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*Physicists have gathered evidence that space-time can behave like a fluid. Mathematical evidence, that is, but still evidence. If this relation isn’t a coincidence, then space-time – like a fluid – may have substructure.*

We shouldn’t speak of space and time as if the two were distant cousins. We have known at least since Einstein that space and time are inseparable, two hemispheres of the same cosmic brain, joined to a single entity: space-time. Einstein also taught us that space-time isn’t flat, like a paper, but bent and wiggly, like a rubber sheet. Space-time curves around mass and energy, and this gives rise to the effect we call gravity.

That’s what Einstein said. But turns out if you write down the equations for small wiggles in a medium – such as soundwaves in a fluid – then the equations look exactly like those of waves in a curved background.

Yes, that’s right. Sometimes, waves in fluids behave like waves in a curved space-time; they behave like waves in a gravitational field. Fluids, therefore, can be used to simulate gravity. And that’s some awesome news because this correspondence between fluids and gravity allows physicists to study situations that are otherwise experimentally inaccessible, for example what happens near a black hole horizon, or during the rapid expansion in the early universe.

This mathematical relation between fluids and gravity is known as “analog gravity.” That’s “analog” as in “analogy” not as opposed to digital. But it’s not just math. The first gravitational analogies have meanwhile been created in a laboratory.

Most amazing is the work by Jeff Steinhauer at Technion, Israel. Steinhauer used a condensate of supercooled atoms that “flows” in a potential of laser beams which simulate the black hole horizon. In his experiment, Steinhauer wanted to test whether black holes emit radiation as Stephen Hawking predicted. The temperature of real, astrophysical, black holes is too small to be measurable. But if Hawking’s calculation is right, then the fluid-analogy of black holes should radiate too.

Black holes trap light behind the “event horizon.” A fluid that simulates a black hole doesn’t trap light, it traps instead the fluid’s soundwaves behind what is called the “acoustic horizon.” Since the fluid analogies of black holes aren’t actually black, Bill Unruh suggested to call them “dumb holes.” The name stuck.

But whether the horizon catches light or sound, Hawking-radiation should be produced regardless, and it should appear in form of fluctuations (in the fluid or quantum matter fields, respectively) that are paired across the horizon.

Steinhauer claims he has measured Hawking-radiation produced by an acoustic black hole. His results are presently somewhat controversial – not everyone is convinced he has really measured what he claims he did – but I am sure sooner or later this will be settled. More interesting is that Steinhauer’s experiment showcases the potential of the method.

Of course fluid-analogies are still different from real gravity. Mathematically the most important difference is that the curved space-time which the fluid mimics has to be designed. It is not, as for real gravity, an automatic reaction to energy and matter; instead, it is part of the experimental setup. However, this is a problem which at least in principle can be overcome with a suitable feedback loop.

The conceptually more revealing difference is that the fluid’s correspondence to a curved space-time breaks down once the experiment starts to resolve the fluid’s atomic structure. Fluids, we know, are made of smaller things. Curved space-time, for all we presently know, isn’t. But how certain are we of this? What if the fluid analogy is more than an analogy? Maybe space-time really behaves like a fluid; maybe it is a fluid. And if so, the experiments with fluid-analogies may reveal how we can find evidence for a substructure of space-time.

Some have pushed the gravity-fluid analogy even further. Gia Dvali from LMU Munich, for example, has proposed that real black holes are condensates of gravitons, the hypothetical quanta of the gravitational field. This simple idea, he claims, explains several features of black holes which have so-far puzzled physicists, notably the question how black holes manage to keep the information that falls into them.

We used to think black holes are almost featureless round spheres. But if they are instead, as Dvali says, condensates of many gravitons, then black holes can take on many slightly different configuration in which information can be stored. Even more interesting, Dvali proposes the analogy could be used to design fluids which are as efficient at storing and distributing information as black holes are. The link between condensed matter and astrophysics, hence, works both ways.

Physicists have looked for evidence of space-time being a medium for some while. For example by studying light from distant sources, such as gamma-ray bursts, they tried to find out whether space has viscosity or whether it causes dispersion (a running apart of frequencies like in a prism). A new line of research is to search for impurities – “space-time defects” – like crystals have them. So far the results have been negative. But the experiments with fluid analogies might point the way forward.

