Pure Pedantry

Scientists by have found evidence for the holographic principle in the search for gravity waves:

According to Hogan, the holographic principle radically changes our
picture of space-time. Theoretical physicists have long believed that
quantum effects will cause space-time to convulse wildly on the tiniest
scales. At this magnification, the fabric of space-time becomes grainy
and is ultimately made of tiny units rather like pixels, but a hundred
billion billion times smaller than a proton. This distance is known as
the Planck length, a mere 10-35 metres. The Planck length is
far beyond the reach of any conceivable experiment, so nobody dared
dream that the graininess of space-time might be discernable.

That
is, not until Hogan realised that the holographic principle changes
everything. If space-time is a grainy hologram, then you can think of
the universe as a sphere whose outer surface is papered in Planck
length-sized squares, each containing one bit of information. The
holographic principle says that the amount of information papering the
outside must match the number of bits contained inside the volume of
the universe.

Since
the volume of the spherical universe is much bigger than its outer
surface, how could this be true? Hogan realised that in order to have
the same number of bits inside the universe as on the boundary, the
world inside must be made up of grains bigger than the Planck length.
“Or, to put it another way, a holographic universe is blurry,” says
Hogan.

This
is good news for anyone trying to probe the smallest unit of
space-time. “Contrary to all expectations, it brings its microscopic
quantum structure within reach of current experiments,” says Hogan. So
while the Planck length is too small for experiments to detect, the
holographic “projection” of that graininess could be much, much larger,
at around 10-16 metres. “If you lived inside a hologram, you could tell by measuring the blurring,” he says.

Gravitational wave detectors like GEO600 are essentially
fantastically sensitive rulers. The idea is that if a gravitational
wave passes through GEO600, it will alternately stretch space in one
direction and squeeze it in another. To measure this, the GEO600 team
fires a single laser through a half-silvered mirror called a beam
splitter. This divides the light into two beams, which pass down the
instrument’s 600-metre perpendicular arms and bounce back again. The
returning light beams merge together at the beam splitter and create an
interference pattern of light and dark regions where the light waves
either cancel out or reinforce each other. Any shift in the position of
those regions tells you that the relative lengths of the arms has
changed.

“The
key thing is that such experiments are sensitive to changes in the
length of the rulers that are far smaller than the diameter of a
proton,” says Hogan.

So
would they be able to detect a holographic projection of grainy
space-time? Of the five gravitational wave detectors around the world,
Hogan realised that the Anglo-German GEO600 experiment ought to be the
most sensitive to what he had in mind. He predicted that if the
experiment’s beam splitter is buffeted by the quantum convulsions of
space-time, this will show up in its measurements (Physical Review D, vol 77, p 104031). “This random jitter would cause noise in the laser light signal,” says Hogan.

In June he sent his prediction
to the GEO600 team. “Incredibly, I discovered that the experiment was
picking up unexpected noise,” says Hogan. GEO600′s principal
investigator Karsten Danzmann of the Max Planck Institute for Gravitational Physics
in Potsdam, Germany, and also the University of Hanover, admits that
the excess noise, with frequencies of between 300 and 1500 hertz, had
been bothering the team for a long time. He replied to Hogan and sent
him a plot of the noise. “It looked exactly the same as my prediction,”
says Hogan. “It was as if the beam splitter had an extra sideways
jitter.”  (Links in original.)

Read the whole thing.  It is a bit above my pay grade to explain, but it is very interesting.

Hat-tip: Slashdot

UPDATE:  A thought occurs, and maybe someone with a better background in physics can explain it to me.

The idea in the holographic principle that the
information in a 3D space can be mapped onto a 2D horizon reminds me of
Gauss’s Flux Theorem. Are the two related? Is this Gauss’s law in
information form?

Comments

  1. #1 william e emba
    January 22, 2009

    The idea in the holographic principle that the information in a 3D space can be mapped onto a 2D horizon reminds me of Gauss’s Flux Theorem. Are the two related? Is this Gauss’s law in information form?

