Opposing arrows of time can theoretically emerge from certain quantum systems
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Δs = sqrt(-Δt^2 + Δx^2 + Δy^2 + Δz^2)
There's also Wick rotations, where you can sub `t -> it'`, and then Minkowskian spacetime becomes Euclidean but time becomes complex-valued. Groovy stuff.
I'm not much of a physics buff but I loved reading Julian Barbour's The Janus Point for a great treatment of the possibility of negative time.
The craziest thing I've seen though is the suggestion that an accelerating charge, emitting radiation that interacts with the charge itself and imparts a backreacting force on the charge, supposedly has solutions whose interpretation would suggest that it would be sending signals back in time. [0]
Has any of this been experimentally fit to reality?
> sending signals back in time.
First encode stock movements. Then technological discoveries. If it works like many-worlds, then even NP hard problems.
With sufficient bandwidth and time delta, you'd also have to hope that the future isn't sending anything nefarious that could lead to your demise. A future adversary could final destination you pretty easily and use you as a pawn to enrich itself, and there's not much you could do except stop listening - but it'd know you planned that too. A future adversary would be the scariest adversary.
Fragile universe hypothesis [2].
[1] eg. nucleate vacuum collapse
[2] cf. fragile world hypothesis
Should have written queries into the data mountain of humanity,learn about whats possible and whats not possible. The time we could reuse from ineffective public appeals to work on solveable problems
Messing with your own history, given that most systems are chaotic, seems inherently risky. Even in warfare, you’d have a hard time predicting the outcome over more than a short interval.
It's not time reversal symmetric, but it's probably [CPT][1] (charge-parity-time reversal) symmetric.
If you forget about quantum field theory and consider classical physics in Minkowski space (or Cartesian space), then t -> -t indeed doesn't change the physical laws. You could tell the two apart, though, provided that the system is far from thermal equilibrium (e.g. "why is this egg uncracking spontaneously?").
https://januscosmologicalmodel.com/januspoint
There are other players concerned with similar ideas:
- Negative mass, Farnes: https://en.wikipedia.org/wiki/Dark_fluid
- Mirror-image universe going backwards in time from the big bang, Turok: https://www.newscientist.com/article/mg25734230-100-neil-tur...
It's widely assumed to be true and not at all physically meaningful. If you sub x -> -x then that's just as good a solution as well, i.e. just as you can count x as running from west to east or east to west and the results will be the same, you can also count time as increasing away from the big bang or as decreasing away from the big bang and all your calculations will be the same.
The use of a quadratic to solve the throw is a mathematical model. We say that "the value x describing the when the ball lands must satisfy the quadratic equation F(x)=0" but that does NOT imply the opposite, which is "all x that satisfy F(x)=0 describe a valid motion of the ball."
So when we get two answers, e.g. F(-1)=0 and F(15)=0 for the two points when the ball is at ground level, that means only this: if I had thrown the ball from ground level to follow the same curve land in the same place at x=15, then I would have stood 1m further back when I threw it. It does have physical meaning, but there is nothing curious about the physical meaning.
This throw is symmetrical in time though, in the sense that if I throw the ball with the same speed in the opposite direction starting at x=15 then it will land exactly in my hand. (But the equation here is y=F(x) and not parametrized on time).
The equation we use to describe the motion does not contain a term for the ground being there. That assumption exists outside of the model described by the equation, and you use that assumption after the fact to reject a solution that would otherwise be valid, and describe the movement of the ball that's pulled down by gravity.
In this form, it doesn't really describe a proper orbit, just a trajectory of being pulled down by a constant force. I believe this would correspond to an infinitely-ish heavy object located infinitely far below. The proper equation that gives you an orbital curve has the force of gravity proportional to inverse-square distance and point at the center of the body, which is what makes it possible to describe a circular or elliptical motion this way. Parabolic orbits exist too, but they're interpreted as failed orbital capture - "object is moving so fast that it'll curve around and fly away to infinity before turning around and coming back".
