The arrow of time is hot, baby. I talk about it incessantly, of course, but the buzz is growing. There was a conference in New York, and subtle pulses are chasing around the lower levels of the science-media establishment, preparatory to a full-blown explosion into popular consciousness. I’ve been ahead of my time, as usual.
So, notwithstanding the fact that I’ve disquisitioned about this a great length and considerable frequency, I thought it would be useful to collect the salient points into a single FAQ. My interest is less in pushing my own favorite answers to these questions, so much as setting out the problem that physicists and cosmologists are going to have to somehow address if they want to say they understand how the universe works. (I will stick to more or less conventional physics throughout, even if not everything I say is accepted by everyone. That’s just because they haven’t thought things through.)
Without further ado:
What is the arrow of time?
The past is different from the future. One of the most obvious features of the macroscopic world is irreversibility: heat doesn’t flow spontaneously from cold objects to hot ones, we can turn eggs into omelets but not omelets into eggs, ice cubes melt in warm water but glasses of water don’t spontaneously give rise to ice cubes. These irreversibilities are summarized by the Second Law of Thermodynamics: the entropy of a closed system will (practically) never decrease into the future.
But entropy decreases all the time; we can freeze water to make ice cubes, after all.
Not all systems are closed. The Second Law doesn’t forbid decreases in entropy in open systems, nor is it in any way incompatible with evolution or complexity or any such thing.
So what’s the big deal?
In contrast to the macroscopic universe, the microscopic laws of physics that purportedly underlie its behavior are perfectly reversible. (More rigorously, for every allowed process there exists a time-reversed process that is also allowed, obtained by switching parity and exchanging particles for antiparticles — the CPT Theorem.) The puzzle is to reconcile microscopic reversibility with macroscopic irreversibility.
And how do we reconcile them?
The observed macroscopic irreversibility is not a consequence of the fundamental laws of physics, it’s a consequence of the particular configuration in which the universe finds itself. In particular, the unusual low-entropy conditions in the very early universe, near the Big Bang. Understanding the arrow of time is a matter of understanding the origin of the universe.
Wasn’t this all figured out over a century ago?
Not exactly. In the late 19th century, Boltzmann and Gibbs figured out what entropy really is: it’s a measure of the number of individual microscopic states that are macroscopically indistinguishable. An omelet is higher entropy than an egg because there are more ways to re-arrange its atoms while keeping it indisputably an omelet, than there are for the egg. That provides half of the explanation for the Second Law: entropy tends to increase because there are more ways to be high entropy than low entropy. The other half of the question still remains: why was the entropy ever low in the first place?
Is the origin of the Second Law really cosmological? We never talked about the early universe back when I took thermodynamics.
Trust me, it is. Of course you don’t need to appeal to cosmology to use the Second Law, or even to “derive” it under some reasonable-sounding assumptions. However, those reasonable-sounding assumptions are typically not true of the real world. Using only time-symmetric laws of physics, you can’t derive time-asymmetric macroscopic behavior (as pointed out in the “reversibility objections” of Lohschmidt and Zermelo back in the time of Boltzmann and Gibbs); every trajectory is precisely as likely as its time-reverse, so there can’t be any overall preference for one direction of time over the other. The usual “derivations” of the second law, if taken at face value, could equally well be used to predict that the entropy must be higher in the past — an inevitable answer, if one has recourse only to reversible dynamics. But the entropy was lower in the past, and to understand that empirical feature of the universe we have to think about cosmology.
Does inflation explain the low entropy of the early universe?
Not by itself, no. To get inflation to start requires even lower-entropy initial conditions than those implied by the conventional Big Bang model. Inflation just makes the problem harder.
Does that mean that inflation is wrong?
Not necessarily. Inflation is an attractive mechanism for generating primordial cosmological perturbations, and provides a way to dynamically create a huge number of particles from a small region of space. The question is simply, why did inflation ever start? Rather than removing the need for a sensible theory of initial conditions, inflation makes the need even more urgent.
My theory of (brane gasses/loop quantum cosmology/ekpyrosis/Euclidean quantum gravity) provides a very natural and attractive initial condition for the universe. The arrow of time just pops out as a bonus.
I doubt it. We human beings are terrible temporal chauvinists — it’s very hard for us not to treat “initial” conditions differently than “final” conditions. But if the laws of physics are truly reversible, these should be on exactly the same footing — a requirement that philosopher Huw Price has dubbed the Double Standard Principle. If a set of initial conditions is purportedly “natural,” the final conditions should be equally natural. Any theory in which the far past is dramatically different from the far future is violating this principle in one way or another. In “bouncing” cosmologies, the past and future can be similar, but there tends to be a special point in the middle where the entropy is inexplicably low.
What is the entropy of the universe?
