Already the title of the article has a very high hype content. The tweet of the journal Quanta (a popular journal usually satisfying very high standards) published the following tweet:
Physicists have built a wormhole and successfully sent information from one end to the other. The stormy reception of the article and of the tweet forced Quanta to change the tweet to Experimental physicists built the mathematical analog of a wormhole inside a quantum computer by simulating a system of entangled particles.
The Quanta article contains for instance the statement The team developed quantum software that could reproduce wormhole inspired teleportation on both quantum computers. This was later corrected to Experimental physicists built the mathematical analog of a wormhole inside a quantum computer by simulating a system of entangled particles. This statement is still far from an honest statement telling only what was actually done: Physicists have simulated a model of wormhole in a system argued but not proven to obey AdS/CFT duality by using a quantum computer. This simulation had been done already earlier using an ordinary computer.
Also Scott Aaronson, who is one of quantum computation gurus, expressed his very critical views shared by most quantum computation professionals (see this and this). Here is the core part of Scott Aarronson's commentary.
Tonight, David Nirenberg, Director of the IAS and a medieval historian, gave an after-dinner speech to our workshop, centered around how auspicious it was that the workshop was being held a mere week after the momentous announcement that a wormhole had been created on a microchip (!!) in a feat that experts were calling the first-ever laboratory investigation of quantum gravity, and a new frontier for experimental physics itself. Nirenberg speculated that, a century from today, people might look back on the wormhole achievement as today we look back on Eddington s 1919 eclipse observations providing the evidence for general relativity.
I confess: this was the first time I felt visceral anger, rather than mere bemusement, over this wormhole affair. Before, I had implicitly assumed: no one was actually hoodwinked by this. No one really, literally believed that this little 9-qubit simulation opened up a wormhole, or helped prove the holographic nature of the real universe, or anything like that. I was wrong.
There is also a very nice popular article "The truth about wormholes and quantum computers" representing a harsh criticism (see this).
The combination of all kinds of fashionable pop science related to quantum computation, quantum gravitation, wormholes, EPR= EP, AdS/CFT, etc.... yields this kind of pseudo-science. It has been extremely frustrating to witness the stagnation of theoretical physics to pop science during these more than four decades.
Critics however agree that when one drops all this irrelevant hype away, the work of quantum computer pioneers satisfies the highest standards. It is regrettable that excellent experimentation and engineering is not enough for funding but must be iced with a sugar layer of bad theoretical physics.
Although this kind of hyperhypes do not deserve the attention they receive, I decided to look what I could learn and how could I relate this picture to TGD where holography forced by 4-D general coordinate invariance is also central and defines quantum classical correspondence. Classical physics is an exact part of quantum theory and is realized as Bohr orbitology equivalent to holography. Could I perhaps analyze the experiment in the TGD framework or suggest something analogous and maybe learn something new from TGD?
A. Traversable wormhole dynamics on a quantum processor
In the following I summarize my understanding of the various notions involved with the experiment. These include AdS/CFT duality, traversable wormholes, and negative energy shock waves mentioned in the abstract.
A.1 Abstract of "Traversable wormhole dynamics on a quantum processor"
Here is the abstract of the article "Traversable wormhole dynamics on a quantum processor" Daniel Jafferis et al. (see this).
The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary.
The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev Ye Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography.
We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model.
A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits.
Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics.
Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.
There is a long list of questions to be answered.
- What does the term AdS2 holography mean? How does it relate to ordinary, "real" quantum gravitation?
- What does "traversable wormhole" mean?
- What does the negative energy shockwave, argued to open the wormhole for quantum teleportation, mean in general relativity? What interaction between quantum computers, modelled as blackholes, does the negative energy shock wave correspond at the level of the quantum computer system?
My non-specialist's view of AdS/CFT is the following.
- AdS/CFT is not part of string theory.
- It is not a proposal to describe gravitation but gauge interactions in terms of effective gravitation assigned to effective AdSnx S10-n. AdS5 would have 4-D Minkowski space as boundary and standard model would be dua to a theory of effective gravitation in AdS5.