    Not really. The holographic principle is more like the Fourier transform. A so-called “duality” is conjectured to exist between a certain string theory and a more conventional gauge theory in a certain space-time: two descriptions of the same mathematical situation, but not in the traditional manner of one being the limit of another (like classical mechanics as the h=0 limit of quantum mechanics). Part of what is so remarkable about the duality is they take place in different dimensions, hence the name “holographic”. Just like a holograph is a two-dimensional object packed with three-dimensional information, so too is our world apparently available in a description with one less dimension using notions that at first sight have nothing to do with space-time.

  2. #2 Yes Really
    January 22, 2009

    Yes Really… we physicists commonly use gauss’s law as an (overly simplistic) classical analogy for the holographic principal. Or sometimes, we use the “method of images” technique commonly taught in 1st year electrodynamics courses.

    The point being that physics in the bulk (volume) can have an equivalent formulation on a surface. The main difference being that in classical E&M we know that surface or volume integrals are just different ways of describing the physical phenomena that happen in the bulk… The holographic principal is a little deeper… The holographic principal says that the physics is actually happening on some surface far away

  3. #3 william e emba
    January 23, 2009

    Yes Really… we physicists commonly use gauss’s law as an (overly simplistic) classical analogy for the holographic principal.

    Well then, stop doing that. For an audience appreciative of Gauss’s law, the Fourier transform is a far more apt analogy.

    The point being that physics in the bulk (volume) can have an equivalent formulation on a surface.

    But Gauss’s law is just a conservation law in the end. Ultimately, net flow inside a bulk volume is, because of conservation, the net flow passing the boundary.

    The holographic principle is far more sophisticated. The conjectured correspondence is a duality, where global structures on one side are identified with local structures on the other side, and vice versa. Analogies should be made with other dualities.

    The article Jake linked to refers to what may be noise in a certain part of the gravitational spectrum. Thinking in terms of a Fourier transform, this makes good intuitive sense: in dual space, there’s a spike somewhere. Thinking in terms of the Gauss theorem, it makes no sense whatsoever.

    I haven’t bothered to look at Leonard Susskind’s new book The Black Hole War, but I’ll take a chance and recommend it anyway. It’s a popular account of what the holographic principle is and why it’s so important.

  4. #4 Yes Really
    January 24, 2009

    Hi William,

    I’m not here to argue with you as you are free to believe whatever you feel… But let me just say a few words, on a popular level, about the holographic principal and why it’s so cool (perhaps it’s even THE unifying idea in physics???). The main point here is not duality, since dualities, in one sense of the word, are everywhere in math and physics. As and example (for smooth functions and infinite # of terms) a Fourier series is dual to a Taylor series is dual to a Hermite polynomial expansion is dual to a Bessell function expansion, etc, these are all equilivent descriptions… Or to use your example, a Fourier integral allows us to "pack" all the information from one function into another envelope function in a "dual" space. This is all well and good, but not very interesting, deep, or complicated. It’s all simply a math trick as some problems have a more "natural" representation using certain
    mathematical formulations. On the other hand, the holographic principal is much much cooler.

    For our universe, the holographic principal could very likely tell us that the physical theories we are used to, where things are 3 dimensional (x,y,z) and gravity exists, are dual to theories with 2 dimensions (x,y) and no gravity??? Moreover, the aforementioned article, along with some theoretical results for black holes, could suggest that the 2 dimensional theory with no gravity is the true theory that actually describes reality!!! This is no math trick… A large number of very smart physicists believe that our entire universe exists on a giant 2 dimensional sphere, and our everyday 3 dimensional experience is simply an illusion (along with gravity!).

    So now, this should all make sense. A theory with 2 degrees of freedom should have less information than a theory with 3 degrees of freedom. And when you project a theory with less information onto a theory with a larger information capacity… you would expect the "resolution" to be a bit blurrier. This is what Hogan has predicted.

