Black holes, the information paradox and quantum entanglement: the link between quantum physics and general relativity?
Have you read the preceding page on black holes?
Information theory and the information paradox ….
Information theory and the information paradox ….
For the last several decades, there has been an ongoing debate about what happens to the information a black hole has swallowed. Let’s get things straight. Definitions first.
What is this thing called “information”?
At its basic level, information means distinctions between things - a something that can be measured mathematically in terms of the probability or non-probability of an event or thing’s occurrence, and the information content of an event is proportional to the log (degree) of its inverse probability of occurrence [1], thus:
1 (the information content of the event)
I (information) = log p (the inverse probability of its occurrence).
This formula represents the modern definition of information reduced to its mathematical base. In other words, we only need the presence of two conditions to talk about information: one is the existence of events (something needs to be happening) and the other is being able to calculate the probabilities of events happening.
Under the binary system, the fundamental concept of being able to distinguish between two different states or events is referred to as a bit (binary digit) of information. A binary digit is the smallest unit of information in a computer. It is used for storing information and has a value of true/false, or on/off. An individual bit has a value of either 0 or 1, which is generally used to store data and implement instructions in groups of bytes [2].
A bit is therefore the most fundamental measure of information you can have, and where you have more than two outcomes, you simply use more bits to distinguish them. Information theory boils down to events based on Boolean logic [3]. For an event to happen with several outcomes, each outcome either happens or does not happen – in classical physics at least. Unlikely, low probability words or events contain a very high degree of information, but high probability events contain very little information. They are so likely you don’t really have to describe them in much detail. So in Boolean terms, unlikely or low probability words or events can be encoded with many zeros and ones, depending on how unlikely the occurrence, whereas high probability words or events can be expressed in relatively few such ‘bits’ or pieces of information, or in other words, a shorter code.
In quantum physics, events always occur with probabilities regardless of how much information you have, so the concept of being able to distinguish between events or states needs to be enlarged to account for the bizarreness of quantum effects. A quantum bit can exist in several states at the same time, and can also happen randomly [4].
In recent times, these ideas have found expression in the “it from qubit” project, “it” designating spacetime and qubit representing the smallest possible amount of information, something akin to a computer bit but on a quantum scale. A classical bit can have one or two states: 0 or 1, which can be thought of as the two sides of a coin, but a qubit has many more possible states, which can be thought of as points on a sphere, each point with different co-ordinates. This is known as a superposition of states. [4A]
It is suggested that spacetime itself may actually be composed and knitted together by the quantum entanglement [4A] of these tiny discrete units of information whose units interact with each other, thereby giving rise to spacetime properties such as the curvature that causes gravity. If successfully, pursued, this notion may also help achieve the long-sought after quantum theory of gravity, which would in turn merge general relativity and quantum mechanics.[5]
What happens to information which falls into a black hole? [5A]
According to conventional quantum mechanics, pairs of particles and their antimatter counterparts constantly pop into existence and then disappear almost at once. If this happens just outside the horizon of the black hole, according to Stephen Hawking, the pair could separate; one would fall into the singularity and the other would escape and carry away some of its mass; in this way, eventually the black hole’s entire mass would be depleted, a phenomenon known as Hawking evaporation.
This conundrum exposes two apparent contradictions between general relativity and quantum mechanics: the entropy problem and the information paradox. Does the information (distinctions between things) disappear forever as the black hole evaporates, as Hawking divined in 1975, or does the information re-emerge as the black hole radiates and shrinks, and had Hawking mistaken the scrambling of information for actual information loss? In a recent paper, Joseph Polchinsky elaborates upon these two contradictions. [6]
Firstly, the entropy problem in the context of general relativity:
The radiation spectrum of Hawking emission suggests that black holes have temperatures. Traditionally, heat arises from the motion of atoms within an object. The temperature of black holes implies that they have substructure - some type of building blocks that can rearrange themselves. The possibility of different arrangements gives black holes a measure of disorder or “entropy”, according to the quantum-mechanical picture of Hawking radiation. However, entropy is forbidden to black holes by general relativity, which requires them to be completely smooth, without substructure – “without hair” as the saying goes.
Secondly, the information paradox in the context of quantum mechanics [7]:
Hawking evaporation also conflicted with the standard picture of quantum mechanics, according to which information can never be destroyed, because Hawking radiation implies that black holes destroy the information of the matter that falls into them, since the particles that escape do not depend at all on the properties that initially fell into the black hole – usually a massive star that collapsed. Hawking concluded that the laws of quantum mechanics might need to be modified to allow for such information loss in black holes. In other words, either quantum mechanics needs to be modified to allow information loss, or general relativity requires modification to allow information to escape from the black hole interior. [8]
Polchinsky’s stunning resolution of this conundrum is elaborated towards the end of this page, but I will give the game away right here. The answer is that there is a firewall at the event horizon of the black hole. To understand this, we need to elaborate upon a few basic principles, and the first of these is the holographic principle. The quantum theory of entanglement will come later.
