Physics

A New Look At The Information Paradox

Abstract

This article builds on previous work on the information paradox, but is independent of any of them. The central idea concerning this article is that gravity is not a fundamental force, rather an emergent force. Though this idea is not new in modern physics, the reasoning followed in this paper is unique. The logical reasoning followed in this article leads to the conclusion that gravity might be the result of the universe trying to destroy information.

Basic concepts: the story so far

To start with, what is the significance of the information paradox? Well, this paradox arises out of the ‘combination’ of general relativity and quantum mechanics – the two pillars of modern physics. Further research on the information paradox might reveal the link between these two theories and might lead to a theory of everything – a single theoretical framework that can explain all possible interactions in this universe. The information paradox is a fundamental paradox in physics. For all one knows, further research on the information paradox might alter the course of physics as well. Before we discuss the information paradox, let us discuss some relevant background topics.

Einstein’s theory of gravity

Einstein demonstrated in his general theory of relativity, how gravity can be explained by the curvature of the spacetime continuum (which consists of three space dimensions and an additional time dimension). Spacetime is curved, and the consequence is gravity. General Relativity treats gravity, not as a force, but as the consequence of the movement of bodies in curved spacetime. For instance, the sun “sinks” the spacetime continuum, due to which planets like Earth follow a circular path. The sun is not exactly pulling the earth.

Figure 1: Gravity is a consequence of the curvature of spacetime. The spacetime continuum gets curved near a massive body.

Light follows a bent path due to gravity (also due to atmospheric refraction) and the apparent positions of stars appear higher than their actual position. The apparent position is given by the tangent to the curve nearest to the observer. (Refer to figure 2. Light from the star bends around the gravitational field of another body (the Sun, in this case) and reaches the observer on earth, to whom it appears, on tracing the light backwards in a straight line, that the star is at a different position. Einstein’s predictions regarding this were experimentally verified during a 1919 solar eclipse.)

Figure 2: Light bends near a massive body due to gravity. Although a body of huge mass is required to actually bend light.

Let a body be accelerating upwards with a person in it. If a light is switched on outside it, and the light beam propagates in a straight line, from the accelerating body, the light would seem to be following a bent path (a parabolic curve, to be more precise) to the person inside. As the body accelerates upwards, with time, the light that was near the top of the body seems to have reached the bottom of the body. Gravity also causes acceleration. Thus, light must also follow a curved path under the influence of gravity (that is, in a gravitational field).

Black holes

No discussion on general relativity is complete without some mention of black holes. We saw above that light bends when it comes very close to a strong gravitational field, or in other words, a deep spacetime curvature. What if this curvature is infinite? What if the strength of the gravitational field is infinite? The answer is simply. If light comes too near to such a place, even light – unstoppable light which flies through the vacuum at an alarming and constant speed of about 300000 km per second – can’t escape a black hole. The escape velocity of a black holes is greater than the speed of light.

Time slows down due to gravity, and stops in a black hole.

How does a black hole form? Stars are born in nebulae (massive clouds of hydrogen gas gradually collapsing (to some extent) under gravity). When the nebula turns stable, it is a star, which fuses protons of hydrogen to form helium. But as hydrogen has heavier protons than helium, the excess mass is converted to energy by and this we see as light (and heat). The stars can nucleosynthesize or form heavier elements by fusing subatomic particles and giving out energy. But when stars almost end their nuclear fuel, they collapse further under the effect of gravity. If the star has enough mass, it will finally turn into a black hole, when its gravity would be so strong that its escape velocity will be greater than the speed of light. Thus, light is forced to move around it and can’t escape the event horizon and reach our eyes. This is when black holes are formed.

What is curious about black holes is that the world beyond their event horizons is completely unknown to us. In fact, if you were to fall through the event horizon of a black hole, you wouldn’t immediately feel anything and fall through. (Though of course, your legs (i.e., if you don’t fall headlong) will be exposed to greater gravitational force than your head, since there, the strength of gravity increases downward. This means your legs will be stretched and gradually, your body will turn into spaghetti.) However, since time slows down (to an external observer) as you approach a black hole, an external observer would see you slowing down as you approach the event horizon and at the event horizon, you will seem to be frozen in time (to the observer). This means, you would seem to take an infinite amount of time to fall through. (Though all of this is of course hypothetical.)