    So, to make my point, the main idea here is volume vs surface… Like gauss law or the method of images…

    Disclaimer: this is a tremendously watered down explaination, so it shouldn’t be taken to seriously.

  5. #5 Robert F
    January 25, 2009

    Is the holographic principle related to the AdS-CFT correspondence, wherein a string theory in an anti-deSitter space is dual to a conformal field theory on the asymptotic boundary?

  6. #6 Yes Really
    January 25, 2009

    Hi Robert… absolutely…

    AdS-CFT correspondence was the first convincing theoretical example of the holographic principle (that’s why it’s famous)… it made tons of physicists really start to think about holography more seriously.

    Now, ads/cft doesn’t describe our universe (for several reasons), but that’s not really the point… The point is that holography keeps popping it’s head up…

    Some people start from Einsteins General Relativity and conclude that 3-D space-time may not be fundamental… Others start from semi-classical black holes and derive explicit holographic equations… Yet other people start from quantum mechanics and conclude that the universe must be a gigantic phantasm (like a hologram)… Others started from the mathematical world of string theory and discovered the holographic principle again in ads/cft…. and now GEO600 detects a signal… This could all be coincidence… but then again maybe not???

  7. #7 David A
    January 25, 2009

    As a non-physicist, I know that I am venturing into foreign ground,so if what I say is stupid, you will know why!
    Just two questions.
    Will the size of the minimum units change in an expanding universe (I don’t mean the Planck lengths at the 2D boundary, but their “projection” in local space)?
    What hapened when the radius of the universe was of the order of one Planck Length an instant after the Big Bang?

  8. #8 william e emba
    January 26, 2009

    Disclaimer: this is a tremendously watered down explaination, so it shouldn’t be taken to seriously.

    Well, yes.

    Your response was entirely bizarre. Calling the Fourier transform a “math trick” but then trying to stress that the holographic principle is something wholly different is ridiculous. The HP does involve a dimension shift. So does Gauss’s law. But that’s the extent of their similarity, and every intuition Gauss’s law gives to flows and conservation have nothing to do with HP, and should be nipped in the bud. HP is a Fourier style pairing, albeit involving different dimensions.

    Space-time as we know it is not, according to the HP, the filling inside a lower dimensional space-time as we know it (which is what Gauss’s law would suggest). It’s an illusion of “math tricks” from something without space-time.

  9. #9 Obie1
    January 27, 2009

    doesn’t this extraordinary claim (that the universe is a hologram) require extraordinary evidence?

    … the fact that noise was predicted and noise was found is not confirmation, there may be myriad explanations for the noise that do not involve a holographic universe …

  10. #10 Yes Really
    January 27, 2009

    Hi Obie1,

    Absolutely… you are 100% correct. But that doesn’t me we can’t daydream and get excited about the possibility :-)

    William, feel free to think about things however you feel comfortable.

    David, No one knows the answers to you questions. 1) the “minimum” distance is determine from other fundamental constants… so the question is “do the fundamental constants change as the universe expands???” 2) The physics of the big bang is an open question

  11. #11 william e emba
    January 27, 2009

    doesn’t this extraordinary claim (that the universe is a hologram) require extraordinary evidence?

    It’s only an extraordinary claim when marketed as such, or from the point of view of mathematics. But all of string theory is extraordinary from the point of view of mathematics.

    That is, an “extraordinary claim” in the sense of something that requires “extraordinary evidence” is a claim that seemingly contradicts the well-established, not one that is way off the beaten path.

    … the fact that noise was predicted and noise was found is not confirmation, there may be myriad explanations for the noise that do not involve a holographic universe …

    Such as???

    The detector in question was not built for the sake of the holographic principle, but for detecting gravitational radiation. An independent researcher realized that HP should be noticeable anyway. Stay tuned, there will eventually be a new generation of detectors intended directly for HP.

