Logical arrow of time, 10

Two distinguishable macrostates can both evolve into one indistinguishable macrostate.

— Me@2013-08-11 11:08 AM

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Logical arrow of time, 9.4

The second law of thermodynamics’ derivation (Ludwig Boltzmann’s H-theorem) is with respect to an observer.

How does an observer keep losing microscopic information about a system?

— Me@2017-02-12 07:37:54 PM

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This drew the objection from Loschmidt that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (Loschmidt’s paradox).

The resolution (1895) of this paradox is that the velocities of two particles after a collision are no longer truly uncorrelated. By asserting that it was acceptable to ignore these correlations in the population at times after the initial time, Boltzmann had introduced an element of time asymmetry through the formalism of his calculation.

— Wikipedia on Molecular chaos

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Physical entropy’s value is with respect to an observer.

— Me@2017-02-12 07:37:54 PM

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This “paradox” can be explained by carefully considering the definition of entropy. In particular, as concisely explained by Edwin Thompson Jaynes, definitions of entropy are arbitrary.

As a central example in Jaynes’ paper points out, one can develop a theory that treats two gases as similar even if those gases may in reality be distinguished through sufficiently detailed measurement. As long as we do not perform these detailed measurements, the theory will have no internal inconsistencies. (In other words, it does not matter that we call gases A and B by the same name if we have not yet discovered that they are distinct.) If our theory calls gases A and B the same, then entropy does not change when we mix them. If our theory calls gases A and B different, then entropy does increase when they are mixed. This insight suggests that the ideas of “thermodynamic state” and of “entropy” are somewhat subjective.

— Wikipedia on The mixing paradox

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Logical arrow of time, 9.3

We label the time direction that we can remember as “past”.

If we could remember both time directions, we would remember infinite things, unless the future has an anti-big-bang.

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Also “remembering the future” creates a meta-dox (aka paradox).

— Me@2013-08-11 8:25 AM

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Logical arrow of time, 9.2

To confirm or disconfirm a prediction, you cannot check record; you can only observe the system evolving.

To confirm or disconfirm a retrodiction, you can only check record (or the logical consequence of that retrodiction); you cannot observe that past event directly.

— Me@2013-08-10 08:00 PM

— Me@2021-05-03 12:28 PM

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Logical arrow of time, 9.1

The source of asymmetry:

For prediction of the future, the result is what the observer/calculator can actually see.

For retrodiction of the past, the result is not.

— Me@2017-07-09 12:03:27 PM

— Me@2021-04-04 12:28:34 PM

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Conscious time, 2

If no one has any kind of date, records, memories, or evidence about the past, retro-diction MAY be the same as prediction. But in such a case, it is by definition not our “past” any more.

— Me@2013-08-08 3:11 PM

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If no one has any kind of date, records, memories, or evidence about the past, then consciousness ceases to exist.

We, as conscious beings, cannot exist anymore.

— Me@2021-03-30 4:08 PM

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Logical arrow of time, 6.4.2

Logical arrow of time, 6.1.2

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The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference between prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really making a prediction.

— guess —

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— Me@2013-10-25 3:33 AM

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A difference between deduction and observation is that in observation, the probability is updated in real time.

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each update time interval ~ infinitesimal

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In other words, when you observe a system, you get new information about that system in real time.

Since you gain new knowledge of the system in real time, the probability assigned to that system is also updated in real time.

— Me@2020-10-13 11:27:59 AM

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Memory as past microstate information encoded in present devices

Logical arrow of time, 4.2

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Memory is of the past.

The main point of memories or records is that without them, most of the past microstate information would be lost for a macroscopic observer forever.

For example, if a mixture has already reached an equilibrium state, we cannot deduce which previous microstate it is from, unless we have the memory of it.

This work is free and may be used by anyone for any purpose. Wikimedia Foundation has received an e-mail confirming that the copyright holder has approved publication under the terms mentioned on this page.

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memory/record

~ some of the past microstate and macrostate information encoded in present macroscopic devices, such as paper, electronic devices, etc.

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How come macroscopic time is cumulative?

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Quantum states are unitary.

A quantum state in the present is evolved from one and only one quantum state at any particular time point in the past.

Also, that quantum state in the present will evolve to one and only one quantum state at any particular time point in the future.

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Let

$\displaystyle{t_1}$ = a past time point

$\displaystyle{t_2}$ = now

$\displaystyle{t_3}$ = a future time point

Also, let state $\displaystyle{S_1}$ at time $\displaystyle{t_1}$ evolve to state $\displaystyle{S_2}$ at time $\displaystyle{t_2}$. And then state $\displaystyle{S_2}$ evolves to state $\displaystyle{S_3}$ at time $\displaystyle{t_3}$.

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State $\displaystyle{S_2}$ has one-one correspondence to its past state $\displaystyle{S_1}$. So for the state $\displaystyle{S_2}$, it does not need memory to store any information of state $\displaystyle{S_1}$.

Instead, just by knowing that $\displaystyle{t_2}$ microstate is $\displaystyle{S_2}$, we already can deduce that it is evolved from state $\displaystyle{S_1}$ at time $\displaystyle{t_1}$.