The holographic principle was elaborated by Leonard Susskind and Gerard ’t Hooft (a theoretical physicist at Utrecht University in the Netherlands who went on to win the Nobel Prize) largely in response to Hawking’s views. It holds that what happens in any volume of spacetime can be explained by what happens on its boundary. Although we usually think of objects as zipping around three-dimensional space, we can equally well think of them as flattened blobs sliding across a two-dimensional surface. [9]
What happens is that the information sucked into the black hole (consisting of binary units or “bits” that give rise to the universe and live on the Planck scale) is preserved and imprinted on a two-dimensional surface around its event horizon. In the meantime, the black hole continues to emit radiation for extended periods, and eventually opens up to reveal the information within. Since information comprises distinctions between things, these distinctions never disappear, says Susskind. “They might get scrambled or all mixed up, but they never go away”.
Using a modern day analogy, even after this paper gets dissolved into pulp at the recycling plant, in principle the process can be reversed, and the pulp reconstructed into words and photographs, even if, in principle, the task appears impossible [10].
The black hole’s event horizon – the point of no return – thus serves double duty as a ledger and information is not lost. So, in 2004, Hawking duly came on board and revised his previously held view and agreed that black holes only appear to form but later open up and release information about what’s inside. “So we can be sure of the past and predict the future” [11]. In other words, Hawking’s new black holes never completely destroy everything that falls in. Instead, they continue to emit radiation for extended periods, and eventually open up to reveal the information within.
In the elaboration of this theory, Susskind and ‘t Hooft also proposed a solution to the original information problem that involved a kind of relativity principle called black hole complementarity, which holds that there is an inherent ambiguity in the fate of objects that fall into a black hole. From the point of view of the falling object itself, it passes without incident through the hole’s perimeter or horizon, and is destroyed when it reaches the hole’s centre, or singularity, whereas from the point of view of an external observer, the falling object is incinerated at the horizon.
Otherwise expressed, an observer who jumps into a black hole sees the information inside, whereas one who stays outside sees it come out, there being no contradiction because these two observes cannot communicate. So which is the true reality: the boundary or the interior? The theory does not say. Reality, in this holographic conjecture, is perspectival [12]. The two observers are seeing things from different perspectives and both interpretations are valid [12.1]. The holographic principle is the consequence.
It has been conclusively demonstrated - a least to the satisfaction of those who hand out the Nobel Prize in physics, says Vlatko Vedral – that the theory actually works and that two dimensions are sufficient to store all the information about three dimensions [13].
The wider ramifications of the holographic principle [14]
In information theory, the governing principles derive from entropy. The physical entropy of the universe is ever increasing, says the Second Law of Thermodynamics. The Second Law was elaborated in the context of heat but the same principles apply to the information content of the universe as well. In information theory, the higher the entropy of a system, the more information it carries.
How is one to measure how much information the system carries to produce this entropy?
Somewhat surprisingly, when one compares the information content of different systems, one of which is inherent within the other (as a molecule is embodied within the larger universe), the task is not performed by reference to the number of atoms in the system itself, but by reference to the total number of atoms on the surface – a significantly smaller ratio. For example, if you compare the degree of quantum mutual information in fact held by a molecule and the rest of the universe, a proportional comparison can only be made in relation to something that is common to them both, in this instance, the boundary or surface of them both. So the information content lies not within the object, but on its surface area and becomes a relational property of the object in connection with the rest of the universe.
This is the relationship - the scaling between area and entropy (information) - which Susskind describes in the holographic principle, and these principles, he suggests, are also capable of being elevated to a wider principle applicable to anything in the universe which carries energy, for example, matter and light - and perhaps also to gravity as well.
Space curvature derives from quantum information theory
The hypothesis is that Einstein’s energy-curvature relationship that describes gravity (Gμν = 8πTμν, without reference to the cosmological constant) – or as Wheeler would have it: matter tells space-time how to curve; curved space-time tells matter how to move) is derived from quantum information theory.
In thermodynamical terms entropy is proportional to the geometry of the system – that is, the entropy of a system multiplied by its temperature is the same as the energy of the system - so a larger mass (= a larger energy based on the mass-energy equivalence) also implies a larger curvature in space-time.
So entropy encapsulates geometry in the sense that a simple energy conservation statement between entropy and energy under the Second Law converts into Einstein’s gravitational equation relating mass to curvature, and the more massive the object, the larger the indentation of the surrounding area. In the same way, under the holographic principle, massive objects with greater entropy affect the area that the light travels which will then have to bend to take into account the change in geometry. This was how space-time curvature was first used by Arthur Eddington in 1919 to test Einstein’s theory of general relativity, and the same principles also apply to the gravitational influence on light wrought by black holes.
By these means, information, as measured by entropy, underpins both quantum mechanics and gravity, and the fact that quantum entropy is proportional to area can then be coupled with the First Law of Thermodynamics that energy is conserved, to infer the equations of gravity. In other words, there is a relationship between quantum physics and gravity which were previously thought to be incompatible, and the properties of quantum information are the same with or without gravity.
