# B Big Crunch, Big Bang and information loss

1. Jul 12, 2017

### BernieM

In compression of information, once any patterns have been 'condensed' as much as is possible, the information appears entirely random. Any further compression produces loss of information and the quantity of information required to encode it is increased.

In one theory it is supposed that all the mass and energy in the universe will eventually collapse back on itself and eventually get so dense that it will again make another big bang. If so the following question comes to mind:

There is information at the time of the big bang, such as the information of the conditions of the event itself (which I would assume would be maximum possible theoretical density for the information at the moment of the big bang but I have no proof of this,) and after the expansion, further information is able to be stored, as the universe expands (essentially decompression of the information.)

As the universe progresses in time, and eventually again reaches that point of a big bang (given that this will happen) you now have all of the information from the initial big bang, and the information from the entire period of time between the two big bangs to contend with if you will again compress it.

Does the relative increase of the information that must now be compressed, now dictate how dense the information can be packed when it creates a second big bang? Since there is now more information, would it prevent a duplicate of the first big bang from happening, the second big bang being lesser in magnitude than the first?

Or do the laws of physics make the second big bang occur at the same densities of the first one? What then of the additional information carried into the second big bang not contained in the first? Is it lost? Or is the second big bang's information, as well as all of the information gained between the initial big bang and the second one, actually contained in the initial big bang?

It is supposedly theoretically possible to determine exactly what will happen (or what did happen,) at any or all points in the universe (or events) if one knows all the particles and their energies and directions, etc., (all the information,) if one had a powerful enough computer to calculate it. So, was every event that occurred subsequent to the initial big bang already contained in the big bang itself? It seems one merely only need extrapolate the data from it after uncompressing it. Isn't that what the universe is doing now in essence? Uncompressing all the data contained in the big bang?

It seems to me that at the moment of the big bang, all the information that will ever occur must be present. This then would also contain all future big bangs (if in fact they will occur) and any information that has been gained in the interim. A third big bang? Fourth? That too would have to be included in the first. So as the number of possible big bangs the universe might undergo increases, the total information contained in the first then also increases as well.

So as one approaches the magic value of energy density, and certainty of a big bang is 100%, at that moment, if there will be future big bangs, all of that information must then also be forced into the already compressed information present, further increasing the total information, information that was not present until certainty of a big bang was achieved. And if collapse into another big bang would result later, even further increasing the information density, etc. It seems it would reach infinite information requiring to be compressed into that same initial energy package. If not why not?

So in short, I guess the question is, is information lost in a big bang, theoretically, or do we fall back on the 'we don't know because it breaks all the laws of physics.' And is all future information contained as well. Is it infinite information or simply an algorithm that yields an infinite sequence, that there is no additional information required to be stored?

2. Jul 12, 2017

### Staff: Mentor

My first thought is that at very high densities the probabilistic nature of quantum theory would "erase" most information anyways. But I can't really say much beyond that.

3. Jul 12, 2017

### BernieM

Wasn't there a big disagreement between Hawking who proposed that information was lost in a black hole, and Susskind regarding this? That Hawking eventually came around to stating that information was not lost after all? And as I recall, Susskind really hated the idea that everything could be known about any event if one had the data. That the future is nothing more than an extension of the events and interactions that occur in the present, and that in essence then, there was no free will. I recall him making that statement how much he disagreed with the predetermination aspect of quantum mechanics in one of his lectures I saw online. Perhaps I can locate it again. Here is a link to the disagreement between them (Hawking and Susskind.)

4. Jul 12, 2017

### windy miller

i dont think anyone can claim the information paradox is fully solved so whether information is lost or not I think an open question.
There are many models implying a pre big bang universe but as far I can see no consensus as to what happens to information from the pre to the post big bang phase.
So at the moment that again is an open question. Of course we dont know there was a pre big bang universe, so even that is an open question.

5. Jul 12, 2017

### rootone

Big crunch is not looking likely,
Eternal expansion looks more likely it me,
No information gets lost but distance can make information meaningless.

6. Jul 13, 2017

### jerromyjon

I'm far from an expert, but from what I know about the quark-gluon plasma era shortly after the big bang is like Drakkith said, quantum fluctuations would make information a probabilistic jumble with no apparent structure. The only inhomogenous indication we have is the CMB "cold spot" which isn't much to go on and might not even be from the early universe "structure" which would be relevant "information". To clarify what if we could sum the contents of the universe in terms of relevant information (simply hypothetical statement) as 51% matter 49% antimatter randomly by volume and everything we can see evolved from that simple information alone?

I think this is why mainstream science sticks to the big bang theory, because it is as far as the observable universe will allow us to see with reasonable certainty...