We’re not precisely sure. We do not understand quantum gravity well enough to write down a general formula for the entropy of a self-gravitating state. On the other hand, we can do well enough. In the early universe, when it was just a homogenous plasma, the entropy was essentially the number of particles — within our current cosmological horizon, that’s about 1088. Once black holes form, they tend to dominate; a single supermassive black hole, such as the one at the center of our galaxy, has an entropy of order 1090, according to Hawking’s famous formula. If you took all of the matter in our observable universe and made one big black hole, the entropy would be about 10120. The entropy of the universe might seem big, but it’s nowhere near as big as it could be.
If you don’t understand entropy that well, how can you even talk about the arrow of time?
We don’t need a rigorous formula to understand that there is a problem, and possibly even to solve it. One thing is for sure about entropy: low-entropy states tend to evolve into higher-entropy ones, not the other way around. So if state A naturally evolves into state B nearly all of the time, but almost never the other way around, it’s safe to say that the entropy of B is higher than the entropy of A.
Are black holes the highest-entropy states that exist?
No. Remember that black holes give off Hawking radiation, and thus evaporate; according to the principle just elucidated, the entropy of the thin gruel of radiation into which the black hole evolves must have a higher entropy. This is, in fact, borne out by explicit calculation.
So what does a high-entropy state look like?
Empty space. In a theory like general relativity, where energy and particle number and volume are not conserved, we can always expand space to give rise to more phase space for matter particles, thus allowing the entropy to increase. Note that our actual universe is evolving (under the influence of the cosmological constant) to an increasingly cold, empty state — exactly as we should expect if such a state were high entropy. The real cosmological puzzle, then, is why our universe ever found itself with so many particles packed into such a tiny volume.
Could the universe just be a statistical fluctuation?
No. This was a suggestion of Bolzmann’s and Schuetz’s, but it doesn’t work in the real world. The idea is that, since the tendency of entropy to increase is statistical rather than absolute, starting from a state of maximal entropy we would (given world enough and time) witness downward fluctuations into lower-entropy states. That’s true, but large fluctuations are much less frequent than small fluctuations, and our universe would have to be an enormously large fluctuation. There is no reason, anthropic or otherwise, for the entropy to be as low as it is; we should be much closer to thermal equilibrium if this model were correct. The reductio ad absurdum of this argument leads us to Boltzmann Brains — random brain-sized fluctuations that stick around just long enough to perceive their own existence before dissolving back into the chaos.
Don’t the weak interactions violate time-reversal invariance?
Not exactly; more precisely, it depends on definitions, and the relevant fact is that the weak interactions have nothing to do with the arrow of time. They are not invariant under the T (time reversal) operation of quantum field theory, as has been experimentally verified in the decay of the neutral kaon. (The experiments found CP violation, which by the CPT theorem implies T violation.) But as far as thermodynamics is concerned, it’s CPT invariance that matters, not T invariance. For every solution to the equations of motion, there is exactly one time-reversed solution — it just happens to also involve a parity inversion and an exchange of particles with antiparticles. CP violation cannot explain the Second Law of Thermodynamics.
Doesn’t the collapse of the wavefunction in quantum mechanics violate time-reversal invariance?
It certainly appears to, but whether it “really” does depends (sadly) on one’s interpretation of quantum mechanics. If you believe something like the Copenhagen interpretation, then yes, there really is a stochastic and irreversible process of wavefunction collapse. Once again, however, it is unclear how this could help explain the arrow of time — whether or not wavefunctions collapse, we are left without an explanation of why the early universe had such a small entropy. If you believe in something like the Many-Worlds interpretation, then the evolution of the wavefunction is completely unitary and reversible; it just appears to be irreversible, since we don’t have access to the entire wavefunction. Rather, we belong in some particular semiclassical history, separated out from other histories by the process of decoherence. In that case, the fact that wavefunctions appear to collapse in one direction of time but not the other is not an explanation for the arrow of time, but in fact a consequence of it. The low-entropy early universe was in something close to a pure state, which enabled countless “branchings” as it evolved into the future.
This sounds like a hard problem. Is there any way the arrow of time can be explained dynamically?
I can think of two ways. One is to impose a boundary condition that enforces one end of time to be low-entropy, whether by fiat or via some higher principle; this is the strategy of Roger Penrose’s Weyl Curvature Hypothesis, and arguably that of most flavors of quantum cosmology. The other is to show that reversibilty is violated spontaneously — even if the laws of physics are time-reversal invariant, the relevant solutions to those laws might not be. However, if there exists a maximal entropy (thermal equilibrium) state, and the universe is eternal, it’s hard to see why we aren’t in such an equilibrium state — and that would be static, not constantly evolving. This is why I personally believe that there is no such equilibrium state, and that the universe evolves because it can always evolve. The trick of course, is to implement such a strategy in a well-founded theoretical framework, one in which the particular way in which the universe evolves is by creating regions of post-Big-Bang spacetime such as the one in which we find ourselves.
