Can the Holographic Principle Explain All Physical Information in a Surface?

[Lapidus]

What is the reason/ explanation (possibly in a nutshell!) that all the physical information of a volume can be encoded in the surface surrounding that volume?Because, you know, that sounds silly, at first! I browsed some introductory sources, but could not find any quick answers.

Also, if someone knows any links to good material on that subjects (popular up to first year graduate level), that would be great, too.

many thanks in advance

 

[Simon Bridge]

all the physical information of a volume can be encoded in the surface surrounding that volume?

Where did you get this idea from?
Do you mean the Holographic principle from string theory?
http://en.wikipedia.org/wiki/Holographic_principle

There are no quick answers - look to the connection between entropy and information, the terms are being used in a specific way. The rest is maths.

 

[Naty1]

THE BLACK HOLE WAR; My battle with Stephen Hawking to make the world safe for quantum
mechanics by Leonard Susskind is an excellent non mathematical book for the general public...
history,arguments, insights into how scientific theories come about...all in all fascinating.
According to his accounting, Hawking eventually agreed information is not 'lost' via BH...but put up a sustained 'battle',,,,

a few snippets I saved in my notes:

Black Hole Complementarity

In this view, all the information ever accumulated by a BH is encoded on a stretched horizon...a Planck length or so outside the event horizon and about a Planck length thick. This is a reflection of the Holographic principle: all the information on the other side of an event horizon is encoded on the surface area of that event horizon...

[pg 434] Of every 10,000,000,000 bits of information in the universe, all but one
are associated with the horizons of black holes. [So if you can lose information via black holes, it a really,really,really big deal….]


(p238) Today a standard concept in black hole physics is a stretched horizon which is a layer of hot microscopic degrees of freedom about one Planck length thick and a Planck length above the event horizon. Every so often a bit gets carried out in an evaporation process. This is Hawking radiation. A free falling observer sees empty space.

(p258) From an outside observer’s point of view, an in falling particle gets blasted apart….ionized….at the stretched horizon…before the particle crosses the event horizon. At maybe 100,000 degrees it has a short wavelength and any detection attempt will ionize it or not detect it!

(p270)…. eventually the particle image is blurred as it is smeared over the stretched horizon and….and the image may (later?) be recovered in long wavelength Hawking radiation.

 

[friend]

What is the reason/ explanation (possibly in a nutshell!) that all the physical information of a volume can be encoded in the surface surrounding that volume?

Why should we limit ourselves to "physical information"? Isn't entropy and information part of any probability distribution? And aren't there distributions that involve 2,3, or more variables? Could it be more generally that a holographic principle applies to these distributions as well?

 

[mitchell porter]

What is the reason/ explanation (possibly in a nutshell!) that all the physical information of a volume can be encoded in the surface surrounding that volume?

Black hole thermodynamics (entropy proportional to area of the event horizon) was the beginning of it. It implied that entropy in a theory of quantum gravity can't scale with the volume (as entropy scales in an ordinary quantum field theory), because the black hole thermodynamics will be wrong (entropy would be proportional to the volume of the black hole, not its area).

However, if we look at the concrete example of holographic duality that was discovered in AdS/CFT, twenty years later, we see an important extra detail, which is that the main extra dimension (the radial dimension of the AdS space, as opposed to compact, Kaluza-Klein-style extra dimensions) comes from renormalization group flow in the boundary theory - the scale dependence of quantities in a QFT. To some extent, you can think of the AdS space as a stack of copies of the boundary theory, each corresponding to a different energy/length scale. The longer the length, the deeper into the new radial direction you go. Large quantum structures in the boundary theory correspond to objects deep in the extra dimension, just like large shadows on a wall indicate an object far from the wall and close to a source of light.

So the deeper reason for holography is something like this, that gravity and space-time generically emerge from RG flow in lower-dimensional theories. When you project what is happening within a volume onto its surface, you are taking a step back towards a pre-space-time level of description. But the ultimate details and logic of that level remain obscure.

 

[Naty1]

From an earlier discussion on this subject:
Mitchell Porter:

... the idea is that the interior of the black hole has a dual (holographic) description [of the interior] in terms of states on the horizon; a lot like AdS/CFT, with the horizon being the boundary to the interior. So when someone crosses the horizon from outside, there's a description which involves them continuing to fall inwards, until they are torn apart by tidal forces and their degrees of freedom redistributed among the black hole's degrees of freedom, all of which will later leak away via Hawking radiation; but there's another description in which, when you arrive at the horizon, your degrees of freedom get holographically smeared across it, mingling with all the black hole's prior degrees of freedom (also located on the horizon), which all eventually leak away as Hawking radiation

 

[Naty1]

Ok, found more interesting passages from my notes:

Holographic Principle: The Black Hole War Chapter 18

EVERYTHING INSIDE A REGION OF SPACE CAN BE DESCRIBED BY INFORMATION BITS ON THE BOUNDARY.

