man, watch the PBS YouTube channel SpaceTime. They're short, informative, and very well done. they dedicate a handful of episodes to getting you ready for Hawking radiation.
Seconding that recommendation. The clear explanations allowed me to grasp several concepts that I've been trying to understand for decades, for example the "one-electron universe"
"Why Quantum Information is Never Destroyed" re: determinism and T-Symmetry ("time-reversal symmetry") by PBS SpaceTime
https://youtu.be/HF-9Dy6iB_4
Classical information is 'collapsed' quantum information, so that would mean that classical information is never lost either.
There appear to be multiple solutions for Navier-Stokes; i.e. somewhat chaotic.
If white holes are on the other side of black holes, Hawking radiation would not account for the entirety of the collected energy/information. Is our visible universe within a white hole? Is everything that's ever been embedded in the sidewall of a black hole shredder?
Maybe even recordings of dinosaurs walking; or is that lemurs walking in reverse?
Do 1/n, 1/∞, and n/∞ approach a symbolic limit where scalars should not be discarded; with piecewise operators?
> The important thing is that all evolution equations that we know of are time-reversible.
I've heard this before, but it's so surprising to me, when one of the simplest mathematical operations - addition - is not reversible. e.g. if a+b=4, you can't infer the values of a and b (beyond their linear relationship). This non-injectivity is a kind of summarising, with less information, where more than one state maps to one.
So "evolution equations" (reality) are not like addition; state changes never summarise.
It is not reversible because you’re ereasing information. If you want to have a reversible addition you are not allowed to destroy the information.
The same happens if you apply the standard AND operator to two bits because the output is only one bit, therefore it is impossible to figure out the two input bits. To have a reversible AND operator you can define it like this: f(x1, x2, b) = (x1, x2, b XOR (x1 AND x2)). E.g: f(1,1,0) = (1,1,1).
From this output you can get back to the input. This way you can implement a NOT gate as well, and all others gates. At the end you can implement addition using bits and your summation becomes reversible :)
You can see that with this definition we are not ereasing any information, hence it becomes reversible.
Actually addition is reversible, as long as you do it inline. The inverse of `a += b` is `a -= b`.
An example of an action that's not reversible is masking: `a &= b`. But if you dig deep enough into the physics, you find that these kinds of irreversible actions are actually always implemented in a way analogous to the following:
// a &= b
acquire zero'd register z from environment
z ^= a & b
z ^= a
a ^= z
z ^= a
discard z into environment
Which can be reversed if you're able to get the discarded `z` register back.
That quote is not exactly correct, there are plenty of evolution equations which are not time-reversible beginning with the linear heat equation. If you look at the solution given by convolution (usually taught in first PDE course) you see that this equation has infinite speed of propagation. Any parabolic/dissipative equation is not time-reversible (which is analogous to addition not being reversible... dissipation involves an averaging process).
Elsewhere the author says "all fundamental evolution equations in physics are time-reversible." By fundamental I'm assuming she means: Maxwell's equations, Einstein's field equations and the Schrodinger equation.
Your state changes from two numbers to one number, such a transition is of course not going to be bijective unless carefully designed. In physics most states stay the same "shape", making invertibility easier to achieve.
Insofar as addition is an abstract representation of merging two collections, we are abstracting away the information that links each element of the resulting collection to the one it came from.
So for example one typical quantum gate is called for physicists CNOT, or you would call it in computing a generalization of the XOR gate. We physicists would not think “Oh XOR is irreversible because A ⊕ B = B ⊕ A even when A ≠ B, so the same output can come from two different outputs.” That is just not what reversibility means to us.
Contrast this with boolean AND, which we would say is irreversible. What’s the difference? It's that we think of all of our operations as being automorphisms, they map a system back to itself. So when we are looking at CNOT/XOR, we are thinking about a system which looks like this:
(t increasing)-->
A ---.-----
\
\
B ------⊕--
and if you have the output "1, 0" from this system you can infer that the input was "1, 1". In that automorphic sense XOR is reversible, even though given the output on wire B alone you cannot decide what A or B was.
Contrast with boolean AND, where if I give you the output "0, 0" you cannot genuinely determine whether that came from "0, 1" or "0, 0". It could have come from either place.