If space-time is made of smaller things, this could solve a major problem: How to describe the quantum behavior of space time. Unlike all the other interactions we know of, gravity is a non-quantum theory. This means it doesn’t fit together with the quantum theories that physicists use for elementary particles. All attempts to quantize gravity so-far have either failed or remained unconfirmed speculations. That space itself isn’t fundamental but made of other things is one way to approach the problem.

Not everyone likes the idea. What irks physicists most about giving substance to space-time is that this breaks Einstein’s bond between space and time which has worked dramatically well – so far. Only further experiment will reveal whether Einstein’s theory holds up.

Time flows, they say. Maybe space does too.

*This article previously appeared on iai.news.*

## 41 comments:

Sounds weird. Something almost but not complete unlike luminous eather?

tyy,

Not stuff in space, but stuff that behaves like space. But, yes, it bears some similarity to aether theories.

Historically, I take the 19th Century concept of aether to carry the presumption of Galilean invariance. Although one could update the concept in the light of experience and say that the (effective) dynamics of the aether, as of the vacuum, is Lorentz invariant, it seems good to me not to forget why "the aether" didn't work but "the vacuum" does.

The point of these experiments is that there is an effective Lorentzian dynamics at laboratory scales, but with the speed of sound instead of the speed of light (right?), which gives us another example of a significantly different effective dynamics even across only 10 orders of magnitude. Where I'm curious is whether there is a narrow range or a broad range of conditions for which an effective Lorentzian dynamics is universal.

Some of these ideas go back a long way: https://arxiv.org/abs/cond-mat/9711031

"All attempts to quantize gravity so-far have either failed or remained unconfirmed speculations"

I want to ask whether there is a mathematical model where this is not true. This is, whether anyone wrote down equations for a hypothetical world with different physics, say gravity that follows a relation other than the inverse square one, where the space time could be reduced to quantum objects whose classical limit reproduces the original equations.

Such a model may be easier to find than one that reproduces real physics, and could fertilize the creativity of solutions for the QG problem in the real world.

"

the same cosmic"brainbrane"

equations look exactly like those of waves in a[n achiral] curved background." or chiral spacetime torsion background. Embedded enantiomorphic atomic mass distributions then afford diastereomorphic divergences."

evidence of space-time being a medium" Massless boson photon Michelson–Morley is 10^(-17) null, arXiv:1002.1284, 0706.2031. Massed fermion hadrons are unexamined. Geometric Eötvös experiments contrast visibly and chemically identical single crystal test masses in enantiomorphic space groups to 10^(-12) divergence.P3(1)21 right-handed versusP3(2)21 left-handed α-quartz. Unit cell chiral emergence volume is 0.113 nm³, three SiO_2. Forty grams of single crystal test masses compare 6.68×10^22 pairs of opposite shoes (pairs of 9-atom enantiomorphic unit cells, the Eötvös rotor's opposed vertical sides).Lookhttps://inspirehep.net/record/1121871/files/WEP_figure3.png

An "untouchable" aether that is, since it doesn't seem obvious what substance should be based upon and yet, it should differ for both "matter" and "radiation". It sounds similar to previous attempts to substantiate the wavefunction itself as a "real" entity. What more, such a space-time substance could be as a liquid "screen" with us, the "cartoons" inside!

Is this part of your work on loop quantum gravity or would this be a separate subject like granular space-time?

" What irks physicists most about giving substance to space-time is that this breaks Einstein’s bond between space and time which has worked dramatically well – so far. Only further experiment will reveal whether Einstein’s theory holds up."

The challenge here, I believe, is to interpret 'time' in GR as an emergent property of space, to preserve the space and time connection in this 'fluid' of a nature as yet unknown.

Using the fluid analogy and L. Prandtl's findings, we could have an angle to reinterpret time as follows :

(Link: Prandtl://en.wikipedia.org/wiki/Prandtl%E2%80%93Glauert_transformation)

Ludwig Prandtl already provided the analogous mathematical formalism of the kinetic time dilatation factor, using the speed of sound, serving as a compensation to express the pressure more correctly, for a sphere moving

through a compressible fluid instead of an incompressible one : Cp = Cp0 (1/β).