This is the reason why physicists have become so excited about the holographic principle - because it is said to articulate a deep connection between information, matter and gravity. In the end, the holographic principle could reveal how to reconcile the two tremendously successful yet mutually incompatible pillars of twentieth century physics: quantum mechanics and general relativity. So, the holographic principle may in fact afford a signpost to quantum gravity [15]
What is this thing called “information”?
At its basic level, information means distinctions between things - a something that can be measured mathematically in terms of the probability or non-probability of an event or thing’s occurrence, and the information content of an event is proportional to the log (degree) of its inverse probability of occurrence [1], thus:
1 (the information content of the event)
I (information) = log p (the inverse probability of its occurrence).
This formula represents the modern definition of information reduced to its mathematical base. In other words, we only need the presence of two conditions to talk about information: one is the existence of events (something needs to be happening) and the other is being able to calculate the probabilities of events happening.
Under the binary system, the fundamental concept of being able to distinguish between two different states or events is referred to as a bit (binary digit) of information. A binary digit is the smallest unit of information in a computer. It is used for storing information and has a value of true/false, or on/off. An individual bit has a value of either 0 or 1, which is generally used to store data and implement instructions in groups of bytes [2].
A bit is therefore the most fundamental measure of information you can have, and where you have more than two outcomes, you simply use more bits to distinguish them. Information theory boils down to events based on Boolean logic [3]. For an event to happen with several outcomes, each outcome either happens or does not happen – in classical physics at least. Unlikely, low probability words or events contain a very high degree of information, but high probability events contain very little information. They are so likely you don’t really have to describe them in much detail. So in Boolean terms, unlikely or low probability words or events can be encoded with many zeros and ones, depending on how unlikely the occurrence, whereas high probability words or events can be expressed in relatively few such ‘bits’ or pieces of information, or in other words, a shorter code.
In quantum physics, events always occur with probabilities regardless of how much information you have, so the concept of being able to distinguish between events or states needs to be enlarged to account for the bizarreness of quantum effects. A quantum bit can exist in several states at the same time, and can also happen randomly [4].
In recent times, these ideas have found expression in the “it from qubit” project, “it” designating spacetime and qubit representing the smallest possible amount of information, something akin to a computer bit but on a quantum scale. A classical bit can have one or two states: 0 or 1, which can be thought of as the two sides of a coin, but a qubit has many more possible states, which can be thought of as points on a sphere, each point with different co-ordinates. This is known as a superposition of states. [4A]
It is suggested that spacetime itself may actually be composed and knitted together by the quantum entanglement [4A] of these tiny discrete units of information whose units interact with each other, thereby giving rise to spacetime properties such as the curvature that causes gravity. If successfully, pursued, this notion may also help achieve the long-sought after quantum theory of gravity, which would in turn merge general relativity and quantum mechanics.[5]
What happens to information which falls into a black hole? [5A]
According to conventional quantum mechanics, pairs of particles and their antimatter counterparts constantly pop into existence and then disappear almost at once. If this happens just outside the horizon of the black hole, according to Stephen Hawking, the pair could separate; one would fall into the singularity and the other would escape and carry away some of its mass; in this way, eventually the black hole’s entire mass would be depleted, a phenomenon known as Hawking evaporation.
This conundrum exposes two apparent contradictions between general relativity and quantum mechanics: the entropy problem and the information paradox. Does the information (distinctions between things) disappear forever as the black hole evaporates, as Hawking divined in 1975, or does the information re-emerge as the black hole radiates and shrinks, and had Hawking mistaken the scrambling of information for actual information loss? In a recent paper, Joseph Polchinsky elaborates upon these two contradictions. [6]
Firstly, the entropy problem in the context of general relativity:
The radiation spectrum of Hawking emission suggests that black holes have temperatures. Traditionally, heat arises from the motion of atoms within an object. The temperature of black holes implies that they have substructure - some type of building blocks that can rearrange themselves. The possibility of different arrangements gives black holes a measure of disorder or “entropy”, according to the quantum-mechanical picture of Hawking radiation. However, entropy is forbidden to black holes by general relativity, which requires them to be completely smooth, without substructure – “without hair” as the saying goes.
Secondly, the information paradox in the context of quantum mechanics [7]:
Hawking evaporation also conflicted with the standard picture of quantum mechanics, according to which information can never be destroyed, because Hawking radiation implies that black holes destroy the information of the matter that falls into them, since the particles that escape do not depend at all on the properties that initially fell into the black hole – usually a massive star that collapsed. Hawking concluded that the laws of quantum mechanics might need to be modified to allow for such information loss in black holes. In other words, either quantum mechanics needs to be modified to allow information loss, or general relativity requires modification to allow information to escape from the black hole interior. [8]
Polchinsky’s stunning resolution of this conundrum is elaborated towards the end of this page, but I will give the game away right here. The answer is that there is a firewall at the event horizon of the black hole. To understand this, we need to elaborate upon a few basic principles, and the first of these is the holographic principle. The quantum theory of entanglement will come later.
