Interestingly (at least, I think it's interesting), I'd always felt that way about time, before I learned about quantum mechanics. That's what a four-dimensional spacetime means, isn't it? And so science fiction stories that involve, say, changing the past have never made any sense to me. You can't change the past; it is. And no one can come from the future to change now, because the future is as well. Although now that I think about it more, I realize how this makes slightly more sense in this version of many-worlds than it does in a collapse theory.
Belatedest answer ever: don't think of it as changing the past, think of it as establishing a causal link to an alternate version of the past that had you appear in a time machine (and obeys other constraints, depending on the time travel rules of the story).
And yes, you can not only fit General Relativity into this paradigm, it actually comes out looking even more elegant than before.
Eliezer, do you realize the difference between Barbour's treatments of classical mechanics and GR? In GR, he bases everything not just on relations between matter, but on relations between matter and space itself (at least its metric structure). When he calls his theory "relational" he is engaging in wordplay. The Pooley paper I linked in yesterday's comments goes into gory philosophical detail on this.
I think some people (not including Eliezer) see that Barbour says "there is no time" and imagine that he invented the idea of a block universe (which I personally don't see any philosophical problems with). But it's everyone else who believes in block universes; Barbour's universe is an unsorted-pile-of-block-slices universe. Barbour's theory de-unifies space and time. Ouch!
Lee Smolin is one of the people behind relational QM, and he's a naive Popperian. To me he's the closest thing that physics has to a philosophical anti-authority.
Asking "What happened before the Big Bang?" is revealed as a wrong question. There is no "before"; a "before" would be outside the configuration space. There was never a pre-existing emptiness into which our universe exploded. There is just this timeless mathematical object, time existing within it; and the object has a natural boundary at the Big Bang. You cannot ask "When did this mathematical object come into existence?" because there is no t outside it.
This has been true of the standard (FRW) big bang models since, what, the 1920s?
Ah. And suppose I snapped my fingers and caused all the stars and galaxies to move into the appropriate positions for 2108?
"You'd be arrested for violating the laws of physics."
But suppose I did it anyway.
I get so frustrated when you write stuff like this because you also wrote: http://lesswrong.com/lw/if/your_strength_as_a_rationalist/
Therefore at this point my answer is no you did not.
However, funnily enough, once you changed all the atoms in the universe my response was "Okay now it is 2108" (maybe because I found the universe in a consistent believable state including my memories of the intevening 100 years).
And by the way since I would have survived for another 100 years I might just have overwhelming personal evidence that Many Worlds is true. I guess that would be your purpose for the exercise. (Of course if you are still there with me after that 100 years then the overwhelming personal evidence doesn't happen).
I have been learning a lot from your quantum mechanics series. Thanks. Please keep it up.
You've drawn many vague conclusions (read: words, not equations or experimental predictions) about the nature of reality from a vague idea promoted by a non-academic. It smacks strongly of pseudo-science.
Julian Barbour's work is unconventional. Many of his papers border on philosophy and most are not published in prominent journals. His first idea, that time is simply another coordinate parameterizing a mathematical object (like a manifold in GR) and that it's specialness is an illusion, is ancient. His second idea, that any theory more fundamental than QM or GR will necessarily feature time only in a relational sense (in contrast to the commonly accepted, and beautiful, gauge freedom of all time and space coordinates) is interesting and possibly true, but it is most likely not profound. I can't read all of his papers, so perhaps he has some worthwhile work.
This post, however, appears to be completely without substance. What is the point?
"We don't need the t.
It's redundant.
The r never repeats itself."
While this seems to be true given the expansion of the universe, is it strictly necessary? What if some value R does repeat, throwing the universe into an endless loop? At some point, the chains of r's leading up to R0 and R1 would differ; wouldn't we need another variable to encode that?
I can't help but feel that you are wading into waters which are above your expertise.Wading?
Eliezer is not beckoning, but drowning.
But your argument is flawed. Discarding an argument because you don't feel it's 'profound' is an error. There are scores of mundane truths that go ignored because they're not 'profound' enough to interest the self-styled philosophers, and countless empty 'profundities' that mean nothing.
Most of the 'eternal questions' have already been answered. The trick is to recognize this and move on.
Interesting aesthetic question raised by Caledonian's comment: "not beckoning, but drowning" versus "not wading, but drowning". I think the latter would have worked much better, but presumably C. thought it too obvious and wanted to preserve more of Stevie Smith's semantics. :-)
Arthur, what would keeping a time coordinate buy you in your scenario? Suppose, simplifying for convenience, we have A -> B -> C -> B [cycle], and suppose each state completely determines its successor. What advantage would there be to labelling our stat...
Stop it!
If I intuitively took on board your timeless MWI view of the world... well, I'm worried that this might endanger my illusion of consciousness.