The maximum amount of information that can be stored in any region of space is determined by the area of the boundary enclosing the space rather than the enclosed volume. All information is stored on the boundary of space. Where a particular bit of information is located does not have a unique answer. At each level of space, everything enclosed may be described as a holographic image but when we go looking for the hologram it is always out at the next level

Reread the last sentence...then imagine going to the cosmological event horizon of our universe...everything, you, me, my dogs, earth...is encoded there!

Also note that the horizon of a black hole is null...lightlike...read on for a 'two sided horizon'...

As Porter posts above :

the ultimate details and logic of that ...remain obscure.

And from another reputable source:

Holography in a quantum spacetime
Fotini Markopoulou and Lee Smolin†

http://arxiv.org/PS_cache/hep-th/pdf/9910/9910146v1.pdf

we need a framework for a cosmological quantum theory which incorporates causal structure. .. As each observer receives information from a distinct past, the algebra of observables they can measure, and hence the (finite-dimensional) Hilbert spaces on which what they observe can be represented, vary over the history. Consequently, the algebra of observables of the theory is represented on a collection of Hilbert spaces. These replace the single wavefunction and single Hilbert space of other approaches to quantum cosmology… . We find below that this has two important consequences. First, the additional structure in a screen network which follows from the two-sided nature of the elementary screens allows a distinction between null and timelike propagation, something that an ordinary causal set history does not provide..., a cosmological holographic theory must be a many-screens theory, each screen recording information about its causal past. It is important to note that such a many-screens theory gives us the possibility to dispense with the notion of the bulk theory...We expect that no cosmological form of the holographic principle, even one that holds in the semiclassical limit, can escape the fact that many screens are necessary to give a complete description of a cosmological spacetime.,,, A causal set C is a locally finite, partially ordered set of events…

Musing: Separately, although no one seems to have made this connection that I have so far found in the literature, it is an interesting 'coincidence' that the appearance of an event horizon during cosmological expansion [and one now, today] apparently converts vacuum perturbations into particles...particle waves are 'confined' and so change from fields 'everywhere' to particles 'here' so maybe there is a
bit more to ADS/CFT than we have so far uncovered... where matter is replicated more concretely on horizons.

If anyone has a peer reviewed source discussing such a connection, I'd be very interested to get the link...[I am VERY careful about that now since I got demerits for posting one that wasn't!]

For a good discussion on "Particle creation in an accelerating Universe?"
see here https://www.physicsforums.com/showthread.php?t=590798&page=2
but I don't recall the discussion extending to holographic domains.

 

[mitchell porter]

Reread the last sentence...than imagine going to the cosmological event horizon of our universe...everything, you, me, my dogs, earth...appears there!

And of course this is bizarre. Obviously you and your dogs are located here, not 50 billion light-years away. What holography in this case suggests, is that there is some 2+1 dimensional theory (2 space, 1 time), which is holographically equivalent to the 3+1 dimensional theory (standard model plus gravity plus ?) describing what happens inside the cosmic horizon. Although unlike AdS/CFT, no-one would currently be able to write down for you, a specific 2+1 dimensional theory with this property. AdS space has a genuine boundary, whereas the cosmic event horizon is observer-relative, which means that galaxies can disappear into it, which means that the 2+1 dimensional theory would have degrees of freedom that disappear over time.

The more plausible candidate for the holographic dual of the real world, would be a "3+0" dimensional theory in which time is the emergent dimension. So we'd have a "Euclidean quantum field theory" which has no time, but which has properties (correlation functions) which depend on scale - i.e. the resolution with which space is described, just like in ordinary renormalization - and the way the correlation functions change, as you "increase the resolution", gives you the evolution of time. That would be the fundamental form of cosmic holography. The "2+1" perspective ought to be possible too, but it would somehow be a truncated version, with a change of variables from the "3+0" theory. All the papers on "dS/CFT" are where they try to make this stuff work in detail.

