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.