The holographic principle was elaborated by Leonard Susskind and Gerard ’t Hooft (a theoretical physicist at Utrecht University in the Netherlands who went on to win the Nobel Prize) largely in response to Hawking’s views. It holds that what happens in any volume of spacetime can be explained by what happens on its boundary. Although we usually think of objects as zipping around three-dimensional space, we can equally well think of them as flattened blobs sliding across a two-dimensional surface. [9]
What happens is that the information sucked into the black hole (consisting of binary units or “bits” that give rise to the universe and live on the Planck scale) is preserved and imprinted on a two-dimensional surface around its event horizon. In the meantime, the black hole continues to emit radiation for extended periods, and eventually opens up to reveal the information within. Since information comprises distinctions between things, these distinctions never disappear, says Susskind. “They might get scrambled or all mixed up, but they never go away”.
Using a modern day analogy, even after this paper gets dissolved into pulp at the recycling plant, in principle the process can be reversed, and the pulp reconstructed into words and photographs, even if, in principle, the task appears impossible [10].
The black hole’s event horizon – the point of no return – thus serves double duty as a ledger and information is not lost. So, in 2004, Hawking duly came on board and revised his previously held view and agreed that black holes only appear to form but later open up and release information about what’s inside. “So we can be sure of the past and predict the future” [11]. In other words, Hawking’s new black holes never completely destroy everything that falls in. Instead, they continue to emit radiation for extended periods, and eventually open up to reveal the information within.
In the elaboration of this theory, Susskind and ‘t Hooft also proposed a solution to the original information problem that involved a kind of relativity principle called black hole complementarity, which holds that there is an inherent ambiguity in the fate of objects that fall into a black hole. From the point of view of the falling object itself, it passes without incident through the hole’s perimeter or horizon, and is destroyed when it reaches the hole’s centre, or singularity, whereas from the point of view of an external observer, the falling object is incinerated at the horizon.
Otherwise expressed, an observer who jumps into a black hole sees the information inside, whereas one who stays outside sees it come out, there being no contradiction because these two observes cannot communicate. So which is the true reality: the boundary or the interior? The theory does not say. Reality, in this holographic conjecture, is perspectival [12]. The two observers are seeing things from different perspectives and both interpretations are valid [12.1]. The holographic principle is the consequence.
It has been conclusively demonstrated - a least to the satisfaction of those who hand out the Nobel Prize in physics, says Vlatko Vedral – that the theory actually works and that two dimensions are sufficient to store all the information about three dimensions [13].
The wider ramifications of the holographic principle [14]
In information theory, the governing principles derive from entropy. The physical entropy of the universe is ever increasing, says the Second Law of Thermodynamics. The Second Law was elaborated in the context of heat but the same principles apply to the information content of the universe as well. In information theory, the higher the entropy of a system, the more information it carries.
How is one to measure how much information the system carries to produce this entropy?
Somewhat surprisingly, when one compares the information content of different systems, one of which is inherent within the other (as a molecule is embodied within the larger universe), the task is not performed by reference to the number of atoms in the system itself, but by reference to the total number of atoms on the surface – a significantly smaller ratio. For example, if you compare the degree of quantum mutual information in fact held by a molecule and the rest of the universe, a proportional comparison can only be made in relation to something that is common to them both, in this instance, the boundary or surface of them both. So the information content lies not within the object, but on its surface area and becomes a relational property of the object in connection with the rest of the universe.
This is the relationship - the scaling between area and entropy (information) - which Susskind describes in the holographic principle, and these principles, he suggests, are also capable of being elevated to a wider principle applicable to anything in the universe which carries energy, for example, matter and light - and perhaps also to gravity as well.
Space curvature derives from quantum information theory
The hypothesis is that Einstein’s energy-curvature relationship that describes gravity (Gμν = 8πTμν, without reference to the cosmological constant) – or as Wheeler would have it: matter tells space-time how to curve; curved space-time tells matter how to move) is derived from quantum information theory.
In thermodynamical terms entropy is proportional to the geometry of the system – that is, the entropy of a system multiplied by its temperature is the same as the energy of the system - so a larger mass (= a larger energy based on the mass-energy equivalence) also implies a larger curvature in space-time.
So entropy encapsulates geometry in the sense that a simple energy conservation statement between entropy and energy under the Second Law converts into Einstein’s gravitational equation relating mass to curvature, and the more massive the object, the larger the indentation of the surrounding area. In the same way, under the holographic principle, massive objects with greater entropy affect the area that the light travels which will then have to bend to take into account the change in geometry. This was how space-time curvature was first used by Arthur Eddington in 1919 to test Einstein’s theory of general relativity, and the same principles also apply to the gravitational influence on light wrought by black holes.
By these means, information, as measured by entropy, underpins both quantum mechanics and gravity, and the fact that quantum entropy is proportional to area can then be coupled with the First Law of Thermodynamics that energy is conserved, to infer the equations of gravity. In other words, there is a relationship between quantum physics and gravity which were previously thought to be incompatible, and the properties of quantum information are the same with or without gravity.
