Quantum Arrow of Time Solution

[dmtr]

There have been a proposed solution to the Quantum vs Thermodynamic arrow of time problem published in the Phys. Rev. Letters. If my understanding is correct, the idea is very simple - time flows symmetrically in both directions, but observers only can remember the forward flow.

http://link.aps.org/doi/10.1103/PhysRevLett.103.080401
http://arxiv.org/abs/0802.0438

Abstract. The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

It sounds reasonable, but wouldn't it break unitarity (at least in a subjective observer view)? It also seems to me that it would bias the wave function collapse - an elementary outcome which leave a "larger trail of information behind" would be more likely to be observed.

 

[Com3t]

Umm. Two things:
1) If time flows symmetrically, then why would an observer only remember the "forward" flow? Shouldn't it be possible for an observer to live in the symmetric flow and remember only the "backward" flow?
2) Entropy increases in a CLOSED system. If you draw a box around the Earth, entropy could decrease as long as the Sun keeps giving us energy, since the Earth is not a closed system. [Of course, the Sun's increased entropy can be shown to overcome Earth's decreased entropy, and the Sun will run out of fuel eventually...]

The two comments I made above are illustrative rather than presented in rigor, but I think you can see what I am pointing out.

 

[Dmitry67]

1. The arrow of time has cosmological explanation: low entropy at the Big Bang. So, 'past' always pointing to the Big Bang. So correct, laws of physics are invariant for time inversion, but initial conditions are not.

2. But... this is not quite true... laws of physics are ALMOST invariant for time inversion. Our Universe has CP voilation. Based on CPT theorem, there is direct T-assymetry, 'quantum arrow of time', which exists independently from the thermodynamics and information. T-assymentry is a big mystery, at least for me. I don't understand why it is not discussed here.

 

[Com3t]

The tread in the philosophy forum describes theories of why consciousness seems to go in the same direction as other arrows of time: https://www.physicsforums.com/showthread.php?t=124119

The T-asymmetry that we observe in the Universe is not explained, any more than why E=cmc is explained--it is a description that fits our observations.

 

[sokrates]

" physics cannot study those processes where entropy has decreased, even if they were commonplace"

It didn't make sense to me. We *could* observe processes that decrease entropy if second law wasn't there at all.

What would prevent us from measuring the temperatures of a hot body getting hotter and cold body getting colder?
Plus, there are reasonable resolutions to the arrow of time paradox in statistical mechanics. The entropy increases because it's more likely to happen.

The proposed tautology sounds absurd to me, but this being published in PRL and all...

 

[Dmitry67]

The T-asymmetry that we observe in the Universe is not explained, any more than why E=cmc is explained--it is a description that fits our observations.

We don't observe T-symmetry violation. The effect is tiny and it is detectable on very high energies. However, it exists.

We observe 'macroscopic' arrow of time (2nd law). 2nd law is well explained. I don't understand why you say "it is not explained"

 

[Dmitry67]

What would prevent us from measuring the temperatures of a hot body getting hotter and cold body getting colder (just imagining a situation that violates second law) ?

I believe the point was, if we enter some magic 'bubble', where 2nd law is inversed, then we can't remember what happened inside. If we witness inversed 2nd law we can't have any memories about the event, because our memory requires 2nd law to store information.

Of course, we could see a violation if we observed it from the outside.

 

[sokrates]

Why would our memory need 2nd law to store information?

Our memories could have evolved in a very different manner. And are we expected to believe that this is all about our memories?

Edit: there are dynamical memory schemes where thermodynamics plays no role at all... For instance, our memories could have consisted of tiny ferromagnetic bits that store binary information - which would correspond to a time-reversible switch.

 

[Dmitry67]

Why would our memory need 2nd law to store information?

Our memories could have evolved in a very different manner. And are we expected to believe that this is all about our memories?

