In both the physical and intellectual meanings of the word, their information has been destroyed. However, if we accept conservation of information, then, in principle if not in practice, the trajectories of the smoke and ash particles could be plotted and reversed, and the books recreated. But often we think of a higher-level macroscopic concept of information, one that can indeed come and go: if a book is burned, the information contained in it is lost to us, even if not to the universe.
Examining what conservation of information may mean in various contexts may be a useful tool in elucidating relations between the idea of information in different domains. There is a similarity between the forms of information in this theory, and those put forward earlier by authors such as Marcia Bates and Tom Stonier. The example given by Burgin and Rainer Feistel is of scientific research, whereby structural information essentially regularities in the physical world is extracted and converted into symbolic information, in the form of articles, books, etc.
They argue that, although we do not possess any theory for the formulation of precise information conservation laws applicable to this context, we feel intuitively that the amount of symbolic information produced cannot exceed the amount of structural information in the part of the physical world being studied.
This linkage between the form of physical and social information, in the form of a qualitative approach to a conservation law which essentially limits the production of meaningful information to available physical information, seems attractive, but has been challenged by the introduction of different information-related entities. It seems clear that the answer to the question as to whether information is conserved is still an open one.
But any answer must inevitably begin with the caveat that, first and foremost, it depends what we mean by information. This need not be a sterile argument about the meaning of words, but rather a means of exploring different concepts of information, and — crucially — the ways in which information of different kinds may interact, and provide linkages between the physical, biological and social worlds.
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Share this: Twitter Facebook. Like this: Like Loading Published by dbawden. These are known, for mathematical reasons, as saddle points, and they look like fairly placid geometries. They used the path integral mostly as a vehicle to identify the saddle points.
The next step, after applying the path integral to the black hole and its radiation, was to calculate the entanglement entropy. This quantity is defined as the logarithm of a matrix — an array of numbers. For that, they busted out another mathematical trick. They could instead imagine performing a repeated series of measurements on the black hole and then combining those measurements in a way that retained the knowledge they needed.
One of the authors of the new work, Tom Hartman of Cornell University, compared the replica trick to checking whether a coin is fair. If this happens half the time, the coins are fair. This is analogous to not knowing the full matrix for the black hole, yet still evaluating its entropy.
Tom Hartman right discusses replica wormholes with his co-author Amirhossein Tajdini, who is now at U. Santa Barbara. Trick though it is, it has real physics in it. It takes them literally. This activates some of the latent topologies that the gravitational path integral includes.
The result is a new saddle point containing multiple black holes linked by space-time wormholes. It competes for influence with the regular geometry of a single black hole surrounded by a mist of Hawking radiation.
The wormholes and the single black hole are inversely weighted by, basically, how much entanglement entropy they have. Wormholes have a lot, so they receive a low weighting and are thus unimportant at first.
But their entropy decreases, whereas that of the Hawking radiation keeps climbing. Eventually the wormholes become the dominant of the two, and they take over the dynamics of the black hole. The shift from one geometry to the other is impossible in classical general relativity — it is an inherently quantum process.
The extra geometric configuration and the transition process that accesses it are the two main discoveries of the analysis. In November , two teams of physicists — known as the West Coast and East Coast groups for their geographical affiliations — posted their work showing that this trick allows them to reproduce the Page curve.
In this way, they confirmed that the radiation spirits away the informational content of whatever falls into the black hole. By these calculations, the radiation is rich in information. Somehow, by measuring it, you should be able to learn what fell into the black hole. But how? Theorists in the West Coast group imagined sending the radiation into a quantum computer. After all, a computer simulation is itself a physical system; a quantum simulation, in particular, is not altogether different from what it is simulating.
So the physicists imagined collecting all the radiation, feeding it into a massive quantum computer, and running a full simulation of the black hole. And that led to a remarkable twist in the story. Because the radiation is highly entangled with the black hole it came from, the quantum computer, too, becomes highly entangled with the hole.
Within the simulation, the entanglement translates into a geometric link between the simulated black hole and the original. Put simply, the two are connected by a wormhole. This idea is an example of a proposal by Maldacena and Leonard Susskind of Stanford in that quantum entanglement can be thought of as a wormhole.
The wormhole, in turn, provides a secret tunnel through which information can escape the interior. Juan Maldacena has spent over two decades at the center of efforts to understand information in and around black holes. Theorists have been intensely debating how literally to take all these wormholes. The wormholes are so deeply buried in the equations that their connection to reality seems tenuous, yet they do have tangible consequences. But rather than think of the wormholes as actual portals sitting out there in the universe, Mahajan and others speculate that they are a sign of new, nonlocal physics.
By connecting two distant locations, wormholes allow occurrences at one place to affect a distant place directly, without a particle, force or other influence having to cross the intervening distance — making this an instance of what physicists call nonlocality.
