Black holes, wormholes and the secrets of quantum space-time

This equivalence may have profound consequences. It raises the possibility that space-time itself may have emerged from the interweaving of even more fundamental microscopic components of the universe. It also raises the possibility that intertwined objects - although they have long been considered as objects that have no physical connection between them - they may actually be connected in much less imaginative ways than we thought.

Moreover, the connection between entanglement and wormholes may help to develop a unified theory of quantum mechanics and space-time - a theory that physicists call Quantum gravity - where the physics of the macroscopic universe is derived from the laws governing the interactions that prevail in the atomic and subatomic realms. We need such a theory to be able to understand the Big Bang and what happens inside black holes.

It is interesting to note that both quantum entanglement and wormholes are phenomena that were first described in two papers written by Albert Einstein and his colleagues in 1935. Apparently, the articles seem to deal with two very different phenomena, and it is likely that Einstein never suspected that there could be a connection between them. In fact, entanglement was a feature of quantum mechanics that greatly troubled the German physicist, calling it "ghost action at a distance." How ironic that today she might offer a bridge that would extend his theory of relativity into the quantum realm.

Black holes and wormholes

To explain why I believe there may be a connection between quantum entanglement and wormholes, we must first describe some properties of black holes that are closely related to this idea. Black holes are regions of curved space-time, radically different from the relatively undisturbed space we are used to. The most distinct characteristic of a black hole is that we can divide its geometry into two regions: the outer part, where space is curved but objects and messages can still escape, and the inner part, which lies beyond the point of no return. The inner part is separated from the outer part by the surface of the machine the event horizon. General relativity teaches us that the horizon is nothing more than an imaginary surface: an astronaut crossing it will not feel anything special in that place. But from the moment he crossed it, the space tourist was destined to be squeezed into an area of ​​enormous curvature without any ability to escape. (Actually, the inside is actually in the future compared to the outside, so the space traveler won't be able to escape because he can't travel to the past.)

Only a year after Einstein published the theory of general relativity, the German physicist found Carl Schwarzschild The simplest solution to Einstein's equations, describing what would later be called black holes. The geometry formulated by Schwarzschild was so unpredictable that it was not until the 60s that scientists were able to truly understand that what it was describing was a wormhole connecting two black holes. From the outside, black holes look like separate entities sitting far apart, but they share a common interior.

In 1935, Einstein wrote a paper on the subject with his colleague Nathan Rosen, who was then working at the Institute for Advanced Research in Princeton, New Jersey (and who immigrated to Israel in 1953 and founded the physics faculty at the Technion). In their paper they suggested that this shared interior is probably a type of wormhole (although they did not fully understand the geometry predicted by him), and for this reason wormholes are also called Einstein-Rosen bridges (ER bridges).

The wormhole in Schwarzschild's solution differs from black holes that form naturally in the universe, because it contains no matter at all: it is nothing more than a curved space-time. However. True black guys, which are naturally formed, have substance and therefore only have one outer part. Most researchers see the complete Schwarzschild solution, on its two outer parts, as nothing more than a mathematical curiosity that does not concern the black holes found in the universe. Nevertheless, it is still an interesting solution and physicists have tried to understand what its physical meaning is.

The Schwarzschild solution teaches us that the wormhole connecting the two outer parts of black holes changes with time. It lengthens and becomes thinner as time progresses, as in the situation where a piece of flexible dough is stretched. At the same time, the two horizons of the black holes, which at some point touched each other, are rapidly separating. In fact, they're moving away from each other so fast that we can't use such a wormhole to travel from one outer part to another. Another way to describe it would be to say that the bridge collapsed before we could cross it. In the parable of the stretched dough, the collapse of the bridge is parallel to the situation where the dough becomes infinitely thin as it is stretched further and further.

It is important to note that the wormholes we are talking about are consistent with the laws of general relativity, which do not allow travel at a speed that exceeds the speed of light. In this way, they differ from the wormholes that we find in science fiction works that allow an immediate transition between two distant areas in space, such as in the movie between stars. The science fiction versions therefore often violate the known laws of physics.

A science fiction story involving a wormhole of our kind might look like this: Imagine a couple of lovers, Romeo and Juliet. Their families don't like each other, so they put Romeo and Juliet in different galaxies, and forbade them to travel. However, our pair of pigeons is very resourceful and they managed to build a wormhole. From the outside, the wormhole looks like a pair of black holes, one in Romeo's galaxy and the other in Juliet's galaxy. The lovers decide that they will each jump into the inside of their own black hole. Now, from their families' point of view, they just killed themselves by jumping in and will never be heard from again. But unbeknownst to the outside world, the geometry of the wormhole is such that Romeo and Juliet actually meet in the shared interior! And they can live there for a while in happiness and wealth, until the bridge collapses, destroying the inside and killing them both.