Edit: there are dynamical memory schemes where thermodynamics plays no role at all... For instance, our memories could have consisted of tiny ferromagnetic bits that store binary information - which would correspond to a time-reversible switch.

http://en.wikipedia.org/wiki/Arrow_of_time#The_psychological.2Fperceptual_arrow_of_time

The psychological arrow of time is thought[who?] to be reducible to the thermodynamic arrow: it has deep connections with Maxwell's demon and the physics of information; In fact, it is easy to understand its link to the Second Law of Thermodynamics if we view memory as correlation between brain cells (or computer bits) and the outer world. Since the Second Law of Thermodynamics is equivalent to the growth with time of such correlations, then it states that memory will be created as we move towards the future (rather than towards the past).

I added bold to answer your question. It is not enough to use t-reversible cells.

 

[sokrates]

I don't consider this a rigorous definition, it's somebody's opinion.

My point is : a fundamental physical law cannot depend on how WE perceive time.
Our memories could have been very different.

The explanation should start from a hot body getting hotter and cold body getting colder - and THEN conclude that this cannot be true because if it were, then we wouldn't remember it.

But if your brain consisted of single spins to store information - you would be able to go back and forth in time without erasing information.

Edit: computer bits are not reversible. Why isn't it enough to use t-reversible cells? The WHOLE argument collapses if an alien with time reversible (thus zero-entropy) memory existed somewhere in the universe.

 

[Dmitry67]

So:
1. We see the entropy increasing.
2. If for some magic reason entropy was decreasing, we can't remember such event.
3. Big Bang, as a state with low entropy, is always in the past.

 

[Dmitry67]

I don't consider this a rigorous definition, it's somebody's opinion.

My point is : a fundamental physical law cannot depend on how WE perceive time.
Our memories could have been very different.

No, it is vice versa, WE perceive time based on the initial conditions given by the Big Bang.
Our 'future' always points to the state with higher entropy
For the nature it is irrelevant in what direction we assign positive sign for t

 

[sokrates]

So:
2. If for some magic reason entropy was decreasing, we can't remember such event.

WHY? (Please read my previous post)

Information can be stored in many different ways - and you don't necessarily INCREASE entropy JUST TO STORE information.

You need to ERASE information to increase entropy.

But are we resorting to entropy to understand entropy?

 

[sokrates]

No, it is vice versa, WE perceive time based on the initial conditions given by the Big Bang.
Our 'future' always points to the state with higher entropy
For the nature it is irrelevant in what direction we assign positive sign for t

So second law is violated all the time, but we don't remember it? (Because for nature it is irrelvant and time-symmetric?)

 

[Dmitry67]

So second law is violated all the time, but we don't remember it? (Because for nature it is irrelvant and time-symmetric?)

I don't say that it is actually violated.
It is just a reminder to be careful. If we don't see anything, then it does not exist or we can't have any tracks about it.

Remember a joke:

One day a mathematician, a statistician, and a philosopher were out having a walk in the countryside when they saw a brown cow in a field.
The statistician said, "See that cow. From that we can conclude that all cows in this country are brown."
"Oh no," the mathematician replied, "we can only conclude that at least one cow in this country is brown."
But the philosopher shook his head. "Both of you are wrong. The only thing that we can conclude is that the side of this particular cow which is facing us appears to be brown at this moment in time."

So it is about the last part...

 

[sokrates]

Well, the premise of the paper is quite strong, but I am not convinced at all. I'll study the paper later and try to understand it, better.

Currently, it seems like I don't get it fully.

 

[Dmitry67]

Information can be stored in many different ways - and you don't necessarily INCREASE entropy JUST TO STORE information.

No
http://en.wikipedia.org/wiki/Landauer's_principle

any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information bearing degrees of freedom of the information processing apparatus or its environment

But you are partly right:

there is no thermodynamic objection to a logically reversible operation potentially being achieved in a physically reversible way in the system. It is only logically irreversible operations — for example, the erasing of a bit to a known state, or the merging of two computation paths — which must be accompanied by a corresponding entropy increase. When information is physical, all processing of its representations, i.e. generation, encoding, transmission, decoding and interpretation, are natural processes where entropy increases by consumption of free energy

So yes, one can imagine SOME logical systems which do not increase entropy, but our thinking use irreversible operations too.

 

[Fredrik]

Information can be stored in many different ways - and you don't necessarily INCREASE entropy JUST TO STORE information.