  12. #12 mark jamison
    February 16, 2009

    Hi:

    I am a non scientist but I have had an interest in physics for many years. Around 1991 Michael Talbot wrote a book called the Holographic Universe based on the work of physicist David Bohm and Neurophysiologist Karl Pibram. At the time no one took them serious. Maybe, Susskind should take a look at some their work. I found it very interesting how Karl Pibram describes how the brain interprets and processes these information holograms throughout the brain and not in specific structures. As Talbot says: “the holographic theory provides a profound new way of looking at the world: Our brains mathematically construct objective reality by interpreting frequencies that are ultimately projections from another dimension, a deeper order of existence that is beyond both space and time: The brain is a hologram enfolded in a holographic universe.

    Very interesting if true.

  13. #13 juzzy
    May 30, 2009

    ok, not a physicist but hugely interested in high level theoretical physics, and this is my very simple take on it. I never experience 3 dimensions, anything i see, or any direction i move in, can be replicated on a 2 dimensional monitor. also, the brain in a jar situation? If i placed someones brain in a jar and kept it alive artificially, then connected it to a snazzy computer and wrote a cool program which could send electrical pulses along neurons, I could, theoretically, make that brain enjoy (or not) a full existence, experiencing sight, motion, emotions, sounds, touch and all the rest of it, even though in my reality it never left the jar (it could experience everything i experience through information alone without any true physical reality). Is the universe holographic? In my opinion it must be. Also the fact that the entropy of a black hole is proportional to its surface area and NOT its volume is another clue (showing that the information explaining a black hole exists on its 2 dimensional event horizon). The fact that this background noise has been detected is very interesting indeed.

  14. #14 Daniel
    January 15, 2010

    I’ve been reading Leonard Susskind’s book The Black Hole War and I think that the “holographic principle” is junk created by circular reasoning. First he asked what happens when you drop a bit into a black hole. He then defined a bit as a photon with a wavelength as large as the black hole in order to avoid adding the additional information of where it went in. Since he linked the wavelength to the size of the black hole and wavelength is connected to how much energy gets thrown into the black hole. So the bigger the black hole the less energy he threw in. Multiply the circular logic together and you see why he came up with the wrong answer.

  15. #15 james
    February 11, 2010

    The HP is a very interesting way of looking at the universe. Could this principle lead to the Theory of Everything? Any thoughts? Thanks

  16. #16 Daniel
    February 22, 2010

    Each Planck area have 0.25 bit (1/4 bit) information, not 1 bit. (Yes, “bit” is a unit in physics)

  17. #17 Nicole Tedesco
    June 12, 2010

    I am not a “Holographic Principle” fan as I think too much is being read into what amounts to a flaw in the way dimensionality is determined in modern topology theory (degrees of freedom between densely packed unit balls). Substitute “unit balls” with, potentially “unit strings” or even “threads of control”, then you get the idea of why the usual set-theoretic concept of dimensionality ought to be a little “fuzzy” at the quantum level.

    I have yet to be mathematically convinced that “all of reality” *is* written on a 2-D surface with an infinite radius. (Yes, I’ve seen the math, but I think the basic lemma it relies upon are flawed.)

  18. #18 Joe Zworld
    November 19, 2010

    The holographic principle is a property of the convergence of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon. First proposed by Gerard t’Hooft, it was given a precise interpretation by Leonard Susskind.
    In a larger sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three-dimensions we observe are only an effective description at macroscopic scales and at low energies. Cosmological holography can not be made mathematically precise, partly because the cosmological horizon has a finite area that grows with time and partly because of Heisenberg’s ‘uncertainty principle’.
    The holographic principle was inspired by black hole thermodynamics, which implies that the maximum amount of entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the description of all the objects which have fallen in can be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black-hole information paradox within the framework of string theory.

