Sunday, March 01, 2009

Holographic Noise

Craig Hogan, from the University of Chicago, has written several papers predicting a noise that gravitational wave interferometers would be able to detect. This noise would be a signature of Planck-scale uncertainty if a certain type of holography was realized in Nature. The GEO600 interferometer near Hannover, Germany, would due to its construction details be particularly well suited to detect this noise.

And indeed, the experimentalists seem to be seeing such "holographic noise" in the frequency range between 300 and 1500 Hertz, even tough its detection is unpublished. Its occurrence is quoted in Hogan's paper (0806.0665) as “private communication,” but implicitly acknowledged on the website of the Astrophysics and Space Research Group at the University of Birmingham, a partner of the GEO600 collaboration: “To test the theory of holographic noise, scientists from Hannover and Birmingham will shift the frequency of GEO600's maximum sensitivity towards higher frequencies," and they carefully add “Even if it turns out that the mysterious noise is the same at high frequencies as at the lower ones, this will not constitute proof for Hogan's hypothesis. It would, however, provide a strong motivation for further study.”

Ununderstood noise in experiments is a good prediction to make, especially with large detectors. CERN's Large Electron Positron Collider (the tunnel of which is now reused for the LHC) was sensitive to the tides in Lake Geneva, and GEO600 is sensitive to the tides in the North Sea, and registers even smallest Earthquakes in the South Sea.

But still, we are all looking, waiting, hoping for signatures of Quantum Gravity.

Thus, NewScientist reported that our world may be a giant hologram, in a quite balanced article which quotes Karsten Danzmann of the Max Planck Institute for Gravitational Physics in Potsdam: “We work to identify [the] cause [of the noise], get rid of it and tackle the next source of excess noise. In this respect I would consider the present situation unpleasant, but not really worrying.”

Graviational Wave Interferometry

The idea underlying Hogan's prediction is that our world might have holographic properties, in which case not all three dimensions of our spacetime would encode really independent degrees of freedom. This conjectured property would become noticeable only at very large distances. A device that was able to measure distances in orthogonal directions at long distances and to high precision could be sensitive to this fundamental limit of encoding details, and be subject to a new kind of uncertainty. Gravitational wave interferometers provide exactly such a device. The holography would show up as noise in the detector.

Gravitational waves create distortions in our space-time that make themselves felt as tiny changes in lengths which are not the same for all three spatial dimensions. Interferometers lead a laser through a beam-splitter that splits the beam into two orthogonal directions into the “arms” of the interferometer, bounce the beam back on mirrors at the end of these arms, and compare the phases of the light when it comes back. This procedure can detect tiny deviations in the arm lengths which will change the phase shift. A common way to enhance the sensitivity of interferometers are “recycling techniques” that basically artificially increase arm lengths by reflecting the beam several times back and forth. GEO600 would be particularly sensitive to the holographic modification of quantum mechanics Hogan is proposing because the laser is reflected through both arms several times, whereas LIGO, VIRGO and TAMA use so called Fabry-Perot arms that reflect the beam in each arm separately. You find a very useful illustration of this difference between LIGO and GEO600 in Peter Shawhan's presentation, slide 19 and 20.

That is how the narrative goes.

Stefan and I then looked up Hogan's papers and tried to find out what the underlying model is. Since many points remained unclear to us, I wrote an email to the author who replied almost immediately and patiently answered my questions. He also agreed to be quoted here, which I hope will clarify some points better than Stefan and I could have done.

Holography

Hogan works with a modification of quantum mechanics in which position operators at different times fail to commute and instead the commutator is proportional to the Planck length lp and a measure of distance between the positions
[x1, x2] = lp L (1)

(Eq (3) from 0706.1999) In the cases considered in the paper x1 and x2 are taken for different events 1 and 2 on a lightcone, and denote the coordinates in a direction orthogonal to the lightpath connecting 1 and 2. While the proper distance between the events actually is null, L measures the spatial length of the connecting lightpath. In usual quantum mechanics, the commutator (1) vanishes. In Hogan's theory it can deviate arbitrarily much from the ordinary case, depending on how large L is, but this deviation would only become noticeable at large distances. One obtains from this commutator an uncertainty relation
Δ x1 Δ x2 > lp L/2 (2)

(Eq (7) from 0706.1999), which is then basically the origin of the noise in the interferometer*.