This claim has been brought up a few times, and I don't doubt that it's accurate. I wouldn't be surprised if there are physical systems for which this holds true, but I would be very surprised if it turned out to be true for biological memories. A brain is hardly optimized to story memories without an associated increase of entropy.

But are we resorting to entropy to understand entropy?

Is that what's going on here? I thought the idea was to explain the apparent increase of entropy in a universe where the laws of nature are time-reversal invariant (or at least CPT invariant) without resorting to the assumption that the universe was in a state of extremely low entropy in the past. (I don't get this article either. I've only had a quick look at it).

 

[sokrates]

Information can be stored in many different ways - and you don't necessarily INCREASE entropy JUST TO STORE information.

No
http://en.wikipedia.org/wiki/Landauer's_principle

Well, I am very familiar with Landauer's principle, and if you read it right you'll see that nowhere in his argument does he propose that STORING information results in an entropy increase.

You can refer to Feynman Lectures on Computation, Charles Bennett and many others to see this.

ERASING is different than STORING and this is the crowning achievement of Landauer - this is what's surprising.

From the wiki article you posted:

"any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information bearing degrees of freedom of the information processing apparatus or its environment".

Logically irreversible manipulation of information: reversible logic doesn't count!..
http://en.wikipedia.org/wiki/Reversible_computing

 

[sokrates]

This claim has been brought up a few times, and I don't doubt that it's accurate. I wouldn't be surprised if there are physical systems for which this holds true, but I would be very surprised if it turned out to be true for biological memories. A brain is hardly optimized to story memories without an associated increase of entropy.

There are a few physical examples that, I think, Bennett first came up with. Feynman's Lectures on Computation has an excellent discussion on this.

The idea is this to do the switching very slowly -- think about charging a capacitor through a resistor where the input voltage is increased so slowly that there's never a voltage drop across the resistor and hence no dissipation. This doesn't increase entropy either - it's a perfectly time-reversible process, no information is lost, no energy is dissipated.

Similar examples have been given for magnetic bits, - the key is to do it SLOW.Edit: Fredrik, I agree that it's probably not true for the brain, but it seems to me that the argument given in the paper, then, becomes disturbingly anthropo-centric... But as I said, I need to check further.

 

[sokrates]

Is that what's going on here? I thought the idea was to explain the apparent increase of entropy in a universe where the laws of nature are time-reversal invariant (or at least CPT invariant) without resorting to the assumption that the universe was in a state of extremely low entropy in the past. (I don't get this article either. I've only had a quick look at it).

Oh, I was thinking that while trying to explain entropy (= time reversibility dilemma), the author was reducing the argument to the entropy related information storage in our brains.

 

[Dmitry67]

sokrates, our brain can not JUST STORE information. Because brain don't record RAW information. For example, if our eyes provide (on the low level) 10megapixels each 25frames per second then we get 10M*2*25*3=150Mbytes per second! But we remember only few bytes like 'someone was sitting on the chair' etc.

This is what our brain does: it makes IRREVERSIBLE information compression. The same is true for ANY photocamera: just by taking the image (with finite megapixel resolution) you are already doing IRREVERSIBLE operations.

Except few ARTIFICIAL examples, ALL realistic devices (inculding our brains) are significantly IRREVERSIBLE.

 

[sokrates]

So the fundamental resolution of the arrow of time works well except for a few artificial examples?

Do you expect me to believe in a FUNDAMENTAL theory that works for human brains, normal computer bits and pixels of a camera, but NOT for reversible computers?

If you check the reversible computing article I posted from Wikipedia, you'll observe that it's about performing FULL computations, not just to store information. If you inferred it from my posts, sorry I was misleading you. What I really meant was that one CAN process-store-manipulate-divert logic bits without dissipating ANY energy and not increasing entropy. True, these are highly theoretical examples but hey, you are linking QM - Second Law and Human Brains in this article, so I don't worry about my artificial examples. At least they are on solid ground.We are talking about fundamental laws here, this is not an engineering problem, or whether those schemes are practically implementable or not.

As I said, I don't fully understand the paper. But if you do, and if it comes to the point that the theory depends on the fact that HUMAN brain is irreversible - then that theory isn't worth anything. Because a fundamental law is very unlikely to be critically related to human consciousness.