Secondly, now use the equivalence principle to transfer the logic to the gravitational field, and realize that this pressure from the compressible fluid entails energy density. Hence concluding that time in GR emerges from a comparison of local energy density to energy density 'at infinity', relating to the gravitational time dilatation factor.

As they say " the duration of a second 'here' as compared to 'infinity' "

Such an extremely specific analogous mathematical formalism is by no means to be treated as a mere coincidence I believe. And it directly points to a compressible substance as being space itself, extrapolating the analogy.

One should realize that time can mean 2 things : a tool of the mind to structure and order events. Or time in GR, where time is what clocks measure, atomic clocks, not hour glasses or pendulums, it's not an independent universal entity. Proof links it to the transition between the two hyperfine levels of the ground state of a.o.the cesium. Time here is not abstract at all. Confusing these two definitions or meanings leads to misinterpreting time and not connecting to a scientific clear explanation of 'time' in GR.

Best, Koenraad

More like liquid crystal? One of its properties is chirality.

If space is itself made of substance, where does the space-substance lie?

How did a GR analogy alone reproduce analogy of Hawking radiation when the original radiation required QM and GR both. Does it mean that GR alone can cause the radiation?

Michael,

I do not work on Loop Quantum Gravity and have never worked on Loop Quantum Gravity and have no idea why you think otherwise.

orezeno,

It's not GR alone. The analogy is between quantum fields in a curved background (ie quantum fields plus GR) and quantum fields as perturbations over a background of quantum fields. It's the background that mimics the curved space-time. So the perturbations move in the background ("the fluid") as if they are in a curved space-time. (It also works with classical fields. It's not necessary they are quantum fields but it's more interesting.)

tytung,

Depends on the model. The cleanest versions are usually network-based. In this case you do not have any space at the beginning, you merely have nodes of the networks and some interaction between them. In some limit, the network must reproduce to good accuracy the space-time we usually have in general relativity. But the notion of 'distance' that you get then is derived from the structure of the network. So the substrate isn't anywhere. Instead, it defines what you mean by "here" and "there".

Here is something about how distorted spacetime may create entanglement in photons traveling near spinning black holes. Just like beam splitters and prisms could create photonic entangled states.

https://doi.org/10.1016/j.newast.2017.09.001

How does a fluid analog of general relativity avoid having a preferred reference frame?

Thanks for the great blog. It's written at just the right level for me as the maths of most of what you discuss would be beyond me these days! I just have a question about loop quantum gravity.

Have you never worked on it because that's just the way things worked out? Or have you looked at it and decided that it's not the route to quantum gravity? And if so why not?

If you have already blogged on this then just let me know and I'll go Google it.

Thanks

Dan

Arun,

It doesn't. It's why I write it breaks the union between space and time.

Dan,

I looked at it but wasn't convinced, so I stayed away from it. Same with string theory I may add. I pay for my scientific atheism by being basically unemployable now.

@Paolo "

More like liquid crystal? One of its properties is chirality."Chiral optical effects do not measure geometric chirality, stereograms below, or even require it (achiral silver thiogallate's 522°/mm rotation). Physics' chirality excludes chiral geometric Eötvös experiments. Given baryogenesis, this should set off alarms.

http://www.mazepath.com/uncleal/norone.png

...Atomic mass distribution and optical rotation are not coupled.

Would love to read a blog post outlining your reasons for not being convinced ;)

This fluid "substrate" analogy seems to chime with the older analogy of viewing space as having a variable refractive index (determined by matter distributions) p, that gravitational induced light bending can be viewed according to an aether based Snell's law. What makes it more instructive as an analogy is not clear. Perhaps, that polarisation states of gravitational waves can be naturally described by chiral self dual forms of Einstein-Cartan theories?

By analogy, would sound also be similar?

The "perfect fluid" comes to mind.