- The fact that has been forgotten is that the list of physics successes of AdS/CFT duality is very short, actually non-existing. Even if AdS/CFT is regarded as mathematically well-defined, this does not save it from the ultimate fate of wrong theories.
- The basic statement is a field theory with conformal symmetries at the boundary of AdS (say 4-D Minkowski space) is dual to a theory of gravitation in the interior of Ads.
- In the beginning AdS/CFT with n=5 so that the boundary is 4-D Minkowski space, was tried to apply QCD, to nuclear physics and many other cases. The idea was to deduce predictions from the physics of the AdS side. The attempts failed.
- The probable reason is that the basic mathematical framework, although probably correct using physics standards, does not correspond to the physical situation.
For instance, AdS is a pathological space-time geometry having time-like loops violating cosmic censorship and spoiling the initial value problem. In fact, the SYK model simulated in the experiments, postulates an interaction between blackholes which prevents the occurrence of these time-like loops and this interaction would make possible quantum teleportation!
- The real reasons for the failure are at a much deeper level. Quantum field theory (QFT) itself is to be blamed. QFT relies on the notion of a point-like particle and fails (of course divergence problems and the non-existence of path integral have tried to tell this to us for more than half a century).
- The idea that 4-D conformally symmetric field theory is something fundamental rather than mere approximate QFT limit is probably wrong. Also the Einsteinian view of gravitation has a fundamental problem: one loses basic conservation laws of special relativity. Both sides of the duality are sick.
One can learn of traversable wormholes from the thesis of Alex Simpson (see this). The thesis describes a family of solutions of Einstein' equations characterized by one parameter a. The solutions have time translations and rotations as symmetries and in contrast to naive expectations the radial coordinate varies from -∞ to +∞ rather than from 0 to ∞.
The general solution of the family is given by
ds2= (1-2GM/X)dt2- dr2/(1-2GM/X)+ (r2 +a2)(dθ2) +sin2(θ)dθ2)
The coordinates r and t vary in the range (-∞,+∞). rS= 2GM is Schwartschild radius.
Some comments are in order.
- a=0 gives Schwarzschild solution and in this case r=0 corresponds to a single point as the singularity of spherical coordinates. For 2>0 r=0 corresponds to a sphere with radius a. In the TGD framework this would be obtained if there is a magnetic monopole flux through the monopole throat.
- The study of radial geodesics provides information about the object. One has for the radial velocity dr/st= +/- (1-X). For a>rs this is always nonvanishing. Therefore the radiation from r< 0 blackhole can propagate to r> 0 blackhole.
For Schwartschild solution with a=0, dr/dt it vanishes at Schwartschild radius so that light cannot classically escape from blackhole interior.
For a< rs, dr/dt vanishes for two radii r+/-= +/- (rS2 -a2)1/2 so that these acts as horizons and the two blacholes are isolated.
A.4. What negative energy shock waves are and why they are needed?
The basic problem against the idea of quantum gravitational view of teleportation is that wormholes are unstable against splitting. Neither space ships nor information can travel from blackhole to another one. Wormholes are not traversable: geodesics cannot connect the blackholes but stop at the horizon.
The introduction of the article "Traversable wormholes via a double trace deformation" by Gao et al (see this) describes how traversable wormholes might be generated.
The conditions making wormholes traversable would look like follows.
- Negative energy shock waves are needed to open the wormhole throat so that classical signals can propagate between the blackholes and make quantum teleportation possible. One says that the wormhole becomes traversable. What do these negative energy shock waves mean in GRT context?
- Quantum gravitational deformation of metric such would make the average energy density negative. The first problem is that QFTs do not allow this. Second problem is that after the sad fate of superstring theory, no generally accepted theory of quantum gravitation exists. The third problem, not usually noticed, is that the notions of energy and other Poincare charges are lost in GRT.
- One can however forget these little nuisances and assume that negative energy densities are possible. Negative energy condition means technically that there exists an infinitely long null geodesic going through the blackhole-like entity such that the integral of the trace of energy momentum tensor is negative along the geodesic. This means that negative energy signals can propagate through the entire geodesic and make possible classical communications necessary for teleportation.
