Andromeda: No Escape

Gravitationally you are stronger bonded to Andromeda than you are to Earth


If one of these days you find yourself under a dark night sky, have a look at the constellation Andromeda. With bare eyes you should just be able to spot a faint smudge in this constellation. You need sharp eyes that are well-adapted to the dark. It definitely helps if you happen to carry with you a pair of binoculars. And the dark should be real dark. That means a spot far away from city lights. Also the moon, with its overwhelming brightness, needs to be out of sight.

Once you have spotted it, look more closely at that faint smudge. It is the furthest object you can see with bare eyes. You are looking at a galaxy comparable to but somewhat larger than our Milky Way galaxy. It is the enormous distance you are away from Andromeda that reduces it to a faint fuzzy in the night sky. The light from this galaxy has been traveling an amazing 2.5 million years to reach you. In comparison, no human has ever reached a spot from which light would need to travel more than 1.3 seconds to reach Earth. The distance traveled by light in two-and-a-half million years is a distance way beyond human comprehension. Yet you are more strongly bonded to Andromeda than to Earth.


You read that correctly. You are gravitationally more strongly bonded to Andromeda than you are to earth.

Andromeda: a faint smudge in the night sky


Let me make that more precise. Gravitation makes you stick to earth. And this gravitational binding to earth is pretty strong. To escape earth’s gravitational pull from your present position, you would need to jump up at a speed of about 11 km per second (7 mi/s). No small task. And that is ignoring any drag due to Earth’s atmosphere. However, to escape that faint smudge in the sky, you need to jump much more fiercely. In fact, you need to jump such that you achieve a speed of 88 km/s (55 mi/s) relative to the same smudge. And no, I am not cheating, it’s a like-for-like comparison. It is you again jumping from your same present position, and that is again ignoring atmospheric drag.

Few people realize the amazing reach of gravity. Gravity adds up. Andromeda with its trillion stars is incredibly more heavy than earth, and an overwhelming gravitational attraction comes with it that easily compensates for the enormous distance. The fact that you are gravitationally bound to Andromeda, makes everything around you – earth, the solar system and the whole Milky Way – bound to Andromeda. It should therefore not surprise you that the Milky Way is on a head-on collision course with Andromeda. Both galaxies are falling into each other. Don’t be worried, this is a long fall, and you and I won’t witness the final stage of it, and neither will your children, your grand-children, your grand-grand-children, … , and so on including your grand-to-the-power-100,000,000-children. And when the galaxy merger finally takes place, it will perhaps be a most welcome event as around that time we – if indeed we still exists – will need some forceful intervention to pull us away from sun, which soon thereafter will blow up and turn into a red giant.

Verlinde’s Dark Universe

Verlinde’s stab at the dark universe remains a stab in the dark

Lots of people have asked me for my views on Erik Verlinde’s latest paper “Emergent Gravity and the Dark Universe“. This fifty-one pages long preprint has attracted a fair bit of media attention. Particularly in the Netherlands, Verlinde’s name being attached to the draft paper has caused a true hype. Un-Dutch roaring headlines in the Dutch national newspapers include: “Breakthrough Theory: Dark Matter Is Utter Illusion – Dutch Professor Rivals Einstein“, “We Are at the Brink of a Revolution that could be larger than Quantum Physics and Relativity Combined“,  and “Breakthrough Article on Gravity Renders Verlinde the Most Celebrated Scientist of 2016“.

Last week I found myself standing in the back of a room somewhere in the south of the Netherlands. Erik Verlinde kicking off the session on dark matter at physics@veldhoven was the probable cause for the room being packed.