And in all cases, the solutions make physical sense (+/- infinity), on the assumption the trajectory doesn't cross the ground, as there's no term for it there :). If you want, you can describe the ground as another equation (or inequality), and solve the resulting system - it'll then be clear what exactly is it that rejects some of the solutions.
What both solutions correspond to is the completion of the orbit the ball is briefly in while it is in free fall, in both directions. Every body in free fall (ignoring air resistance) is for that time in orbit around the center of gravity of the Earth. It's just the the body can not complete that orbit due to the fact it impacts the ground, and in the time-reversed direction, couldn't have come from that orbit initially because of the ground.
It's not mystery getting in the way of the equations, it's the physical ground.
(There are many other deviations from the highly idealized "orbit the Earth as if it was a stationary body in perfect Newtonian physics" but compared to air resistance you will not be able to witness any of those effects with anything you can throw with your arm from the ground.)
https://www.scribd.com/doc/287808282/Bearden-Articles-Mind-C... ... https://scholar.google.com/scholar?hl=en&as_sdt=0%2C43&q=%22... ... "p sychon ergetics" .. /? Torsion fields :
- "Torsion fields generated by the quantum effects of macro-bodies" (2022) https://arxiv.org/abs/2210.16245 :
> We generalize Einstein's General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed by the Cambridge group. GTG is a "spin-torsion" theory, according to which, gravitational effects are described by a pair of gauge fields defined over a flat Minkowski background spacetime. The matter content is completely described by the Dirac spinor field, and the quantum effects of matter are identified as the spin tensor derived from the spinor field. The existence of the spin of matter results in the torsion field defined over spacetime. Torsion field plays the role of Bohmian quantum potential which turns out to be a kind of repulsive force as opposed to the gravitational potential which is attractive [...] Consequently, by virtue of the cosmological principle, we are led to a static universe model in which the Hubble redshifts arise from the torsion fields.
Wikipedia says that torsion fields are pseudoscientific.
Retrocausality is observed.
From "Evidence of 'Negative Time' Found in Quantum Physics Experiment" https://news.ycombinator.com/item?id=41707116 :
> "Experimental evidence that a photon can spend a negative amount of time in an atom cloud" (2024) https://arxiv.org/abs/2409.03680
/?hnlog retrocausality (Ctrl-F "retrocausal", "causal") https://westurner.github.io/hnlog/ )
From "Robust continuous time crystal in an electron–nuclear spin system" (2024) https://news.ycombinator.com/item?id=39291044 ;
> [ Indefinite causal order, Admissible causal structures and correlations, Incandescent Temporal Metamaterials, ]
From "What are time crystals and why are they in kids’ toys?" https://bigthink.com/surprising-science/what-are-time-crysta... :
> Time crystals have been detected in an unexpected place: monoammonium phosphate, a compound found in fertilizer and ‘grow your own crystal’ kits.
Ammonium dihydrogen phosphate: https://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphate :
> Piezoelectric, birefringence (double refraction), transducers
Retrocausality in photons, Retrocausality in piezoelectric time crystals which are birefringent (which cause photonic double-refraction)
Is it gauge theory, though?
From https://news.ycombinator.com/item?id=38839439 :
> If gauge symmetry breaks in superfluids (ie. Bose-Einstein condensates); and there are superfluids at black hole thermal ranges; do gauge symmetry constraints break in [black hole] superfluids?
Probably not gauge symmetry there, then.
it doesn't say anything about time evolution because it isn't something you solve. given a spacetime, you can lay down axes and the metric tells you intervals between events.
it says nothing about allowed trajectories through spacetime.
If you have a casual system, then statistically, things will tend to become more disordered over time, because there are just more ways to be disordered than ordered.
Lots of clever people seem to agonise about this, but I don't see any problem. What am I missing?
The apparent arrow of time is commonly thought to have to do with initial conditions. Entropy was low right after the Big Bang, creating an asymmetry between the two time directions.
0. Technically, the laws of physics are symmetric under stimultaneous inversion of time, flipping of all charges, and a mirror reflection of space.