But I have a feeling that there's more to it, so I'd like to read more.I think we should both step back a little and read the paper again. A PRL paper cannot possibly be handling human brain, irreversibility, second law and QM at the same time. Max Tegmark does that, but he's very special so he doesn't count.

Good night.

 

[dmtr]

So the fundamental resolution of the arrow of time works well except for a few artificial examples?

Do you expect me to believe in a FUNDAMENTAL theory that works for human brains, normal computer bits and pixels of a camera, but NOT for reversible computers?

It doesn't matter if the observer is a regular observer or a reversible computer ('superobserver' in the article), either one wouldn't be able to observe (and keep memory) of a process where coarse-grained (or fine grained) entropy is decreasing. Fundamentally this decrease of entropy requires the erasure of the observer memories.

The Born rule is the only place
where quantum mechanics allows irreversibility, but the
correlations that stem from such rule can be undone, at
least if one treats both the observer and the apparatus
quantum mechanically. This means that the measure-
ment can be undone, at the price that all the observer’s
memories must be erased.
What we have seen up to now is that any decrease in
entropy of a system that is correlated with an observer
entails a memory erasure of said observer, in the absence
of reservoirs (or is a zero-entropy process for a super-
observer that keeps track of all the correlations). That
might seem to imply that an observer should be able to
see entropy-decreasing processes when considering sys-
tems that are uncorrelated from her. In fact, at micro-
scopic level, statistical fluctuations do decrease occasion-
ally the entropy. However, the correlations between any
two macroscopic systems build up continuously, and at
amazing rates [22]: this is how decoherence arises [8].
Then no observer is really factorized with respect to any
macroscopic system she observes. This implies that en-
tropy decreases of a macroscopic system becomes unob-
servable (unless extreme care is taken to shield the system
under analysis). Only microscopic systems can be con-
sidered factorized from an observer for a period of time
long enough to see entropy decrease from fluctuations.

Conclusions. In this paper I gave a quantum solu-
tion to the Loschmidt paradox, showing that all physical
transformations where entropy is decreased cannot re-
linquish any memory of their having happened from the
point of view of any observer: both normal observers that
interact with the studied systems and external super-
observers that keep track of all the correlations. Thus
they are irrelevant to physics.

 

[Dmitry67]

I see your point.

I agree, to some extent it is possible. BUT the paper talks about the information ALREADY INSIDE the machine. And how INPUT DEVICES are working?

Lets look at it from the CI perspective (I hate CI, but FAPP we can use it). Input device IS measurement device because it performs a collapse, which is irreversible operation. So even if machine is reversible inside, its input devices are still irreversible.

Of course, the next step is to say that we can create reversible inputs too. Such device will be 100% quantum computer as there should be no collapse elements inside: you can pass any superposition on inputs, and get superposition of outputs. You can play all sorts of nasty games with this device, like putting output into quantum eraser etc.

I can even provide a very simple example of such machine: mirror labyrinth. You pass light ray there... and it reflects many times.

With the reversible inputs such device simply translates the inputs, like glass translates light. If becomes completely decohered with the environment. Like glass or a mirror does not change when reflects light.

 

[dmtr]

Except few ARTIFICIAL examples, ALL realistic devices (inculding our brains) are significantly IRREVERSIBLE.

On the contrary. According to the article all the devices are essentially PASSIVE and REVERSIBLE. Including observers. Including the real ones, like you. It is just that any observers are unable to observe the erasure of their own memory, and thus are unable to observe the decrease of entropy (and reverse time flow). So you don't need to invent reversible quantum computers and simulate consciousness to get you answer, you are as reversible as these computers, and the time flows for you in both directions, but you (and any other observer) fundamentally unable to remember the reverse flow.

 

[sokrates]

Erasing information increases entropy. This is well known and it's the celebrated Landauer's principle.

If I am not wrong the article is "assuming" or somehow justifying the converse argument:
"Decreasing entropy must necessarily erase information and therefore such a phenomenon cannot be tracked."

If he gave a concrete, PHYSICAL example -- as to why and how the information is erased from the "observer's" memory - that would be more striking.