There are many different types of black holes. They can form as a result of stellar evolution (from a collapsing star whose remaining mass is a few times the mass of our Sun). Some are supermassive – found at the center of most galaxies, including our own Milky Way galaxy (Sagittarius A*). However, the formation of supermassive black holes is still largely unknown. On 22 November, 2014, a tidal disruption flare (X-ray burst) was observed from the center of a distant galaxy. It is theorized that a supermassive black hole captured a passing star, which caused the flare. On gulping up such stars, black holes may also gain angular velocity and spin. In fact, most black holes are spinning. The faster ablack hole spins, the more likely nearby objects may travel to the event horizon, without running the risk of being pulled in. Thus, the smallest radius of ISCO (see later) corresponds to the maximum spin.

The Event Horizon telescope (a network of a number of telescopes spread across the Earth) succeeded in capturing a photograph of a black hole in April 2019. The picture appears blurry due to the sheer distance of the black hole. Although black holes do not allow light to escape and thus, cannot be directly detected (since light cannot reach our eyes from the black hole), one may get some indication of the presence of a black hole by incidents like flares, etc. in that region.

Figure 3: The picture of the black hole obtained by the Event Horizon.

Spacetime is warped near a black hole, giving rise to interesting effects. Light, sufficiently away from the event horizon, may safely orbit the black hole and even escape from that region. But due to the intense spacetime curvature there, one can actually see the black hole from all the angles, at once, since light would bend around and then escape. Also, a huge ring of dust and particles swirl around the black hole, at a safe enough distance from the event horizon that it doesn’t get sucked in immediately. This is called the Innermost Stable Circular Orbit (ISCO). Light can orbit the black hole at an even nearer distance to the event horizon, and thus a photon ring exists between the event horizon and the ISCO. Also, due to Doppler (relativistic) beaming , one side of the black hole might appear brighter than the other. If we see a black hole edge-on to the ISCO, light from the back of the ISCO bends over the black hole and travels to us, allowing us to see the back of the ISCO. This happens both upward and downward the black hole, and it might resemble the picture below.

Figure 4: The black hole as depicted in the movie “Interstellar.”

Entropy

The concept of entropy is arguably the most important concept in modern physics. Simply put, the more disorder, the more entropy. As per the second law of thermodynamics, the entropy of a system must always either remain the same or increase. Any machine, for instance, must always waste some energy on its functioning and become less efficient over time. The idea of a perpetual motion machine, thus, is not just an engineering problem – it is prohibited by the laws of physics. Thus, there is a fundamental limitation to the efficiency of anything. For example, take Lindemann’s 10% law. It states that, in a food chain, when we move from one trophic level to the next only 10% of the total energy of the former trophic level can be utilized by the organism at the latter trophic level. No process is possible whose sole result is the transfer of heat from a colder object to a hotter object. For this to occur, some external work must be done on the system. (This is obvious, since everything tends to achieve an equilibrium state. Heat always flows from a hotter object to a colder object.)

Entropy can be defined as being directly related to the number of ways a particular state can be achieved. In our universe, it is clear that entropy increases with time. It seems reasonable to assume that entropy is a measure of disorder but that is not exactly so. For instance, if we have 5 differently colored balls and 2 jars, then the lowest entropy state would be achieved if we keep all 5 balls in 1 jar and thus, no balls in the other. This state is not an equilibrium configuration, obviously, for the concentration of the balls is more on one side. (An equilibrium state cannot be achieved in this case, since that would require each jar to have 2.5 balls in it!) If we decide to keep 2 balls in 1 jar and 3 in the other, by taking into account the 5 different colors, there are many different ways we could achieve this state. Thus, in this case, the entropy of the system is more than in the previous case, when there were only 2 possible ways to achieve our state (that is, either all the balls in the first jar or in the second jar, while keeping the other jar(s) empty).

 

As is obvious, the entropy of the initial configuration (the highly ordered one) is much lower as compared to that of the final configuration.