So the automorphism (x, y) ⇒ (x, x + y) in fact is reversible in this sense; there is an automorphism which undoes it. The weirdness that you are identifying comes from the fact that you were actually considering the automorphism (x, y) ⇒ (0, x + y), which is a composition of the addition gate above with an ERASE gate, (x) ⇒ (0). Ignore the erasure and you get a reversible process again.
You might know that AND, OR, and NOT are universal: you can write any circuit from N bits to 1 bit by enumerating all of the inputs which could set the bit to 1, using AND and NOT to build “masks” for those inputs, and then using a final big OR-gate to see if any of the masks was triggered. By de Morgan's laws, you can build an OR gate out of NOT and AND; and then it is not too hard to see that you can build both NOT and AND from NAND: so we say that “NAND is a universal boolean gate.”
To get a universal reversible system you just need to go to three bits. Two working options are the Toffoli gate “doubly controlled NOT” and the Fredkin gate “controlled swap,”
Toffoli = ([x, y, z]) => [x, y, (x && y)? z : !z]
Fredkin = ([x, y, z]) => [x, x? z : y, x? y : z]
The universality of Toffoli is very easy to see from the universality of NAND: because Toffoli(x, y, 0) is actually just (x, y, x NAND y). However the fact that you start with an “isolated” bit and then it becomes “involved” in the computation, this is where you eventually start to need to erase bits if you do not have unlimited amounts of memory. [Fredkin is a little more difficult to reason about but for example Fredkin(x, 0, y) = (x, x AND y, (NOT x) AND y) and so you can then build both an AND gate directly from this construction and a NOT gate with y=1.]
> Think of mixing dough. You’ll never be able to unmix it in practice. But if only you could arrange precisely enough the position of each single atom, you could very well unmix the dough. The same goes for burning a piece of paper. Irreversible in practice. But in principle, if you only knew precisely enough the details of the smoke and the ashes, you could reverse it.
This is literally what the holographic principle addresses... https://youtu.be/B2ksDczJOAs Leonard Susskind has enough accessible vids and lectures to give a conceptual idea of how it works out.
The other major example of a time-irreversible operation/object is much more mundane: the collapse of a wave function. I've never been able to find a decent layperson's explanation of what the wave function collapse really means, and why physicists seem to have no issue with it being time irreversible but seem quite concerned with black holes
It is a problem. Quantum mechanics, as it's normally taught, basically has two components:
1. Schrödinger's equation, which governs how the wavefunction (or quantum state) evolves in time. This equation is time-reversible: given a state at time t, you can calculate what the state was at time t-T. Technically, that means that the "time evolution operator" is invertible. All the information about the history of how system's state is contained in the present state. No information is ever destroyed.
2. Observation. A quantum state looks like a_1 * psi_1 + a_2 * psi_2 + ... + a_n * psi_n, where psi_i are all the possible states of the system and a_i are complex numbers called "amplitudes." When you observe a state (I'm obviously leaving out some mathematical details here, so anyone with physics knowledge please forgive me), you observe it to be in one of the possible states, psi_i, with i between 1 and n. The probability of observing it to be in state i is proportional to |a_i|^2. This operation destroys information, because the state collapses to psi_i, and all the amplitudes, a_j, j≠i, are lost. You can no longer reconstruct the previous state of the system.
I think most physicists who "seriously" think about quantum mechanics do not believe that step 2 above actually happens. It is a simplification of a much more complicated process called "decoherence." In order to understand decoherence, you have to change your perspective on what observation means. If you treat the observer as a system governed by Schrödinger's equation, which interacts with the system that's being measured, you find that the observer becomes entangled with the system under observation. The observer ends up in a superposition of states, each of which has observed a different outcome. It appears to each state of the observer as if there has been wavefunction collapse, but there actually is a larger quantum system containing both the observer and thing being observed, in which no information has been lost.
The theory of decoherence and the "many-worlds interpretation" began to be developed in the 1950s by one of Wheeler's students, Everett. Somehow, it hasn't really made it into undergraduate physics yet, and most physicists can get by without thinking too deeply about what observation means. You can do most calculations assuming wavefunction collapse happens.
Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a different energy level.
Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover the state at time t1 or even know just when t1 was. That is, the reversible time evolution equation of state at time t2 can't tell us the random time t2 - t1 or t1 so cannot recover the state at time t1 -- at time t2, we just do not know just when or how we got to the state at time t2.
So, the time evolution equation is time reversible but the event of the emission of the photon is not time reversible.
This thought experiment seems to conflict with the OP. Where am I going wrong?
You are collapsing the wave function at t1 and t2. At t1 explicitly by stating that the state is known, and by t2 implicitly by defining that you have a defined distance t2- t1.
The emission of an photon at an explicit time t2 is not reversible, the emission of an photon according to the wave function of the atom leads to an photon entangled with the atom and the total has a reversible wave function. (For illustrative purposes, when you measure and you find the photon at a distance (t- t2)*c from the atom, then you will also find the atom in a state that has emitted a photon at t2, no Idea if that is especially illustrative.)
It is a bit more difficult to see this because you are describing a continuous time process, however, the answer is that yes you would be able to to figure out the time t1 given you knew had a snapshot of the whole system through the time evolution equation.
Perhaps your confusion stems from the fact that the time t2 is observed, and it seems like you can't go back after that. An easier to grasp manifestation of this problem is that if you find Schrodinger's cat dead you can't tell if was always dead or if was dead only after your experiment. The reason is because that's only with the narrow knowledge of that cat being dead (maybe the would call this the cat state subsystem). It might be unsatisfactory to you, but in the theory of quantum mechanics, if you knew the state of everything (say the room, measurement apparatus, and so on), then you would be able to trace back to whether the cat was alive or dead. The moral is that the measurement looks irreversible if you look only at the system you are observing, but overall, people accept that there is a overarching greater space (the "environment, universe" where everything is just a unitary operation in motion according to the time evolution equation [1]). To be clear, the time evolution equation only admits reversible solutions. So with full knowledge, of say, the room and measurement apparatus, it would be possible to deduce the original state of the cat.
The final state wavefunction, which you need to recover the initial state, contains an exponentially decaying distribution of different t2s. The final state wavefunction is not "here's a definite t2"---that requires measurement.
(I am not a physicist.) One thing I've struggled with around black holes is what it means for anything to fall into a black hole.
From a reference frame outside the black hole, observing an object falling into the black hole, don't we observe time slowing down as the object approaches the event horizon? In this reference frame, does it ever cross the event horizon, or does it just asymptotically approach it? If it doesn't cross the event horizon, how can anything ever fall into the black hole?
(From the reference frame of the object falling into the black hole, my understanding was that the event horizon shrinks away from you as you approach it.)
The object has physically fallen through the event horizon and long disintegrated but the imprint of its falling toward the event horizon is slowing down to the outside observer. The falling object emits photons along the way which are what the observer sees. These photons of the falling object shining toward the observer have to travel greater and greater distance in the warped spacetime as the object getting near the event horizon so the photons appear to slow down. The spacetime is being "stretched" (warped) more as getting closer to the blackhole. The event horizon is at the point where the spacetime is "stretched more than" the distance the photons can travel to come out.
(also not a physicist) I think you're correct that objects falling into a black hole never cross the event horizon from our reference frame, but at the same time the light from the object red shifts towards zero energy as it approaches the event horizon as well.
There is a somewhat recent theory that supports this idea. It is unclear whether or not things actually fall-in, but the idea is that the entire surface is a hologram, and the surface alone is sufficient to describe the entire contents. (Thus preventing any information loss).
Simple: the laws of most physics say you can look at something now and work it backwards. Once it falls into a black hole the previous state of what falls into it isn't able to be derived from working backwards because it just fell into a black hole. This isn't rocket science! (Maybe eventually though)
I’ve heard this idea a lot and it always strikes me as one of those things that’s technically true but wildly off base. I get that the equations are mathematically reversible. Presumably we’re more interested in the world than we are the math though, and in real life almost nothing can be worked backwards. There’s a lamp on the dresser for example. How did it get there? Go ahead and run the kinematics in reverse and tell me which of the infinite solutions is the truth.