When I started to think about all this, I provisionally took the view that the version with more dimensions unfolded is the realer and truer description of things, and that the holographic description is just a compression. I already pointed out the absurdity of saying that everything around us is really billions of light-years away. According to this "compression" interpretation of holography, all that's true is that all the physics of the real world has an alternative compressed description, in terms of the gigantic "shadows" we would cast on the cosmic horizon, if you projected our images there. Similarly, time is real, I have no qualms about asserting that, and so the holographic timeless description must also just be a compression, an exercise in math, but not a lesson that time isn't real.

For people trying to understand the practical or ontological implications of holography, I still think that is probably a healthier attitude to take - space and time are basically as they appear, holography is just a type of compression of information that's possible. But I suspect that ultimately we might arrive at a sort of intermediate position, a "semi-nonlocal" view of reality in which e.g. lightlike paths are viewed as single objects. That's already the twistor perspective! And holography would reflect the fact that the start and the end of the path can be regarded as the same point in twistor space... But we're not there yet. I think we still only have glimpses of what "semi-nonlocal realism" would be like.

 

[Naty1]

Mitchell:

the whole idea of holographic information is, as you say, bizarre:

..whereas the cosmic event horizon is observer-relative...

yes...

Susskind mentions something like ' Every time you go to look for information on a boundary it appears somewhere else...' so there are observer dependent boundaries within observer dependent boundaries within...etc,.etc...

Have you any insights into the prior quote:

Of every 10,000,000,000 bits of information in the universe, all but one
are associated with the horizons of black holes.

[So if you can lose information via black holes, it a really,really,really big deal.]

I've posted that several times, nobody has commented yet.

I was shocked when I read that but have never understood any of the basic assumptions underlying it. It reminds me in a sense of the apparent imbalance between matter and anti matter early in the universe where most apparently annihilated and we are all simply a minute portion of what was there...we are all just 'leftovers' so to speak! As if that is not humbling enough, if the 1 part in 10¹⁰ that Susskind claims has also been hidden from us for a while,in BH, it offers a new perspective on the relative insignificance our entire universe! Then mix in the limited causal history for each of us...I feel like I am almost blind!

 

[mitchell porter]

Have you any insights into the prior quote

Presumably Susskind gets the number of bits from entropy. Entropy is sort of a measure of how much invisible detail there is to the physical state of an object - details that you can't see and don't know, and which are usually boring details. It's associated with the loss of order because the main boring invisible detail of a physical system is how all the unusable energy is distributed inside it. The unusable energy is the background heat, that e.g. passes from molecule to molecule and doesn't do anything except circulate randomly and which gives the object its average temperature.

An example is a gas in a box. Microscopically it might consist of a large number of molecules flying around and bouncing off the walls, and every molecule always has a specific position and velocity. But we have no way to know those details or to use all that energy in a microscopically coordinated way - it just gets passed unpredictably from one molecule to another as they collide. What we can know are rough macroscopic properties like the pressure and temperature of the gas, and from this we can also estimate how many different detailed microscopic states of the gas would manifest that pressure and temperature. By a microscopic state of the gas, I mean a full inventory of what each molecule is doing - this one is here moving that way, the next one is over there and moving in that direction, and so on through a very large number of molecules. These are the "invisible boring details", and the entropy is proportional to the number of bits it would take to actually specify all those details. So a crystal lattice has low entropy because we roughly know where all the atoms are, and a gas has much higher entropy because the individual atoms are all over the place and could be doing anything.

Ever since the late 19th century, and long before anyone thought of black holes, we had this picture of the world's entropy increasing. Somehow stars, wherever they came from, were a big long-lived source of energy which kept injecting new "usable" energy into the universe, but meanwhile, down on the planets, the energy from the stars would spread out into the material environment, perhaps after first being used by living beings or machines, and then it would be lost into the thermal background. Eventually the stars would burn out, all life would die, everything would subside into a featureless homogeneous state of uniform temperature, and that would be the heat death of the universe.

Since the 1970s, black holes have been regarded as the highest-entropy objects in the universe. But the curious thing is that there was no model of what the "microscopic states" of a black hole are. A black hole was just a point in space surrounded by a zone of no return, and when you considered the energy of the black hole and the temperature of the Hawking radiation using the usual laws of thermodynamics, it suggested an enormous entropy which just happened to match the size of the event horizon. In the 1990s, string theory came up with an answer to where the entropy is: a black hole is a bundle of branes, with a gas of attached strings circulating around the branes, and the high entropy of the black hole comes from the enormous number of possible states of that string-gas. It's a lot like the molecules in the box, except here it's strings moving along the branes, a bit like wandering electric arcs.