Since the second case is more toward equilibrium and stability, and as everything in this universe tends to remain stable, entropy increases in our universe. Entropy defies all attempts at manipulation and always increases with time in this universe. (For instance, even if we try to compress some atoms in a smaller space so that the number of possible arrangements (and consequently, entropy) decreases, the energy of the atoms will increase, increasing the number of possible arrangements. Even if we forcibly prevent a system to reach equilibrium, that is, the highest entropy state, we must be aware of the states of the particles to achieve the feat. Here, the information in our brains is equivalent to entropy.)

(Interestingly, life is a state of thermodynamic disequilibrium, or low entropy. To maintain such a state, we need energy. During the hypothetical heat death scenario, our universe reaches a state of maximum entropy or thermodynamic equilibrium.)

The fact that entropy is increasing in our universe is itself a testimony to the fact that we started off in an orderly state, that is, at low entropy. If we go by the Big Bang theory, at the very beginning, when a tiny fluctuation in the vacuum gave rise to the expansion of an infinitely dense point and led to the formation of this universe, the Big Bang state must have been symmetrical. It was just a point. And you can’t exactly define asymmetry for a point. Yet that stage was clearly not in equilibrium with the surroundings (that is, zero energy vacuum). Thus, entropy was low then, for it was a fundamental state. Over time, with its expansion, the universe has advanced more toward equilibrium, and has lost symmetry in the process.

Information

Entropy is equivalent to information. But, to start with, what exactly do we mean by information here?

You can think of information in terms of reduction of uncertainty. If someone is about to send you a message, you are uncertain about what the message would say. But once you read it, the information in the message reduces your uncertainty. The information ( ) in the message is defined as the logarithm, to the base two, of the total number of messages that might possibly have been sent ( ). The logarithm is taken to the base two, since in this model, one gets information by asking questions that can have two answers – true or false. Thus, . If the answer to a question can be either true or false, then the answer can be assumed to contain one bit of information. For answers that cannot be defined using just true and false, we may assume that the information associated with it is just the number of questions one needs to ask (whose answer can be either true or false), to have enough data to make a successful guess as to the answer.

The existence of variation (obviously, with respect to something) is a sufficient condition to conclude that information is present. This is because, a variation invariably points at some difference. This difference is perceptible, is itself evidence enough that there is some information about the different objects there. It is this information that ‘separates’ the objects, in some sense.

The more different the objects you are trying to describe are, the more the amount of information you need to completely describe the objects. For example, suppose A and B are similar in all respects except one. Then, you need to only describe either A or B and mention this one difference. If A and B are different in two aspects, you need more information to describe A and B, and so on. 11111111 and 0000000 contain less information than 01100011111111011100000000101. You can describe 11111111 as “eight ones.” This is not possible for 01100011111111011100000000101. (Interestingly, the human mind is hardwired to feel that chaotic numbers that contain more information are more random. 14556327 seems more random than 10000000. Mathematically, if you are asked to pick a number between 1 and 10, each number has an equal chance of being chosen. However, most people choose 7. And very few choose 5 and 10, since numbers like 5, 10, 15, 20, 25… are intuitively viewed as important numbers, and seem less random than 7. We try to make our choice look random.)

Now consider another aspect of information. Redundancy. “If you can read this message then you are just like everyone else” is just “If u cn rd ths msg u r jst lke vryne lse.” It is sufficient to convey the message, grammatical formalities aside. Thus, English (like most other languages) is a redundant language.

The black hole information paradox

Information is responsible for the existence of the different objects in the universe. For instance, it is the information of the arrangement of atoms/molecules that differentiates a wooden plank from an iron rod, or water. More fundamentally, it is the difference in the arrangement of electrons and number of protons in an atom that defines whether the atom is a hydrogen atom or a carbon atom (etc.).

Recall that particle-antiparticle pairs can pop up in vacuum. However, they must soon annihilate each other. Now consider that a particle A and its antipartner B emerges in such a manner that A falls inside a black hole, while B remains outside the black hole. Now, before the particles have a chance to annihilate each other, A is sucked by the black hole. But then, who annihilates B? Who accounts for the energy of B? Doesn’t that violate the law of conservation of energy? Stephen Hawking concluded that the black hole contributes part of its own energy. The black hole emits radiation – the Hawking radiation. After a very long amount of time, the black hole evaporates away completely.