I do not think the issues raised here are so simple that you can answer the question without mentioning entropy, which, at first sight, might appear to show that information loss is routine.
Perhaps this is why we perceive time to be going in one direction. The fact that a black hole exists in our universe means that there is only that direction.
To save you the read, the summation is in the second-to-last paragraph:
>As you have probably noticed, I didn’t say anything about information. That’s because really the reference to information in “black hole information loss” is entirely unnecessary and just causes confusion. The problem of black hole “information loss” really has nothing to do with just exactly what you mean by information. It’s just a term that loosely speaking says you can’t tell from the final state what was the exact initial state.
[+] [-] chasd00|6 years ago|reply
https://youtu.be/qPKj0YnKANw
[+] [-] dharmab|6 years ago|reply
[+] [-] stallmanite|6 years ago|reply
[+] [-] westurner|6 years ago|reply
Classical information is 'collapsed' quantum information, so that would mean that classical information is never lost either.
There appear to be multiple solutions for Navier-Stokes; i.e. somewhat chaotic.
If white holes are on the other side of black holes, Hawking radiation would not account for the entirety of the collected energy/information. Is our visible universe within a white hole? Is everything that's ever been embedded in the sidewall of a black hole shredder?
Maybe even recordings of dinosaurs walking; or is that lemurs walking in reverse?
Do 1/n, 1/∞, and n/∞ approach a symbolic limit where scalars should not be discarded; with piecewise operators?
[+] [-] hyperpallium|6 years ago|reply
I've heard this before, but it's so surprising to me, when one of the simplest mathematical operations - addition - is not reversible. e.g. if a+b=4, you can't infer the values of a and b (beyond their linear relationship). This non-injectivity is a kind of summarising, with less information, where more than one state maps to one.
So "evolution equations" (reality) are not like addition; state changes never summarise.
[+] [-] myaccount80|6 years ago|reply
The same happens if you apply the standard AND operator to two bits because the output is only one bit, therefore it is impossible to figure out the two input bits. To have a reversible AND operator you can define it like this: f(x1, x2, b) = (x1, x2, b XOR (x1 AND x2)). E.g: f(1,1,0) = (1,1,1). From this output you can get back to the input. This way you can implement a NOT gate as well, and all others gates. At the end you can implement addition using bits and your summation becomes reversible :) You can see that with this definition we are not ereasing any information, hence it becomes reversible.
[+] [-] Strilanc|6 years ago|reply
An example of an action that's not reversible is masking: `a &= b`. But if you dig deep enough into the physics, you find that these kinds of irreversible actions are actually always implemented in a way analogous to the following:
Which can be reversed if you're able to get the discarded `z` register back.[+] [-] dls2016|6 years ago|reply
Elsewhere the author says "all fundamental evolution equations in physics are time-reversible." By fundamental I'm assuming she means: Maxwell's equations, Einstein's field equations and the Schrodinger equation.
[+] [-] kmm|6 years ago|reply
[+] [-] OscarCunningham|6 years ago|reply
[+] [-] mannykannot|6 years ago|reply
Insofar as addition is an abstract representation of merging two collections, we are abstracting away the information that links each element of the resulting collection to the one it came from.
[+] [-] crdrost|6 years ago|reply
So for example one typical quantum gate is called for physicists CNOT, or you would call it in computing a generalization of the XOR gate. We physicists would not think “Oh XOR is irreversible because A ⊕ B = B ⊕ A even when A ≠ B, so the same output can come from two different outputs.” That is just not what reversibility means to us.
Contrast this with boolean AND, which we would say is irreversible. What’s the difference? It's that we think of all of our operations as being automorphisms, they map a system back to itself. So when we are looking at CNOT/XOR, we are thinking about a system which looks like this:
and if you have the output "1, 0" from this system you can infer that the input was "1, 1". In that automorphic sense XOR is reversible, even though given the output on wire B alone you cannot decide what A or B was.Contrast with boolean AND, where if I give you the output "0, 0" you cannot genuinely determine whether that came from "0, 1" or "0, 0". It could have come from either place.