Why do we remember the past, but not the future?
Because of the arrow of time.
Why do we conceptualize the world in terms of cause and effect?
Because of the arrow of time.
Why is the universe hospitable to information-gathering-and-processing complex systems such as ourselves, capable of evolution and self-awareness and the ability to fall in love?
Because of the arrow of time.
Why do you work on this crazy stuff with no practical application?
I think it’s important to figure out a consistent story of how the universe works. Or, if not actually important, at least fun.
Greg wrote:
I answered that in the last paragraph of #112: you’d always be moving towards the horizon, but never catching up with it (not in your proper time, or by anyone else’s coordinates). Trying to cross a horizon the “wrong way” is like trying to catch up with a pulse of light — and if you remember that the horizon itself consists of potential world lines of photons this becomes a bit less mysterious.
Ah, that makes sense, thanks. So that would seem to imply that you can decide whether a given massive object is a black hole or a white hole without paying any attention to the thermodynamic arrow of stuff around it (aside from the arrow of your own brain and measuring equipment), just by seeing whether an object dropped into it reaches the horizon in finite proper time or not. For example, if you’re on a platform hovering above the horizon you could drop a probe over the edge which constantly sends back radio messages of its current clock reading, calculate what its final clock reading would be as it crossed the event horizon if the object were a black hole, and then if you continue to receive messages of greater clock readings than that you know the object must be a white hole…is that right? If so, that would suggest a possible way of making sense of the notion that an object could still be called a “white hole” even if the entropy around it were increasing rather than decreasing (which would also imply a way of making sense of the notion that an object could still be called a ‘black hole’ even if the entropy around it were decreasing).
By the way, do you have the Misner-Thorne-Wheeler “Gravitation” handy? There’s a section there that seems related to the question of whether a single object can behave like a black hole and a white hole at different points in its history, which you had said something about in comment #116…on p. 826 they describe the construction of the Novikov coordinate system, and it seems to be based on considering a collection of particles which are emitted from the singularity and rise up out of the event horizon like a white hole, but then fall back downwards through the even horizon like a black hole, and with the condition that “Every particle in the swarm is ejected in such a manner that it arrives at the summit of its trajectory (r = rmax, tau =0) at one and the same value of the Schwarzschild coordinate time; namely, at t=0”. The coordinate system is constructed in such a way that each of these particles has a constant radial coordinate throughout its “cycloidal life”. So what I’m wondering is, does this mean that from the point of view of Schwarzschild coordinates, the object is behaving like a white hole from Schwarzschild time -infinity to 0, and then behaving like a black hole from Schwarzschild time 0 to +infinity? In #116 you said that an object could be a black hole for one segment of its life and then a white hole for the next segment, is this the same sort of thing?
Jesse,
Your scheme where you drop a probe with a clock, and you monitor its signals reporting back its proper time does make sense to me as a way of distinguishing “black” holes from “white” — where these words take their meaning entirely by reference to the arrow of time that you (and also the probe) possess.
The Novikov coordinates as described in MTW are actually leading into a separate issue, which is that the Schwarzschild solution for a perfect eternal classical black hole can be extended from what we’d normally think of as a black hole and its exterior into a larger solution that also includes a white hole and its exterior elsewhere. This is a kind of (non-traversable) wormhole known as the “Einstein-Rosen bridge”, that would “join” either two universes, or two parts of one universe. But (a) this is a mathematical idealisation that doesn’t apply to astrophysical black holes, (b) you could never travel through the “bridge” anyway, and (c) this is completely separate from the issue of considering the single exterior region around a hole undergoing a change in name because the people naming it at different times are subject to different thermodynamic arrows.
MTW don’t explain any of this in the section on Novikov coordinates; you have to keep on reading through sections 31.5 and 31.6 before all of this is made clear. In particular, look at the curve that includes the points F, F’ and F” in figure 31.4(b) on page 835. If you follow this curve back in time prior to “the summit” at F, you’ll see that it actually has to cross t=-infinity before it can ascend from the horizon (let alone the singularity)! There’s a kind of symmetry in Novikov and Kruskal-Szekeres coordinates which is very beautiful, but a bit misleading, because this extended Schwarzschild geometry that they describe (if you take in the full range of their coordinates) is twice what would actually be there in reality.
Appreciated your thoughts John…
I have become more and more impressed by the common sense and significance of relativity and QM in explaining the world we observe.