7. Jul 13, 2017

### kimbyd

Information is definitely effectively lost during inflation. That is, the early universe was sufficiently randomized that almost no feature of the universe before a certain point during inflation has any measurable impact on our observable universe.

There may be a sense in which the information is not actually lost, where it's just randomized so well that it seems to be lost but is actually preserved. If so, that's not likely to have any impact on any observations, making it more of a philosophical question. Ultimately we just don't know whether or not information is lost in this deeper sense. In large part it comes down to one question: are the fundamental laws of physics unitary. The ultimate answer likely has close ties to the black hole information paradox.

8. Jul 14, 2017

### Staff: Mentor

9. Jul 14, 2017

### BernieM

I agree that it is very close to the situation of the information paradox of the black hole.

I don't know if it is a satisfactory analogy, but I visualize it like say a blue starburst firework. The initial blast I equate to the big bang and the starburst being the resultant universe caused by it. Each spark that travels out from the initial blast is there because of information that was in the initial conditions of the big bang that set it all in motion. So isn't the information there after the big bang, regardless of whether we can discern it, measure it or differentiate it from noise later? Dilution of the information does not destroy the information right? If the information was lost in inflation, how could the universe continue to develop without a major disconnect from the big bang? How could you link what you see today to the big bang then? That the big bang then was an entirely dis-related event not connected to the universe around us?

I agree that it is more a philosophical question, but then science itself relies on a variety of 'beliefs.' For example, there is a lot of debate regarding time and whether or not it is an actual property of the universe or if it is something mankind has created for convenience.

On the face of it, it seems that the big bang has caused a universe which went through certain phases and is continuing on in a direction that may or may not end up in a big crunch. And though information may be becoming diluted (or was diluted in inflation,) the actual information is yet there in the current state of the universe, isn't it? If it wasn't how could you ever connect the current state of the universe to the big bang at all?

But if the information is there, then this information will eventually get compressed again if we undergo contraction later (along with all the diluted random garbage ... but isn't that information too? Information about the inflation phase of the universe?) and at some point may in fact become dense enough to spawn another big bang. OK it's all hypothetical, I give you that. But given this scenario, the question becomes whether or not what occurs is simply the unfolding of a sequence of events, (the information regarding which was contained in the big bang,) so that all subsequent information is merely the manifestation of the decompression of the original highly compressed information in that big bang?

Or is the information that is gained after the big bang, actual separate information that was not present in the initial big bang? Do I need to supply all the digits of pi or can I just give you a formula to generate it? If I give you a formula, I do not need to compress all the digits of pi for you in the big crunch later. I just compress the formula. Or perhaps to put it in a more relevant way; do I have to compress the information for all particles in the universe, and all it's energy, or can I get away with simply storing the energy itself, and the laws of physics that will apply in the universe (information) to get the universe to unfold properly and contain all the information I want it to have, for it to manifest in the way it has? If so, then there is no free will right? Wasn't that Leonard Susskind's fundamental disagreement with quantum mechanics?

10. Jul 14, 2017

### Staff: Mentor

Well, for starters, I suppose it depends on what you mean by information. My preferred description is from the wikipedia article on information: At its most fundamental level, information is any propagation of cause and effect within a system.

However, there's an implied idea here that you need to be able to discern previous events by observing some number of successive states of a system. In other words, you need to be able to make observations in the present and be able to discern the past to some degree of accuracy. And that's with the other implied idea that you can't observe all successive states of a system. Only some. So you're working with incomplete knowledge of these missing states. Nor can you observe all of the causes of the events in even a single state, making things even more uncertain.

Assuming the laws of the universe hold in such a way as to allow us to discern the previous states of a system, then no matter what happens you should be able to get some kind of information about the previous states of the universe. However, whether this is achievable in practice is a different story. Noise, which is loosely defined as a random variation in a signal, is extremely important and is essentially one of the root causes of information being "lost". Obviously cause and effect held completely, but we cannot say with any real degree of confidence what the previous state of a system was if the noise heavily swamps the signal we're interested in.

But that's just my mostly uneducated view on this topic. Take it with a grain of salt.
Also, I just took some meds and I'm a bit loopy, so I hope all of that makes sense.

11. Jul 14, 2017

### kimbyd

It's definitely not achievable in practice.

If the laws of physics are unitary, then the universe is described by the many worlds interpretation of quantum mechanics. In the many worlds interpretation, decoherence causes information to be "lost" to the environment in such a way that wavefunctions appear to collapse. It doesn't take much for a system to decohere so much that retrieving the "lost" information becomes ludicrous. In principle it still exists, but it is inaccessible in any meaningful sense.

Similar rules apply for inflation, or black holes.

