend a lot of time grappling with – not that there’s anything wrong with that.

Further reading:
Gough Holographic Dark Information Energy.

Astronomy Without A Telescope – Black Hole Entropy

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An easy way to think about the entropy of black holes is to consider that entropy represents the loss of free energy – that is, energy that is available to do work – from a system. Needless to say, anything you throw into a black hole is no longer available to do any work in the wider universe.

An easy way to think about the second law of thermodynamics (which is the one about entropy) is to consider that heat can’t flow from a colder location to a hotter location – it only flows the other way. As a result, any isolated system should eventually achieve a state of thermal equilibrium. Or if you like, the entropy of an isolated system will tend to increase over time – achieving a maximum value when that system achieves thermal equilibrium.

If you express entropy mathematically – it is a calculable value and one that tends to increase over time. In the seventies, Jacob Bekenstein expressed black hole entropy as a problem for physics. No doubt he could explain it much better than I could, but I think the idea is that if you suddenly transfer a system with a known entropy value past the event horizon of a black hole, it becomes immeasurable – as though its entropy vanishes. This represents a violation of the second law of thermodynamics – since the entropy of a system should at best stay constant – or more often increase – it can’t suddenly plummet like that.

So the best way to handle that is to acknowledge that whatever entropy a system possesses is transferred to the black hole when the system goes into it. This is another reason why black holes can be considered to have a very high entropy.

Then we come to the issue of information. The sentence The quick brown fox jumped over the lazy dog is a highly engineered system with a low level of entropy – while drawing out 26 tiles from a scrabble set and laying them down however they come delivers an randomly ordered object with a high level of entropy and uncertainty (to the extent that it could be any of a billion possible variations).

Throw your scrabble tiles into a black hole – they will carry with them whatever entropy value they began with – which is likely to increase further within the black hole. Indeed it’s likely that the tiles will not only become more disorganized but actually crushed to bits within the black hole.

Now there is fundamental principle in quantum mechanics which requires that information cannot be destroyed or lost. It’s more about wave functions than about scrabble tiles – but let’s stick with the analogy.

You won’t violate the conservation of information principle by filling a black hole with scrabble tiles. Their information is just transfered to the black hole rather than being lost – and even if the tiles are crushed to bits, the information is still there in some form. This is OK.

But, there is a problem if in a googol or so years, the black hole evaporates via Hawking radiation, which arises from quantum fluctuations at the event horizon and has no apparent causal connection with the contents of the black hole.

The Hawking radiation story. A quantum fluctuation proximal to a black hole's event horizon produces a particle and an antiparticle. The antiparticle enters the black hole and annihilates when it collides with a particle in there. The remaining particle is free to join the rest of the universe outside the event horizon. To an external observer, the black hole appears to have lost mass and radiated a particle. Over time this process would result in the black hole evaporating. To date - good story, evidence nil, but watch this space. Credit: NAU.

A currently favored solution to this problem is the holographic principle – which suggests that whatever enters the black hole leaves an imprint on its event horizon – such that information about the entire contents of the black hole can be derived from just the event horizon ‘surface’ – and any subsequent Hawking radiation is influenced at a quantum level by that information – such that Hawking radiation does succeed in carrying information out of the black hole as the black hole evaporates.

Zhang et al offer another approach of suggesting that Hawking radiation, via quantum tunneling, carries entropy out of the black hole – and since reduced entropy means reduced uncertainty – this represents a nett gain of information drawn out from the black hole. So Hawking radiation carries not only entropy, but also information, out of the black hole.
But is this more or less convincing than the hologram idea? Well, that’s uncertain…

Further reading: Zhang et al. An interpretation for the entropy of a black hole.

Astronomy Without A Telescope – Is Time Real?

Time is an illusion caused by the passage of history (Douglas Adams 1952-2001).

The way that we deal with time is central to a major current schism in physics. Under classic Newtonian physics and also quantum mechanics – time is absolute, a universal metronome allowing you determine whether events occur simultaneously or in sequence. Under Einstein’s physics, time is not absolute – simultaneity and sequence depend on who’s looking. For Einstein, the speed of light (in a vacuum) is constant and time changes in whatever way is required to keep the speed of light constant from all frames of reference.