Now, information. Information differentiates things. On the other hand, black holes suck in things and crush them into the singularity. Or in other words, the difference between a pen and a pencil, as they fall into a black hole is lost in the sense that, inside a black hole, we have no means to differentiate a pen and a pencil. You can also understand it this way: there is no time in a black hole. Time has dilated infinitely there. You must, however, perceive variations according to time. This is a highly important concept. For instance, if I put before your eyes a picture showing a red ball and a blue one; although the balls are not changing with respect to time, you must perceive that they are different with respect to time. First, your eyes send the data to your brain, which then compares it with your sense of color and tells you that one ball is red, and the other blue. No matter how fast all these take place, it needs some time. But inside a black hole, time does not even exist. Theoretically. Thus, as far as we are concerned, there is no way to retrieve information from a black hole. If you fall through a black hole, your existence is simply deleted. This means that the information associated with you is lost. (In fact, in popular scenarios regarding the end of our universe, over time, when every star in our universe will either become a black hole, or be sucked into one (and all planets will be destroyed). So if the information associated with objects that fall into black holes is indeed lost, all the information associated with this universe may be deleted entirely.) But what exactly is paradoxical about all these?

Information can’t be destroyed. This is a fundamental law. The quantum information associated with a particle can’t be destroyed. Every object in the universe is composed of particles with unique quantum properties. And no matter how much we try to destroy these objects, the quantum information related to them can never be entirely deleted. In theory, it even is possible to recreate the object.

But deep down in a black hole, there exists nothing but a singularity. Or perhaps, rather than using that fancy term, it would be better to say that we don’t know what is down there. But we should know. The information must be present somewhere. Oh well, maybe we can’t perceive this information. But it exists inside the black hole alright. But once we learn that even black holes are not permanent, the possibility of the information resting peacefully in there gets ruled out, too.

Thus, the information paradox [1].

Possible solutions

Perhaps black holes pass on the information to baby universes, which stores the information. Some have suggested that the paradox is a result of our misunderstanding of how general relativity and quantum field theory interact. Or maybe, the information is contained in the Hawking radiation in such a manner that we cannot perceive it.

But all these are mere possibilities. These do not offer anything as definite as the holographic principle [2]. Holographic duality demonstrates how holography could explain and link two very different kinds of theories in physics. It has significantly improved our understanding of modern physics, and may even take us a long way toward a theory of everything. AdS/CFT correspondence is one prominent realisation of holographic duality, where AdS refers to Anti de Sitter spaces, while CFT refers to Conformal Field Theory. All this is technical, but the concept is really simple. Imagine a sphere. CFT is related to the boundary, while the AdS space sits inside the sphere. Everything in the AdS space has a counterpart in the CFT boundary. The AdS/CFT correspondence is often described as a holographic duality because this relationship between the two theories is similar to the relationship between a three dimensional object and its image as a hologram. Although a hologram is two dimensional, it encodes information about all three dimensions of the object it represents.

The three dimensional black hole, thus, perhaps has a two dimensional counterpart. A three dimensional universe contains black holes and strings governed solely by gravity, whereas the two-dimensional boundary of this three dimensional universe contains ordinary particles governed solely by standard quantum field theory. When studied in the framework of the AdS/CFT correspondence, the black hole information paradox can be, to some extent (i.e. under string theory), resolved.

 

Figure 5: A two-dimensional surface “projects” the information contained to give rise to the illusion of a three-dimensional sphere.

In the above picture, a two dimensional surface ‘projects’ the information it contains to give rise to the illusion of a three dimensional sphere.

The most desperate assumptions would be either to assume that information is irretrievably lost, or maybe there is some fundamental flaw in our understanding of the universe, and we need to rebuild physics from scratch.

Recent researches suggest that black holes can emit information [3]. Information is not lost as black holes radiate. This is because the entanglement entropy of the radiation does not go on rising infinitely as was previously believed, but rises and then falls. Recent calculations have shown that a quantum extremal surface appears inside a black hole’s event horizon, and everything inside this surface no longer remains a part of the black hole. How this happens exactly is still shrouded in mystery.