12. Jul 14, 2017

### Staff: Mentor

What does "unitary" mean in this context?

13. Jul 14, 2017

### kimbyd

Unitary evolution means that if you had the complete wavefunction of the universe for one slice of time, then you could in principle calculate the complete wavefunction of the universe at any other point in time.

Newtonian laws of physics are unitary in this sense, as are the Schroedinger equation and its relativistic variants (e.g. the Dirac equation). Wavefunction collapse is not, and General Relativity is not.

Newtonian laws are unitary because if you know the position and motion of every particle in the universe, as well as all of the forces between the particles, you can calculate their position at any other point in time.

The Schroedinger equation can be proven to be unitary in that time evolution of the system can be represented by a unitary operator ($e^{-Ht/\hbar}$).

Wavefunction collapse isn't unitary because information is lost. General Relativity isn't unitary because of the existence of event horizons, such as the black hole's event horizon, which are one-way.

14. Jul 14, 2017

### Staff: Mentor

It's not the event horizon that breaks unitarity, it's the singularity. An event horizon is just a null surface; unitary evolution works fine across null surfaces. The problem is what happens to a piece of the wave function that hits the singularity: there is no unitary transformation that handles that.

15. Jul 14, 2017

### Staff: Mentor

As so many others have said, it depends on what you mean. Information is not the same as knowledge.

If information is related to the number of possible microstates, then randomization has no effect on it even when useful knowledge is destroyed.

Bus Leonard Susskind says that conservation of information is the same thing as saying that micro physical laws must be time reversible. That and unitarity and causality are all restrictions on time evolutions. That suggests that whatever information is, it is not a static property, but rather something that must be conserved in time evolutions. Susskind calls that the minus first law of physics.

But there seems to be no symmetry associated with that conservation law. No Noether's Theorum. Nor is there an observable for that thing that is conserved. It makes the whole topic slippery.

Susskind is giving lectures called ER=EPR describing the research direction of his institute. They are looking at information to unite QM with GR. If and when they succeed (a long shot for sure), I wager that a new definition of information will be an essential part.

16. Jul 15, 2017

### Haelfix

There is a bit of a debate about this. To see why it's not that simple, consider the case of our pre 1976 understanding of black holes. There you had an event horizon, a singularity and so forth. However there wasn't an information loss problem. When a super observer would analyze the system he could say the information was partially in the black hole, and partially in the rest of the universe, and the two systems would purify each other, regardless of the fate of information near the singularity.

The root of the problem now, is crucially that black hole evaporates. An observer at infinity, now detects a real problem of principle! He either sees a Planckian remnant (a thermodynamically vile object with almost no energy but enormous entropy) or the information is fundamentally transformed into a mixed state and quantum mechanics appears to be violated.

17. Jul 15, 2017

### Staff: Mentor

To put this somewhat more technically, if the black hole is eternal, the super observer can always choose a Cauchy surface for the spacetime that covers both the exterior and the interior of the hole, and evaluate the state on that Cauchy surface, making the overall state pure and the overall evolution unitary. You are correct that, strictly speaking, this does not pose a problem for unitarity.

To rephrase this in line with the above: after the hole evaporates, there are Cauchy surfaces for the spacetime that do not cover the interior of the hole at all, and there is no unitary transformation that takes you from the state on a Cauchy surface before evaporation, to the state on a Cauchy surface after evaporation, unless you allow a Planck-size remnant to continue to exist at $r = 0$ so that it is present on the after-evaporation Cauchy surface and holds all of the states of everything that fell into the hole before it evaporated.

18. Jul 15, 2017

### stefan r

Suppose we take a newspaper and burn it. Stir the ashes. Not all information is lost. We could, for example, do a chemical analysis on the ash and measure the amount of ink. Radioactive isotopes might leave clues to the origin of the tree that was turned into pulp. You could also carbon date the ash if there was any soot left. However, the chemical analysis will not differentiate the word "dog" from the word "god". Knowing the total mass of the ink does not let you calculate the thoughts of the reporters/editors. You can not read stirred ash.

The statement "all information is lost at the event horizon of a black hole (except spin, mass, charge) " is not the same as "some information is lost when a solid object turns into plasma". If all information is lost then you could not distinguish between a newspaper, lead batteries, or an apple.