At first glance, this is very surprising. Einstein constructed general relativity with the express purpose of eliminating nonlocality from physics. Gravity does not reach out across space instantly. It has to propagate from one place to another at finite speed, like any other interaction in nature. But over the decades it has dawned on physicists that the symmetries on which relativity is based create a new breed of nonlocal effects.
This past February, Marolf and Henry Maxfield , also at Santa Barbara, studied the nonlocality implied by the new black hole calculations. They found that the symmetries of relativity have even more extensive effects than commonly supposed, which may give space-time the hall-of-mirrors quality seen in the black hole analyses.
The new calculations say much the same thing, but without committing to the duality or to string theory. Wormholes crop up because they are the only language the path integral can use to convey that space is breaking down. Physicists not involved in the work, or even in string theory, say they are impressed, if duly skeptical.
But some feel uneasy about the tottering pile of idealizations used in the analysis, such as the restriction of the universe to less than three spatial dimensions. She has argued that wormholes need to be expressly forbidden if the integral is to give sensible results. Skeptics also worry that the authors have overinterpreted the replica trick. In supposing that replicas can be connected gravitationally, the authors go beyond past invocations of the maneuver. Given the uncertainties of the calculation, some are unconvinced that a solution is available within semiclassical theory.
He has championed models in which stringy effects prevent black holes from forming in the first place. But the upshot is broadly similar: Space-time undergoes a phase transition to a very different structure. Skepticism is warranted if for no other reason than because the recent work is complicated and raw. It will take time for physicists to digest it and either find a fatal flaw in the arguments or become convinced that they work. Indeed, they thought the paradox was their fulcrum for prying out that more detailed theory.
But assuming that the new calculations stand up to scrutiny, do they in fact close the door on the black hole information paradox? The recent work shows exactly how to calculate the Page curve, which in turn reveals that information gets out of the black hole.
So it would seem as though the information paradox has been overcome. The theory of black holes no longer contains a logical contradiction that makes it paradoxical. But in terms of making sense of black holes, this is at most the end of the beginning. This article was reprinted on Wired. Get highlights of the most important news delivered to your email inbox. Quanta Magazine moderates comments to facilitate an informed, substantive, civil conversation. Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected.
Moderators are staffed during regular business hours New York time and can only accept comments written in English. We care about your data, and we'd like to use cookies to give you a smooth browsing experience. Please agree and read more about our privacy policy. Read Later. By George Musser October 29, In a landmark series of calculations, physicists have proved that black holes can shed information, which seems impossible by definition.
The work appears to resolve a paradox that Stephen Hawking first described five decades ago. Ashley Mackenzie for Quanta Magazine. But then a year later you come to that box and all the cords are tangled up in a big hairball.
The initial ordered state has low entropy. You put the cables in on top each other in some order, so supposedly you should know some information about the arrangement of the contents of the box, even if you don't know all the specifics. Now over time, people might poke around in the box looking for one cable or another so stirring around the contents, and pushing things aside and vibrating the contents in various ways. This is disordered unknown environmental information that is being added to the box contents.
Its a random bunch of forces on various cables over time, and you are not making any note of that information. So the entropy of the system hidden information from the external random perturbations is being increased. In the end you have a whole bunch of cables that are knotted together in various ways, instead of being independent and simply organized.
The information encoded in all those knots and tangles came from the random environmental information that was added. This is the increase in entropy. So then not being happy with this situation, you decide to organize them. But in practice what that means is that you have to undo all the knots by perceptually following each cable through the system and becoming cognizant of the information that was added, in order to unthread all the tangles and separate them again.
So this process of sorting that you do is lowering the entropy of the system because you are exhaustively cataloging and rapidly forgetting exactly how the hidden information was encoded in the cable tangles. But also note that this process required energy and time on your part. And the information that was encoded in the cable tangles went into your brain, and then was forgotten, and dissipated as thermal energy.
But the weird thing is that entropy is related to your state of knowledge. So that means you and I can potentially ascribe different entropy to the same system depending on what we know in advance. For example if I receive a million bits of information, I can calculate the frequency of the 1s and 0s and other statistics, and that gives me some information, but then the rest I consider to be hidden and therefore I can put a large entropy number on it.
In the same way if someone had somehow noted how each interaction with the box of cables over time had affected them, then at the end the entropy would be low from the viewpoint of that person even though the cables would still be tangled.
It's just that that person who watched how they got tangled didn't allow the information to become hidden, and in theory doesn't need to actually analyze the cables at the end in order to understand them, they could mechanically untangle them like a robot with zero or low levels of perception. It's the ideal because physical transforms can, at best, discriminate between as many states before the transform as after it; anything more is impossible while anything less looks like an opportunity for improvement.
So, the very best a physical model can ever do is conserve information. For example, if 10 bits of information are known about a physical system and no more information is gained e. By contrast, it's easy to lose information. Worth noting that information is a property of a model and not the universe itself, so different observers can perceive different information leaks.