So that is the cosmology that Susskind is describing. The early universe (which started with very low entropy for some unknown reason) gave us a universe of stars which warm up the planets and nebulae, and so the nonluminous bodies get to see some action before entropy wins and the long boredom sets in; but the number of boring interchangeable states of the atoms in a dead planet, while enormous by human reckoning, are still minute compared to the number of states in a collapsed star, where a mass equal to millions times that of the Earth is locked up in a shrunken bundle of quivering branes whose energy fluctuations create a gas of attached strings trapped behind the event horizon. And the long term history of the universe consists of these black holes swallowing everything else, merging to make bigger black holes with bigger entropies, and then very slowly shrinking through Hawking radiation, until at the end you just have the Hawking radiation dispersing through space.

OK, what I just recited is a sort of modern-day scientific catechism, most of which would be familiar, even if the details about what entropy really means, and about the microstates of black holes, are not familiar. I'm far from being 100% confident that that is how the universe is and will be. But I just wanted to spell out what that statement about "most information is in black holes" really refers to. It's saying that most of the invisible boring details of the universe's exact microscopic state are to be found in the details of what happens inside the black holes.

What about holography? Well, all of this cosmic evolution ought to have a dual holographic description (on the cosmic horizon, or at the beginning of time, depending on which version you use). I might say something about it later. But I must say that the ideas of holography don't seem to have contributed any insight to this entropic history of the universe. I was able to tell the story without digressing to say, "and here's the holographic description of what I just talked about". It could just be that outside of black holes, holography isn't very interesting. Here you are in three dimensions, you have a doppelganger description smeared onto two dimensions, ho hum. It might be more interesting if the twistorial, semi-nonlocal description of physics played a role, but that didn't happen either. Still, maybe that's something to expect in the future, that we'll have a cosmic historiography in which nonlocality plays more of a role.

In an earlier comment you talked about particle creation in the early universe, I might try to say something about that too, but later, I need to sleep right now. :-)

 

[Naty1]

Needing sleep is NO excuse!

If we are leftovers of baryogenesis from the early universe, and I can't find THAT figure [the ratio of particles to antiparticles, maybe 10²⁰ or 10¹⁰⁰ to one...and then Black Holes swallowed all the remaining good stuff to the tune of 10¹⁰ to one...well, let's face it, we are like the dregs from a great feast...I do NOT like the idea of being relegated to 'garbage of the universe' status.

 

[Paulibus]

Mitchell Porter: I find your posts Nos. 5, 8 and ten, taken together, most illuminating. Thanks for writing so fully and clearly about what, for antediluvian me, is not an easy subject. In particular, I'm not familiar with RG, the "renormalization group flow in the boundary theory - the scale dependence of quantities in a QFT" ,and would be grateful if you could amplify this aspect of your description.

I have very simple-minded ideas about the importance of scale in descriptions of the real world of our experience, and have trouble believing that scale-free (conformal?) theories can easily describe the reality we experience and perceive. It's too full of hierarchical and scale-related stuff.

For example take a really simple physics phenomenon, like the surface tension of a drop of water. When describing the surface tension of a drop, it's essential to be able to distinguish the environment of its constituent water molecules "near" its surface from that of others "deep" inside it. To do this we must be able to use a scale that refers to the reality we want to describe --- a scale to relate the sizes of molecules and water drops, such the S.I. system. In a scale-free conformal world the phenomenon of surface tension in drops made of molecules, whose sizes couldn't be compared by means of a physical scale, wouldn't even exist to be described.

Nor, I guess , would there be much else for physics and perhaps even QFT to describe without referrring to some physical scale. What price then of dogs here, or reality as shadows of a kind on the surface of a remote event horizon?

 

[mitchell porter]

I'll use a common terminology and speak of a "boundary theory" and a "bulk theory". The bulk is the space-time we live in and experience. Physics there is described by standard model plus gravity plus unknowns. The boundary is the distant space of one less dimension, on which a different physics can be described, which is nonetheless holographically equivalent to the bulk physics. Thus, in the conception that Naty1 introduced, our everyday world has a dual representation in a 2+1 dimensional theory which we would regard as defined on our cosmic event horizon. Or, in the version of holography in which time is the emergent dimension, our world of 3+1 dimensions is holographically equivalent to a static 3+0 dimensional "universe" in which there is no change, but in which there is this "scale dependence" which ends up being time by another name.