I don't want to be ignorant since this is published and all but I just don't buy it at the moment. It doesn't make sense.

 

[dmtr]

Erasing information increases entropy. This is well known and it's the celebrated Landauer's principle.
If I am not wrong the article is "assuming" or somehow justifying the converse argument:
"Decreasing entropy must necessarily erase information and therefore such a phenomenon cannot be tracked."

Landauer's principle is: "erasing information increases entropy of the environment". And it is in no way is converse with the argument in the article: "a reverse time flow requires the memory erasure of the observer" or "decreasing entropy must necessarily erase observer memory".

 

[sokrates]

Landauer's principle is: "erasing information increases entropy of the environment". And it is in no way is converse with the argument in the article: "a reverse time flow requires the memory erasure of the observer" or "decreasing entropy must necessarily erase observer memory".

First, environment is not very well defined. What is environment in Landauer's principle? Without CONCRETE, physical examples - this will not get clear at all.. I have clear examples on that, which would require another discussion. Physics of information is still a widely researched subject and there are many subtle points.

Back to the point:
Is there a reasonable system that you (or the author) can imagine where decreasing entropy results in the erasure of information from the observer's head?

 

[Dmitry67]

Is there a reasonable system that you (or the author) can imagine where decreasing entropy results in the erasure of information from the observer's head?

No, of course. For me it is some kind of logical excercise.

If Nature in fact was 'secretly' violating 2nd law then we would feel some strange gaps in our memory.

 

[dmtr]

I can even provide a very simple example of such machine: mirror labyrinth. You pass light ray there... and it reflects many times.

With the reversible inputs such device simply translates the inputs, like glass translates light. If becomes completely decohered with the environment. Like glass or a mirror does not change when reflects light.

Note, that potentially, you can make an observer out of such a machine. That observer would be a completely passive, reversible device. And note that it is not really different from a real human observer, which in a sense is too, completely passive, reversible device. Fundamentally, there is no such thing as 'irreversible', 'active' device.

 

[dmtr]

No, of course. For me it is some kind of logical excercise.

If Nature in fact was 'secretly' violating 2nd law then we would feel some strange gaps in our memory.

Yes, of course.
The author was talking about the real human observers. Enjoying the symmetric backward/forward time flow. Completely unable to remember the former.

 

[Dmitry67]

Note, that potentially, you can make an observer out of such a machine. That observer would be a completely passive, reversible device. And note that it is not really different from a real human observer, which in a sense is too, completely passive, reversible device. Fundamentally, there is no such thing as 'irreversible', 'active' device.

Hm... no...

Say, you invented a 'mirror camera'. Mirror camera has a matrix with ideally reflecting cells. At some moment also reflecting covers are quickly closed, trapping light inside. So light is contained within the cells without any decoherence and collapse, to be released later and analyzed.

However, it only appears that that 'mirror camera' is able to store information. Without decoherence, light (or darkness) inside cells is still in superposition. Bob's actions far away from the device can change thru entanglement the properties of the light inside. Can we say that it is actually 'storing' something?

 

[dmtr]

Hm... no...

Say, you invented a 'mirror camera'. Mirror camera has a matrix with ideally reflecting cells. At some moment also reflecting covers are quickly closed, trapping light inside. So light is contained within the cells without any decoherence and collapse, to be released later and analyzed.

However, it only appears that that 'mirror camera' is able to store information. Without decoherence, light (or darkness) inside cells is still in superposition. Bob's actions far away from the device can change thru entanglement the properties of the light inside. Can we say that it is actually 'storing' something?

It doesn't matter that from the outside point of view the photons inside are still in superposition. There would be the inside observer point of view, observer, which 'state of mind' corresponds to the intricate interference patterns in this mirror labyrinth. Note, that these interference patterns correspond to the classical information - bits, not qbits.

 

[Demystifier]

Umm. Two things:
1) If time flows symmetrically, then why would an observer only remember the "forward" flow? Shouldn't it be possible for an observer to live in the symmetric flow and remember only the "backward" flow?

Exactly! This is also the basis of this comment:
http://xxx.lanl.gov/abs/0912.1947