Schoedinger's holography and quantum gravity
Holographic Earth by Kevin Gill.
Years ago I bought a hologram making kit (from Litiholo). This came with a red diode laser, instant hologram film which worked sort of like Polaroid film, and some plastic pieces that you put together so as to get all the right alignments. Exposure in a darkened room produced red holograms on the instant film.
Holograms were developed in the 1940s as a byproduct of electron microscopy. Electrons were fired at very tiny objects. The key to how it all worked was to create an interference pattern between the incoming beam of electrons and the scattering of the electrons off the tiny object. The interference pattern gives you visual information about the object.
Radar actual works the same way although the interference is usually done digitally there days. You send out pulses of radio waves which scatter off of an object. You then collect the scatterings and create an interference pattern between those and the original signal. The result gives you information not only in angle but also in range which means the information is 3D. Thus, radars are really making radio holograms of their surroundings.
Visual holograms were not possible until the development of the laser in 1960 which allows for precise control of the frequency of the light. That allowed for interference patterns to be recorded on film or plates.
To create the interference pattern, you shine the laser both directly at the film and at a mirror that bounces the laser onto an object. The reflection of the laser off the object travels to a photographic plate where it interferes with the original beam.
When you shine the original laser onto the plate, it will produce an image of the 3D object including all the original characteristics of the light you created the image with.
Kit holograms are a little different in that they produce an image by shining a laser at a specialized diffraction grating plate, which is a plate that, if you zoomed in on it, would look like a corrugated roof. It has bumps on it that diffract the light at different wavelengths. The laser interferes with its own reflection off an object on the plate itself. After the plate develops, it produces the 3D image without needing a laser shined on it again because it is diffracting the ambient light in the room to produce light at a particular wavelength or set of wavelengths. This diffracted light doesn’t reproduce the original exactly but our eyes can’t tell the difference.
Interference patterns are possible not only using light waves but any kind of wave, including quantum waves. You may be familiar with the double slit experiment where a particle is fired at a barrier with two slits and is made to interfere with itself.
Electron microscopes use the wave-like properties of electrons to do exactly this, creating a hologram of tiny objects. Since electrons have such small wavelengths, they can be used to image very small objects.
Anything can be used to make a hologram, provided you can use its wave-like property to do it. Obviously, for practical purposes, you can only do this with particles.
Taking this further, you might ask, if I can make a hologram of an object using wave interference patterns, is it possible that there might be some things in our universe that appear to be real objects but are, in fact, holograms created from wave interference?
What about black holes?
A black hole is produced when matter collapses in on itself to the point where no force is capable of counteracting the pull of gravity. They are black because light cannot escape. This happens when large stars reach the end of their lives. We now have images of two black holes: one in another galaxy M87 and one in our own Milky Way, in Sagittarius.
General relativity explains that black holes are not simply stars that are dark. They warp space and time so that time effectively ends at the singularity inside.
Theoretical calculations by Bekenstein and Hawking also showed that the amount of information in a black hole is proportional to its surface area, not its volume. Everything in the universe contains information, so all the mass inside a black hole must contribute to its information content.
In normal, non-black hole space, we tend to think of information as increasing with volume. After all, if I have a book, the amount of information is spread in two dimensions, on each page, and also from page to page, along the thickness of the book. To add information, we either have to make the pages bigger, add pages, or make the type smaller (which increases the information density in the volume).
The fact that black hole information increases with surface area and not volume is confusing. It is as if that 3rd dimension of the black hole doesn’t really exist or ceases to be a dimension that stores information. That wasn’t the case when the black hole was a star.
It is as if I have a book, and, as I keep adding more and more to it, eventually it collapses and becomes a poster while at the same time getting smaller.
That black holes have this property has been used to argue that the universe in general has a holographic property. By holographic, we simply mean that all the information in a volume or hypervolume is contained on a surface or hypersurface.
There are numerous popular science articles all with some variation of the title: “Are we living in a hologram?”
What’s interesting about the holographic principle is that, while it draws on the analogy of projecting from a 2D plate into a 3D space, it rarely makes use of the other features of real holograms: the interference pattern that makes it possible.