Time itself does not exist, we merely experience it because it is how our consciousness experiences reality
It just doesn’t matter on a universal level.
Kurzgesagt – In a Nutshell has a very good video on it:
Did The Future Already Happen? - The Paradox of Time
"To be honest, no one knows. What we’ve learned are two possibilities to describe time, but they're not the only ones. Some scientists think that the idea of “now” only makes sense near you, but not in the universe as a whole. Others think that time itself doesn’t even exist – that the whole concept is an illusion of our human mind. And others think that time does exist, but that it's not a fundamental feature of the universe – rather, time may be something that emerges from a deeper level of reality, just like heat emerges from the motion of individual molecules or life emerges from the interactions of lifeless proteins."
They touch on block universe: https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time...
…and growing block universe: https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time...
"The growing block universe, or the growing block view, is a theory of time arguing that the past and present both exist, and the future as yet does not. The present is an objective property, to be compared with a moving spotlight."
Excellent video worth your time.
What I mean is that since our brains store memories and generally process information utilizing entropic systems, we perceive time as always moving forward. There is no fundamental physical direction to time... But since our experience slides along an axis of increasing entropy, we perceive the whole universe sliding on that axis as well.
That's backwards: Time exists to allow our consciousness to experience change over time. This is because time exists to allow change over time to the physical universe.
That said, there is only the ever-present Now in a constantly evolving universe.
Time does not exist so we experience it, our experience of existence is a function of our brains integrating and recalling state via entropy. Therefore, our moment of consciousness is sliding along in the direction of entropy, and our entanglements with the universe around us are likewise evolving with entropy
That being said, there are still plenty of unanswered questions around time in physics. Even just open questions about block vs growing block universe are unanswered, and tied into the ultimate nature of time.
Also, we know that entropy was much lower in the past, but we don't know WHY.
I feel the same way. The past is just the direction where things were more ordered (to be glib about it.)
Even though the large scale implications of the statistics are profound, star fusion, rivers, etc. the “cause” is statistics.
The one place (that I am aware of) where the statistics -> time effect still needs explicit work is how the timal fabric dimension operates differently (but very similarly) to the 3 spacial fabric dimensions of space-time in the very large scale. Often represented by a negative (for time) and three positive (for space) signs in equations. But I assume when we understand how space in the small works, the topology will still have a statistical explanation.
—
A very close topic, and the same forehead slap feeling for me, is all the contortions many physicists go through to avoid the many worlds quantum interpretation. Which is the parsimonious interpretation.
(Should more accurately be called the “quantum field web” interpretation, according to … me.)
Again statistics: we just think there is a “collapse” in possibilities when super-positioned information becomes to mixed up for us to remix.
The alternative: a mysterious collapse with yet unexplained cause, with deep problems regarding how this introduces another unique “time” effect, of nearly infinite new information constantly being injected into every interaction everywhere and everywhen in the universe! And this information is supposed to be causeless or self-caused in some mystical (but don’t ever say “mystical”), way.
And don’t point out the mockery this makes of “conservation of information” if 99.99…99% of information now wasn’t there just one quantum event ago, for all quantum events.
Again, statistics completely explains why us biggies experience fields making choices, based on the field equation defining field connection (we experience as event) point distributions, and … statistics.
Yet every day physicists who can’t admit to themselves that we are ourselves constantly expanding webs of superpositions, take for granted that anything they can scale up in the lab will have superpositions, subject to experimental practicalities.
Because anything else would violate the field equations.
The only problem is that this ignores the fact that we still don't know WHY entropy was lower in the past. It's an open question in physics.
Due to time-reversal symmetry, you could easily do a t<-->-t substitution, flipping the time axes around. Now entropy decreases over time, with the big bang being the point of minimum entropy, located far ahead in time. But regardless of the convention, our memories exist along the direction between us and the big bang, rather than the other direction.
So if increasing entropy is to be the arrow of time, it needs to relate to why we form memories of the past but not of the future.
