Memories can only form in the increasing entropy direction.
Or, to be more precise, higher entropy states can contain memories of lower entropy states, but not vice versa. This remains true regardless of how the memory is represented.
So the arrow of time (and second law) are not facts about the universe, but about observers' ability to represent it.
Even if you wound back time past t=0 and kept the simulation going, you would see the same thing in the reverse direction, such that the negative time direction should now be considered futureward.
IOW, it's not that "time goes forward, entropy goes up, such coincidence". It's "if entropy were not higher, we could not regard it as the future."
 what Barbour calls "time capsules" and Drescher calls "[metaphorical] wakes"
1) observed, macroscopic arrow of time
2) microscopic, fundamental particle physics level arrow of time.
Thermodynamic solution is satisfactory solution only for macroscopic arrow of time.
Time reversal in general is not symmetric. There are particles that are violate CP and T-symmetry called kaons. That's completely different arrow of time.
Each row of the grid represents the state of the universe at a certain "time". Given any two adjacent rows, we can compute the row above them or the row below them according to a predefined rule, which is symmetric in "time". So we randomly generate the two initial rows and then from there derive the rest of the pattern. However, by default the two initial rows are mostly empty, corresponding to a low-entropy initial state. From this initial state, applying the rule either forward or backward in time leads to states of higher and higher entropy. So the system exhibits "arrows of time" flowing from the low-entropy initial state forward and backwards in time to the high-entropy equilibrium states.
Indeed it is:
I wonder if the FloWave people ever considered Popper's argument and tried to eject an object from the bottom.
Reminded me of a side remark from another context:
The past only exists in our memory, therefore in some sense we can't recall incorrectly.
For sure we can all agree that this encoding is irreversible - i.e. we can't reconstruct the past state from the present.
And due to the combination of chaos in macroscopic systems and quantum uncertainty, I think it's highly likely that we can conceive of two slightly different past states that give present states indistinguishable even to $deity_of_unlimited_power.
So how is it "faithful"?
A good question! I mean that future states are produced by past states according to physical laws.
> For sure we can all agree that this encoding is irreversible - i.e. we can't reconstruct the past state from the present.
Not with full accuracy, no. But past states are constrained by present states in useful and interesting ways.
Yes, that is exactly what I'm saying.
> but we can't calculate those functions ourselves with full accuracy.
Yes, that is also true. The universe as a whole is not constrained by the limits of what we humans can compute.
Sorry to be a stickler for detail, but earlier you defined "faithful" to mean the future is a function of the present, and now you're saying that "the past and future are functions of the present" is exactly what you are saying. Perhaps you mean that it's exactly what you intended to say?
I'm not intending to undermine anything with "gotchas." It just seems to me that more precision will help your arguments.
One thing I do not see, in your essay, is how reducing "memory" to "entanglement" means time is asymmetric. What is it about entanglement that is asymmetric that isn't just "that's how entanglement is defined"?
I also do not understand how the thought experiment implies time travel cannot happen. Has anyone proved that the wave equation has no solutions when there are closed timelike curves? (I assume not since there are papers studying quantum computations possible in the presence of closed timelike curves, for instance.)
> What is it about entanglement that is asymmetric that isn't just "that's how entanglement is defined"?
Entanglement is symmetric. You can reverse an entanglement. But only by returning the entangled particles to the same physical location.
The reason that this symmetric quantum process gives rise to (what appears to us to be) a time-asymmetric classical universe is that what we classical entities actually are is massively entangled systems of vast numbers of quantum particles (or, to be as precise as I can, we are quantum systems with a vast number of mutually entangled degrees of freedom). All those entanglements can be reversed, but if you reverse them, the result is not "moving backwards in time" as humans commonly conceptualize it. The result is rewinding the whole universe to a previous state. That is actually possible in principle. As I note at the end of the essay, there is no way to distinguish a universe that is constantly being rewound and replayed from the universe we live in. But what most people think of as going backwards in time is rewinding the whole universe with the exception of themselves to a previous state. That's not possible.
I don't actually know what the consequences are of applying this idea to CTCs. I don't understand CTCs well enough to do it myself. There's probably a thesis or two in there somewhere. Mixing QM and GR is a rare skill.
Isn't the loss of information, i.e. the breaking of quantum determinism, at the centre of the black hole information paradox ? It's a paradox because quantum determinism and reversibility imply information can never be destroyed.
Yes, but entropy can make it asymetrical - in practice past usually have less legal states (a lower entropy point) than the future.
Past and future can be completely encoded by the direction of entropy change, if we start from, or end in one legal state.
(You can exactly tell the past of the Logo turtle (or something similar physical thing) by following its trajectory line. You can have an inverse turtle that follows and erase an existing line, then you can tell its future, but not its past by looking only its present state)
This kind of entropy increase is very common in human life - like forming memories, filling empty screens and white papers with signs, leaving footsteps in the snow etc... So the subjective feeling of asymetry is not completely ungrounded.