    Common misconceptions of THP (The Holographic Principle):

    That the principle’s wording as described above (entire universe) can be misinterpreted as not inclusive of the observer’s location in current space-time. In other words the holographic principle’s description is cosmic in nature only (and therefore outside of us) and so does not encompass or include our day-to-day consciousness and experience.
    That the event horizon does not contain the information (measured by area not volume) rather than the more commonly understood “black hole” into which information falls, irretrievably. The “hole” is not a hole at all rather a surface of fluctuating information that grows over time and with gravitational capture and shrinks as energy is released over time until the mass no longer serves as a strong enough gravitational mechanism to retain information thereby radiating it away by the evaporative process. Energy is conserved according to thermodynamic law and information becomes available albeit at maximal entropy minus residual nuclear radiation that finds its anti-particle partner which then mutually annihilate.
    That time is elastic rather than fixed as a function of quantized event-momenta. That a distinct definition of events of the past and of the present exist but do not include the events (the future) that have yet to be encountered due to the event-horizon of a black hole which is also the cosmic horizon?

    A Description of Time

    A singularity is the compression of quantum event-momenta (time) and it is this compression that distorts localized space. A singularity causing distortion of space-time is equivalent to saying that space-time distorts space-time. Events happen over time and when the stretched horizon can not support additional events the momenta move closer and closer together but eventually force non-conforming time off of the fluctuating surface warping the surrounding space as it captures the time freed from the spatial boundary that encompassed it. This further compresses the event-momenta adding to the gravitational field and increases it’s mass (E=mC2) until all information (gas clouds, stars, other black-holes, planets, moons and people) within it’s Schwarschild radius are captured and space is pushed back away from the accretion disk by strong gravity waves (spatial distortion in the vicinity of a black-hole) and the “hole” stops feeding. The black-hole is a representation of the stretched horizon. There is no “hole”. Instead, there is a surface/a stretched horizon.

  19. #19 Joe Zworld
    November 19, 2010

    Following is a possible combination of concepts that help validate the queasy feeling one can encounter when contemplating the Holographic Principle.

    Quantum Gravity
    The Evolution of Time
    The preferred approach in classical canonical quantum gravity is to impose mathmatical constraints after quantizing. In this ‘constraint quantization’ approach, akin to Paul Dirac’s* theorem, one treats the constraints themselves as operators A, and demands that “physical” states ψ be those which are solutions to the resulting equations A ψ = 0. The problem of time is associated with the super-Hamiltonian constraint. The super-Hamiltonian H is simply a description of time-evolution in the classical theory, yet its counterpart in the constraint-quantized theory, H ψ = 0, would prima facie seem to indicate that the true physical states of the system do not evolve at all. Trying to understand how, and in what sense, the quantum theory describes the time-evolution of something, be it states or observables, is the essence of the problem of time.
    Symbology: H = Time-Evolution
    A = Operator ( the interface between an observer and what is observed )
    ψ = Physical States
    Therefore: H ψ = 0 which implies no operator in connection to a pysical state, the resulting equation having a value of zero/ zero which has no resolution and is therefore inconsistent leaving a resulting product of infiniti which is unsatisfactory to most theoreticists.
    The super-Hamiltonian constraint for time-evolution is scewed as is that for Q-gravity. These equations leave no mathmatical solution and are self-serving, ie: if one describes a system or a calculation coupling the so-called constraints, they imply a wave- cancelling function with only probabilities for degrees-of-freedom, the very reason for calculating the theorems and formulations to begin with.

    So it follows that the prima facie needs no further explanation as it states that: H ψ = 0 “the true physical states of a system do not evolve at all” indicating no span of time need be measured beyond the Planck time to solve for the evolution of physical states or systems.