We know it well, but it is easy to forget that these concepts are, first and foremost, descriptive with extremely precise experimental veracity, in the case of GR for example, to more than 10 decimal places. That is easy to recite, but when we consider that the diameter of an atom is perhaps 10 to the minus 8th Cm, we can see how GR works right down to levels of scale where quantum effects dominate.
I said in another thread that a recent practical test of GR in an airplane was accurate to “a few centimeters”. What I did not say was that that level of accuracy had nothing to do with the precision of GR…the accuracy problem was our guestimate of the distance between the antennae on the windows on each side of the cabin of the aircraft!
GR accurately measures continental drift, the recession of the moon…with an accuracy of much less than one millimeter. The limits of measurement are essentially the limits of our instrumentation. This kind of accuracy is at the same time, awesome and profound.
Gravitational time dilation for example, is not some esoteric idea but is at the heart of the way we observe the universe…a reason why we exist as we do. The grand proportion, the principles of binomial expansion, the observed speed of light, the behavior of the photon and the origins of particulation within observed scale are all interrelated concepts, and…as you point out, result in the way we observe the arrow of time.
Jesse
I’m afraid I was completely wrong when I claimed that the proper time for an observer to fall to a white hole horizon was infinite. MTW section 25.5 makes it clear that the proper time to ascend from any r coordinate r1 to rest at a maximum r-coordinate R is exactly the same as the proper time to fall from R to r1. That those two times are the same for a black hole means they’ll also be the same for a white hole, and will involve finite proper times to cross between the singularity, the horizon, and the r-coordinate R outside the horizon.
The twist is, particles that “ascend from the singularity” must ascend from a different singularity than the one particles fall into; also, ascending particles cross through a different horizon. (See Fig 31.4b of MTW page 835) I think that if you’re going to have an eternal classical black hole (eternal in both time directions), you really do have to consider the full Schwarzschild geometry, which inevitably contains a black hole / white hole pair. And that pair is time-symmetric!
My statements about the light cones at the horizon were correct as far as they went, but when you have an eternal BH/WH pair like this, what happens when you time-reverse it is the white hole becomes a black hole, and an observer who falls from the exterior falls into what is now the black hole! So you never find yourself stuck outside a white hole unable to cross into the interior.
Sorry for the confusion.
Obviously the finite case will be different, but I’m not really clear as to what constitutes sensible formation and destruction events for white holes (unless we’re just going to time-reverse the normal processes of stellar collapse and Hawking decay for black holes, which would defeat our whole goal of figuring out what it means if you don’t time-reverse the whole universe along with the black hole). I’ll have to think about this some more.
Sam,
I’m certainly not arguing with the math, rather making the point that too much focus on the details does distort our understanding of the larger picture. I’ve been arguing that time is a consequence of motion, similar to temperature, rather then dimensional basis for it, like space. Consider a thermal medium, say a pot of hot water, with lots of water molecules moving about. If we were to determine a time keeping process out of this situation, we would take the motion of one of these points of reference and measure it against the medium it is moving through. The point is the hand and the medium is the face of the clock. Obviously all the other points are hands of their own clocks, but are medium/face for all other clocks. As Newton said, “For every action, there is an equal and opposite reaction.” So the motion of any point/hand is balanced by the reaction of the medium/face of the clock. To the hands of the clock, the face goes counterclockwise.
Time is described as a dimension because it has direction from past events to future ones, but these events go from being future potential to past circumstance. Tomorrow becomes yesterday. In the thermodynamic medium, the relationships of these points constitute an event, even though the perspective is different for every point. While any and all of the points go from past events to future ones, the medium against which any point is being judged is the overall context, which once created, is displaced by the next, so this event goes from present to past. Mass is the face of the clock. As form it is information that goes from future potential to past circumstance. The energy is the hand of the clock, going on to the next unit of form and time, as it leaves the old.
This collapsing wave of future potential turning into past circumstance, is distilled out as linear narrative. The quantum event, the bottle of poison, the cat, the box, our eyes. This linear progression is a stream of specific detail, like the path of a particular molecule traveling through the larger medium and the series of encounters involved. Yet there are innumerable other points of reference also describing their own narrative and all this activity exists in an equilibrium, so there are waves of all these other narratives crashing around as potential turns to actual and then is replaced, nothing really collapses to a point, just continues on its merry way, because every narrative amounts to the center of its own coordinate system, to which the circumstances determine the rate of change and there is no one dimension of time. The only absolute temperature is the complete absence of it and the same applies to time.
While the math may be accurate down to the last decimal point, the real question is what is being measured. Time is a measure of motion, not the other way around.
The answer I gave to this previously (in #124) was incomplete. If the black hole has an infinite past, you do see particles that escaped in the past from the white hole half of the extended Schwarzschild geometry, at the same time as you see particles falling in, destined for the black hole horizon and singularity. Some of these particles will be the same, i.e. they go from the white hole singularity to the black hole singularity; others will go out to, or come in from, infinity.