This is the reason why physicists have become so excited about the holographic principle - because it is said to articulate a deep connection between information, matter and gravity. In the end, the holographic principle could reveal how to reconcile the two tremendously successful yet mutually incompatible pillars of twentieth century physics: quantum mechanics and general relativity. So, the holographic principle may in fact afford a signpost to quantum gravity [15]
[1] Vlatko Vedral, Decoding Reality – The Universe as Quantum Information, Oxford University Press (2010), New York, see generally pp 28-36; 111-115.
[2] Cory Janssen. For further elaboration on the binary system, see his post at http://www.techopedia.com/definition/2678/binary-digit-bit.
[3] Named after George Boole, the writer of Laws of Thought (1854).
[4] Vedral, op cit, 137.
[4A] Neil Savage, "What are the limits of manipulating nature?", Scientific American, June 2018, 64 at 67. At 66, Savage explains entanglement by comparing it to two balls in a box, one red and one blue. If you take out the one ball without looking at it and place it in your pocket. After travelling on distance, you take it out of your pocket and look at it, discovering it is red, which immediately tells you that its counterpart in the box is blue. That is entanglement. "The effect, translated to a quantum realm, can transmit information instantaneously and across vast distances". The concepts of collapse, decoherence, superposition and quantum entanglement are also separately considered on the page Schrodinger's probability wave equation
[5] Clara Moskowitz, “Tangled up in Spacetime”, Scientific American, January 2017, 28-31 at 28. See also George Musser, "What is Spacetime?" Scientific American, June 2018, 51-54. The article appears online at https://www.nature.com/articles/d41586-018-05095-z The author's conclusion: all theories of quantum gravity (loop quantum gravity, String/M theory, for example) dictate that the building blocks of spacetime must consist of something more than our present state of knowledge dictates at the moment. Physicists need to find some new foundational structure, and when they do, they will have completed the revolution that began just more than a century ago with Einstein.
[5A] All the issues explored here - black hole radiation, the information paradox, the holographic principle and quantum entanglement - are also covered in George Musser's article cited above.
[6] “Burning rings of fire”’, Scientific American, April 2015, 23-27. See also Sabine Hossenfelder, "Head Trip - Einstein's thought experiments left a long and somewhat mixed legacy of their own", Scientific American, Special Issue - 100 years of General Relativity, September 2015, 37 at 38-39.
[7] Ibid.
[8] Ibid.
[9] From Leonard Susskind as interviewed by Peter Byrne, “Bad Boy of Physics”, Scientific American, Scientific American, Special Collector’s Edition, op cit, August 2013, 108 at 110.
[10] For the development of this argument, see Michael Moyer, “Is space digital?” Scientific American, February 2012, 21 at 25.
[11] ‘Hawking changes his mind on black holes’, MSNBC website, 16 July 2004; ‘Black holes turned ‘inside out’’, BBC News, 19 Sep 2004; ‘Meet the Indian who took on Stephen Hawking’, in rediff.com/news/2004/aug/03hole.htm, 19 Sep 2004.
[12] Susskind, op cit, 110.
[12.1] This difference in perspective between outside observers and someone who is falling into the black hole along with a book containing information, is also well explained by Yasunori Nomura in "The quantum multiverse", Scientific American, June 2017, 22 at 28. The article is noted on the page Branes and multiple universes
[13] Vlatko Vedral, Decoding Reality, Decoding Reality – The Universe as Quantum Information, Oxford University Press (2010), New York, op cit, Chapter 11, see generally and pp 28-36; 111-115.
[14] Unless otherwise indicated, what follows is an abbreviation drawn from Vlatko Vedral’s Decoding Reality, op cit, Chapter 11.
[15] Moyer, “Is Space Digital?” Scientific American, February 2012, 20, 25.
As it turns out information is not lost from an evaporating black hole after all [1]
According to the concept known as known as Maldacena duality (a duality representing a surprising equivalence between two things that seem very different), the mathematics of a theory combining quantum mechanics and gravity (a quantum theory of gravity) based on string theory are equivalent to the mathematics of an ordinary quantum theory under a special set of circumstances: in particular the quantum physics of a black hole is equivalent to that of an ordinary gas of hot nuclear particles.
This also means that spacetime is fundamentally different to what we perceive: something like a 3-D hologram (the one in which we live, for example) is projected from the conventional 2-D surface of a sphere. If Maldacena’s assumptions are true, then ordinary quantum laws would apply to gravity as well and information cannot be lost. Evaporating black holes cannot leave behind any remnants, so it must be that the information gets out with the Hawking radiation and is therefore not lost. [2]
The role of quantum entanglement:
The laws of quantum mechanics dictate that particles entangled with one another cannot be described individually—instead, a quantum state may only be given for the system as a whole. When scientists measure the properties of one entangled partner, the measurement also determines the characteristics of its partner.