Erik Verlinde facing a packed room at physics@veldhoven
Just like other physicists, I am eagerly awaiting results from the various dark matter detection experiments. I certainly do not consider myself to belong to the group described by one of the subsequent speakers as ‘dark matter deniers’. At the same time, I do feel the standard model of cosmology contains too many coincidences to convince me dark matter is real. On balance, I remain sympathetic towards papers that provide an alternative to the somewhat baroque ‘gravity + dark matter + dark energy’ description of our universe. Verlinde’s paper states that this trinity can be reduced to the duo ‘gravity + dark energy’. In other words, Verlinde claims that in a universe with dark energy, the long-range effects of gravity get modified such that dark matter appears to be present

With a lot of hand waving I can dumb-down Verlinde’s position as follows:

1)  Spacetime (and gravity, its curvature) is emergent from the information captured in quantum correlations. This in itself represents by no means a new concept. Emergent spacetime is best understood for a model universe containing nothing else than ‘dark anti-energy’ (so-called AntiDeSitter space) and goes under the cryptic label ‘ER=EPR’.

2) In a more realistic spacetime solely containing dark energy (so-called DeSitter space), the ER=EPR correspondence still applies, albeit with a significant complication: non-local quantum correlations play up. This claim is new. If correct, this implies the breakdown of the much celebrated holographic principle first proposed by Erik’s MSc thesis adviser Nobel laureate Gerard ‘t Hooft.

3) Due to competition between local and non-local quantum correlations, emergent DeSitter spacetime does not thermalize over large length scales, thereby causing a ‘glassy behavior’ and ‘elastic dynamics’ which lead to long-range deviations in the gravitational behavior commonly attributed to dark matter.

So, to eliminate dark matter, Verlinde requires fundamental degrees of freedom that are non-holographic in nature and that also feature non-equilibrium behavior. Particularly at point 3) the paper is rather impenetrable (at least for me) and it is unclear to me how exactly the ‘glassy dynamics’ emerges. In his talk Verlinde didn’t address this point.

For the time being, we may step over any issues in the derivation, as in the end what matters is how successful Verlinde is in quantifying the apparent dark matter. The formula he proposes (equation 7.40 on page 38 in Verlinde’s preprint) adds to the gravitational acceleration a ‘dark acceleration’. The equation he provides applies to static mass distributions with spherical symmetry only, and can be condensed into:

<a2> =  c Ho g /2

Here, g denotes the (constant) gravitational acceleration over a spherical surface  centered around a spherically symmetric mass distribution, the angular brackets denote averaging over the whole sphere, a represents the apparent ‘dark acceleration’, c is the speed of light and Ho the current value for the Hubble constant. This represents a MOND-type modified gravity. Just like the phenomenological MOND description, Verlinde’s equation can be expected to struggle in describing dark-matter phenomena such as the acoustic oscillations in the cosmic microwave background (CMB).

My final ordeal? I had hoped Verlinde’s lengthy paper to culminate in an equation with wider applicability. Cosmology has evolved into a high-precision scientific discipline thanks to a wealth of quantitative information on the CMB. Verlinde’s paper doesn’t address dark matter effects in the CMB. It is unlikely that Verlinde’s approach will attract a professional following anywhere near to what the Dutch newspaper headlines suggest, unless Verlinde manages to apply his approach successfully to the acoustic oscillations in the CMB or any other area where MOND fails.

Until that happens I am most happy with my tax money going to dark matter detection experiments.


Holographic Dark Universe

Dark energy in a holographic universe.

When Albert Einstein constructed his general theory of relativity he decided to resort to some reverse engineering and introduced a ‘pressure’ term in his equations. The value of this pressure was chosen such that it kept the general relativistic description of the universe stable against the gravitational attraction of the matter filling the universe. Einstein never really liked this fudge factor, but it was the only way to get the equations of general relativity to describe a universe that is static in size.

More than 10 years later, Edwin Hubble’s observations showed that the universe is in fact not static, but rather expanding. With this, the need for the pressure term disappeared. Einstein must have felt floored: if only he would have sticked to the bare equations without the fudge factor, he could have predicted the universe to be non-static. Throughout his later life, Einstein kept referring to the introduction of the pressure term as his ‘biggest blunder’.