But if it’s an astrophysical black hole that formed some finite time ago from a collapse, then rather than seeing particles that left a white hole singularity (which is no longer part of the solution), you’ll see the massively red-shifted light that was emitted from the surface of the collapsing star just before it fell through the horizon. The luminosity of that surface emission drops exponentially with time, so in effect it very rapidly becomes the blackness of the black hole.
It’s that case — where there’s only one horizon and one singularity, which must be seen by a given observer either as purely a black hole or purely a white hole according to the observer’s arrow of time — that I was describing in my answer in #124.
And if you time-reverse a black hole formed by a collapsing star, then if you let yourself fall freely towards the white hole produced by the reversal, you never cross the horizon; rather, after a finite proper time, you collide with the time-reversed collapsing star emerging from the white hole.
Since no one has yet commented on my post above (121), I assume that it may be due to unfamiliarity with the works of Gustafson or Zhu.
Perhaps a quote from Zhu will help stir things up:
Huaiyu Zhu, On the Physical Reality of Wave-Particle Duality
“It will be shown that mathematical justification of entropy must always rely on a quantum assumption.
Unfortunately, the standard quantum theory…was still reversible, save for the measurement process, so the paradoxes became even more acute: (1) The measurement process is irreversible, so it could not, even in principle, be described as part of the physical world. (2) Because of the uncertainty principle the second law could not be attributed to the lack of precision in measurements.
The purpose of this letter is to explore the idea that the difficulties mentioned above may be overcome by a single postulate, that the random quantum jumps, hitherto confined to measurement alone, if admitted at all, are inherent in the physical world.”
“(Unfortunately), the standard quantum theory…was still reversible, save for the measurement process, so the paradoxes became even more acute: (1) The measurement process is irreversible, so it could not, even in principle, be described as part of the physical world.”
Len, the field work in this area I have studied indicates that at the quantum level of scale, the measurement process itself is reversible, not irreversible. We can observe and measure events to occur a certain way, change our minds and proceed to observe and measure them to happen differently, with a different measurable outcome.
At the quantum level of scale, CPT symmetry is a fact of life, save for a few sub-atomic particles. Since these symmetry breaking particles nevertheless appear in predictable numbers, it can be presumed that even they emerge from a process inherent in the universal structure. The implication, of course is that even these “violations of symmetry”, since they repeat and are predictable, are part of an overall symmetrical system.
Chirality is a given..it has to be a part of any universe where information exists and a arrow of time can be observed at some frame of reference. What seems a flat (or curved) and uniform surface when observed from one scale, as the Earth’s curvature observed from a distance, may, when observed from a less remote coordinate, be correctly observed to be quite asymmetrical…
I’m not really sure there is a paradox here…
I don’t personally understand why quantum reversibility is (unfortunate) either…it just is…it is behaviour we observe. Moreover this observed reality dovetails very nicely with the mathematical symmetry of most of the laws of physics…including GR and of course, Quantum Mechanics…
“The purpose of this letter is to explore the idea that the difficulties mentioned above may be overcome by a single postulate, that the random quantum jumps, hitherto confined to measurement alone, if admitted at all, are inherent in the physical world.”
Len, I think you make a very valid point…”are inherent in the physical world”.
White holes! What are they? Egan (if I remember the name) is on the right track. The Penrose diagram for the Schwarzschild solution is a pentagon with an X crossing from the top to bottom corners. Try to draw it or look it up. The bottom and top horizonal edges are the singularity at r = 0, which curiously is a three dimensional space where the Weyl curvature diverges. There are two timelike regions, the squares on either side of the X and two tirangular wedges that are spacelike regions. The top one is the black hole, and the bottom is the white hole. Both the black hole and the while hole are “eternal” and the white hole is a source of stuff coming out and the black hole an absorber. If you can find a Finkelstein diagram for a black hole and turn it upside down you have the white hole.
Is the white hole physical? No. The problem is that black holes are not eternal, they are formed by collapsing matter and this truncates the Penrose diagram so there is just one timelike wedge and only the black hole remains. Some time back I thought about using black holes, white holes and euclideanized gravity solutions as a model for instantons and excitons, but abandoned the effort. There was some talk back in the early 70s about white holes as being “creation fields” in the universe, which spew out material and cause the expansion of the universe. None have been found and the idea is no longer regarded as even theoretically stable.
Sam:
Please note:
Both sections of your response were not to my words, but to part of the quoted excerpt from Zhu’s 8-page letter.