The averaged null energy condition (ANEC), presumably stating the vanishing or even non-negativity of the trace, is said to fail if this is the case. It is also mentioned that physically the failure of the condition implies that light-rays focused at the other end of the wormhole, defocus at the other end. I didn't quite understand how this follows from the condition.
- The existence of this kind of defocusing of geodesics is excluded by several conditions. As already noticed, the averaged null energy condition (ANEC) denies their existence. Neither does the generalized second law, stating that the area of blackhole horizon increases, allow them. It would seem that the hopes for traversable wormholes are rather meager.
- Here comes however AdS2 to rescue. Before continuing, note that AdS2 duality is not for gravitation but for the gravitational dual of a conformally invariant QFT, such as gauge theories. Therefore we can allow things which we would condemn as nonsense in real quantum gravitation.
The problem is that AdS has 1 time-like dimension but has closed time-like directions. AdS is imbedded in 3-D space with line element ds2= dt12 + dt12 -dz2 containing 2 time-like directions and a 2-sphere with time-like metric containing circular time loops.
These time-like loops imply at the level of AdS a violation of cosmic censorship and global hyperbolicity. As a consequence, the standard initial value problem with 3-D initial data is ill-defined since the signals from the surface of initial data return back. This also implies that the blackhole horizon extending through the wormhole intersects itself. The radial direction for AdS between the blackholes is time-like and effectively a compact circle. One has a causal anomaly. This is bad.
- One must save the causality. The postulated interaction between the boundaries of the wormhole comes to rescue at this time and solve the problem that we have created. This interaction would save causality and would also imply failure of ANEC, and therefore make the wormhole traversable. Negative energy is interpreted in terms of effective Casimir effect.
Of course, it would be much easier to not postulate at all the AdS duality and be satisfied with the fact that we have been able to simulate certain quantum model using quantum computers.
B. The TGD view
In the following I describe a possible TGD based interpretation of the experiment.
B.1 The TGD counterpart of AdS/CFT duality
TGD is a proposal, which solves the energy problem of general relativity and generalizes string models by replacing strings with 3-D surfaces. In the TGD framework, 4-D general coordinate invariance leads to a holography and analog of AdS/duality having interpretation as quantum classical correspondence.
- In the TGD framework, light-like 3-surfaces appear as fundamental objects and are metrically effectively 2-D. These 3-D objects are related by holography (forced by general coordinate invariance in TGD) to 4-D objects defining space-time as a 4-D surface in M4×CP2.
These 3-D surfaces possess a conformal symmetry which is much larger than the usual 2-D conformal conformal symmetry, which is already infinite-D.
- In AdS/CFT, the dimensions related by holography are wrong: in AdS5 one has 4→5 and AdS5 is non-physical unless one wants to believe in the emergence of space-time, a second fashionable but remarkably unsuccessful idea.
- In TGD holography corresponds 3→4, which is the case also in the duality proposed between blackhole horizon and interior. In this duality everything has precise physical meaning and both sides of the duality can be tested unlike in AdS/CFT duality for which AdS is a completely fictitious notion.
- The TGD variant of duality is forced by the 4-D general coordinate invariance and is not a separate principle.
- In quantum theory this duality corresponds to Bohr orbitology: space-time surface is analogous to Bohr orbit of 3-surface generalizing the notion of particle.
- Classical theory as Bohr orbitology becomes an exact part of quantum theory.
- This duality leads to what I call zero energy ontology in which these 4-D Bohr orbits replace time=constant snapshots as basic objects. This leads to a solution of the basic paradox of quantum measurement theory and has profound implications in quantum biology and theory of consciousness.
Could these traversable wormholes have TGD analogues and could they provide a dual or a classical correlate for the quantum description as the quantum classical correspondence suggests. One must remember that the TGD view of quantum differs considerably from the standard view.
- New view of space-time predicts topological field quantization and the notion of field body. The notion of magnetic body (MB) consisting of flux tubes and flux sheets is in a central role in TGD.