So the automorphism (x, y) ⇒ (x, x + y) in fact is reversible in this sense; there is an automorphism which undoes it. The weirdness that you are identifying comes from the fact that you were actually considering the automorphism (x, y) ⇒ (0, x + y), which is a composition of the addition gate above with an ERASE gate, (x) ⇒ (0). Ignore the erasure and you get a reversible process again.
You might know that AND, OR, and NOT are universal: you can write any circuit from N bits to 1 bit by enumerating all of the inputs which could set the bit to 1, using AND and NOT to build “masks” for those inputs, and then using a final big OR-gate to see if any of the masks was triggered. By de Morgan's laws, you can build an OR gate out of NOT and AND; and then it is not too hard to see that you can build both NOT and AND from NAND: so we say that “NAND is a universal boolean gate.”
To get a universal reversible system you just need to go to three bits. Two working options are the Toffoli gate “doubly controlled NOT” and the Fredkin gate “controlled swap,”
The universality of Toffoli is very easy to see from the universality of NAND: because Toffoli(x, y, 0) is actually just (x, y, x NAND y). However the fact that you start with an “isolated” bit and then it becomes “involved” in the computation, this is where you eventually start to need to erase bits if you do not have unlimited amounts of memory. [Fredkin is a little more difficult to reason about but for example Fredkin(x, 0, y) = (x, x AND y, (NOT x) AND y) and so you can then build both an AND gate directly from this construction and a NOT gate with y=1.][+] [-] improv32|6 years ago|reply
[+] [-] ailideex|6 years ago|reply
Maybe there is some recent development I am not aware of an Susskind is wrong though.
More:
- https://physics.stackexchange.com/questions/450326/why-is-th...
[+] [-] ben_w|6 years ago|reply
[+] [-] stochastimus|6 years ago|reply
[+] [-] soulofmischief|6 years ago|reply
This was a nice description of entropy.
[+] [-] Ultimatt|6 years ago|reply
[+] [-] platz|6 years ago|reply
which explains the paradox and several different competing theories at a high level.
[+] [-] openasocket|6 years ago|reply
[+] [-] DiogenesKynikos|6 years ago|reply
1. Schrödinger's equation, which governs how the wavefunction (or quantum state) evolves in time. This equation is time-reversible: given a state at time t, you can calculate what the state was at time t-T. Technically, that means that the "time evolution operator" is invertible. All the information about the history of how system's state is contained in the present state. No information is ever destroyed.
2. Observation. A quantum state looks like a_1 * psi_1 + a_2 * psi_2 + ... + a_n * psi_n, where psi_i are all the possible states of the system and a_i are complex numbers called "amplitudes." When you observe a state (I'm obviously leaving out some mathematical details here, so anyone with physics knowledge please forgive me), you observe it to be in one of the possible states, psi_i, with i between 1 and n. The probability of observing it to be in state i is proportional to |a_i|^2. This operation destroys information, because the state collapses to psi_i, and all the amplitudes, a_j, j≠i, are lost. You can no longer reconstruct the previous state of the system.
I think most physicists who "seriously" think about quantum mechanics do not believe that step 2 above actually happens. It is a simplification of a much more complicated process called "decoherence." In order to understand decoherence, you have to change your perspective on what observation means. If you treat the observer as a system governed by Schrödinger's equation, which interacts with the system that's being measured, you find that the observer becomes entangled with the system under observation. The observer ends up in a superposition of states, each of which has observed a different outcome. It appears to each state of the observer as if there has been wavefunction collapse, but there actually is a larger quantum system containing both the observer and thing being observed, in which no information has been lost.
The theory of decoherence and the "many-worlds interpretation" began to be developed in the 1950s by one of Wheeler's students, Everett. Somehow, it hasn't really made it into undergraduate physics yet, and most physicists can get by without thinking too deeply about what observation means. You can do most calculations assuming wavefunction collapse happens.
[+] [-] KSS42|6 years ago|reply
See : https://backreaction.blogspot.com/2019/08/the-problem-with-q...
Sabine Hossedfelder also discusses it in her book Lost in Math.
Two books on the subject are reviewed in the Booklab podcast, episode 20:
http://booklabpodcast.com/booklab-020-what-is-real-and-beyon...
Featured Books:What is Real? by Adam Becker; and Beyond Weird by Philip Ball.