Entanglement comes in many different forms. Conventional entanglement involves taking a single characteristic (a particle’s spin, for example) in multiple particles of the same type spread out in space. But there are many other forms of entanglement. Particles of a certain kind at one location may be entangled with particles of a different kind at the same location – an entanglement that does not involve space. And there remains the confusing complexities of entangling larger numbers of particles. All these are relevant, especially in the context of reconstructing spacetime. [3]
The conundrum is that if one particle, say a photon (B), escapes from a black hole after it is at least halfway evaporated, leaving its entangled partner (A) behind and the outgoing photon B to end up in a definite quantum state, if the information is not be lost, then B must be entangled with some combination (C) of the other Hawking particles that had already escaped, otherwise the output would not preserve the information. But this entanglement with another particle is forbidden by the laws of quantum mechanics.
It has recently been demonstrated that strings and higher dimensional objects called D-branes with tiny hidden dimensions too small for us to detect together provide the precise number of bits to account for black hole entropy. So string theory solutions lead to a surprising conclusion: black holes may be surrounded by of a firewall of high energy particles that would obliterate any object that encountered them.
The price of saving quantum mechanics - keeping the entanglement between B and C - is the loss of entanglement between A and B. The Hawking photons A and B began just inside and outside the event horizon when they arose as an ephemeral particle-antiparticle pair, and in quantum theory, the cost of breaking this entanglement, like the costs of breaking a chemical bond, is energy. [4]
The Polchinsky conclusion [5]
Breaking the entanglement for all the Hawking pairs implies that the horizon is a wall of high-energy particles termed a firewall. This represents a large departure from general relativity – a wall of energy in a place where nothing unusual should be happening. Rather than the subtle effects of complementarity, there is a drastic breakdown of general relativity and the laws of physics at the boundary of black holes. If these strange firewalls do exist, information may not be destroyed, but perhaps some rewriting of quantum mechanics may be required. And if this firewall does exist, what is it? Does space and time end at the event horizon? And what do firewalls imply for real life black holes, like the one in the centre of the Milky Way?
More about the rapprochement between general relativity and quantum entanglement
Hawking had proposed that general relativity works for black holes but that quantum mechanics breaks down, whereas Juan Maldacena concludes that quantum mechanics is unmodified, but that spacetime is holographic.
Maldacena provides another area where they may possibly be seen to work together [6]. As we have just seen, the laws of quantum physics allow for distant objects to be entangled so that their actions on one affect the other, even though they lack a physical link. At the same time, the equations of general relativity, which describe the geometry of spacetime, allow for wormhole shortcuts between distant regions of space time. The equations of general relativity suggest that wormholes can connect two black holes, even those located vast distances apart, to create a bridge in spacetime. From the outside the two black holes would appear to be separate entities, but they would share an interior connecting them. However, no person or signal could travel through.
Might these two phenomena be different versions of the same thing and a clue for developing a quantum description of spacetime? Asks Maldacena [7]: if two black holes were to become entangled, all the microscopic elements inside the first black hole would be correlated with those in the second, and if so, the black holes would form a spacetime in which a wormhole joined their interiors. So entanglement and wormholes might actually be equivalent.
Because black holes look like ordinary quantum systems from the outside, nothing prevents us from considering an entangled pair of them. “Imagine a pair of very distant black holes”, suggests Maldacena. “Each has a large number of possible microscopic states. Now imagine an entangled pair of black holes in which each quantum state in the first black hole is correlated with the corresponding quantum state of the second. In particular, if we measure a certain state for the first hole, the other hole must be in exactly the same state”.
“The interesting thing is that, based on certain considerations inspired by string theory [8] (one approach toward a theory of quantum gravity) we can argue that a pair of black holes with their microstates entangled in this way (an EPR entangled state) would produce a spacetime in which a wormhole (an ER bridge) links the interior of both black holes. In other words, quantum entanglement creates a geometric connection between the two black holes. This result is surprising because entanglement, we thought, involves correlations with a physical connection. But the two distant black holes in this case are physically connected through their interior and brought close via the wormhole”. [9]
Another stunning conclusion: entanglement is the basis of spacetime
In this way, entanglement may be viewed as a thread connecting the two systems. When the amount of entanglement becomes larger, we have lots of threads and these threads could weave together to form the fabric of spacetime. “In this picture, Einstein’s relativity equations are governing the connections and reconnections of these threads; quantum mechanics is not just an add-on to gravity – it is the essence of the construction of spacetime”. [10]
Maldacena concludes with the comment that at present all this is just wild speculation, but at the end of the tunnel there may perhaps be lurking a long-awaited unification of general relativity and quantum mechanics.
Same result, different perspective: entanglement and the holographic principle leads to the shaping of spacetime
And in this fast developing field, that is not all. In fact this is where we came in with the “it from qubit” project looking at the same issues from an entirely different perspective with scientists from quantum computing working with scientists from the disciplines of general relativity and string theory: the idea that spacetime itself may actually be composed and knitted together by the quantum entanglement of tiny discrete units of information whose units interact with each other, thereby giving rise to spacetime properties such as the curvature that causes gravity.[11]
Once again, this notion, if successfully pursued may also help achieve the long-sought quantum theory of gravity, which would in turn merge general relativity and quantum mechanics. The planks of this project are essentially the same, embodying as they do the concept of entanglement and the holographic principle. “Perhaps what we think of as gravity and spacetime is just another way of looking at the end product of entanglement – in mother words entanglement might somehow encode the information from the 3-D bulk into bits stored on the 2-D boundary”.