    Stated even more simply: The evolution of time on a physical system = 0. Only the scaler for the Planck time is quantifiably applicable
    The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provides a description of elementary spin 1 – 2 particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. The equation demands the existence of antiparticles and actually predated their experimental discovery. This made the discovery of the positron, the antiparticle of the electron, one of the greatest triumphs of modern theoretical physics.
    Positronium: The electron and it’s anti-matter equivalent; the Positron annihilate via a number of channels, each producing one or more gamma rays. The gamma rays are produced with a total energy of 1,022 keV (since each of the annihilating particles have mass of 511 keV/c2,) the most probable annihilation channels produce two or three photons, depending on the relative spin configuration (spin 1 – 2) of the electron and positron. Gamma rays exert radio-spectral pressure.
    1 kiloelectron volt = 1.60217646 × 10-16 joules

    Therefore: Time may be expressed as a force of pressure (or as a wave) moving across quantized Planck units.
    Planck time:
    In physics, the Planck time, (tP), is the unit of time in the system of natural units known as Planck units. It is the time required for lightwaves (quanta) to travel, in a vacuum, a distance of 1 Planck length.
    The Planck time is defined as:

    where:
    is the Planck constant
    G = gravitational constant (Feynman schematics indicate that this force is variable)
    c = speed of light in a vacuum (Feynman Schematics indicate that c is variable)
    s is the SI unit of time, the second.
    The two digits between parentheses denote the standard error of the estimated value.

    The Coupling of Time and Light

    Varying c in quantum theory : Variation in the speed-of-light constant.
    In quantum field theory the Heisenberg uncertainty relations indicate that photons can travel at any speed for short periods. In the Feynman diagram interpretation of the theory, these are known as “virtual photons”, and are distinguished by propagating off the 1.mass shell. These photons may have any velocity, including velocities greater than the speed of light. To quote Richard Feynman “…there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn’t go only in straight lines; now, you find out that it doesn’t go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c.” These virtual photons, however, do not violate causality or special relativity, as they are not directly observable and information cannot be transmitted acausally in the theory. Feynman diagrams and virtual photons are interpreted not as a physical picture of what is actually taking place, but rather as a convenient calculation tool (which, in some cases, happen to involve faster-than-light velocity vectors).
    Richard Feynman’s lecture was presented prior to the conceptualization and general acceptance of The Holographic Principle.
    1. Mass shell –

    The mass shell condition simply stated is the square of linear momentum component (p) equal to the square of the rest mass (m): p = m. This condition is totally relativistic by simply rationalizing the speed of light to unity: c = 1 instead of 300 000 kilometers per second or about 7 times around the earth in one second. Furthermore, since relativistic linear momentum is defined as p = E/c and mass energy equivalence is defined as E = mc, for c = 1, then p = m = E is always true. However, this square of energy (E) makes more sense if it is quantized at the infinitesimal domain of the spacetime continuum.

    Varying time, Planck time, Relative time and the Holographic Principle.

    Event-momenta can propagate to a region of space-time according to FTL, or at the Planck time. Occupying areas surrounded by light-like boundaries, Black-holes are not holes but surfaces that grow as information is attracted across the Schwarschild radius. Since Heisenbergs Uncertainty Principle allows for FTL (Faster Than Light) travel, then energies are free to escape from the black-hole: one example is the jets of plasma: high-energy particles (radiating at optical wavelengths) backed up in space-time waiting to be “swallowed” by the black-hole. The Holographic Principle provides a solution for this seeming contradiction as the three dimensional jets are merely two-dimensional pixelated areas of information occupying only the Planck time/distance. If there is only the Planck time/distance to traverse than the principle of simultaneity applies to event-momenta and the equation H ψ = 0 suffices as an accurate description.

    H = Time-Evolution
    A = Operator ( the interface between an observer and what is observed )
    ψ = Physical States

    H ψ = 0

    Relativity of simultaneity:
    In physics, the relativity of simultaneity is the concept that simultaneity—whether two events occur at the same time—is not absolute, but depends on the observer’s reference frame.
    H ψ = 0
    The speed-of-light according to Relativity is equivalent to the transit of the Planck time/unit expressed as a waveform –
    Therefore: Time may be expressed as a force of pressure (or as a wave) moving across quantized Planck space.

  20. #20 A Question
    February 5, 2011

    Can anyone suggest a good summary work on the Holographic Principle that would be an accessible read to a non theoretical physicist with a good mathematical background (preferably something that excludes all the religious, paranormal and other various extensions that most books seem to venture into!).

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