Under general relativity (GR) you are able to experience living for three score and ten years regardless of where you are or how fast you’re moving, but other folk might measure that duration quite differently. But even under GR, we need to consider whether time only has meaning for sub-light speed consciousnesses such as us. Were a photon to have consciousness, it may not experience time – and, from its perspective, would cross the apparent 100,000 light year diameter of the Milky Way in an instant. Of course, that gets you wondering whether space is real either. Hmm…

Quantum mechanics does (well, sometimes) require absolute time – most obviously in regards to quantum entanglement where determining the spin of one particle, determines the spin of its entangled partner instantaneously and simultaneously. Leaving aside the baffling conundrums imposed by this instantaneous action over a distance – the simultaneous nature of the event implies the existence of absolute time.

In one attempt to reconcile GR and quantum mechanics, time disappears altogether – from the Wheeler-DeWitt equation for quantum gravity – not that many regard this as a 100% successful attempt to reconcile GR and quantum mechanics. Nonetheless, this line of thinking highlights the ‘problem of time’ when trying to develop a Theory of Everything.

The winning entries for a 2008 essay competition on the nature of time run by the Fundamental Questions Institute could be roughly grouped into the themes ‘time is real’, ‘no, it isn’t’ and ‘either way, it’s useful so you can cook dinner.’

The ‘time isn’t real’ camp runs the line that time is just a by-product of what the universe does (anything from the Earth rotating to the transition of a Cesium atom – i.e. the things that we calibrate our clocks to).

How a return to equilibrium after a random downward fluctuation in entropy might appear. First there was light, then a whole bunch of stuff happened and then it started getting cold and dark and empty.

Time is the fire in which we burn (Soran, Star Trek bad guy, circa 24th century).

‘Time isn’t real’ proponents also refer to Boltzmann’s attempt to trivialise the arrow of time by proposing that we just live in a local pocket of the universe where there has been a random downward fluctuation of entropy – so that the perceived forward arrow of time is just a result of the universe returning to equilibrium – being a state of higher entropy where it’s very cold and most of the transient matter that we live our lives upon has evaporated. It is conceivable that another different type of fluctuation somewhere else might just as easily result in the arrow pointing the other way.

Nearly everyone agrees that time probably doesn’t exist outside our Big Bang universe and the people who just want to get on and cook dinner suggest we might concede that space-time could be an emergent property of quantum mechanics. With that settled, we just need to rejig the math – over coffee maybe.

I was prompted to write this after reading a Scientific American June 2010 article, Time Is An Illusion by Craig Callender.

What is Entropy?

Perhaps there’s no better way to understand entropy than to grasp the second law of thermodynamics, and vice versa. This law states that the entropy of an isolated system that is not in equilibrium will increase as time progresses until equilibrium is finally achieved.

Let’s try to elaborate a little on this equilibrium thing. Note that in the succeeding examples, we’ll assume that they’re both isolated systems.

First example. Imagine putting a hot body and a cold body side by side. What happens after some time? That’s right. They both end up in the same temperature; one that is lower than the original temperature of the hotter one and higher than the original temperature of the colder one.

Second example. Ever heard of a low pressure area? It’s what weather reporters call a particular region that’s characterized by strong winds and perhaps some rain. This happens because all fluids flow from a region of high pressure to a region of low pressure. Thus, when the fluid, air in this case, comes rushing in, they do so in the form of strong winds. This goes on until the pressures in the adjacent regions even out.

In both cases, the physical quantities which started to be uneven between the two bodies/regions even out in the end, i.e., when equilibrium is achieved. The measurement of the extent of this evening-out process is called entropy.

During the process of attaining equilibrium, it is possible to tap into the system to perform work, as in a heat engine. Notice, however, that work can only be done for as long as there is a difference in temperature. Without it, like when maximum entropy has already been achieved, there is no way that work can be performed.

Since the concept of entropy applies to all isolated systems, it has been studied not only in physics but also in information theory, mathematics, as well as other branches of science and applied science.

Because the accepted view of the universe is that of one that is finite, then it can very well be considered as a closed system. As such, it should also be governed by the second law of thermodynamics. Thus, like in all isolated systems, the entropy of the universe is expected to be increasing.

So what? Well, also just like all isolated systems, the universe is therefore also expected to end up in a useless heap in equilibrium, a.k.a. a heat death, wherein energy can no longer be extracted from anymore. To give you some relief, not everyone involved in the study of cosmology is totally in agreement with entropy’s so-called role in the grand scheme of things though.

You can read more about entropy here in Universe Today. Want to know why time might flow in one direction? Have you ever thought about the time before the Big Bang? The entire entropy concept plays an important role in understanding them.

There’s more about entropy at NASA and Physics World too. Here are a couple of sources there:

Here are two episodes at Astronomy Cast that you might want to check out as well:

Source:
Hyperphysics