The aim at the end of all this is a quantum theory of gravity, but even if that does not come about, there are still likely to be beneficial offshoots, says Moskowitz “Bringing the techniques and ideas of string theory and general relativity to bear on questions of quantum information can, for instance help to better define the different types of entanglement, both for understanding spacetime and for construction quantum computers”. [12]
[1] For what appears hereafter, see Joseph Polchinsky, “Burning rings of fire”’, Scientific American, April 2015, 23-27. See also Sabine Hossenfelder, "Head Trip - Einstein's thought experiments left a long and somewhat mixed legacy of their own", Scientific American, Special Issue - 100 years of General Relativity, September 2015, 37 at 38-39.
[2] Ibid.
[3] Clara Moskowitz, "Tangled up in Spacetime", Scientific American, January 2017, 26 at 29.
[4] It should be noted that Einstein never accepted the principles of quantum entanglement which he described derisively as "spooky action at a distance". However, experiments conducted since the 1970s confirm that it is real but that it cannot be used to transmit action faster than the speed of light: Sabine Hossenfelder, op cit, 38. See also Juan Maldacena, “Black holes, wormholes and the secrets of quantum spacetime”, Scientific American, November 2016, 20 at 26: “correlations caused by quantum entanglement cannot be used to send messages faster than the speed of light”. On the reality and non-spookiness of entanglement, see also http://www.abc.net.au/news/2015-10-22/einstein-was-wrong3a-spooky-entanglement-is-real/6876262
[5] Joseph Polchinsky, Burning rings of fire”’, Scientific American, April 2015, 23-27.
[6] In "Black holes, wormholes and the secrets of quantum spacetime", Scientific American, November 2016, 20-25.
[7] Ibid.
[8] Noted above as referred to in the Polchinsky article.
[9] EPR refers to the 1935 Einstein, Rosen and Podolsky paper whose authors argued that quantum mechanics allows for the existence of certain strange correlations between distant physical objects which would later be referred to as entanglement. ER refers to another 1935 paper written by Einstein and Rosen describing the shared interior of two black holes via a bridge called a wormhole. Leonard Susskind and Maldacena's 2013 discovery that if two black holes became entangled, they would create a wormhole, a shortcut in time predicted bt general relativity, has therefore been christened ER=EPR: Clara Moskowitz, "Tangled up in Spacetime", Scientific American, January 2017, 26 at 29.
[10] Maldacena, op cit at [6].
[11] Clara Moskowitz, “Tangled up in Spacetime”, Scientific American, January 2017, 28-31 at 28.
[12] Ibid.
[2] Ibid.
[3] Clara Moskowitz, "Tangled up in Spacetime", Scientific American, January 2017, 26 at 29.
[4] It should be noted that Einstein never accepted the principles of quantum entanglement which he described derisively as "spooky action at a distance". However, experiments conducted since the 1970s confirm that it is real but that it cannot be used to transmit action faster than the speed of light: Sabine Hossenfelder, op cit, 38. See also Juan Maldacena, “Black holes, wormholes and the secrets of quantum spacetime”, Scientific American, November 2016, 20 at 26: “correlations caused by quantum entanglement cannot be used to send messages faster than the speed of light”. On the reality and non-spookiness of entanglement, see also http://www.abc.net.au/news/2015-10-22/einstein-was-wrong3a-spooky-entanglement-is-real/6876262
[5] Joseph Polchinsky, Burning rings of fire”’, Scientific American, April 2015, 23-27.
[6] In "Black holes, wormholes and the secrets of quantum spacetime", Scientific American, November 2016, 20-25.
[7] Ibid.
[8] Noted above as referred to in the Polchinsky article.
[9] EPR refers to the 1935 Einstein, Rosen and Podolsky paper whose authors argued that quantum mechanics allows for the existence of certain strange correlations between distant physical objects which would later be referred to as entanglement. ER refers to another 1935 paper written by Einstein and Rosen describing the shared interior of two black holes via a bridge called a wormhole. Leonard Susskind and Maldacena's 2013 discovery that if two black holes became entangled, they would create a wormhole, a shortcut in time predicted bt general relativity, has therefore been christened ER=EPR: Clara Moskowitz, "Tangled up in Spacetime", Scientific American, January 2017, 26 at 29.
[10] Maldacena, op cit at [6].
[11] Clara Moskowitz, “Tangled up in Spacetime”, Scientific American, January 2017, 28-31 at 28.
[12] Ibid.
Putting Einstein to the test: these scenarios now capable of being tested by the EHT and LIGO [1]
And so it is that a variety of explanations have been tendered to come to terms with Hawking’s 1974 hypothesis that black holes evaporate (which incidentally Steven Giddings describes as perhaps his greatest discovery) and its corollary that everything that falls into them is ultimately destroyed including the information contained in the matter that fell in. This so-called classical explanation actually contradicts the laws of quantum mechanics and energy conservation which state that information cannot be destroyed.