So, the ideal's perfect information preservation. Whenever we fail to preserve information, we can't be sure that our models are complete. Then, the assertion that information's indestructible is basically the idealistic demand that the laws of physics reach that theoretical optimality.
As an ideal, it's worth noting that it's not necessarily a practical truth. We can construct hypothetical laws of physics that would practically not preserve information; if any of those happen to be the case, then the claim that information's indestructible would continue to be unrealized.
Regardless, systems that appear to lose information are glaring targets for scientists for two big reasons:. Any sort of prediction that can be made based on the " lost " information constitutes a novel discovery.
Most of the current laws of physics purport to conserve information, so they're ready tools to attack the lossful system with. The black hole stuff is an example of the second point. If black holes appear to leak information whereas current theories don't, then that seems like a prime opportunity to attack black hole models with other theories and see what falls out of it. My understanding was always that this was a result of time evolution preserving measure in state space.
Now let's consider the time evolution of the entropy. Another case to look at is quantum mechanics. Notice here that it wasn't sufficient for the dynamics to be reversible. The dynamics really need to preserve volume in state space. ANY current state of matters is an 'effect' that resulted from infinite amount of causes.
And it also is a cause for subsequent effects itself. In short, just like matter, information also transforms, changes into different states through cause and effect mechanics. So, what we call 'chaos' or 'entropy' or any other seemingly incomprehensible and un-trackable state of existence, is also a state which results from infinite numbers of causes leading to effects. That we are not able to track, distinguish, calculate, comprehend, explain such states of existence does not mean that they are outside the cause-effect mechanic and other mechanics that make existence.
So any state in a chaotic, entropic state should be theoretically traceable to earlier states, should actually be coming to being due to cause-effect mechanics that can be observed, calculated if you had the means to, and also should naturally be linked to any earlier state of information - including the state where the entropy, chaos or 'destroyed information' did not come to being yet, and the earlier information we were observing was there as it was.
Conservation of information, if you will. Information is also subject to the cause-effect mechanics that is inviolable anywhere in existence. That some cases seem to 'violate' cause and effect relationships - like some quantum physics experiments - does not mean that they violate the mechanic in regard to general existence itself, leave aside universe.
If you would look at black holes and explanation susskind and others brought, there is no exception - information is protected and conserved and linked in this or that way. Therefore it is indestructible : you should be able to reconstruct any information which led to the CURRENT state of information by analyzing current state of information and deconstructing it. Which includes anything falling into black hole and merging into singularity.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why is information indestructible? Ask Question. Asked 9 years, 5 months ago. Active 2 years, 2 months ago. Viewed 25k times. Is that information that is lost, through the increase of entropy really recoverable?
Improve this question. MarianD 2, 2 2 gold badges 10 10 silver badges 18 18 bronze badges. Is it based on a popularization? The only context the question if information could get destroyed left therefore is therefore in the context of black holes which the OP does not want to hear about. But even in this case, the issue has been solved as can be read for example on [many] site:motls.
Show 4 more comments. Active Oldest Votes. The 'field equations' consist of a set of allowed colorings for each 2x2 block of cells: A total of 27 local color patterns are allowed. Suppose that when looking "North" or "West" along the lattice directions, you hit a horizon beyond which an infinite sea of yellow squares stretches: "North" and "West" we label as 'light rays from the past'.
Given this 'snapshot', and using the field equations the allowed 2x2 colorings , we can start reconstructing the past: Here, the rule applied to color the cell follows from the square at the bottom of the center column in the overview of the 27 allowed 2x2 squares. Continuing like this, we obtain the full past of the universe up to any point we desire: We notice that we constructed the full past knowing the colorings of 'light ray cells' in the 'snapshot' that, excluding the uniform sea beyond the horizons, count no more than 25 cells.
Now we reverse the dynamics, and an interesting thing happens: knowing only 9 color values of light rays to the future again excluding the uniform sea beyond the horizon : We can reconstruct the full future: We refer to these 9 trits that define the full evolution of this cellular automata universe as the 'information content' of the universe. These observations, however, go well beyond the questions asked. Improve this answer. Johannes Johannes Can you make the reconstruction part more specific?
Where are some of the numbers coming from? The 9 trits are clearly the ones that are hidden. And thank you for reviving this thread. It was fun working out this toy model and turning it into an "entropy growing universe". As I noted above, the patterns and rules that he introduces define a cellular automata that creates a pattern known as a Sierpinski carpet.
Here is an image generated from the rules: Sierpinski Carpet. I don't think deterministically generating a image from a set of rules and an inital pattern really sheds much light on the issue. Show 6 more comments. The statement "information is indestructible" is a strange one, I would like to understand what it refers to, My question is how an 'hypothetical information' not recoverable by any mean can be still called information? As I said, I guess he was probably just talking about unitarity.
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