Let me start with the question of motivation. The Holographic Principle is the conjecture that all the information about a volume of spacetime is actually encoded on its surface. This conjecture originated from black hole thermodynamics: the entropy of the black hole is proportional to its surface. The Holographic Principle is supported by string theoretical considerations. There is no experimental evidence for it. The Wikipedia entry on the Holographic Principle interestingly refers to the NewScientist article as an experimental test.

There is however no derivation of Hogan's modified commutator in any of his papers from the Holographic Principle, there are just many references to papers by Susskind, t'Hooft, Bekenstein, Busso and so on. We are thus actually dealing with an approach that is conjectured to be related to a conjecture. The motivation Hogan provides is from the black hole entropy. He is claiming that his modified version of position uncertainty is necessary for consistency in the black hole entropy and that of its radiation, a conclusion I could not follow (see estimate, comments are welcome).

To be fair, this motivation from the black hole entropy does not appear in Hogan's later papers. And despite the missing relation to the usual Holographic Principle one might consider his particular sort of holography and its consequences.

Lorentz Invariance

But let us have a closer look at the modification of quantum mechanics Hogan is proposing. In his approach, the Planck length plays a special role; combined with the distance L it determines when the new effects would become important. One should be wary of any framework that does such since lengths are not invariant under Lorentz transformations - there is a restframe in which the Earth is of Planck length. Thus, by merely writing down an equation that renders the Planck length special, one creates a problem (see eg my post on The Minimal Length Scale). This is already a serious issue in “Deformed Special Relativity” (DSR) which claims to have found a way to leave the Planck length invariant under a modified sort of Lorentz transformations. Unfortunately, this doesn't work well in position space (see paper) and creates all kinds of unappealing secondary problems, such as the need for a modified addition law of momenta and a missing macroscopic and multi-particle limit. Hogan doesn't mention any of this in his papers.

The problems with Hogan's approach are actually worse than that of DSR, as one can see by looking at (1) and (2). In (1) we have two quantities of dimension length on the left side that undergo Lorentz-contraction, while on the right side there is only one, since lp is supposedly invariant. But as becomes particularly clear from (2), there is an additional problem, since L is orthogonal to the x axis - recall that it was a projection down along this axis. Thus, if one performs a boost in direction x, the left side of the inequality (2) can become arbitrarily small, but the right side remains as it is. This equation thus can clearly either not hold in all reference frames or requires some serious modification of Lorentz transformations. The former would imply Lorentz invariance is broken, and this case is very closely studied and tightly constrained by experiment. The latter implies all the problems of DSR and more, since there needs to be taken care of the unusual way orthogonal directions are treated.

Hogan clarifies in an email that he is considering the latter. With regard to the question of the invariance of the Planck length, he writes “The theory itself does not violate Lorentz invariance, but a particular apparatus or measurement does, by singling out a particular frame. There is no preferred direction in the theory.” And “I am working with the idea is that the Planck length really is fundamental and the same to all observers. An object can't Lorentz-contract below that; instead, some other physics kicks in, such as Matrix degrees of freedom in M theory.”

(Which I believe might refer to this recent paper.) With regard to the question of the relation of transverse boosts, he adds:

“In a holographic theory, you can't boost transversely; the wavefront is already moving at c. A boost would change the direction of the wavefront, and the observables.

I admit to writing down the relations in an arbitrary lab frame. The relationships of the position states depend on the frame; if L is Lorentz contracted by a longitudinal boost, the indeterminacy is less. In a highly boosted frame, L becomes the Planck length, and the indeterminacy is also a Planck length, reducing to the Planck scale noncommutativity. You can't boost more than that; in a holographic theory, once you have boosted that much, you have reached the 2D dual description, essentially living on the light sheet.”

Incidentally, Giovanni Amelino-Camelia considered that gravitational wave interferometers might detect Planck scale noise already in a 2003 paper “Quantum-gravity-motivated Lorentz-symmetry tests with laser interferometers". Without the holographic twist however, he concluded that the necessary sensitivity is out of reach.