In the study of holography, it's the boundary theory which is scale-free - not always, but it is so, in numerous standard examples of holographic duality - and this is actually required to allow objects of fixed size to move in the extra dimension of the bulk, towards and away from the boundary. This can be understood in terms of Plato's cave (or any situation where there is a light casting shadows on a wall). The cave is the bulk, the wall of the cave is the boundary, and the "boundary theory" would be a flatland physics which described the interactions of the shadows on the wall without any reference to the cave's interior.

Suppose we have an object - perhaps a rock, since it's in a cave - and a fixed candle to cast shadows. As we move the rock around, it doesn't change size; but its shadow on the wall changes size, as the rock moves closer to the candle, or away from it. So the "physics of the wall-shadows" must allow for a rock-shaped shadow of arbitrary size, small or large on the wall; and the same for all other types of shadow, for the types of object that can exist in the cave.

This is a property of a scale-invariant theory - if an object can exist at one size, it must be able to exist at all sizes, or else the theory would have a preferred scale. As you point out, the physics we experience has preferred scales. But that is the physics of the bulk! It's the holographic dual theory, defined on the spatial boundary or at the beginning of time, which has scale invariance, because the same-sized objects must be able to exist anywhere in space (at arbitrary distances from the horizon) or anywhere in time (at arbitrary "time-distances" from the timeless boundary). Therefore, their images in the dual theory must be of all sizes; which is unlike what we're used to, but then we're not used to thinking of everything in terms of its projection onto a boundary of one less dimension.

One of many things that I find unsatisfactory about my account of holographic dualities in this thread, is that I don't think I have properly motivated it. A sensible person, who refuses to be mystified and who feels that they must have some concept of what this holographic business is about, might reasonably conclude that it's all just an odd and even pointless change of variables, vaguely analogous to a cartographic projection, except that instead of stretching and distorting a two-dimensional surface, one is starting from three-dimensional space and just losing a dimension entirely, by making a picture in which everything that extends into the lost dimension is just drawn on top of each other. Harder to visualize than the cartographic case, but nothing metaphysically special.

And seriously, if there's anyone out there who is in a hurry to get a working concept of holography and then move on, I think that's an entirely reasonable way to think about it: as just a rewrite of the laws of physics so that they describe the "shadows on the wall of the cave" rather than the objects in the cave (but they are special sorts of "shadows" which contain information about the whole depth of the object, and not just its outline); just a mathematical trick; done.

But... even if it's just another way to talk about the same physics, it's a very un-obvious one. The physics of the ordinary world, the bulk world, may be made of certain fundamental fields, but the "shadows on the boundary" are made of a different set of fields, that obey a different fundamental equation. Each fundamental field in the bulk space, corresponds to a specific combination of the boundary fields, and figuring out the boundary fields from the bulk fields is a highly nontrivial task - i.e. in general we don't know how to do it.

Paulibus, you asked what "renormalization group flow" is. You're probably familiar with the idea of virtual particles, and virtual particles that bud from virtual particles, and so on - this is part of the modern picture of particle physics, that an electron, for example, moving through space, is actually a quantum superposition of innumerable virtual-to-the-nth-order configurations of particles that are being emitted and absorbed. One may decide to care only about a certain level of detail in these configurations; fluctuations which are smaller than a chosen length - which will also mean, fluctuations which are bigger than a corresponding energy - might just be ignored by the calculating physicist, trying to find a tractable approximation. The renormalization group flow describes the dependence of this approximate physics on the length scale or energy scale of the cutoff.

In holographic dualities, the geometry of the emergent dimension of space reflects the renormalization group flow of the boundary theory. For example, when the boundary theory is conformal, all its scales behave the same, there is no RG flow, and the emergent dimension is homogeneous in its properties - e.g. it is a curved space of constant curvature, and things can move back and forth along the emergent direction without a change in the geometry they experience.

I have to say that my understanding of all this is rather brittle, heuristic, and intuitive. The best-understood examples of holographic duality are only partly understood, and they involves spaces and theories very unlike reality. The hope is that they will be a testbed in which the mathematics and the principles of it are worked out. Already holography is used to approximate otherwise intractable calculations in physical systems of interest, but there the "extra dimension" really is a mathematical construct. The ultimate application of holography would be to the real world in its totality - to discover that "standard model + gravity + ..." is genuinely equivalent to some other set of fields in a space of one less dimension, an equivalence which might in turn just be a step towards some other, new, semi-nonlocal description of physics, like the "twistor diagrams" which were the mainstay of twistor theory before Witten's twistor string.