The holographic principle, however, is a property that all waves have, and all things in our universe, by dint that they are made of particles or fields, have a wave-like nature. Therefore, it is natural to ask whether the holographic principle arises from the waves themselves.
Suppose that all matter are composed of interference patterns of waves, constructively interfering, but those waves are projected from the boundary of the universe, infinitely far away.
The matter in the black hole is projected into it, therefore, from the universe boundary.
This may sound an awful lot like AdS/CFT correspondence and it is a similar idea although not exactly the same. That correspondence does say that gravity and quantum theories are dual to theories at the boundary of the universe. A duality or correspondence means that you have something equivalent to something else in some way but those things are conceptually different.
In AdS/CFT you have some fields that exists in spacetime as well as at the boundary. You have a quantum field theory on the boundary that you calculate and this corresponds to a theory that obeys the classical equations of motion, an “on-shell” theory, meaning it has no virtual particles. Thus, you have a correspondence between a theory with virtual particles on the boundary and one in the bulk of spacetime with no virtual particles.
In string theory, you interpret that “on-shell” theory using something called an S-matrix, which stands for Scattering matrix, and get a quantum theory of gravity in the bulk instead of a classical theory.
AdS/CFT doesn’t say anything about holographic projection because it isn’t a projection. Rather it obeys a “holographic principle” because information encoded on the boundary corresponds to information in the bulk.
A projection theory would imply that waves come from the boundary creating a field theory based on information on the boundary.
If you look at this picture above of how a hologram is projected, you can see that the 2D photographic plate contain all the information for the waves that create the illusion of the 3D object.
If you imagine this plate is the boundary of the universe, then waves containing this information, projected from the boundary into the bulk of spacetime, can produce particles and therefore objects. If those waves are Schroedinger or other kinds of field theoretic waves, then these objects would appear to us to be real. In fact, we ourselves would be made from them, from the mere interference pattern of Schroedinger waves.
This is fundamentally different from AdS/CFT which is a duality not a genuine projection.
I haven’t brought in gravity yet either.
There is just one small problem with that:
How can space and time be projected through space and time?
One solution is the imagine that space and time do not project through space and time but something else. While things like light and electrons are waves that spread through spacetime, space and time have to spread through a much larger, in fact infinite dimensional, space called superspace. In superspace, every possible point is an entire potential spacetime.
In the same way that a Schroedinger wave can be spread through all space, and at every point is a potential particle, so you can have a wave spread through superspace where every point is a potential space or spacetime.
The same idea we had for particles, of projecting them from the boundary of the universe, also applies in superspace.
If we project waves from the boundary of superspace into it, then the interference pattern can create spacetime itself, or, many spacetimes, an infinite multiverse of spacetimes. Nevermind that the boundary of an infinite dimensional space is also infinite dimensional.
The problem with this approach, which was favored in the 1960s, is that you get an infinite regress. You have to ask where superspace comes from.
We could shrug and say it doesn’t matter, or we could take the route the string theorists take that as long as we understand gravity, it doesn’t matter where space and time come from.
This latter view is philosophically problematic for a lot of physicists, particular adherents of Loop Quantum Gravity, but it can be put on stronger footing. In 1925 when he developed his view of quantum mechanics Heisenberg took the view that space is not something that Schroedinger waves are “spread over”. (Heisenberg absolutely hated Schroedinger’s wave mechanics when he first read about it.) Rather, position is a property of particles themselves.
Gravity, then, is how gravitons behave as they couple to one another and to particles. Einstein’s theory is an effective field theory that emerges from the coupling of gravitons to the position (and other) property of particles.
In this case, our holographic projection idea is, in some sense, a fiction because it is over a fictionally conceived “spacetime” that is really made up of the position observables of actual matter. The difference, however, is for the most part metaphysical whether you ascribe to spacetime existence of its own and attach it to particles. We cannot perceive spacetime, only the matter that we interpret to be in it. If spacetime is really an intrinsic property of matter, it is all the same as far as we are concerned.
What we gain from this is a decoupling of gravity from spacetime so that we can interpret all matter and forces, including gravity, as being over a background spacetime which is fictitious. This is what string theorists do although perhaps not with as much metaphysical rigor.
From this we can also interpret gravity as being projected from the boundary of a spacetime in the same way as other matter without the need for infinite regress into superspaces.