Bottomline

Hogan is proposing an interesting modification of quantum mechanics that is holographic in the sense that it constrains the precision of measurements connected by lightpaths into directions orthogonal to each other. It is expressed through a modified commutation relation for position operators. The relation to the common Holographic Principle is not entirely clear to me, but it is an approach one can consider nevertheless. It does however necessitate a modification of Special Relativity in order to accommodate the invariance of the Planck length, and an appropriate transformation behavior of orthogonal directions. So far, Hogan's model has not addressed these issues that I believe pose significant challenges as to its consistency. Though I find the possibility that Planck scale physics might already have been detected exciting, I would appreciate an exposition of the framework that clarifies these points. It is certainly a long shot but, you see, if your shot is long enough, you might reach a stable orbit.

In reply to my suggestion to blog about it, Hogan wrote “On the blog, you are certainly welcome to post a piece on this --- indeed I hope it will help raise more discussion about it. Up to now I am interacting more with the experimental community, who seem to have a more urgent need to understand it!” Thus, having done my part, your comments are welcome.

Update: Thomas Dent points out that unlike what I wrote the GEO600 noise was published in The status of GEO 600, H Grote et al 2008 Class. Quantum Grav. 25 114043, and plots can be found online here and here. It is unclear to my why Hogan's papers do not refer to these publications.




* Let me add here that it is not clear to me what L is in the general case, since we are talking about a "distance" between wave-functions whose position is an operator, whereas L is a c-number. If you look at the definition of L in Fig (2) of Hogan's paper you find that the operators x1 and x2 have suddenly lost their operator-hats. I am further not sure how the approach of this paper corresponds to that of later papers. Thus, despite this pictorially making sense, I am missing an operationally well-defined explanation what L is in the general case of this modification of quantum mechanics.

26 comments:

Plato said...

I had just finished up at my blog with this posting on Gravity Wave Spectrum and thought to come over to check and see what was new, to find that you were dealing with similar work?

I am going to have to have a good look at yours , while mine is most generalized indeed. Don't know if you will learn anything.

Best,

Phil Warnell said...

Hi Bee,

A nice article which discusses a current proposal in physics which I must admit I certainly find difficult to grasp. To consider everything we recognize as being real as a projection that originates and resident at the boundaries of our universe gives ones mind more then a single twist. The worst of it for me is it seems to generate more questions then it provides answers.

Best,

Phil

Anonymous said...

Thanks, Bee, for the summary and for reporting on your exchange with Hogan! I presently have nothing to add, but will download the papers.

Plato said...

"Dyson, one of the most highly-regarded scientists of his time, poignantly informed the young man that his findings into the distribution of prime numbers corresponded with the spacing and distribution of energy levels of a higher-ordered quantum state." Mathematics Problem That Remains Elusive—And Beautiful By Raymond Petersen

If one is able to direct their attention to the idea of "Bekenstein bound" and how interpretation is arrived at Holographically for that space within the blackhole, then what use of CFT if it cannot help to move the mind to consider a "fifth dimensional perspective?" A tomato soup can and it's contents

Hi Phil,

There is no sense I think to give an example of the work of recognizing quality from something from 2002 but rather to exemplify it at work here first.

This is a culmination then as to the "signs of the time" that require an understanding of the "Quality of things." It would be to long in description that I may save one time to consider the discussion between Phil and my self in relation to the "Aristotelean arche" here this theory in consideration, in that, the technical aspects and the quality had to coincide with a balanced view with which is, "self evident."

You are then donning these glasses that I ask you to put on.

I again refer you back to Sean Carroll's view here, and his interpolations with regard to WMAP.

Best,

Plato said...

As you said Bee, I am the new Bacon( Shakespeare). If we are the builders, then what is nature? :)If it doesn't make sense now, it will.