Thank-you for this link. Using a quantum aether condensate for a black hole seems like a really potentially fruitful approach to unification of black hole physics with quantum uncertainty. Of course, there is still a fundamental dephasing necessary a la continuous spontaneous localization to finally complete unification with a quadratic Hamiltonian...or at least, that what seems to work.

sorry..but giving a space-time a material fluidic substructure constituting its continuum (mechanically and explicitly) does not separate space and time as exclusive and does not invalidate Einstein's GRT...it just gives it cause for their dependency. Both the experience of distance and time are emergent from the superfluidic substructure of space, where the curvature of space-time is a distortion in this material substance of density and stress.

Space may not be as immaterial as we thought.... What if the fluid analogy is more than an analogy? Maybe space-time really behaves like a fluid; maybe it is a fluid.This seems puzzling to me. Ordinary material substances (such as fluids) have constituent parts that move inertially in time through some (supposedly empty) space. If space(time) itself is a material (or at least not as immaterial as we thought) fluid, then does it have constituent parts that move inertially in... what? Some kind of meta-spacetime? In other words, if spacetime is a fluid, don't the parts of that fluid have to exist and move in some meta-spacetime? If no, then it doesn't much resemble an actual material fluid, but if yes, then what is the structure of the meta-spacetime in which the fluid of spacetime exists?

For example, in models of analog gravity based on fluids, do the models assume that the fluid exists in a Galilean spacetime, with the locally Lorentzian metric arising purely as an effective "acoustic metric" in the fluid, or is the fluid modeled in a pre-existing Lorentzian spacetime?

Hi Sabine,

I like your ideas about defects in space, and space being made of something. What are your thoughts that matter is the defects in space, and the defects and the fields they create are an alteration in expression of the something that space is made of. Where both the defect and the fields are the only thing that moves through the something, but the actual granular spacetime does not move, except for tiny dislocation adjustments.

The constituents of a space-time substructure material would have to exist... but do not have to be similar to known macroscopic material constituents. Space is not a normal substance therefore it's constituents don't have to be "normal". Been researching this for years from a line of research the branched into this area and could go on at length speaking to what and how space-time is... there is a lot of good research and historical context out there about this very subject ... including on Einstein's own work... pop science has conflated the understanding of many with erroneous assumptions.

Amos

She mentioned networking if you were reading above. Volovik refers to superfluid helium and all his work explicitly shows the similarities between spacetime and condensed matter systems. As far as my opinion, if you have a lattice and each point has time reversal symmetry (protected) it cancels out however if you add frustration based on the spin system (see heisenberg) you get frustration which gives you the stress energy to be conserved into quanta or particles

She mentioned networking if you were reading above.Does mentioning networking really answer the question? I believe (correct me if I'm wrong) the analog gravity models mentioned in the post are based on modeling the fluid, not on an abstract network, but in some underlying spacetime. So, for this case, my question was: Is the underlying spacetime for analog gravity fluid models assumed to be Galilean or Lorentzian? And is the fluid treated with Newtonian or relativistic mechanics? I'm curious because if they claim the Lorentzian metric of spacetime emerges as an acoustic metric in a fluid, then it would be strange for the fluid to be modeled in a Lorentzian background spacetime.

For the more abstract attempts to model spacetime, it was mentioned that

"The cleanest versions are usually network-based. In this case you do not have any space at the beginning, you merely have nodes of the networks and some interaction between them.... So the substrate isn't anywhere. Instead, it defines what you mean by "here" and "there".But doesn't the network with its connections constitute a "space at the beginning?" The network with its interactions defines its own prior space with its own measure of "distance" and "location", etc. It may be a discrete network, with non-local connections, or it may be continuous, etc., but it possesses the structure of some kind of space... and if something is going to be a fluid in this network, it must be a special kind of space(time) to support that.So this brings me back to my question: If we say that "spacetime is a material fluid", then it must have the attributes of a material fluid, and I'm trying to understand how something that exists on the nodes of a network can have those attributes, unless the network is a meta-spacetime. Do the constituent parts of spacetime flow from one node to another? I think that, for something to even exhibit the inertial attributes of a material fluid, it must exist in some kind of space and time, but if the fluid IS space and time, then I'm still puzzled. Doesn't this imply that the network is, in effect, a meta-spacetime?

Amos,

It's Lorentzian and you can treat the fluid both relativistsically and in the non-relativistic limit.