19. Jul 17, 2017

### BernieM

That is to assume that you did not track it's progress from newspaper to ash. If one had a method of storing all the data of all particles and their positions in a single time frame (all the information), one would be able to track it back say one moment in time forward or backward as everything would be determinate would it not? If we then were to track the big bang from the moment it did what it did to cause this universe and we watched all of the information (energy etc.) we would see it progress to the point the universe is today. Is there any new information being added? Or is it all just a result of the original information and events unfolding as they were destined to unfold at them moment the big bang came into existence? If again, we could take all information from every successive moment in time, of every particle in the universe, there would be no random nature to it. Though the position of an electron in the electron cloud is statistical where you may find it, once you do, don't you then know where it will be the next instant in time after that? It's not hopping around in an entirely random fashion is it? It is traveling in a predictable path is it not? And if it is then from one point on that path to the next point x nanoseconds later should be a predictable location as long as all external forces acting on it are known as well.

I am not saying we would ever have such ability to do so. What I am trying to get at is if there really is any new information being generated in the universe, or if the entire cycle of the universe, including a potential future big crunch or big whimper wasn't already predetermined at the moment the big bang came into existence or 'occured.' Once a sky rocket is made what it will do when it explodes is already written in stone, the only thing left is where it will explode and when, but how many blue and white sparks will fly out from it and how far they will fly, etc., was determined by the information stored in the explosives in it. In a way isn't this similar to the big bang? The result of the big bang and the eventual end of the universe itself could be known (theoretically) if one had ALL the information contained there then?

20. Jul 17, 2017

### Staff: Mentor

You are equating information with knowledge.

Suppose I ask how many bits of information does it take to describe the state of a system. That is the information content. It has nothing to do with whether I have knowledge of what the state is. If I do have knowledge and I destroy that knowledge, it still doesn't change.

Take the spin of an electron for example. Up or down. That takes exactly one bit to describe. It never evolves 0 or 0.5 or 2 bits. It always remains 1 bit. Information is conserved. Knowledge of the spin doesn't change that. The probability of spin up plus the probability of spin down must add up to exactly one, never 0.99, never 1.01.

But it gets complex fast. How many bits does it take to completely describe the quantum state of a heavy atom, with all the electrons, nucleons and quarks? I don't know how to calculate that, but it's a lot.

21. Jul 17, 2017

### kimbyd

That's a bit over-simplified.

An electron can be in any quantum superposition of up and down. If we take our current understanding of quantum mechanics at face value, then it requires a complex number (two real numbers) to describe the quantum state*, which represent an infinite number of bits. And any superposition you might think of can have observable consequences through interference patterns.

The issue comes about when that wavefunction collapses. In this case, the electron becomes a pure state: either up or down, nothing in between. Then, and only then, can it be described wholly with the use of a single bit.

If the wavefunction collapse is real, then information is lost: you've gone from a system described by two real numbers to a system described by a single bit.

If the wavefunction collapse isn't real (as is the case in unitary quantum mechanics), then the appearance of collapse results in an effective loss of information. In principle the information still exists, but it isn't accessible by any realistic experimental apparatus. The unitary evolution of the wavefunction guarantees that those two real numbers aren't lost at all, but still exist in the wavefunction of the universe. But it's become inaccessible in the same way that the letters on the burnt page have made the meaning of the text inaccessible.

* The two quantum numbers, for the curious, are the relative magnitude between the two states and the difference in their quantum phases. The magnitude determines the relative probability of measuring one state or another, e.g. 75% to 25%, or an even 50% chance of measuring either state. The probability has to sum to 100%, so this can be described with a single number. The quantum phase difference is more difficult to understand intuitively, but has an impact in how the quantum state interferes. If you're creative and understand quantum mechanics, you can produce systems where you modify the quantum phase so that the two are out of phase, and then use interference to eliminate one of the states. This will result in a wave that is a pure state of one spin state or the other without any wavefunction collapse.

22. Jul 17, 2017

### jerromyjon

Define "one moment in time"... as far as I know time doesn't have discreet steps!

23. Jul 17, 2017

### Staff: Mentor

Simplified I agree. I did not intend to get into interpretations of QM, some of which feature wave function collapse. Perhaps we could compromise by saying 1 qubit?

But we agreed on the part essential to conservation of information, that the sum of all probabilities is identically 100% (which is an over simplified way to express unitarity).

24. Jul 17, 2017

### kimbyd

I don't think that's accurate. The sum of all probabilities is always 100%, regardless of whether or not your underlying model is unitary.

Unitarity implies something much deeper: that the state at any one time uniquely identifies the state of the system at any other time. A unitary system, in other words, is fully deterministic.

Certainly some aspects of our universe appear to be very much non-deterministic (such as wave function collapse). The question becomes whether this collapse is real, or whether it is just an illusion. Either way, the strong appearance of non-determinism in quantum mechanics remains.

25. Jul 17, 2017

### rootone

Time particles!, hey well you can never know for sure where quantum mechanics is involved,
and that's not a lot weirder than other QM stuff.