That much is very well understood.
Order from the past is what we harness to make memories. That’s why you can’t have memories the other direction.
Think of a computer. It takes ordered energy, organized as a stream of electrons, which end up in a less energetic form we can’t use and heat we can’t use.
But in the eddies of that entropy, the computer calculates a few things. Uses up that order to store a few things.
The net is massive loss of order. One electron can go either way on a wire. With (usually) or against (mostly) voltage. (Because we randomly decided electrons are negative.)
But a trillion electrons statistically can only go one way.
The order we build in our minds and computers is a fraction of the order from the past. Which is just saying, we get order from the direction there was more order.
You could set up a tiny few particle experiment, shield it from interactions, and operations can randomly go either direction.
But our neurons and brains are built out of countless particles. We can only do ordered things with them by consuming order from the direction there was order.
A windmill can do work, but only if you let higher water push the wheel. If the river stops from above, no amount of water below is going to power it. Statistically to the level of certainty.
The order in the universes origin, statistically cascades away in all directions. And all those directions, radiating from order, away from order, are what lets us think, store memories, and have an experience we call time.
But with a constant total net loss of order. We are just those eddies that defy the rivers flow, but only fractionally, by harnessing the rivers flow.
(For how there can be places where order “first” appears, see my other comment. Unlike this one, it is highly conjectural.)
And this is why when the universe has a temporal entropy gradient, the direction of decreasing entropy gets labeled "the past". It's not because the past is the direction of "-t", but because the past is the direction of "-dS/dt". Otherwise we wouldn't form memories of it.
This dissolves the mystery of why the past has lower entropy than the future despite the laws of physics being time-reversible, and replaces it with the question "why does the universe have an entropy gradient at all?"
Did you read my other sibling comment about ordered regions of reality being inevitable?
(Not being snarky, just that was the question I have a conjectural answer too.)
It reminds me of Feynman's QED, where he explains how a photon can take every path to its destination, and the end result looks almost like it's taking just one path, because all the other paths end up with scrambled phases that cancel each other out when you sum them up.
My provisional answer would be that reality is a web of constraints, which most certainly is essentially (deterministic chaotic) noise almost everywhere. But like the Mandelbrot set, has pockets where the chaos gets expressed as order.
Because no order at all would actually be impossibly ordered.
The same effect as proofs that if you simply add random edges to a graph, ordered patterns will emerge. What patterns is still random! But that patterns emerge is a certainty.
Except instead of random, reality just churns and spans so many variations that there has to be pockets of order and of arbitrarily large size.
You're ignoring all of the major problems which require additional assumptions for MWI to appear so parsimonious. The biggest of which being the preferred basis problem: a quantum system isn't just in a superposition of states along one axis, it's in a superposition of states along the axis you choose to measure. If you and I both choose to measure the same system along different axis, we'll get different (but correlated) kinds of results about the same particle pair (which is the root of the Bell inequalities).
Take an entangled pair of polarized photons, such that they must have opposite polarization, and send one towards you and one towards me. You'll measure the polarization of your photon along some axis, and I'll pick an axis that is 30% off yours. If we repeat the experiment many times, we'll conclude that percent of photons was polarized along the axis we each chose, and some percent was perpendicular. The percentages will be different, of course, and if we compare measurement results for individual events, we'll find that they correlate perfectly. But what can't be done, even in principle, is decide along which axis the photons were "actually" polarized.
So, the problem for MWI is: how come classical objects have real properties independent of measurement choice, and they all happen to have properties along the same axis, given that the quantum objects they're made of don't, and there is no collapse?
And this can't be explained away by statistics or entropy, because the amplitude of the wave function in QM is the same regardless of the choice of measurement axis. Even decoherence doesn't solve this problem, because lack of self-interaction doesn't affect the choice of basis.