Einstein and Hubble

Would Einstein have lived till the very end of the 20th century, he would certainly have changed this ordeal. Sure, our universe is expanding, but since the end of the 90’s we know that this expansion is accelerating. Today the universe is expanding faster than yesterday, and tomorrow it will be expanding again faster than today. Without Einstein’s fudge factor, a decelerating expansion is to be expected, and the pressure term is needed to switch from a description yielding a decelerating universe to one that yields an accelerating universe.

What is causing this pressure that is pushing space apart at ever accelerating rates? Cosmologists refer to ‘dark energy’ permeating space as what propels this cosmic acceleration. In order to explain the observed accelerated expansion of the universe, this dark energy should comprise the vast majority of the total energy content in the universe. Recent observations lead to a dark energy density in the universe corresponding roughly to one Planck energy (or equivalently: one Planck mass of about 20 microgram) per 1000 km cubed. The fact that this tiny density constitutes the dominating component of our universe just demonstrates the vast emptiness of space.

But what is this dark energy? No one knows. The most likely explanation is that dark energy is quantum mechanical in origin. In fact, most physicists would probably agree that dark energy results from quantum fluctuations, if only this would lead to predictions of the right magnitude of the dark energy effect. However, the standard quantum field-theoretical (QFT) approach leads to an overestimate of the dark energy density. How much of an over estimate? Well, any statement one can make on this will be an understatement. Applying standard quantum field theory considerations, vacuum fluctuations can be estimated to lead to an energy density of one Planck energy per Planck length cubed. That is a Planck energy per cube with sides of 0.000 000 000 000 000 000 000 000 000 000 000 016 m. A volume a wee bit different from 1000 km cubed.

Where have we gone wrong?

Some simple dimensional analysis hints at a potential solution. There are two key length scales entering the problem: the Planck length ℓ and the cosmic scale L (read: the diameter of the observable universe). The contrast between the two is vast: 61 orders of magnitude. Wouldn’t it be a huge surprise if these two extreme length scales can be combined into a volume of the right size to describe the dark energy density? Well – surprise, surprise – this is easy to achieve. The experimental value of the dark energy density happens to coincide with one Planck quantum per volume of size L2ℓ. Yet, as we saw above, standard quantum field theory predicts a zero point energy density of one Planck quantum per ℓ3. Can we change two of the ℓ’s in this equation into L’s?

Yes we can. Key is to realize that the ℓ3 volume enters into the theoretical description because standard QFT assumes one degree of freedom per Planck cube. So according to QFT our universe has a total of (L/ℓ)3 degrees of freedom. This however ignores the holographic nature of our universe that was postulated by Gerard ‘t Hooft in 1993. The holographic principle states that standard QFT vastly overestimates the number of degrees of freedom available. More precisely, the holographic principle forbids a system of linear size L to have more than (L/ℓ)2 degrees of freedom. So, this in itself already changes one ℓ in the equation for the dark energy density into an L. But there is more. QFT associates a zero-point energy of one Planck unit with each degree of freedom. This does not necessarily carry over into a holographic description. The degrees of freedom in the holographic description are non-local, and the wavelengths corresponding to the zero-point motion can probably be linked to the macroscopic length L, rather then to to the microscopic length ℓ. This effect (embodied in the so-called ‘UV/IR connection’) gives us another swap between ℓ and L in the equation for the dark energy density so that with all holographic effects incorporated we arrive at ℓ/L Planck energies per volume of size ℓ2L, or equivalently, one Planck energy per volume of size L2ℓ.

Is this all the correct way to look at the expansion of our universe? Or is the Planck energy per volume L2ℓ some coincidence? I don’t know the answer. What I do know, is that if the above is in essence correct, holographic considerations will be an integral element of the still elusive theory of quantum gravity. It is also clear that the strict holographic cut-offs to the number of degrees of freedom and the allowed energies per degree of freedom will be of immense help to regularize this theory of quantum gravity. History tells us that experimentally demonstrated discrepancies in our understanding of the fundamental laws of physics never last for more than a few decades. So I dare to make the prediction that in the first half of this century we will witness a revolution in our thinking about the universe in the form of a fully consistent theory of quantum gravity. These are exciting times!