All The World's A Stage by William Shakespeare
From: As you Like It, Act II Scene VII

Jaques:All the world's a stage,
And all the men and women merely players:
They have their exits and their entrances;
And one man in his time plays many parts,
His acts being seven ages. At first the infant,
Mewling and puking in the nurse's arms.
And then the whining school-boy, with his satchel
And shining morning face, creeping like snail
Unwillingly to school. And then the lover,
Sighing like furnace, with a woeful ballad
Made to his mistress' eyebrow. Then a soldier,
Full of strange oaths and bearded like the pard,
Jealous in honour, sudden and quick in quarrel,
Seeking the bubble reputation
Even in the cannon's mouth. And then the justice,
In fair round belly with good capon lined,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part. The sixth age shifts
Into the lean and slipper'd pantaloon,
With spectacles on nose and pouch on side,
His youthful hose, well saved, a world too wide
For his shrunk shank; and his big manly voice,
Turning again toward childish treble, pipes
And whistles in his sound. Last scene of all,
That ends this strange eventful history,
Is second childishness and mere oblivion,
Sans teeth, sans eyes, sans taste, sans everything.


Best,

Thomas D said...

It's not clear to me exactly when Hogan found out that GEO 600 had unexplained noise in the few-hundred Hz range.

The New Scientist article implies that he was "in the dark" until last June - when he sent his prediction to the experimentalists and got back a noise spectrum that matched it perfectly.

But he already referred in March 2008 (latest arxiv version of 0712.3419) to an earlier GEO600 talk which explicitly mentioned mystery noise in this range. Something looks screwy with the New Sci timeline.

It might possibly refer to the fact that the predicted spectrum isn't exactly flat but turns up at lower frequencies - this extra feature could possibly have been what the GEO people confirmed in 2008, although it was already visible in GEO600 talks and papers in 2007-8
eg
http://www.iop.org/EJ/abstract/0264-9381/25/11/114043
http://www.iop.org/EJ/article/0264-9381/25/11/114043/cqg8_11_114043.pdf

Uncle Al said...

Ununderstanding Lovely! All discovery is insubordination. Yang and Lee made a mockery of deep symmetries dictating all observation. Theory predicts what it is told to predict.

Lorentz invariance is not tighty constrained. Massless EM is hugely tested to extradordinary sensitivity. Massed sector violations remain untested. Physics is achiral by postulate and mathematics, then repeatedly embarrassed real world.

If left and right shoes violate the Equivalence Principle GR, isotropic vacuum, conservation of angular momentum, and Lorentz Invariance suffer an exquisitely selective violation. Eotvos balances are ready, single crystal left- and right-handed quartz is commercial.

Your problems can arise from a Weak postulate, like Euclid's Fifth Postulate. Somebody should do a Yang and Lee on spacetime. Somebody should look.

Plato said...

Uncle Al,

You should look at the analogy of the waterfall....False vacuum to the true? Energy topology?:)

You look then at the "sound of" billiard balls in new ways.:)

Best

Aaron said...

Wouldn't the Unruh effect make a better prediction of noise in gravitational interferometry? So that one would find a thermal spectrum of noise due to the acceleration. Now the really clever thing would be to look for diurnal oscillations in the thermal noise spectrum corresponding to axis change with respect to the sun.

Of course I'm just a crack-pot so what do I know anyway?

Peter said...

Isn't this principle

"The Holographic Principle is the conjecture that all the information about a volume of spacetime is actually encoded on its surface."

also true for other field theories ?

I'm not a physicist but I am aware
that in linear field theories, e.g., electromagnetism, you can
remove a volume if you know the tangential fields on the boundary of this volume. Is this similar to
the holographic principle ?

Aaron said...

Peter,

Interesting that you should point out Stokes Theorem. It was Stokes Theorem (the solutions to a differential form in a volume are enumerated by their boundary values) that initial was used to argue that black holes don't have entropy (they have a unique state).

The reason was that the Einstein Field Equations are a differential form, whose solutions are specified by the boundaries, which in the case of the Schwarzchild solution was unique and vanishing at infinity, and having a point singularity.

But by incorporating quantum effects at the event horizon Hawking showed that a black hole must be degenerate with entropy proportional to the event horizon area.

Thus either the assumptions about the boundary are incorrect (perhaps the singularity is not uniquely specified) or the Einstein Field Equations are not valid in the black hole regime.

Did I get that about right?

(As an aside, Stokes Theorem is also used to derive the adjoint of momentum operators in Quantum Mechanics).