Then we have the “soft fair”’ hypothesis which says that information does not fully enter the black hole, but instead leaves an “imprint”” just outside the event horizon. Most experts do not regard this as convincing. Then there is the “fuzzball” explanation which postulates a kind of massive remnant stemming from string theory in which the black hole is replaced by strings and higher dimension geometry. All these latter scenarios require modification of the conventional notion of “locality” – the idea that nothing, including information, can travel faster than the speed of light.
And then we have Polchinsky’s firewall idea of a massive remnant in which a “wall” of high-energy particles replaces the horizon, there being no black hole interior. And latterly the hypothesis that a quantum black hole interacts with its surroundings, possibly through small fluctuations in spacetime, allowing information to transfer out. Giddings postulates two versions of this scenario. “In one, the geometry of spacetime near a black hole is altered, making it bend and ripple in a way that depends on the information in the black hole—but gently, so that it does not, for example, destroy an astronaut falling through the region where the horizon would ordinarily be found. In this “strong, nonviolent” scenario, such shimmering of spacetime can transfer the information out”.
But he also discovered that there is “a subtler, intrinsically quantum way for information to escape the black hole. In this “weak, nonviolent” scenario, even tiny quantum fluctuations of the spacetime geometry near the black hole can transfer information to particles emanating from the hole. The fact that the information transfer is still large enough to save quantum mechanics is related to the huge amount of possible information a black hole can contain. In either picture, a black hole effectively has a “quantum halo” surrounding it, where interactions pass information back to its surroundings”.
If this quantum-halo scenario is correct, with its concomitant component of the modification of locality, Giddings postulates that it probably represents an approximate description of a deeper reality. The exciting part is that these theories have come to the surface at the same time as two direct observational windows on black hole behaviour, the EHT and LIGO with the capacity to detect gravitational waves from collisions between apparent black holes. Perhaps they may detect a departure from Einstein’s traditional description of black holes.
“A large part of the theoretical community has now reached the consensus that some changes to the current laws of physics are needed to describe phenomena not just deep inside a black hole but all the way out past the horizon”. Just as with the atom and quantum mechanics, a better understanding of black holes is likely to help guide the next conceptual revolution in physics.
[1] This is a condensation of Steven B Giddings' article, "Escape from a black hole", Scientific American, December 2019, 42-49.
And so it is that a variety of explanations have been tendered to come to terms with Hawking’s 1974 hypothesis that black holes evaporate (which incidentally Steven Giddings describes as perhaps his greatest discovery) and its corollary that everything that falls into them is ultimately destroyed including the information contained in the matter that fell in. This so-called classical explanation actually contradicts the laws of quantum mechanics and energy conservation which state that information cannot be destroyed.
Then we have the “soft fair”’ hypothesis which says that information does not fully enter the black hole, but instead leaves an “imprint”” just outside the event horizon. Most experts do not regard this as convincing. Then there is the “fuzzball” explanation which postulates a kind of massive remnant stemming from string theory in which the black hole is replaced by strings and higher dimension geometry. All these latter scenarios require modification of the conventional notion of “locality” – the idea that nothing, including information, can travel faster than the speed of light.
And then we have Polchinsky’s firewall idea of a massive remnant in which a “wall” of high-energy particles replaces the horizon, there being no black hole interior. And latterly the hypothesis that a quantum black hole interacts with its surroundings, possibly through small fluctuations in spacetime, allowing information to transfer out. Giddings postulates two versions of this scenario. “In one, the geometry of spacetime near a black hole is altered, making it bend and ripple in a way that depends on the information in the black hole—but gently, so that it does not, for example, destroy an astronaut falling through the region where the horizon would ordinarily be found. In this “strong, nonviolent” scenario, such shimmering of spacetime can transfer the information out”.
But he also discovered that there is “a subtler, intrinsically quantum way for information to escape the black hole. In this “weak, nonviolent” scenario, even tiny quantum fluctuations of the spacetime geometry near the black hole can transfer information to particles emanating from the hole. The fact that the information transfer is still large enough to save quantum mechanics is related to the huge amount of possible information a black hole can contain. In either picture, a black hole effectively has a “quantum halo” surrounding it, where interactions pass information back to its surroundings”.
If this quantum-halo scenario is correct, with its concomitant component of the modification of locality, Giddings postulates that it probably represents an approximate description of a deeper reality. The exciting part is that these theories have come to the surface at the same time as two direct observational windows on black hole behaviour, the EHT and LIGO with the capacity to detect gravitational waves from collisions between apparent black holes. Perhaps they may detect a departure from Einstein’s traditional description of black holes.
“A large part of the theoretical community has now reached the consensus that some changes to the current laws of physics are needed to describe phenomena not just deep inside a black hole but all the way out past the horizon”. Just as with the atom and quantum mechanics, a better understanding of black holes is likely to help guide the next conceptual revolution in physics.
[1] This is a condensation of Steven B Giddings' article, "Escape from a black hole", Scientific American, December 2019, 42-49.