The world is made up of overlapping relationships at multiple scales. Time is what we call changes in the configuration of these relationships. Acceleration also causes changes in relationship between things. I agree that time is a product of motion, specifically acceleration. Gravity and acceleration are both attributes associated with moving mass. So, maybe moving mass creates time and a temporal reference frame that is consistent for that system as long as that system exists. If so, initial conditions come into play, but not low entropy.
Why do we attribute the arrow of time to entropy when we are surrounded by examples of entropy both increasing and decreasing? We don’t observe the future affecting the past. We see causality going in one direction (though relativity of reference frames gives me pause on that one). That is the view from here, now.
On the issue of “Blackhole>
Ok, lets see On the issue of “Blackhole-Whitehole” distinction, as sort of stated by Lawrence post 136, in which Penrose has a new idea of perceptive solution to the problem.
If one was to derive a collapse of a Stellar object(star) of certian Mass, then a Blackhole remnant becomes the end product in GR. Now for Galactic Blackholes, the process is reversed, as observer paramiters are introduced into the solutions, I believe Smolin introduced this into one type of model. So how does one differentiate between Stellar collapse Blackholes and Galactic Blackoles, with the corresponding Whitehole solutions?
Using cyclic models, the solutions intertwine at a “crunch”, and out of the solutions comes another Universe with amongst other factors, Times Arrow being instrumental in determining what WAS and what WILL be, that is what happened before the crunch, and what happened after the crunch.
If one looks up into the night sky, where there are a lot of “White” holes visible, its just we call them Stars, these Stars/StellarWhiteholes, will emerge out of this universe (when seen by following observers in the “next” universe), as the primordial Blackholes in Smolins model. The time reversal ONLY occurs within the paramiters of close to a crunch/bounce.
You can derive stellar collapse blackholes, if you could physically reverse the process within our Universe as a single isolated system, then the Star would re-emerge from the collapsed blackhole. But the laws of thermodynamics do not allow this, except at a Universal critical “end” phase.
On the “other” side of a bounce,(which can only be retraced by observers WITHIN that cosmic horizon) what were Galactic blackholes appear to be spitting out vast quantities of whitholes, or Stars.
So Penrose’s idea basically, in it’s simplest form works thus:Our local stars, are “Whiteholes” to any previous or post observers in any “other” Universe. Our Galactic blackholes, are Time’s Arrow starting points of a Previous singular point, wherby White holes become Blackholes, and Blackhole become Whiteholes. Entropy, of a previous Universe cannot but influence, with absolute precise form and function, as the remnant energy of our Universe disperses and wanes towards a crunch/bounce, there is less particles available, so there are very little colliding events, Time as we now it appears to be settling down into a process of absolute “order” rather than chaos.
Out of “this>
Greg, thanks for the clarification, this discussion and that section of the MTW book are giving me a better understanding of Schwarzschild black holes. I think I can follow the basics of what’s going on in the Kruskal-Szekeres diagram on p. 834, from this it seems like my earlier suggestion of an observer hovering at a fixed radius above the horizon and seeing a constant stream of both ingoing and outgoing particles would be possible, so as seen from the outside the object is more like a “gray hole”, neither purely black nor purely white. But I erred in imagining that the worldlines of ingoing and outgoing test particles would ever cross inside the horizon–in fact, each ingoing test particle that passes the observer will subsequently cross the worldlines of all the infinite number of outgoing particles that the fixed-distance observer will receive after that moment, before the ingoing particle reaches the horizon (in finite proper time, of course). Likewise, after crossing the horizon each outgoing test particle crosses the worldline of every ingoing particle that has passed the fixed-distance observer up until the moment the outgoing particle reaches him.
As you said, the Kruskal-Szekeres diagram shows that the region of spacetime that the ingoing particles find themselves in after crossing the horizon is different from the region of spacetime that the outgoing particles came from before crossing the horizon, so I guess it is only in these interior regions that it really makes sense to talk about a “white hole” and a “black hole” as fundamentally different objects. Or at least they’re potentially different–MTW mention on p. 840 that in principle one could identify these two distinct regions on the diagram with one another, but they mention two objections, one involving a “conical singularity” where there is no local Lorentz frame, and one involving causality violations where observers can meet themselves going backward in time. But another physicist, Andrew Hamilton, also mentions the possibility of identifying the regions in this way here, and argues that the conical singularity is not really a reason to reject this possibility out-of-hand, and also says the objection about causality violations is incorrect, I think because any time an “ingoing” object interacts with an “outgoing” one, it will only influence the part of the “outgoing” object’s worldline that is closer to the singularity than the interaction-event. Unless we assume that the matter coming out of the black hole is at maximum entropy, though, it seems to me there could still be weird issues of objects with different thermodynamic arrows of time meeting inside the horizon, or of outgoing objects having to flip their arrow of time at the moment they cross the horizon.