Bee said...

Hi Peter,

I'm not sure what you mean with 'removing' the volume. Are you talking about the static case? Best,

B.

Bee said...

Hi Thomas,

Thanks for the info, I have added an update. Best,

B.

Bee said...

Hi Phil,

Well, one can get very philosophical about that, but one way to think about it is that we are subject to the illusion of having more possibilities than it is the case. I'm waiting for the beauty industry to pick up the idea that the surface tells you everything already ;-) Best,

B.

Bee said...

Hi Aaron,

Regarding Unruh effect: what is accelerated in an interferometer? I don't quite get it. Best,

B.

Aaron said...

The actual detectors are not sensitive to the Unruh effect because they are not in a freely falling geodesic; however the light particles themselves are freely falling near to the Rindler horizon of the gravitational acceleration (the light cannot be accelerated to higher velocities), and so would scatter off a thermal background whose temperature is proportional to the component of gravitational acceleration in the direction of the the beam. The scattering increases with beam intensity, but is of extremely low intensity.

The two arms of the beams are in orthogonal directions, so they scatter off different thermal backgrounds, resulting in different spectra. But interferometry only measures frequency difference, so the observed noise is the (anti-symmetric) convolution of the spectra, which is how the experiment can gain in sensitivity over direct measurements (nearly equal spectral modes are canceled while very different modes are amplified).

I only bring this up because it is worthwhile to look for noise sources plausible in standard physics before jumping into more speculative terrain.

Neil' said...

Maybe the holographic concept will link gravity and QM but more important: solve the collapse of the wave function. The current use of decoherence as a pretense for solving collapse is pitiful IMHO. Decoherence involves pretending that the mixture definable for a set of multiple cases (like, various runs of an experiment with varying phases each time) can be bastardized onto a given single event - "A coherent superposition becomes an incoherent mixture."

And, "they don't interfere with each other anymore." Well, "interference" is a global way of talking about patterns created by the superposition principle. The SP is supposed to apply in any case, even if it makes nice patterns one time and messy combinations another time - and in any case, both wave contributions continue to at least exist. So what does decoherence say happens to the other, "lost" state that used to be in combination with the first? No good answer is given.

Phil Warnell said...

Hi Bee,

This would seem to suggest that the larger the universe gets so the fussier it will become. We could have in future the projected Planck length the diameter of basket balls. What sort of world would this represent?

"I'm waiting for the beauty industry to pick up the idea that the surface tells you everything already ;-)"

Yes it would destroy the adage which cautions beauty is not only skin deep yet ugly goes clear to the bone:-)

Best,

Phil

Phil Warnell said...

Hi Bee,

Of course the other consequence is that every section of a hologram is representative of the larger whole, yet with less detail (more course grained). It is then to ask what this limit is as to when the overview is entirely lost and also to ask what information actually represents being when not complete when looked at from the segmental perspective rather then in its entirety. This alone has one end up in paradoxical positions. It seems to me that projection brings with it more then an illusion yet rather enough space to exist. This is like to ask what is a DNA sequence without a body in which to be manifested?

Best,

Phil

Plato said...

Sometimes it is necessary to shake the "rhetorical tree of science" in order for it to enjoy the "continuity of expression of beauty" as some fruit fallen, while it seeks to value the intricateness of complexity and call it a "sight to the bone," of what is at the surface.

Neil,

Credit: Weiqun Zhang and Stan Woosley

This image is from a computer simulation of the beginning of a gamma-ray burst. Here we see the jet 9 seconds after its creation at the center of a Wolf Rayet star by the newly formed, accreting black hole within. The jet is now just erupting through the surface of the Wolf Rayet star, which has a radius comparable to that of the sun. Blue represents regions of low mass concentration, red is denser, and yellow denser still. Note the blue and red striations behind the head of the jet. These are bounded by internal shocks.

The sun's distributive corona discharged are predictive from seeing only this side of the sphere? How so?

What is the fundamental value of geometrics of bubble nucleations but to see this in context of cosmological events "part and parcel" expressed and somehow is thought to be ugly? A foundational framework?

Such "static imaging" in this case, reveals a larger scope of the event then what is only apparent to the those being less than superficial?