Finally, it is always important to realize that we can always go back and speculate on accepted theories. For instance, though we cannot make sense of it yet, maybe information is destroyed. However, we should resort to such desperate explanations and assumptions only when we have exhausted all other possibilities.

Entropic gravity: a radical revision

It is widely believed that a unified field theory, dubbed “the theory of everything,” might resolve paradoxes like the information paradox. The idea is to reconcile gravity with the other three fundamental forces of nature, so that in a single framework, it becomes possible to predict all possible interactions that can take place. But, although the electromagnetic, strong nuclear and weak nuclear forces have been unified in quantum field theory; gravity, which is described by general relativity, has always avoided a reconciliation [4]. Gravity is intimately connected with the curvature of spacetime. It is considerably difficult, if not impossible, to combine gravity with quantum field theory.

The attempts to unify gravity with other forces at a microscopic level may not be the right approach as it leads to many contradictions and paradoxes. Gravity might not be a fundamental force in the first place. Thus, when we try to unify it with quantum field theory, paradoxes arise. Quantum field theory describes forces as taking place due to exchange of particles called bosons. Just like the discovery of atoms and molecules unified ice, liquid water and water vapor into a single compound: ; quantum field theory unifies these three forces. However, gravity is a different story altogether. It is described by the geometry of spacetime, and not by the exchange of any particle. Although some people have theorized the existence of the so-called graviton (or the boson responsible for the gravitational force), no experimental data confirms this, and for all we know, might never do so.

Erik Verlinde argued that gravity can be explained as an emergent entropic force[5]. He proposed to interpret the force in Newton’s second law and gravity as entropic forces. An entropic force in a system is a force that results from the entire system’s thermodynamic tendency to increase its entropy, rather than from a particular underlying microscopic force. The idea is that gravity is not a fundamental interaction, but emerges from the universe trying to maximize disorder.

Modern cosmology states that the expansion of the universe is accelerating and therefore the universe has its entropy being increased every moment [6]. With more expansion, disorder, information contained, and the number of ways a particular arrangement can be achieved increase. And so, entropy is increasing too, at a tremendous rate. During this expansion, some particles may come closer and will have gravitational attraction between them, thus establishing stable behavior. Galaxies are formed in those regions where the regional density is high. Entropy may not increase at that particular portion of space, but it is at the expense of increase in entropy in its surroundings so that the net entropy still increases. Moreover, as the universe is expanding, the effective gravity between galaxies is decreasing, because of the increase in distances among matter.

Gravity tries to keep things together through attraction and thus tends to lower statistical entropy. The entropy of an isolated system which is not in equilibrium will tend to increase with time, approaching a maximum value at equilibrium. At equilibrium, entropy change is zero. If we assume the universe to be an isolated system, once it attains equilibrium, or maximum entropy, the gravity has to vanish from it altogether because if it does not, the entropy will start moving from high to low and time’s arrow will reverse. Another possibility is that the net effect of entropy due to gravity and the net effect of entropy because of expansion of the universe have to cancel each other at equilibrium, which is unlikely since the net effect of gravitational entropy is negligible as compared to the latter one. The idea is that entropy and gravity are essentially two sides of the same coin. At the Big Bang, entropy was minimum and gravity maximum. Today, the universe is expanding to maximum entropy, while gravity is slowly decreasing to zero. At the peak, perhaps, the universe might begin to contract and gravity would again take over. However, most probably, this change is unidirectional. [6]

As always in science, there are some problems with this argument. Appealing as it seems, there are still some obstacles that must be overcome before this can be established. Of course, it is easy to see why gravity and entropy are, in some sense, the opposite of each other. With increasing distances, gravity decreases. However, more the distance increases, more is the increase in entropy.