I’m still pretty much in the dark about the ingoing vs. outgoing issue in the case of non-Schwarzschild black holes that don’t exist forever. From the Kruskal-Szekeres diagram of a collapsing star on p. 848, I think I see what you meant in comment #132 about the only outgoing light being light emitted by particles in the collapsing star before they crossed the event horizon; there’s only one event horizon here, and it lies along the diagonal r = 2M, t = + infinity coordinate line, so the only way for a diagonal light ray to cross the horizon is for it to be parallel to the other diagonal r = 2M, t = -infinity coordinate line, which will make it an “ingoing” ray. But I wonder if things would change if you took into account Hawking radiation which allows the horizon to shrink after the star has collapsed. In terms of the diagram, it seems like a shrinking horizon would be represented by a line closer to vertical than the r = 2M, t = +infinity coordinate line, in which case it might be possible to have “outgoing” photon worldlines parallel to this t = + infinity coordinate line which crossed the shrinking event horizon (though these photons would not actually emerge from the singularity, if I’m picturing it right…maybe they’d be able to enter the horizon from ‘region III’ and leave it in ‘region I’ without ever running into the singularity?) But then again, I’m not sure if it even makes sense to have a Kruskal-Szekeres diagram in which you don’t have an event horizon lying along the diagonal coordinate line, or whether light beams would necessarily still be diagonals in this case (could you describe an ordinary flat Minkowski spacetime in terms of Kruskal-Szekeres coordinates, and if so would all light beams still be diagonals?)
It might also be interesting to consider the hypothetical case of a perfectly time-symmetric black/white hole with a finite lifetime, which initially forms from a collapsing shell of matter (or converging time-reversed Hawking radiation), lasts for some time, then blows apart in a time-reversed version of its formation. I’m not sure if this is physically allowable in general relativity, although it must at least be allowable to have a white hole which has lasted from t = – infinity but then blows apart in the time-reversed version of a normal black hole’s formation. If it is possible to have a time-symmetric black-white hole with a finite lifetime, then I wonder if it could have both outgoing and ingoing photons crossing the horizon, and whether it would potentially have two distinct inner regions like a Schwarzschild black hole (and if so, maybe you’d need a different set of coordinates than the Kruskal-Szekeres ones to make this clear, just as the Schwarzschild coordinates don’t really work for depicting the two inner regions of a Schwarzschild black hole).
Len, I agree that quantum fluctuations are inherent to the sub-microscopic universe, but I’m not sure a single postulate explains such behavior- or that such a postulate is neccesary anyway. Sometime when I have a chance, I’ll look it over…I don’t like to pre-judge something I have not studied, but those are first impressions based on the content of what you posted…Sam
Sandy,
It is a pleasant surprise to see someone else questioning whether time is fundamental. The institutional effect on science makes it acceptable to project established theory in the most fantastical, convoluted and complex forms imaginable, but fresh insights based on basic observation are too pedestrian to consider.
The discussion of black and white holes is a good example; Gravitation contracts. Radiation expands. Everything else is detail, perspective, or some combination thereof and when the two columns are added up and the loose ends tied together, there won’t be any need for all the supernatural phenomena currently proposed, from extra universes and additional meta-dimensions, to Big Bang theory and its various patches, from Inflation to Dark energy.
To those whom this may offend, it is another attempt to crack the facade and start a discussion. Surely I’m too stupid to be right and with all the intelligent people in this conversation, someone should have the wherewithal to set me straight. I may be too thick to understand, but it would be good test of communication skills.
Jesse
I don’t want to comment further on this until I’ve done some more reading, but if you want to see a Penrose diagram (aka conformal diagram) of an evaporating black hole, there’s one on page 413 of Wald’s General Relativity. (BTW, in the Wikipedia article I just linked to, they do actually call the infinite Schwarzschild geometry a “grey hole”.) Penrose diagrams are a great way of keeping track of causal relationships, and if you know when light signals can get from one event in spacetime to another, you also know that any material particles around will have to travel between the two sides of the (two-dimensional version of the) light cones.
The arrow of time could be like a coil spring, a coil spring design allows for a closed loops that start and end in the same place, (but these closed loops have to be observed on one side). If there is a closed loop in the centre of the spring, then it could prevent the universe from changing direction but also allows for the possibility of time travel (but in a rather frightening way). I think the arrow of time entirely depends on the ability of a observer, to deal with the vast amount of information that’s needed to produce a closed loop half way through a universe.
Qubit
The future can affect the present where there is consciousness (free will) or any plan or algorithm working towards a predetermined goal (a program). Only the past is out of reach. What attribute(s) does the past have that the present and future don’t? One thing is a lack of uncertainty.
There is an arrow of time from the past to the present and future, but there is also an arrow of time from the future to the present, with the past walled off.