Thinking about it is already making me feel a bit weird.
g, I'm not sure how it all works out in terms of ψ, as the mathematics of multi-dimensional configuration spaces is way over my head. What I'm not clear on is, in the absence of t, why do we have to read the function from "left to right?" When you read in the other direction, State C can "lead to" A or B. Don't we need a variable to differentiate between the C that leads to A, and the C that leads to B, to as Eliezer put it, "keep things straight"?
Doesn't the Lorentz invariant already pretty much take care of the relativity of time? As long as we're using the Lorentz invariant, we're free to reparameterize the universe any way we want, and our description will be the same. So I don't see what this Barbour guy is going on about, it seems like standard physics. Whether you write your function f(x,t) or f(y) where y = g(x,t) or even just f(x) where t = h(x) is totally irrelevant to the universe. It's just another coordinate transformation just like translating the whole universe by ten meters to the left.
Now, if you have a new invariant to propose, THAT would amount to an actual change in the laws of physics.
@Jess
Your comments on Barbour (non-academic etc) are ad hominem, I say so what? Being an academic may be an indicator for good work, but not more. And he did his Ph.D in physics anyway.
Julian Barbour's work is unconventional.
Yes! Fine. Lovely. Science needs more unconventional thinkers. Let the evidence sort them out, but let's not be against "unconventional" theories. Especially not when they are explanatorily powerful.
Many of his papers border on philosophy
There are two kinds of philosophy: the bad kind (Essay by Paul Graham criticising philoso...
Whence comes the experience of a present moment?The after-the-fact processing done by the brain of the data accumulated in that moment, of course.
If that storage is disrupted - by sudden trama or an experiential shock, such as that which might occur in a car accident without leaving lasting damage - there are no experiences at all.
If there are no lasting consequences of an event that our physiology can react to, it's as though it never happened at all, at least as far as our awareness is concerned. If you have no high-level memory representation of an e...
Caledonian, you miss the point. The present moment seems distinguishable from the past or future, singular, and in constant motion. Experience exists in the present and describes the past via memory and the future via speculation. The content of experience changes.
Even if this is a cognitive illusion, it needs a reason.
But the main thing that's different about time is that it has a clear direction whereas the space dimensions don't. This is caused by the fact that the universe started out in a very low-entropy state, and since then has been evolving into higher entropy. I don't know if it's even possible to answer the question of why the universe started out the way it did -- it's almost like asking why anything exists at all. But whatever the reason, the universe is very uniform in its space dimensions, but very non-uniform in its time dimension.
In philosophy "four dimensionalism" is probably the dominant view of time. We're all spacetime worms in a block universe. I don't know what to make of some of Barbour's ideas but I can swallow timelessness.
It's worth noting, regarding Jadagul's comment, that time travel should be possible in a block universe without paradox and without resorting to many-worlds. The closed time-like curve just exists as part of the block universe and the illusion of paradox stems from our foreknowledge of events. It's not required that we be able to change things ...
The present moment seems distinguishable from the past or future, singular, and in constant motion.
The 'present' is always the immediate past. We're not aware of things happening in the true present, because our nervous system doesn't have anything to process. It can only receive data corresponding to the very recent past, and then it takes even more time to process it.
The reality is that our awareness operates on a measureable time-lag.
For some reason, this view of time fell nicely in place in my mind (not "Aha! So that's how it is?" but "Yes, that's how it is."), so if it's wrong, we're a lot of people to be mistaken in the same way.
But that doesn't dissolve the "What happened before the Big Bang?" question. I point at our world and ask "Where does this configuration come from?", you point at the Big Bang, I ask the same question, and you say "Wrong question.". Huh?
The thing about the concept of a block universe that bothers me is the question of the reversibility of the Schrödinger equations. I have been told that they are so, but I have to take it on faith that they are completely time-symmetric since they are just beyond where I am comfortable in Mathematics.
So, if one looks at the current configuration space for a point of 'now', and works the equations backwards, does one get only one possible past, or an large number of possible pasts? If its the former, how can one claim that the equations are time symmetric? If its the latter, why don't we remember all of those quantum possibilities?
I point at our world and ask "Where does this configuration come from?"There is no phenomenon within time that can be used as an explanation for the configuration, as is required by the phrase "come from". Furthermore, if we try to explain a thing by referring to another thing, we then need an explanation for the other thing.
There is no reason for the configuration of time within time, and even if we adopt a timeless perspective, we can never find an ultimate resolution to the question. The universe simply is what it is. Your question is surely asked in good faith, but it's not meaningful.
Günther: Of course my comments about Barbour were (partially) ad hominem. The point was not to criticize his work, but to criticize this post. Very few people are qualified to assess the merit of Barbour's work. This includes, with respect, Eliezer. In the absence of expertise, the rational thinker must defer to the experts. The experts have found nothing of note in Barbour's work.
Albert Einstein was not performing philosophy when he developed GR. He was motivated by a philosophical insight and then did physics.