Quantum entanglement

The 1935 paper that discusses the second phenomenon that interests us, the quantum entanglement phenomenon, was written by Einstein, Rosen andBoris Podolsky (who also worked at the Institute for Advanced Research at the time), the three authors who were published by the initials of their names: EPRR. In this famous work, the physicists claimed that quantum mechanics allows the existence of certain strange correlations between distant physical objects, a feature that would later be called "entanglement".

Correlation between distant objects can also exist in classical physics. Imagine for example that you leave the house with one glove because you forgot the other one at home. Before you check your coat pocket, you won't know if the glove you brought with you is your right or left. But as soon as you find out that you took the right glove with you, you will immediately know that the glove left at home is the left one. But entanglement includes a different type of correlation, a correlation that exists between quantities governed by quantum mechanics, and subject toHeisenberg's uncertainty principle. According to this principle, there are pairs of physical variables that are impossible to know both precisely at once. The most familiar example involves the location and velocity of a particle: if we accurately measure its location, its velocity will become uncertain, and vice versa. The three authors of the EPR paper wondered what would happen if we decided to measure either the locations or the velocities of each pair of distinct particles, with a large distance separating them.

The conventional wisdom that nothing can escape a black hole is too simplistic.

The sample analyzed in EPR consisted of two particles of the same mass moving in one dimension. Let us imagine that the lovers, Romeo and Juliet, are the ones who will perform the measurements, so we will call the particles after them, R and J. We can prepare the particles in such a way that their center of mass will have a well-defined place, which we will call x_cm, equal to half the sum of x_R (the place of R) and another x_J (JJ's place). We can demand that the center of mass be equal to zero, in other words, we can say that the two particles are always equidistant from the beginning of the axes. We can also decide that the relative velocity of the particles, v_rel, compare to the speed of (R (v_R minus the speed of (J (v_J, you will get an exact value; For example, it is said that v_rel is equal to some number called v₀. In other words, the difference between the two speeds must remain constant. Here we determine location and speed accurately, but not for a single object, therefore we do not violate Heisenberg's uncertainty principle. If we have two different particles, nothing prevents us from knowing the location of the first and the speed of the other. Similarly, once we determine the location of the center of mass, we cannot say anything about the velocity of the center of mass, but we are free to determine the relative velocity.

And now we come to the most amazing part: the thing that makes quantum entanglement seem so strange. Suppose that our particles are at a great distance from each other, and two distant observers, Romeo and Juliet, decide to measure the locations of the two particles. Now, since the particles have been prepared in advance, if Julia determines some exact value for x_J, Romeo will find that the locus of his particle is the negative value of that locus (x_R = – x_J). Note that Julia's result is random: the location of her particle will change from measurement to measurement. But Romeo's outcome is completely determined by Juliet's outcome. Now suppose that each of them measures the speed of its own particle. If Julia receives a certain value for v_J, Romeo will surely discover that his speed is the value found by Juliet plus the relative speed (v_R =v_J + v₀). Again, Romeo's outcome is completely determined by Juliet's outcome. Of course, Romeo and Juliet are free to choose which variable they will measure. In particular, if Juliet measures the place and Romeo measures the speed, their results will be random and there will be no correlation between them.

The strange thing is that even though Romeo's measurements of the speed and location of his particle are limited by Heisenberg's uncertainty principle, if Juliet decides to measure the location of her particle, then Romeo's particle will have a completely certain location once he knows the result of Juliet's measurement. And the same will happen with the speed. It seems as if as soon as Juliet measured the position, Romeo's particle immediately "knew" that it must have a well-defined location and an uncertain velocity, and the opposite would have happened if Juliet had measured the velocity. At first glance, this situation seems to allow the passing of too much information: Juliet can measure the place, and then Romeo will see a definite place for his particle and infer that Juliet measured the place anyway. But Romeo will not be able to understand that his particle has a definite place without knowing what the actual value that Juliet measured was. So it is practically impossible to use the correlations caused by quantum entanglement to send signals at a speed higher than the speed of light.

Although entanglement has been experimentally confirmed, it still appears to be nothing more than an esoteric property of quantum systems. However, over the past twenty years, these quantum correlations have led to several practical applications and breakthroughs in fields such as cryptography and quantum computing.

equivalence

How could our two strange phenomena, so different from each other, wormholes and quantum entanglement, be related to each other? A deeper look at black guys points the way to a solution. In 1974, Stephen Hawking showed that quantum effects would cause black holes to emit radiation in the same way a hot object does, proving that the conventional wisdom that nothing can escape a black hole is too simplistic. The fact that black holes radiate indicates that they have temperature: a concept that has important implications.