Information conservation in a multiverse system

It is a known idea in physics that the information of the universe may be conserved. Building upon this premise, physicist Scott M. Hitchcock proposes certain ideas on black holes and information. In his article titled “Is There a ‘Conservation of Information Law’ for the Universe?”, he explains:

Black holes might be ‘logic gates’ recomputing the ‘lost information’ from incoming ‘signals’ from outside their event horizons into outgoing ‘signals’ representing evaporative or radiative decay ‘products’ of the reconfiguration process of the black hole quantum logic ‘gate’. Apparent local imbalances in the information flow can be corrected by including the effects of the coupling of the vacuum ‘reservoir’ of information as part of the total information involved in any evolutionary process. In this way perhaps the ‘vacuum’ computes the future of the observable universe.

Let us begin with the assumption that there may exist a Conservation of Total Information ‘law’ for the entire universe. This means that the total information content in the current epoch is the same as that in the early universe regardless of the limitations on what we observe as the ‘visible’ forms it takes. The motivation for this is based in the idea of conservation of total mass-energy for the universe regardless of the forms matter takes during the reconfiguration processes of matter within the framework of an expanding vacuum filled with growing quantum networks. If all current visible structures floating on the sea of the vacuum constitute a very small percent of the total ‘information’ in the entire universe and the ‘expansion’ of ‘space’ combined with local gravitationally driven aggregation of mass into ‘information’ sources and sinks (such as stars and planets for instance) provide a means for ‘computing’ new configurations of matter (biological systems for instance), then perhaps the remainder of the ’invisible information’ is in the vacuum ‘reservoir’. All unstable ‘visible’ physical systems such as atoms and molecules represent the building blocks for complex hierarchical systems. If one were to take this view then the apparent information ‘loss’ by ‘trapping’ in black holes could be recast as the ‘computation’ of new forms of information (Hawking radiation) by the black hole ‘logic gate’ in a quantum computer space (vacuum). The signals emanating from the black hole carry information content about the logical operations performed on the incoming mass ‘signals’ contributing to the process of black hole formation. The black hole recomputed its unstable state (coupled to the vacuum) into a more stable one in which outgoing signals are ‘emitted’. [7]

These ideas assume that the black hole can reconstruct the information of the objects that fall into it. While this may be true, we may also assume that the black hole serves the purpose of ‘leaking out’ the extra information in the universe to some parallel universe, and maintain an overall constant information density. Although recent researches suggest that black holes may emit information [3], it would be interesting to explore the implications of this idea. In any case, this always remains a possibility, and may hold in some parallel universe.

It may be best to assume that information, as a whole, is conserved in the multiverse system. That is, not just in our universe. As we already know, entropy is equivalent to the information. The total information contained in a system as a whole, must be constant.

At a fundamental level, we must assume that information is contained in variations. The more fundamentally different two phenomena are, the greater variation between them, and thus, we would need a greater amount of information to describe the difference between them. Variation and the concept of information, thus, are more fundamental than entropy. We may assume entropy is a natural consequence of varying information densities throughout the system.

Let us assume that our universe, along with other similar systems, ultimately exists as part of a greater and more fundamental system. To exist as a part of this fundamental system, the universe must maintain a minimum ‘fundamentality.’ If the information in the universe continues to increase and at an increasing rate, then a time must come when the information in the universe must exceed the overall constant information of the system as a whole. Even when the information of the universe is equal to the information of the entire system (note that the latter is constant), the resultant information of all the other parts of the system, except the universe, must be zero. This is highly improbable. A minimum amount of information must be present in the other parts even to be distinguishable as parts of the system.

From the above arguments, it is clear that the information of the universe, considering it as one among other universes (in a greater system, say a multiverse), cannot increase infinitely. There must be a limit. However, in many models of the cosmos, the universe does expand infinitely. The only option to resolve this contradiction is to assume that the universe must have some means of reducing the information and passing out some information to a different system. And that must be gravity. (Gravity creates stable and predictable behavior regionally, and in some sense, reduces information. It takes less information to describe a planet moving around a star in a perfectly elliptical orbit than to describe some random particles moving farther and farther away from each other.) It is important to realize that this argument is fundamentally a better one than defining gravity in terms of entropy. (This argument might also, fundamentally, explain why the universe’s acceleration sped up just after the Big Bang. At that point, entropy had just begun to increase, and gravity would not be so dominant. Although gravity is supposed to decrease with increasing distances, fundamentally there was no urgent need for gravity to keep a check on information then, since the universe just began to expand.)