The other problems with MWI have to do with the very notion of doing probability calculations, and then statistics based on them, in a perfectly deterministic world where every outcome of every experiment is fully realized. If you flip a coin and both sides come up, how can you tell if the coin is biased or not? Or, since you prefer the quantity of information concept, in the MWI it seems that there is 0 information from any experimental result, because you know ahead of performing the experiment that all of the possible results will happen with probability 1 (in some "branch"). So yes, information is conserved: it's always 0.
Measurement choice impacts the field equations, because you are field equations too.
So none of those problems exist. Just interpret the field equations as they stand.
Yes, new information is information is conserved, if everything is predictable. Which the field equations are.
That would not be true if collapse was real, as that would impact the system with new, previously unknown, inherently unpredictable information.
(The fact that we as big things end up experiencing what looks like a collapse is explained by the field equations and the statistics of how quickly information, not carefully controlled, gets dispersed.
At this point in the history of physics, we should be able to discard extra explanations for our experiences that are already completely and exhaustively explained by the well tested laws.
The fact that the explanation requires thinking about things differently than ordinary experience, isn’t an excuse for wedging poorly characterized and completely unnecessary fudge effects as shims into our intuition gaps.
I am, of course, not arguing that collapse isn’t a useful concept, with many pervasive practical uses when full systems are not being modeled.
This sounds nice, but doesn't actually work if you try to apply it in practice, because however many experiments you'll perform on classical objects, you'll only ever observe properties for one basis of measurement, whereas you'll get different results for different bases for quantum objects.
In other words, how come when I observe a single atom, I can see it in a state like (1/sqrt(2))|spin up> + (1/sqrt(2))|spin down>, but I can never observe a basket ball in a similar state? If it were just a matter of my field equations happening to only match certain kinds of states, that should apply exactly as much to a single atom as it would to ~6,022*10^23 atoms.
Order requires energy -- i.e. our highly thermodynamic body processes -- so as the temp lowers, disorder will tend to decrease.
Maybe a physicist can correct me, but that seems like a simple yet accurate system-wide summation. Of course, local areas (such as Earth) can retain enough heat for a span of time to maintain complexly organized systems, but in the universe's time scale, it's going to keep winding down towards that CMBR, where ever little complexity will be possible.
I’m not sure I follow your description: as the universe empties, aren’t we at some point left with less and less happening per cubic meter?
Thanks for correcting me.
Your theory:
> If you have a casual system, then statistically, things will tend to become more disordered over time, because there are just more ways to be disordered than ordered.
contains a tacit assumption that states are chosen at random. But assuming that is begging the question. Why are states chosen at random? What is the source of the randomness? Newtonian mechanics doesn't have any obvious source of randomness, and it's an open question whether quantum randomness is "really random". Bohmian mechanics is completely deterministic, and so is (obviously) superdeterminism.
It's true that "there are more ways to be disordered than ordered", but in any time-reversible dynamic there are exactly as many states where entropy decreases as there are states where entropy increases because for any entropy-increasing state, the time-reversed state has decreasing entropy.
> but in any time-reversible dynamic
Now that is making an assumption that the dynamics of an entire system could be thrown into reverse. Everything flipped to its opposite, and then proceeding onwards causally from that point.
It also presumes that the system started in a state of order, got more disordered, and then you reversed it and then order "magically" appears. Your eggs unscramble themselves. If you merely take a disordered system and throw it into reverse, you will still just see a disordered system becoming more disordered, because there was never any surprising ordered state built in to be uncovered later.
This is circular. If the system is becoming more disordered, it follows that playing it in reverse will make it less disordered. Sure, if the initial state wasn't very ordered to begin with, this won't look very different, but that's entirely irrelevant: as long as we accept that "disorder" is a measurable objective property of a system, then there is a quantifiable difference between moving forward and backward in time. And this doesn't match either a deterministic time-reversal symmetric theory like classical mechanics, nor a deterministic CPT-reversal symmetric theory like QFT.