"Beauty is skin deep" takes on new meaning in the "continuity of expression." One has to grok and consume, then one can say, the glasses are put on. It's seen in this new way.

While such creativity would seem less then desired here, it is of value that once you assume a position, this position highlights reality in different ways, and encourages them to develop according to that vision.

If one can never attain that position then they are more or less, mechanical in the repetitiveness of being, being rhetorical from one scientist to another. One would hope they could offer something new in "any dialogue."

Best,

Plato said...

The L4 and L5 points lie at 60 degrees ahead of and behind Earth in its orbit as seen from the Sun. Unlike the other Lagrange points, L4 and L5 are resistant to gravitational perturbations. Because of this stability, objects tend to accumulate in these points, such as dust and some asteroid-type objects.

A spacecraft at L1, L2, or L3 is ‘meta-stable’, like a ball sitting on top of a hill. A little push or bump and it starts moving away. A spacecraft at one of these points has to use frequent rocket firings or other means to remain in the same place. Orbits around these points are called 'halo orbits'.

But at L4 or L5, a spacecraft is truly stable, like a ball in a bowl: when gently pushed away, it orbits the Lagrange point without drifting farther and farther, and without the need of frequent rocket firings. The Sun's pull causes any object in the L4 and L5 locations to ‘orbit’ the Lagrange point in an 89-day cycle. These positions have been studied as possible sites for artificial space stations in the distant future.


So, you have decided to put the glasses on?:)You see now from a fifth dimensional perspective?

Ltool then becomes a method in recognition of "paths of least resistance." Asks then, that you hold events in the cosmos( and the events explained above) as expressive of these "new relations," that you might see it's extreme in, "blackhole participation?"

Best,

Plato said...

The Blackhole Computers

Hawking radiation owes its existence to the weirdness of the quantum world, in which pairs of virtual particles pop up out of empty space, annihilate each other and disappear. Around a black hole, virtual particles and anti-particles can be separated by the event horizon. Unable to annihilate, they become real. The properties of each pair are linked, or entangled. What happens to one affects the other, even if one is inside the black hole.

IN this case, a fifth dimensional view encapsulates and incorporates electromagnetism with gravity. A Gravity Wave Spectrum?:)

Plato said...

Oops! Sorry

Go to bottom of this page on Blackhole Computers

mcc said...

Quick dumb question... if there is "noise" in gravity waves at large scales, then why does this not have a noticeable effect on the gravitational dynamics at large scales?

Bee said...

Hi Mcc,

There is nothing special about gravitational waves in this model. It's just that gravitational wave detectors happen to have the right construction details to detect that sort of holographic noise, which is always there and everywhere. It's a far to weak effect to influence dynamics of planets or whatever you had in mind. Best,

B.

Ben R-G said...

I know this thread is getting a bit stale, but I had some questions/comments.

First, is there any difference between the concept of "holography" and the Bekenstein entropy bound? Usually I think of "holography" as implying some particular physics on some particular boundary, but this paper seems to make hardly any assumptions about boundary physics, and the derived result doesn't depend on the choice of boundary. Assuming this is really about the Bekenstein bound, does anyone seriously doubt that that bound holds? It seems as inevitable as Hawking radiation. Experimental confirmation of it would be like experimental confirmation of Hawking radiation—enormously important but not very surprising. To put it another way, if Hogan's derivation is theoretically sound then how plausible is it that the GEO600 noise is not what he says it is?

Second, you (Bee) object to the idea of a minimum length on the grounds that Lorentz contraction should lead to shorter lengths. Whenever I hear this argument I'm reminded of the fact that classical black holes don't Lorentz contract. That is, in any spacelike slice through a stationary black hole geometry the area and intrinsic curvature of the event horizon are the same. A "moving black hole"—i.e. a stationary black hole considered in different coordinates—is still spherical with the same surface area regardless of speed. Given this I can't help wondering if the minimum length problem solves itself in quantum gravity once you stop treating quantum particles as test particles on a fixed background. You shouldn't need a new deformed special relativity when general relativity already seems to provide the needed "deformation". (I'm aware of the charge/mass ratio problem with treating everything as a black hole, but still.)