Now, we may proceed with this argument in two ways. The first is to assume that over time, the universe will have enough information to exist independently of the fundamental system. This basically means that the universe could continue to expand and gobble up every other system, till it becomes bigger than the fundamental system of which it was a part. That is when it can be called an independent system. However, the fundamental system we are considering must be part of another greater system… And so on. Importantly, though the universe might cease to exist one day, like all other phenomena, something must always exist. Because if we assume that everything will cease to exist at the same time, even then it would mean that information would be irretrievably lost. Thus, in some sense, something always remains, and information can be transferred to these systems from the ones that cease to exist. In this way, the overall information remains constant.

You must also realize that the information required to describe a fundamental system (like the one we assumed our universe to be a part of) is much less than that required to describe a less fundamental system; because in the latter case, there are many ways to achieve that state. We must also realize that it is not always true that a bigger system will have a greater amount of information. Although this cannot be explained using our current understanding of physics, it might be the case that in some parallel universe, information (and entropy) can decrease over time. It may be that concepts of negative information and negative entropy exist beyond our universe. If we assume our universe to be a part of a fundamental system, though the latter is bigger in size than our universe (since it contains our universe), it can still contain less information than our universe. When you are calculating the total information, you must take into account both the positive information and the negative information. For all we know, there may be equal amounts of positive and negative information in the fundamental system, which may contain zero information.)

We can also assume our universe to have information conserved. As the universe expands, and information increases; due to gravitational interaction, black holes are formed and black holes might serve the purpose of ‘leaking’ the excess information outside, that is, to another subsystem (where information is lower) of a fundamental system like the one we have been contemplating above.

In this manner, perhaps, the fundamental system maintains an overall uniform information density. This is essential, since for the entire system to be fundamental, the number of ways that state can be achieved should be minimum. And indeed, there is only one possible state where the system has a perfectly uniform information density. For instance, if the condition was that 50% of the system has a given information density, and the other 50% another given density, then it could be that the left half has the former value of information density. Or maybe, the right half. It can also be the case that 50% of the region near the center has the former value, while the information density of the outer part might be the other given value. On the other hand, there is only one such state where the information density is uniform throughout. Since overall, the information density is perfectly uniform, that can only represent one state, which is achieved by constant manipulations and fluctuations in all the subsystems. It is important to realize that for the information density to be uniform, all the universes in the system must have the same information density, and all the universes must have black holes and other means of keeping a check on the information. But then, these black holes can’t pass on the information to some other universe in this system. Or it may be the case that the black holes of all the universes are transferring information to one another. It may also be the case that each universe maintains a constant information density, and this information density is the same for all the universes, so that the system has an overall uniform information density. However, to maintain a constant information density, the universe can’t transfer the information to one another. They could transfer it out of the system; but if this is a fundamental system, what remains outside it? Finally, we may also assume that the overall information density of this system is not uniform, but these fluctuations are a way to achieve that state. So we are stuck in the middle of the process. (Maybe the universes pass on this information to the empty space which is present between the universes in the system, to increase the information density of this space to achieve an overall uniform information density. It should be noted that this empty space can technically contain information, like the information about the quantum fluctuations which can occur in vacuum etc. It, however, is likely that the information density of this empty space is much lesser than those of the universes. So information flows from regions of higher density to a region of lower density, through black holes.) It should also be noted that these difficulties can be avoided if we assume that the information of the system is zero by introducing the concept of negative information. Although we can’t make sense of that yet.

Conclusion

Essentially, what has been argued in this article is that gravity is not a fundamental force, but rather an emergent and entropic force. More specifically, and in terms of information, one could say that gravity is the consequence of the universe’s attempt to destroy information. This is necessary to conserve the overall information of an entire system of many universes, of which our universe might be a part. The overall entropy increases in this universe, and so does the information, since it is equivalent to entropy. However, black holes might serve the purpose of “leaking away” the information of objects that fall through it to another subsystem of the entire system. This way, there is a check on the increase of the information.