Thanks again Greg, I don’t own Wald’s book but I’ll check out a copy and take a look at that Penrose diagram. As I did some more thinking about this issue, I found it also helped to picture what was going on in terms of the “ingoing Eddington-Finkelstein” coordinates on p. 828-829 of MTW, where ingoing light rays are always represented as diagonals, but outgoing rays can be curved. The outgoing light rays from the center of a collapsing star immediately before it crossed the event horizon shown in the diagram labelled “Eddington-Finkelstein spacetime diagram of the collapsing sphere” on this page; looking at the diagram, I can more easily see what you meant in #132 about a distant observer forever seeing outgoing rays from the moments before the collapsing star crossed the event horizon, in the case of a black hole which lasts forever after the collapse (realistically the observer wouldn’t actually be able to detect them after a while because they’d be too redshifted and anyway light is emitted in discrete photons rather than continuously, but I’m really just talking about what geodesics would represent the past light cone of events on the distant observer’s worldline). For a black hole which subsequently evaporates, I think it would be a modified version of this diagram where the outside observer sees outgoing rays from the moments before the star crosses the horizon for a long time, then suddenly sees light from events at the R=0 coordinate immediately after the black hole finally evaporated completely. I found a paper, The Internal Geometry of an Evaporating Black Hole, which at the very end has a caption for fig. 3 describing the outgoing light geodesics for an evaporating black hole in advanced/ingoing Eddington-Finkelstein coordinates (the diagrams have to be downloaded separately from here), which shows that an outside observer would continue to see light that had been very close to the horizon for a long time until the final evaporation.
I assume, then, that if we turn this sort of diagram upside down, it shows what would happen to the ingoing light rays in the case of a white hole which formed via time-reversed Hawking radiation and then later blew apart as a time-reversed collapsing star, as seen in the outgoing or ‘retarded’ Eddington-Finkelstein coordinates described on pp. 829-831 of MTW (where it’s the outgoing light rays that are always represented as diagonals). So, this also helps me see what you meant at the end of #132 when you said “if you let yourself fall freely towards the white hole produced by the reversal, you never cross the horizon; rather, after a finite proper time, you collide with the time-reversed collapsing star emerging from the white hole.” This also suggests a sense in which a black hole could be differentiated from a white hole regardless of the arrow of time of matter outside–even if we had a black hole that formed via converging light that looked just like time-reversed Hawking radiation, so that its formation and growth appeared symmetrical with its shrinking and evaporation in the ingoing Eddington-Finkelstein coordinates (including a reversal of the thermodynamic arrow outside the hole at its moment of maximum size), it could still be differentiated from its own time-reversed white hole because a freefalling observer on the outside could cross the black hole’s event horizon in a finite time, while for the white hole they’d be flung forward in time on a path that hugged the outside of the event horizon until the white hole had evaporated under them (probably in an amount of proper time comparable to the proper time it took the first observer to fall into the event horizon of the black hole from the same distance, although I’m not sure about that).
The only thing that’s still a little confusing to me is what the black hole would look like in outgoing/retarded Eddington-Finkelstein coordinates, or what the white hole would look like in ingoing/advanced Eddington-Finkelstein coordinates. It almost seems as though in these cases the holes would have to form and evaporate in zero coordinate time in order for the distant observer’s light cones to come out right. I think maybe what was confusing me before was the thought that if a black hole’s formation and growth were symmetrical with its shrinking and evaporation as plotted in the ingoing/advanced coordinate system, then the drawing of its event horizon would look exactly the same in the outgoing/retarded coordinate system, but I suppose there’s no reason to expect that should have to be true. At some point I need to either study a GR textbook on my own or go to graduate school, so I can figure out how to do these sorts of plots myself…
Sandy,
But the present becomes the past(and at an ever increasing rate, the older you get), so that wall is being breached continuously.
Hey, anyone remember about the paper by Einstein and Tolman (?) supposedly saying that the past was not definite due to quantum info issues? I don’t mean, “merely” that we can’t find out all details about it. I mean, literally indistinct despite our observing specific things happening now, etc. I don’t think it was a MW type thing. Is that what most workers think?
I haven’t had time to read through all the comments, so apologies if someone has mentioned this already. But I wouldn’t glibly collapse our lack of memory of the future, our conceptions of cause and effect, and the second law of thermodynamics into the same arrow of time. There is no generally accepted argument for why any of those should cause the others, or why they should all share a common cause. For one, it seems obvious that our psychological arrow of time still applies to observed events that involve systems without a well-defined thermodynamic entropy (which, in fact, includes most systems), suggesting that the psychological arrow of time cannot be explained by the thermodynamic arrow.
A contrary view worth mentioning, I think, is John Earman’s argument that there is as yet no good reason to accept cosmological arguments for a low entropy past.