No, that's not an assumption, that's a mathematical feature of all known laws of physics. An it's not that "the dynamics could be thrown into reverse", it's that for every initial state, there is a corresponding initial state where the system runs in reverse, and hence, for every state from which entropy increases there is a corresponding state where it decreases. For a Newtonian system, it's a state where all the velocities have opposite sign. (For quantum systems it's a little trickier to describe.) So if you choose a state uniformly at random from among all possible states, the odds that you will end up with one where entropy is increasing is exactly 50%.
And it gets even worse than that. In a universe that obeys certain conservation laws (which as far as we can tell ours does) a time-reversible dynamic is unitary, which is to say, there is a one-to-one correspondence between an initial state and its successors. Therefore, for any initial state, the time evolution of that state must eventually loop back to its initial state [1], and so it must eventually enter an entropy-reducing state to get there.
[1] https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
So, while the math is reversable, time is a one-way street by virtue of the construction of the physical universe, which is not reversable. And it's that way because that's how this magnificent universe was instantiated.
It may sound trite, but sometimes Occam is bang-on. As well, there are endless unknowns, but there are also unknowables.
All matter is >99% empty, not counting field interactions. I don't know how much of it can be understood, but some of it is likely to be unknowable.
However, say we receive a video of a billion billion such masses all starting in a single point, staying more or less still for a few seconds, and then moving out at high speed away from each other. It is obvious that this video is almost certainly playing forward in time, since the reverse, a billion billion balls all coming together to form a single object, is very very unlikely.
What if time is a free variable - it can move forward and backwards freely, perhaps like a drunkards walk? To a conscious being, any memory of having been at time t will be erased when t decreases. When t increases again, but you'll have no memory by which to detect the revisitation.
I know that I just postulated that there is a time sequence by which the motion of time can be described. But that is only to make the idea graspable to our ordinary sense of time.
One interpretation of what I described is the slab model of the universe where time is just another axis and the evolution along that line is fixed. Another interpretation would be that as time moves forward and backwards the state of the universe is free to change. In either case, our perception of our personal timelines would always appear to be unidirectional.
What would be the measurable effect of this - would casualty actually be broken? Would we get Dejavu?
And, if you want to suppose objective collapse, I think you can still consider a probability distribution over histories, where each history could be considered as like, something like the described above Psi(t), except that if at time t_i some measurement is made with the outcome of the measurement being described with the projection P, then like, for t > t_i , Psi(t) = U(t-t_i) P U(t_i-t_0) Psi(t_0) = U(t-t_0) (U(t_i-t_0)^* P U(t_i - t_0)) Psi(t_0) = (U(t-t_i) P U(t-t_i)^*) U(t-t_0) Psi(t_0) ,
except add in a projection for each objective-collapse event.
I guess you might also want to add in normalization factors.
Also, I guess maybe one might want to make the collapse be a thing that is happening constantly to some extent or another? I think I saw something about the quantum zeno effect arguing that time evolution could be described in terms of constantly applying continuously varying projection operators.
Now, in these cases, you wouldn't have the future deterministically determining the past, but you also don't have the past deterministically determining the future, so..
I think this seems like it could be considered a "slab model" or "block universe" in a reasonable sense? Though perhaps not in the sense you have in mind, but I don't know what about it fails to satisfy what you have in mind.
Isn't this a bit underspecified? Like a marble in a bowl has plenty of positions it can be in, but it tends to end up in the center due to the whole physical system doing its thing to roll a marble to the center.
Or is there some deeper argument here?
But this is no longer true when the box (now much larger) contains millions of billiard balls. If the balls start clustered together, they will scatter over time about the box and the replay of their paths has only one plausible time direction.
> If the balls start clustered together, they will scatter over time about the box and the replay of their paths has only one plausible time direction.
It is extremely unlikely that all the billiards will, simply by chance at some point in the future, collect together so they are contained within a very small volume. this shows that there is asymmetry in which direction time flows.
I suppose we're now entering into the realm of what happened before the big bang?