Quantum physics has been with us for more than 100 years – but what is it actually telling us about the world?
[+] [-] garmaine|6 years ago|reply
[+] [-] graycat|6 years ago|reply
Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover the state at time t1 or even know just when t1 was. That is, the reversible time evolution equation of state at time t2 can't tell us the random time t2 - t1 or t1 so cannot recover the state at time t1 -- at time t2, we just do not know just when or how we got to the state at time t2.
So, the time evolution equation is time reversible but the event of the emission of the photon is not time reversible.
This thought experiment seems to conflict with the OP. Where am I going wrong?
[+] [-] yk|6 years ago|reply
The emission of an photon at an explicit time t2 is not reversible, the emission of an photon according to the wave function of the atom leads to an photon entangled with the atom and the total has a reversible wave function. (For illustrative purposes, when you measure and you find the photon at a distance (t- t2)*c from the atom, then you will also find the atom in a state that has emitted a photon at t2, no Idea if that is especially illustrative.)
[+] [-] someguy12342|6 years ago|reply
Perhaps your confusion stems from the fact that the time t2 is observed, and it seems like you can't go back after that. An easier to grasp manifestation of this problem is that if you find Schrodinger's cat dead you can't tell if was always dead or if was dead only after your experiment. The reason is because that's only with the narrow knowledge of that cat being dead (maybe the would call this the cat state subsystem). It might be unsatisfactory to you, but in the theory of quantum mechanics, if you knew the state of everything (say the room, measurement apparatus, and so on), then you would be able to trace back to whether the cat was alive or dead. The moral is that the measurement looks irreversible if you look only at the system you are observing, but overall, people accept that there is a overarching greater space (the "environment, universe" where everything is just a unitary operation in motion according to the time evolution equation [1]). To be clear, the time evolution equation only admits reversible solutions. So with full knowledge, of say, the room and measurement apparatus, it would be possible to deduce the original state of the cat.
https://www.quantiki.org/wiki/church-larger-hilbert-space
[+] [-] evanb|6 years ago|reply
[+] [-] maffydub|6 years ago|reply
From a reference frame outside the black hole, observing an object falling into the black hole, don't we observe time slowing down as the object approaches the event horizon? In this reference frame, does it ever cross the event horizon, or does it just asymptotically approach it? If it doesn't cross the event horizon, how can anything ever fall into the black hole?
(From the reference frame of the object falling into the black hole, my understanding was that the event horizon shrinks away from you as you approach it.)
Please correct/inform me!
[+] [-] ww520|6 years ago|reply
[+] [-] jadams5|6 years ago|reply
[+] [-] aeternum|6 years ago|reply
Much better described here:
https://www.youtube.com/watch?v=2DIl3Hfh9tY
[+] [-] misja|6 years ago|reply
[+] [-] GuB-42|6 years ago|reply
[+] [-] platz|6 years ago|reply
[+] [-] mherrmann|6 years ago|reply
[+] [-] acollins1331|6 years ago|reply
[+] [-] danaliv|6 years ago|reply
[+] [-] dchest|6 years ago|reply
That doesn't really explain anything.
[+] [-] mannykannot|6 years ago|reply
[+] [-] ricardo81|6 years ago|reply
[+] [-] maxheadroom|6 years ago|reply
>As you have probably noticed, I didn’t say anything about information. That’s because really the reference to information in “black hole information loss” is entirely unnecessary and just causes confusion. The problem of black hole “information loss” really has nothing to do with just exactly what you mean by information. It’s just a term that loosely speaking says you can’t tell from the final state what was the exact initial state.
[+] [-] JDEW|6 years ago|reply
A summary like this is useful if the underlying article is bloated and clickbait-y but in this case potentially detracts a reader from a good article.
As featured on the front page a few days ago [1]: knowledge without understanding is meaningless.
[1] https://www.theguardian.com/commentisfree/2019/aug/24/dougla...
[+] [-] nice1|6 years ago|reply
[deleted]
[+] [-] vectorEQ|6 years ago|reply
i see no issues there
[+] [-] cellular|6 years ago|reply
[+] [-] ropiwqefjnpoa|6 years ago|reply