It is clear that with increasing distances, and thus increasing entropy, a system approaches an equilibrium state. However, this state is, of course, not the most ordered state and thus, lacks symmetry. Bring in gravity, and everything collapses to a symmetric point.

Finally, it can be said that (very roughly speaking) gravity and symmetry form one side of a coin; whereas entropy and equilibrium form the other side. Essentially, they are the different sides of the same coin. And what holds this coin together? Information, that is, information as in the context of modern physics. Manipulate these two sides of the coin, and out emerges gravity, black holes, and the information paradox.

References

[1] Jon Cartwright. “Information paradox simplified”. 2011. https://physicsworld.com/a/information-paradox-simplified/

[2] Jacob D. Bekenstein. “Information in the Holographic Universe”. 2007. https://www.scientificamerican.com/article/information-in-the-holographic-univ/

[3] George Musser. “The Most Famous Paradox in Physics Nears Its End”. 2020. https://www.quantamagazine.org/the-black-hole-information-paradox-comes-to-an-end-20201029/

[4] T. Padmanabhan. “Combining general relativity and quantum theory: points of conflict and contact”. 2001. https://cds.cern.ch/record/522187/files/0110046.pdf

[5] Johannes Koelman. “It From Bit – Entropic Gravity For Pedestrians”. 2010. https://www.science20.com/hammock_physicist/it_bit_entropic_gravity_pedestrians-66244

[6] Muhammad Hamza Waseem. “On the Relation of Entropy with Gravity”. 2016. https://ysjournal.com/on-the-relation-of-entropy-with-gravity/

[7] Scott Matheson Hitchcock. “Is There a ‘Conservation of Information Law’ for the Universe?”. 2001. https://arxiv.org/abs/gr-qc/0108010

Figure references

Figure 1: Storyblocks. “Animated Visualization of the Effect of Gravity on Space Time Version 2.”Accessed November 12 2020. https://www.storyblocks.com/video/stock/animated-visualization-of-the-effect-of-gravity-on-space-time-version-2-r7d4n0z9eizpfuuuk

Figure 2: Andy Bohn. “Gravitational Lensing.” Accessed November 12 2020. http://andybohn.com/images/science/LightDeflection.jpg

Figure 3: NASA. “Black Hole Image Makes History; NASA Telescopes Coordinated Observations.” Accessed November 12 2020. https://www.indiewire.com/wp-content/uploads/2019/04/shutterstock_10196787a.jpg

Figure 4: Wired. “Wrinkles in spacetime: the warped astrophysics of Interstellar.” Accessed November 12 2020. https://www.wired.com/wp-content/uploads/2014/10/ut_interstellarOpener_f.png

Figure 5: Vox. “Some physicists believe we’re living in a giant hologram — and it’s not that far-fetched.” Accessed November 12 2020. https://cdn.vox-cdn.com/thumbor/uB241sgBJdoC-0ThViBxai10qP4=/0x0:800×600/1200×800/filters:focal(336×236:464×364)/cdn.vox-cdn.com/uploads/chorus_image/image/59620595/csm_holography_cyan_eaea795162.0.0.0.0.jpg

About the Author

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Arpan Dey, aged 15 years, is a student of Delhi Public School, Burdwan, West Bengal, India. He is interested in physical sciences and mathematics. He wishes to pursue quantum mechanics and nonlinear dynamics in the future. He is also an aviation enthusiast. He has always believed that research should not be confined to degree-holders, and is enthusiastic in involving children in research.

2 thoughts on “A New Look At The Information Paradox

  1. Hi Arpan:
    You may want to look at gravity as a surface tension effect of the vacuum sea of energy. For more, look at these:
    https://archive.org/details/myths-of-physics-collection_20210610/page/n11/mode/2up
    https://archive.org/details/feynman-clocksthe-vacuumandand-gravity-waves
    https://archive.org/details/trivac1
    https://archive.org/details/the-missing-dark-massand-energyofthe-universeisinthe-vacuum/page/n5/mode/2up
    My proposed total information law you sited has been expanded into a metainformation paradigm See the following:
    https://archive.org/details/metainformation/mode/2up
    Good luck in your pursuits.
    Cheers,
    SMH

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