- The number theoretic vision of TGD predicts hierarchy of dark matter as phases of ordinary matter labelled by values of effective Planck constant: dark matter would reside at the field body, in particular at MB. These phases of ordinary matter might be highly relevant for quantum computation, which is in the standard framework formulated using standard quantum mechanics.
- TGD predicts zero energy ontology (ZEO) one predict is that the TGD counterpart of ordinary state function reduction (SFR) reverses the arrow of time. Could this give rise to quantal versions of time loops.
- Wormholes of GRT are not stable. Monopole flux tubes are stabilized by the very fact that monopole flux is conserved so that the flux tube cannot be split.
- If one has a pair of flux tubes with opposite fluxes connecting two systems, reconnection can split the flux tubes to U-shaped flux loops. This is a basic mechanism in the TGD inspired quantum biology.
- Could the reconnection of flux tube loops to a flux tube pair generate an analogue ofa traversable wormhole with classical signals propagating along the flux tube pair and making possible quantum teleportation?
- Could thus involve "big" SFR changing the arrow of time and giving rise to effective negative energy signals propagating backwards in time?
Could this correspondence be made more quantitative and detailed.
- Could one assign to wormhole throats and entire wormhole scales which are analogous to rS and the parameter a and could the condition a>rS have an analog in TGD framework.
- The first trial starts from wormhole contacts as they are identified in TGD.
- The expectation is that at least for elementary particles the wormhole throat radius is of order CP2 radius and therefore extremely small. Mass would be of order m=10-4 mPl and could correspond to a mesoscopic mass: a water blob of size 10-4 meters has mass of order Planck mass. Could this give some idea how to proceed?
- The Earth's gravitational field has a key role in TGD inspired quantum biology since gravitational quantum coherence is possible in even astrophysical scales. Gravitational Compton length Λgr= hgr/m GM0 defines a fundamental quantum gravitational size scale. One has scale of about .45 cm for Earth mass ME and v0=c.
- The condition a> rs for the traversability need not generalize as such in the TGD framework. Therefore it is better to start from the physical picture rather than trying to mimic wormhole physics.
This kind condition should tell when the reconnection for U-shaped flux tubes is possible. This suggests that the parameter a characterizes the length of the U-shaped flux tubes connecting the two quantum systems. This length scale should be more than half the distance between the two systems as analogues of blackholes so that the half-distance d/2 would be the counterpart of rS and the typical length of the U-shaped flux tube would be the counterpart of a. The length of the flux tube depends on the value of heff and on the p-adic length scale assignable to the flux tube.
- For an ordinary wormhole, the formula a> rs guaranteeing traversability can be satisfied if the mass parameter m decreases below a but remains unaffected. This would correspond to a generation of negative vacuum energy reducing m below a/2G. Does this have any generalization to the TGD framework?
- Now the distance d between the systems could decrease or the length of U-shaped flux tubes could increase so that reconnection becomes possible.
The postulated interaction between the two systems should give rise to the analog of negative energy shock wave. In the TGD framework, the reconnection of flux tubes could be the interaction generating a communication line. The GRT analogue for the negative energy shock wave could be Hawking radiation. The system at right would receive positive energy and the system at left would receive negative energy, or equivalently, send positive energy.
The positive energy received by the system at right would serve as a metabolic energy feed and would change the distribution of values of heff in it. The values of heff would tend to increase. Therefore also entanglement negentropy content of the system would increase meaning that entanglement is created. At the left side the opposite would occur. One can say that information is transformed between the two systems.
- Could "big" SFR (BSFR, that is the ordinary SFR) in the scale of the entire system be involved. This would imply a change of the arrow of time and one could say that the system at right sends negative energy signals to the system at left and gets positive energy as a recoil acting as metabolic energy. This mechanism is a basic metabolic mechanism in the TGD inspired quantum biology. The energy for dark analogs of Hawking photons would be large although frequencies could be small. For hgr = GMEm/v0, the energies would be in visible range for frequencies of order 10 Hz.