In other words, microstate does not require memory.

— Me@2020-10-28 10:26 AM

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Logical arrow of time, 7.2

Microscopically, there is no time arrow.

— Me@2011.06.23

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No. There is weak force.

— Me@2011.07.22

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Myth: The arrow of time is a consequence of CP-symmetry violation.

The weak nuclear interactions violate the CP symmetry which is equivalent to saying that they violate the T symmetry. Is it the reason why eggs don’t unbreak? Of course not. There are two basic ways to see why. First, the weak interactions much like all other interactions preserve the CPT symmetry – there is extensive theoretical as well as experimental evidence supporting this assertion. And the CPT symmetry would be enough to show that eggs break as often as unbreak. More precisely, eggs break as often as mirror anti-eggs unbreak. ;-)

— Myths about the arrow of time

— Lubos Motl

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Weak force’s T-symmetry-violation has nothing to do with the time arrow.

In other words, microscopic time arrow has nothing to do with the macroscopic time arrow.

— Me@2020-03-21 07:56:01 PM

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About T-violation and the arrow of time: the simple answer is that the weak interactions are perfectly unitary, even if they are not T-invariant. They don’t affect the entropy in any way, so they don’t help with the arrow of time.

A bit more carefully: if you did want to explain the arrow of time using microscopic dynamics, you would have to argue that there exist more solutions to the equations of motion in which entropy grows than solutions in which entropy decreases. But CPT invariance is enough to guarantee that that’s not true. For any trajectory (or ensemble of trajectories, or evolution of a distribution function) in which the entropy changes in one way, there is another trajectory (or set…) in which the entropy changes in precisely the opposite way: the CPT conjugate. Such laws of physics do not in and of themselves pick out what we think of as the arrow of time.

People talk about the “arrow of time of the weak interactions,” but ask yourself: in which direction does it point? There just isn’t any direct relationship to entropy.

— Sean Carroll

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Logical arrow of time, 7

When we imagine that we know and keep track of all the exact information about the physical system – which, in practice, we can only do for small microscopic physical systems – the microscopic laws are time-reversal-symmetric (or at least CPT-symmetric) and we don’t see any arrow. There is a one-to-one unitary map between the states at times “t1” and “t2” and it doesn’t matter which of them is the past and which of them is the future.

A problem is that with this microscopic description where everything is exact, no thermodynamic concepts such as the entropy “emerge” at all. You might say that the entropy is zero if the pure state is exactly known all the time – at any rate, a definition of the entropy that would make it identically zero would be completely useless, too. By “entropy”, I never mean a quantity that is allowed to be zero for macroscopic systems at room temperature.

But whenever we deal with incomplete information, this one-to-one map inevitably disappears and the simple rules break down. Macroscopic laws of physics are irreversible. If friction brings your car to a halt and you wait for days, you won’t be able to say when the car stopped. The information disappears: it dissipates.

— The arrow of time: understood for 100 years

— Lubos Motl

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If there is a god-view, there is no time arrow.

Time arrow only exists from a macroscopic point of view. Microscopically, there is no time arrow.

If there is a god-view that can observe all the pieces of the exact information, including the microscopic ones, there is no time arrow.

Also, if there is a god-view, there will be paradoxes, such as the black hole information paradox.

Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Larus Thorlacius, and Gerard ‘t Hooft.

Leonard Susskind proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and cannot escape, with the catch being no observer can confirm both stories simultaneously.

— Wikipedia on Black hole complementarity

The spirit of black hole complementarity is that there is no god-view. Instead, physics is always about what an observer can observe.

— Me@2018-06-21 01:09:05 PM

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Logical arrow of time, 6.4

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really doing a prediction.

— guess —

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— Me@2013-10-25 3:33 AM

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The existence of the so-called “the paradox of the arrow of time” is fundamentally due to the fact that some people insist that physics is about an observer-independent objective truth of reality.

However, it is not the case. Physics is not about “objective” reality.  Instead, physics is always about what an observer would observe.

— Lubos Motl

— paraphrased

— Me@2019-01-19 10:25:15 PM

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Logical arrow of time, 6.3

“Time’s arrow” is only meaningful when considering with respect to an observer.

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c.f. the second law of thermodynamics

The direction of time is direction of losing microscopic information… by whom?

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“Time’s arrow” is only meaningful when considering with respect to an observer.

— Me@2018-01-01 6:14 PM

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Logical arrow of time, 6.2

Source of time asymmetry in macroscopic physical systems

Second law of thermodynamics

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— Bohr

— paraphrased

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Physics should deduce what an observer would observe,

not what it really is, for that would be impossible.

— Me@2018-02-02 12:15:38 AM

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2. Whatever an observer can observe is a consistent history.

observer ~ a consistent story

observing ~ gathering a consistent story from the quantum reality

3. Physics [relativity and quantum mechanics] is also about the consistency of results of any two observers _when_, but not before, they compare those results, observational or experimental.

4. That consistency is guaranteed because the comparison of results itself can be regarded as a physical event, which can be observed by a third observer, aka a meta observer.