And yes, you can define a distance measure from the network. That isn't the challenge. The challenge is to get the connectivity of the network to resemble a locally flat 3(+1) dimensional space-time. That's highly non-trivial & not any network will do.

Amos, the analog gravity models are based on standard condensed matter theory. One can, of course, also consider relativistic theories of condensed matter theory, but, given that the characteristic speed in these models is the speed of sound, much smaller than the speed of light, this is usually not done. So, the underlying spacetime model is Newtonian absolute space and absolute time.

And even if you use a relativistic model, the relativistic background has nothing to do with the point of analog gravity, because in this case you have two Lorentz symmetries, that of the background, with the speed of light, and that used in the analogy, with the speed of sound as the respective characteristic speeds. So, the emerging Lorentzian metric is very different from that of the background, even if you use one to describe the background.

Amos

There are several ways you can attack the problem

As an example check up Xiao-Gang Wen on spin liquid. He is working on it over decade, and his theory actually uv complete.

Second, you can also study from another direction such us ising model XY universality, magnetic orders etc and gravitational anomalies (see graphene) the superfluid analogue it's just one description.

Look up Grigori Volovik on arXiv he shows the parallel between these scenarios.

I did built network models in 2 and 3 dimensions and tested under unitary transformation, and degeneracy of the system. My results were surprisingly good, I received lots of nice feedback from condensed matter physicists also from Edward Witten himself thanking for my simulations.

I believe string theory need condensed matter physics support and this territory still in the early stages, but it's an intense research topic, especially if you understand the importance of zero temp phases and their difficulties experimentally due effectively you can't ever reach it still.. Trying to describe the system in that state. Recently this year spin liquid and quantum Hall states started to be experimentally shown but it's a long way to go. Regardless its shows that, the theoretical part is eventually successful, especially more successful in condensed matter physics than in cosmology at this moment.

[The underlying spacetime for analog gravity fluid models is] Lorentzian and you can treat the fluid both relativistsically and in the non-relativistic limit.Okay, so in that case I wouldn't say the fluid IS spacetime, I would say the underlying Lorentzian spacetime - within which the fluid exists and moves - is spacetime, and the fluid is, well, a fluid. I suppose one could say that the fluid is a simulated spacetime, if everything we ordinarily deal with is a structure of the fluid with the effective acoustic metric of the fluid. In that sense it reminds me of your other post about living inside a simulation (except it's a natural simulation). But my point is that there's an underlying spacetime that happens to be identical in structure to the simulated spacetime (at least in flat regions), which seems somehow comical.

(I'm setting aside the gravitational curvature here, and just trying to understand the relationship between the usual flat spacetime of our experience and the sub-stratum space(time).)

And yes, you can define a distance measure from the network. The challenge is to get the connectivity of the network to resemble a locally flat 3(+1) dimensional space-time. That's highly non-trivial & not any network will do.Exactly, so again in this case we have our simulated spacetime "fluid" existing in a sub-stratum space(time) that happens to closely resemble the same structure as the simulated Lorentzian spacetime of our normal experience. Maybe the purpose of a substratum is to make it discrete instead of continuous, so the simulated spacetime behaves differently at small scales. It does seem a lot like the "living in a simulation" idea, with the network connectivity comprising the programming.

Yes, except that just like you said its natural computation process in some form underlying all scale. And exactly because of this, thinking parallel about black holes and quantum computation is so much interest, just as ads/cft

Sabine, perhaps you already know about this experiment, but in case you don't, I've already found this article in phys.org:

https://phys.org/news/2017-10-physicists-quantum-gravity-current-technology.html

From some post of yours I've been reading in the last months, I infere that you don't like pop science divulgation that much, but in my humble opinion phys.org is a very interesting website, so I'd like to share this article.

Best regards.

Guillermo (the guy that recently asked you about Maldacena)

Guillermo,

It seems this is a revival of this idea. It was wrong in 2012, it's still wrong.

Sabine, do you think that the Higgs field might turn out to be omnipresent throughout space, connecting everything as a real explanation for gravity? Could we then throw out the metaphysics of the non-entity "spacetime?"

Michael,

The Higgs field (background value) is omnipresent. The rest of your comment doesn't make sense.

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