> > The past state of the universe is encoded in the present state only in the same way, and to the same extent, that the future is.
> Only in a classical universe, not a quantum one.
In in Norton's dome, the indeterminacy extends equally into the past and the future: you can't tell when the ball will leave the dome, and you can't tell when it arrived.
At every moment that the ball is moving, there is indeed an external force due to gravity.
Edit: interesting paper on quantum information theory and measurement vs entanglement!
I was impressed by the article, and it made a lot of sense to me -- but I've also found that, given sufficiently persuasive writing, I'm easily persuaded that something incorrect is correct in QM, and the only way to get the 'right' answer is to do actually the math. This is why I was curious about your background: if I could reasonably surmise that you had 'done the math' so I didn't have to! (:
(Note that I realise this is not how science is meant to work, but is a quite useful filter in practice)
Just because you can't know them doesn't mean they aren't physical. God can know the initial conditions. In a classical world, that's good enough.
> and you can't transpose non-linearities
So? Classical mechanics is linear.
> can you tell where it started moving if its current velocity is constant?
Yes, of course. Just as easily -- and by the exact same method -- as you can tell where it will stop moving.
> What if that particle hits a wall and stays there? How can you know when in the past it stopped moving?
That's a question that is answered in a first-year physics course, but the TL;DR is that any collision must conserve both momentum and energy. If a ball hits a wall and "sticks" then some of its energy must be dissipated as heat. That is the thermodynamic arrow of time, which is exactly what the original post was about.
You cannot know where or when a particle with constant velocity started or will stop moving. Unless you are God, of course. And you cannot know when a particle hit a wall. All you can know is that it happened some time in the past.
What did I say that made you think that initial conditions are not "physical" and what does that even mean? I feel like we are talking about different things...
> Remember, my whole point was the current state of a system does not necessarily encode its past.
Yes, I know. You're wrong about that. The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises, and in quantum mechanics by the wave function of every such particle. That information, together with the same information about the environment, encodes the basketball's past and its future.
"Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system."
"State functions do not depend on the path by which the system arrived at its present state."
MIT lecture on state representation of linear systems: http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf - see Section 1.1.
I got my "Linear Systems and Signals" B.P. Lathi 2nd ed from my shelf and found similar information. See section 10.1 if you have access to that book.
> The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises
I'm no physicist, but I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system. Even if you are just mentioning that as a mental exercise and we assume that we can in fact determine everything there is to know about every particle in a basketball, your theory still won't hold. When your system reaches an equilibrium state (i.e., minimal energy state) it will rest there forever and you will lose the ability to reverse it. In other words:
"The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states."
Obtained from the first paragraph of the original article.
Sorry about that. I'm frustrated, but I really am trying to be constructive here.
> "Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system."
Right. So if your state describes the whole universe, that provides enough information to determine its future behavior because there is nothing external to the universe (by definition!)
> "State functions do not depend on the path by which the system arrived at its present state."
Right. However, because the dynamics of both classical and quantum mechanics are reversible, you can determine the past states of a closed system (like the universe) in exactly the same way you can determine its future states. (That's how we know, for example, that the big bang happened.)
> I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system.
Right. That's why it's important to distinguish between classical and quantum mechanics. In classical mechanics there is a mystery about where the arrow of time comes from because the fundamental equations are all time-symmetric. Quantum mechanics (and more specifically QIT - quantum information theory) solves that mystery.
> "The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states."
This is not a solution to the mystery because it has to introduce this extra axiom about equilibrium states, which does not follow from Newton's equations. QIT is a better solution because the (practical) irreversibility of measurements can be derived from the basic axioms of QM. It doesn't have to be assumed.
Or swim backwards.
TL;DR: the decoherence process by which the classical world emerges from the quantum is necessarily asymmetric with respect to time.
Quantum mechanics can be formulated to be time symmetric. With time symmetric quantum mechanics decoherence happens symmetrically in both directions in time.
If you use many-worlds interpretation as illustrative as metaphor for decoherence,
reality splits also backwards from the current moment in time symmetric quantum mechanics. In fact I think Stephen hawking uses QM backwards in his quantum cosmology theories. Calculating every possible history of the that leads to next event might tell us something about early universe.
As a final point. Quantum decoherence cant' explain existing CP-violations that are not time symmetric.
Quantum mechanics and entanglements have nothing to do with the thing you are trying to explain. It's all thermodynamics and entropy. Memories can formed only by increasing entropy. Thus personal time flows from lower entropy to higher entropy.
> Memories can formed only by increasing entropy
That's right. So? Once again you seem not to have read what I wrote at all (or you did not read the background material that I link to).
Answer to this question:
If you can explain whole stuff using thermodynamics, why you bring QM and entanglement into the picture at all? Time would work exactly same in classical universe.
> Because I feel your tl;dr doesn't reflect it accurately.
Could be. It's really hard to sum this up into a pithy slogan.