Since whenever an observer can observe is consistent, the meta-observer would see that the two observers have consistent observational results.

5. Either original observers is one of the possible meta-observers, since it certainly would be witnessing the comparison process of the observation data.

— Me@2018-02-02 10:25:05 PM

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Logical arrow of time, 6

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really doing a prediction.

However, it may not be possible for such an observer to exist. Me@2018-02-02 09:37:48 PM

— guess —

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— Me@2013-10-25 3:33 AM

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Logical arrow of time, 5

Otherwise your games with the “definition” of initial and final states and with the sign of t are completely immaterial. “Initial” and “final” states are, according to logic, qualitatively different things, and the usual convention for the sign of t is that t_{initial} < t_{final}. But I have never even used this convention.

Even if I had, it wouldn’t matter. One can easily rewrite all proofs to the opposite convention by replacing t with −t; all those things are physically vacuous. The non-vacuous claim is that the future and past don’t play symmetric roles in logic.

— Physics Stack Exchange

— Jan 25 ’12 at 9:49

— Lubos Motl

2013.09.26 Thursday ACHK

Logical arrow of time, 4

That’s why the retrodicted probabilities of initial states pi=P(Hi) always depend on some subjective choices. What we think about the past inevitably depends on other things we have learned about the past. This is a totally new property of retrodictions that doesn’t exist for predictions. Predictions may be probabilistic (and in quantum mechanics and statistical physics, they are inevitably “just” probabilistic) but the predicted probabilities are objectively calculable for certain input data. The formulae that objectively determine these probabilities are known as the laws of physics. But the retrodicted probabilities of the past are not only probabilistic; their values inevitably depend on the subjective knowledge, too!

— Prediction isn’t the right method to learn about the past

— Lubos Motl

The future is not fixed, in the sense that the present chooses among the potential futures to evolve to. Since each higher entropy macrostate by definition is corresponding to more microstates, it has a higher probability to occur.

However, the past is fixed. The probability is subjective probability. The present cannot “choose” among the “potential” pasts from which the present is evolved. The fact that there are more one possible pasts is due to your subjective ignorance about the past. If someone else has more data about the past, his number of possible pasts will be much smaller. If that person has a record of the past, there will be only one possible past.

The probability for predicting the future is objective, because by the definition of the word “future”, no one can have any data about the future. No one can have a record of the future now.

— Me@2013-07-26 6:01 PM

The difference between the future and the past is that logically, no one can have any data of future, but someone may have some data of the past. Also, different people can have different sets of data about the past.

— Me@2013-08-08 8:43 AM

Logical arrow of time, 3

And as we have explained many times, the results of this inference – the retrodictions – always depend on our priors. So the knowledge of the present is enough to calculate the future (classically) or to predict the unique probabilities of various states in the future (quantum mechanically). But it is simply never enough to calculate the unique state or unique probabilities of various states in the past.

The reason has been explained many times. But we can say that at least in the macroscopic context (when some microscopic detailed information is being omitted, e.g. because it’s unmeasurable), different initial states “A,B” in the past may evolve into the same final state “C” in the future.

— Logical arrow of time and terminology

— Lubos Motl

2013.07.20 Saturday ACHK

Logical arrow of time, 2

However, the right definition of the past and the future is independent of these sign conventions for spacetime coordinates. The right definition says that

The future is evolving from the past (and the present).

Correspondingly, the calculations that are designed to theoretically mimic this evolution have the same arrow:

The future is calculated from the past (and the present) as long as we use the usual calculations that resemble the evolution.

It’s important that you can’t exchange the words “future” and “past” in the sentence above.

That doesn’t mean that science can never say anything about the past, by manipulating with the present data or the data from a closer past. But this type of calculation is different from predictions of the future. It follows different formulae, too. They’re the formulae of logical inference, e.g. Bayesian inference.

And as we have explained many times, the results of this inference – the retrodictions – always depend on our priors. So the knowledge of the present is enough to calculate the future (classically) or to predict the unique probabilities of various states in the future (quantum mechanically). But it is simply never enough to calculate the unique state or unique probabilities of various states in the past.

— Logical arrow of time and terminology

— Lubos Motl

2012.02.28 Tuesday ACHK

Time in physics

1.    Time is just another, imaginary dimension of space
2.    The question about the existence of the past depends on our definition of existence
3.    The future doesn’t exist at the present regardless of any definitions
4.    Some units of time are better than others
5.    Among conserved quantities, time has a special relationship with energy
6.    All physical systems with many degrees of freedom inevitably possess a future-time asymmetry, the so-called logical arrow of time
7.    The logical arrow of time implies the asymmetry of all macroscopic processes, i.e. the thermodynamic arrow of time and other arrows of time
8.    An exact time-reversing symmetry which holds in Nature is called CPT and only applies to the microscopic laws
9.    To properly understand the psychological perception of time, one needs to analyze the functions of the brain
10.   When times become as short as the Planck time, \(10^{-43}\) seconds, time develops some wholly unfamiliar properties

— Ten new things modern physics has learned about time

— Lubos Motl

2011.09.06 Tuesday ACHK