The simplest interpretation is that the first BSFR creates reconnection and maximal entanglement between the systems and and the second BSFR corresponds to de-reconnection and the quantum measurement destroying the entanglement. The classical communication during the entanglement period induces the transfer of internal entanglement. One could see this phenomenon also as quantum tunneling for information.
- Prepare an entangled state between two copies of H: one is the left side of the wormhole, and the other is the right side of the wormhole. This entangled state is dual to a wormhole at time t=0. The devised through learning small SYK-like system has 7 Majorana fermions on the left and 7 Majorana fermions on the right; encoding all 14 fermions in superconducting qubits requires 7 qubits. Comment: the initial state is quantum entangled. If the existence of flux tube pair(s) serves as a correlate for entanglement, BSFR changing the arrow of time must take place.
- Evolve the wormhole backwards in time according to H. This moves the horizons of the left and right mouths of the wormhole. Comment: The time evolution backwards in time could correspond to a sequence of SSFR ("small" SFRs as counterparts for "weak" measurements preserving the arrow of time). What could the motion of the wormhole mouths correspond to? Suppose that the half-distance d between the two systems corresponds to the parameter rS and the length L of flux U-shaped flux tubes corresponds to the parameter a. If this is the case, the motion would correspond to the decrease of the length of the U-shaped flux tubes so that the condition L> d/2 as an analogy for the condition a>rS ceases to be true and the U-shaped flux tubes become too short to reconnect anymore.
- Prepare two maximally entangled qubits: call the first one the reference qubit and the other the probe qubit. We later attempt to send the probe qubit through the wormhole, and we will be able to check if it made it through by comparing against the reference qubit. These two additional qubits bring the total circuit size to 9 qubits. Comment: this step could correspond to a BSFR changing the arrow of time to normal.
- Swap the probe qubit with one of the qubits in the left quantum system of the wormhole. This inserts the entanglement probe qubit into the wormhole. Evolve the wormhole forwards in time according to H. As this happens, the information of the probe qubit gets chaotically scrambled throughout the entire quantum system. Comment: This step could correspond to a time evolution by SSFRs with the standard arrow of time.
- Apply an entangling interaction between the two sides of the wormhole. In the gravitational dual, this corresponds to sending an energy shockwave through spacetime. We can apply an interaction that gives this shockwave negative energy to prop open the wormhole and make it traversable, or we can choose a positive energy shockwave to close the wormhole and prevent information from getting across. Comment: This step could correspond to a reconnection of U-shaped flux tubes to a flux tube pair connecting the two systems and entangling them, perhaps maximally.
- Evolve the wormhole forwards in time according to H. As this happens, information of the probe qubit undergoes further chaotic dynamics. The dynamics refocus the information onto the right side of the wormhole. Comment: this step could be a BSFR followed by a sequence of SSFRs with standard arrow of time. The entanglement would become visible for the observer with a standard arrow of time.
- Measure the amount of entanglement between the rightmost qubit of the right system and the reference qubit. More entanglement means more information was transferred from the left system to the right system. In our experiment, we observed more entanglement when a negative energy shockwave was used compared to a positive energy shockwave, which is consistent with the interpretation that some quantum information was transferred via the traversable wormhole mechanism.
There are still some questions to be considered.
- In the TGD framework, the expectation is that the radial coordinate r for the family of blackhole-like objects corresponds to the radial coordinate of E3 ⊂M4 and is therefore non-negative.
One can however ask whether one could have parallel space-time sheets connected by a wormhole contact with an Euclidean signature of the induced metric and whether the negative values of r could be natural for the radial coordinate at the other space-time sheet. Both sheets would be covered by a single coordinate.
- One must also ask whether the connected space-time sheets could correspond to opposite arrows of time, which changes in "big" state function reductions (BSFRs). If so, wormhole contacts would mediate interaction between quantum states with opposite arrows of time. The wormhole throat with Euclidean signature does not have a definite arrow of time and could mediate this interaction. In this picture elementary particles, at least bosons, would be pairs of particles with opposite arrows of time. Can this make sense?
See the article How do AdS/CFT- and TGD based holographic dualities relate?.
For a summary of earlier postings see Latest progress in TGD.