I think this is generally explained as being due to the expansion of space? This is only an extremely loose analogy because the expansion of space is not really all that much like a container getting bigger (because it isn't like it is thought to start with one particular size and get bigger), but, suppose you have a syringe with the tip closed off, where there is some hot gas that is highly compressed in the front bit of the syringe, and then you pull back on the syringe plunger. The temperature of the gas should decrease, right? By the same principle of how refrigeration works by rarefying the coolant in the place you want to make cool, to make it cooler so that it will absorb heat from the environment, and then moving it to the place you want to heat and compressing it so that it will be hot and give off that heat?
But, pulling the plunger back doesn't decrease the entropy of the gas in the plunger, does it? It might require putting in energy in which case it could decrease the energy in the plunger at the cost of increasing it elsewhere, but if the plunger is loose enough the pressure from the gas should be able to push it out, in which case I think the temperature and pressure would still decrease without an external source doing the work, so the entropy definitely shouldn't decrease in that case.
So, going from hot and dense to less hot and dense, keeping the same amount of stuff but more spread out, doesn't always mean a decrease in entropy, and can instead correspond to more entropy?
After all, if there are more places available to be, that seems like more uncertainty, right? At least, in a finite system.
Like, if you are looking at the relative entropy of a distribution of one particle in a 1D box of length L, where the entropy is relative to the Lebesgue measure, and you compare this to the case of a 1D box of length 2L , still measuring the relative entropy relative to the Lebesgue measure, well, the maximum entropy distribution for the position when in the 2L length box, the uniform distribution on [0,2L], has more relative entropy than the uniform distribution on [0,L] , which has the highest entropy for the distribution over position attainable for the length L box. (I say "relative entropy" because for a continuous variable, we don't have like, a countable set of possibilities which each have non-zero probability that we can sum over, and so we can't use that definition of entropy, but instead integrate over possibilities using the density of the distribution with respect to some reference measure, and I think the Lebesgue measure, the usual measure on sets of real numbers, is a good common reference point.)
Though, I guess the thing shouldn't really be just distribution over position, but joint distribution over position and momentum.
"things will tend to become more disordered over time, because there are just more ways to be disordered than ordered."
You can derive all of classical thermodynamics from this one observation.
At a high level, physics is just symmetries and laws, and efforts to poke holes in them. We are "hung up" because they form the base of the core lines of inquiry in the field, not because we don't understand them.
Only if they weren't disordered to begin with. If you start with well stirred coffee and milk and stir it again, it won't be more "disordered" than what you started with.
The problem is that our universe started as "ordered" for reasons we don't understand. We call it the big bang, and that's the origin of the arrow of time.
No big bang means maximum entropy, no arrow of time, and no conscious observer. And if there is, that would be a Boltzmann brain scenario, and no one wants a Boltzmann brain scenario.
The question of the arrow of time is literally the last question of life, the universe, and everything.
“Our findings are consistent with the second law of thermodynamics and emphasise the distinction between the concepts of irreversibility and time-reversal symmetry. Once the arrow of time and a particular low entropy initial condition at have been chosen, then the von Neumann entropy will increase forward in time from the temporal origin. However, a different choice of the arrow of time would have implied the same dynamics. The Markov approximation applied to the time-reversed evolution leads likewise to the same dissipation and entropy increase. Consequently any thermal equilibrium state for a forward-running trajectory is also an equilibrium thermal state for any time-reversed trajectory, and entropy increases in both directions: the system thermalises into both time directions. […]
“Furthermore, we speculate that these results may reflect on the cosmological arrow of time. In fact, the natural assumption that the universe was dissipative from time zero onwards would suggest that a model of it would rely on the Markov approximation performed at the moment of the Big Bang. If so, this would imply that two opposing arrows of time would have emerged from the Big Bang, which would account in turn for the maintenance of time-reversal symmetry despite the ensuing dissipative nature of the universe. We would happen to live in one of them, where dissipation and entropy increase are common experience, but unaware of the existence of the other alternative possibility.”
That sentence is doing a lot of heavy lifting in this article.
this is what they mean by stretching spacetime right?
"Physicists uncover evidence of two arrows of time emerging from the quantum realm"
s/sufficiently/insufficiently/