Since the 19th century, physicists have known that temperature results from the movement of the microscopic components of a system. In a gas, for example, the temperature is created by the frantic movements of molecules. Therefore, if black holes have temperatures, then we can expect them to also have microscopic components of some kind, which can together assume a variety of possible configurations, called microstates. We also believe that, at least as black holes look from the outside, they should behave as quantum systems; That is, they should obey all the laws of quantum mechanics. In conclusion, when we observe a black hole from the outside, we are supposed to find a system that can have many microstates, and the probability of finding it in each of these configurations is basically the same for each and every one of the microstates.

Since black blacks look like ordinary quantum systems from the outside, there is nothing to prevent us from thinking of a entangled pair of them. Imagine a pair of black holes very far apart. Each has a large number of possible microscopic quantum states. Now imagine an entangled pair of black holes where there is a correlation between each of the quantum states in the first black hole and the corresponding quantum state in the other hole. In particular, if we measure a certain state in the first hole, then the second hole must be in exactly the same state.

The interesting point is that, based on certain considerations inspired by string theory (which is one of the approaches striving towards a theory of quantum gravity), we can claim that a pair of black holes whose microstates are entangled in this way (that is, in a state that can be called an entangled EPR state) will create a space-time in which A wormhole (ER bridge) connects the interior of the two black holes. In other words, quantum entanglement creates a geometric connection between the two black holes. This result is surprising because we thought that interweaving involved correlations without a physical bond. However, the two black holes in this case are physically connected through their interior and approach each other through the wormhole.

Leonard Susskind from Stanford University and I called the equivalence of wormholes and entanglement “ER = EPR”, because it links the two papers written by Einstein and his colleagues in 1935. From EPRR's point of view, there is a correlation between the near-horizon observations of each of the black holes because the black holes are in a state of quantum entanglement. From the perspective of ER, there is a correlation between the observations because the two systems are connected through the wormhole.

Now, if we return to Romeo and Juliet from our science fiction story, we can see what the couple in love should do to create an intertwined pair of black holes that will form the wormhole. First, they must create many intertwined pairs of particles, similar to the particles we described before, with one member of each intertwined pair being in Romeo's possession, and the other in Juliet's possession. They then have to build very complicated quantum computers that will manipulate each other's quantum particles and combine them in a controlled manner to form a pair of entangled black holes. This would be an incredibly difficult operation to pull off, but it seems possible according to the laws of physics. Besides, we said that Romeo and Juliet are resourceful!

A universal principle?

The ideas that led us here have been developed over the years by many researchers, starting with a 1976 paper by Werner Israel, who then worked at the University of Alberta in Canada. An interesting work was also done in 2006 on the connection between interweaving and the geometry of space-time by Shinsei Rio וTadashi Takayanagi, both of whom were then working at the University of California, Santa Barbara. What motivated me and Susskind to research the subject was an article they published in 2012 Ahmed Almehairi, Donald Marloff,Joseph Polczynski וJames Sully, who were all working at the University of California at Santa Barbara at the time. They discovered a paradox related to the nature of the interior of an entangled black hole. The ER = EPR idea, which says that the interior is part of a wormhole connecting the black hole to another system, dulls the sting of some aspects of this paradox.

Although we identified the connection between wormholes and entangled states using black holes, it is tempting to speculate that this connection is more general: that in any state where there is entanglement, there is also a kind of geometric connection. This expectation will remain true even in the simplest case, where we have only two entangled particles. But in such situations, the spatial link could include tiny quantum structures that would not fit our usual concepts of geometry. We do not yet know how to describe these microscopic geometries, but the interweaving of these structures may in some way lead to the formation of space-time itself. So to speak, the interweaving can be seen as a thread connecting two systems. When the amount of interweaving increases, we have many threads, and these threads will be able to fit into a plexus that will create the fabric of space-time. According to this picture, Einstein's equations of relativity govern how these strings are tied and retied; Quantum mechanics is not just an addition to gravity - it is the essence of the structure of space-time.

At the moment, this picture is nothing more than a wild hypothesis, but there are several hints pointing in its direction, and many of us physicists are delving into its implications. We believe that the phenomenon of entanglement and the phenomenon of black holes, seemingly unrelated, may in fact be equivalent, and that this equivalence provides an important clue to the development of a description of quantum space-time - and to the long awaited unification, the unification of general relativity and quantum mechanics.