 

[Naty1]

Mitchell Porter posts

Presumably Susskind gets the number of bits from entropy.

yes; but I am still stunned that we get to observe only one bit of every 10¹⁰ or so considering black holes alone. As I already noted, that's apparently after baryogenesis in the early universe eliminates a roughly equivalent proportion of 'matter'just as the universe gets started...and when I was thinking a bit further, remember to add dark matter and dark energy about which we know virtually nothing...smart as we might think we are, nature has so far outfoxed us!

It could just be that outside of black holes, holography isn't very interesting.

Au contraire! Shame on you! I know you don't mean that...[LOL]

I don't know exactly where holographic insights begin and other theories now end, but the finite information content of a volume associated with horizons, the ADS/CFT correspondence linking quantum gravity with string theory, the resulting strong likelihood that spacetime is quantized rather than continuous, is still enough to impress on a rather grand scale. It also leads one to wonder if our universe isn't fundamentally information based...

 

[Paulibus]

Thanks for that prompt amplification, Mitchell Porter. I'm afraid I'll have to be careful not to bite off more than I can chew, as it were. Despite the formidable amount of mathematical theory now sloshing around , I live in hope that it will somehow connect with the golden thread that runs through physics - the melding of theory and observation to make verifiable predictions about the behaviour of the quite real "bulk" world that we find ourselves in, and try to describe. I seem to have been confusing this with an equivalent concept, the boundary, which is not quite so real.

When you say:

One may decide to care only about a certain level of detail in these configurations; fluctuations which are smaller than a chosen length - which will also mean, fluctuations which are bigger than a corresponding energy - might just be ignored by the calculating physicist, trying to find a tractable approximation. The renormalization group flow describes the dependence of this approximate physics on the length scale or energy scale of the cutoff.

you sound a bit like Lisa Randall writing about "effective" theories (in her book "Knocking on Heaven's Door"); This adjective serves a purpose, provided "effective" means "able to generate predictions". I'll drink to that!

 

[Naty1]

Porter posts:

In the study of holography, it's the boundary theory which is scale-free - not always, but it is so, in numerous standard examples of holographic duality - and this is actually required to allow objects of fixed size to move in the extra dimension of the bulk, towards and away from the boundary.

Very nice description; haven't seen such previously...I wonder what the cavemen thought of such analogous shadow displays...perhaps they understood shadows better than we do holographic boundaries??

I'm having trouble associating such a 'flexible' description with the perfect match of surface information display with the enclosed interior volume...that seems so absolute...fixed...and the quantum jitters associated with such boundaries...all different glimpses, I guess, of 'reality'...

 

[Naty1]

Paulibus posts:

I seem to have been confusing this with an equivalent concept, the boundary, which is not quite so real.

Whoaaa there!...Let's not be overly hasty[LOL]...
what's real and 'not so real'...who's to say where the information 'really' resides??

When event horizons or cosmological horizons, that is boundaries, meet vacuum fluctuations REAL particles emerge...so without the 'not quite so real' boundary phenomena we might well not be here.

In addition, Brian Greene has this to say in FABRIC OF THE COSMOS:

..Juan Maldacena found a hypothetical realization of holography within string theory. He showed a particular quantum theory without gravity is a translation of – is indistinguishable from - another quantum theory that includes gravity but is formulated with one more space dimension. (This sounds roughly analogous to Kaluza uniting Maxwell’s equations with Einstein’s 4x4 metric tensor for gravity by adding a fifth special dimension.)

Not only can the size and shape of spacetime change in translation from one formulation to another equivalent form but the number of space dimensions can change too. So it seems the form of spacetime, the number of dimensions for example, is an adorning detail that can change from one formulation to another rather than being a fundamental constituent of reality. Maybe spaEctime is stitched out of fundamental strings, maybe it is limited to a minimum discrete size at Planck Length. Nobody knows spactime’s elemental ingredients.

 

[Paulibus]

Naty1: Yes, I agree; my distinction between 'real' and 'not quite real' above is facile. 'Real'' is a wooly concept. But, as the French say, each to his own taste - chacun a son gout.

Much modern theory, including the physics that Brian Greene so enthusiastically describes, seems to rely on mathematical ratiocination without any obvious physical foundation. My taste is that the cantilevers of theory should not extend beyond solid piers of observation and experiment as as far as they now do. The gulf of ignorance that they attempt to bridge is already something like forty years wide. It's time for a dividend of confirmed predictions, so forgive my hasty impatience!