I wasn't intending to suggest that the timelessness of the universe is an answer to the First Cause puzzle (which itself is certainly a Wrong Question, somehow) because you just point to the whole timeless mathematical object and say, "Why does this 'exist'?"
It's just that you can't answer by tracing to one minute before the Big Bang and some mighty act of the Flying Spaghetti Monster. You'll have to look somewhere else for a resolution to your confusion.
@Stirling: If you took one world and extrapolated backward, you'd get many pasts. If you take the many worlds and extrapolate backward, all but one of the resulting pasts will cancel out! Quantum mechanics is time-symmetric.
@Shane Legg: Good to see that the post had its intended effect.
So, if one looks at the current configuration space for a point of 'now', and works the equations backwards, does one get only one possible past, or an large number of possible pasts? If its the former, how can one claim that the equations are time symmetric? If its the latter, why don't we remember all of those quantum possibilities?
Both. Many possible pasts, because the many worlds are never entirely causally isolated, so we are to some minuscule degree always affected by parallel worlds (though not enough to notice). But one possible past, because only ...
This abstract of one of Barbour's papers may be helpful for those wondering (like me) how exactly Barbour was proposing to get rid of "t":
http://www.iop.org/EJ/abstract/0264-9381/11/12/006
Abstract. A strategy for quantization of general relativity is considered in the context of the timelessness' of classical general relativity discussed in the preceding companion paper. The Wheeler--DeWitt equation (WDE) of canonical quantum gravity is interpreted as being like a time-independent Schrödinger equation for one fixed energy, the solution of which s
...
If you took one world and extrapolated backward, you'd get many pasts. If you take the many worlds and extrapolate backward, all but one of the resulting pasts will cancel out!
I agree. However, at the same time, we don't actually remember the many extrapolated pasts of the one world we inhabit. Of course, "remembering" multiple extrapolated pasts might be indistinguishable from failing to remember any particular past (e.g., if both X and not-X lie in our extrapolated past, then our "remembering" both X and not-X might be nothing other than failing to remember whether X or not-X).
Well, I'm not sure there's no observable difference. I mean, let's say you have universe in state |A> such that the evolution of the state vector would cause it one nanosecond later (whatever the heck that turns out to really mean) to be, oh, say something like (-|A> + |B>)/sqrt(2)
Now, if time was truly nonexistant then those two would interfere with each other, right? ie, it's sortakinda the same sort of test to find out if two particles are really identical or not.
Except, wait, if we're talking total state of reality... how would one perform the...
Is the possibility of life in non conventional coordinates occurring been discarded?
By this i mean evolution were selection is made along some coordinate of space, or backwards in time.
Maybe it would make a good Sci-Fi finding some intelligent life form which evolved from the future to the past, meeting humanity at present.
I agree with those who can't quite see the point of this post (block universe is old and uncontroversial), but I suppose that may because I internalized (mostly) this view some time ago. I see some people are learning from it.
Something like Barbour's timeless physics has to be true, or I'm in trouble: I have forgotten how to imagine a universe that has "real genuine time" in it.
I hope you're not saying this is a good thing, or that others should follow.
I'm a huge fan of the general program of philosophical minimalism (i.e., doing away with epiphenomena). One of my favorite works in this respect is Hartry Field's Science Without Numbers. There's a long line of argument in philosophy for the reality of mathematical abstracta on the grounds of its indispensability to science. Field formulated a version of classical physics without numbers.
Barbour is proposing something quite different from the block universe. I'm not sure if Eliezer is missing the point, or just not carrying it across. Barbour is speculating that if we solve the Wheeler-DeWitt equation, we'll get a single probability distribution over the configuration space of the universe, and all of our experiences can be explained using this distribution alone. Specifically, we don't need a probability distribution for each instant of time, like in standard QM.
I think Eliezer's picture with the happy faces is rather misleading, if it's ...
It's worse than just P-symmetry (parity) violation. There's also CP-symmetry (charge-parity) breaking, which, given CPT symmetry (a fairly reasonable assumption given current knowledge) means that the weak nuclear force also violates T-symmetry. Even without the second law of thermodynamics, you would be able to put an arrow to time by observing the decay of certain particles.
Therefore, we need time.
I went back to the beginning of this series of posts, and found this introduction:
I think I must now temporarily digress from the sequence on zombies (which was a digression from the discussion of reductionism, which was a digression from the Mind Projection Fallacy) in order to discuss quantum mechanics. The reasons why this belongs in the middle of a discussion on zombies in the middle of a discussion of reductionism in the middle of a discussion of the Mind Projection Fallacy, will become apparent eventually.
Eliezer, would you mind telling us the reaso...
We're not? Did I miss a memo?
@Nick Tarleton, anyone questioning the value of this post Prior to this post, my understanding was that there wasn't one 'me' consciously observing the unraveling of our universe over time. Instead, there were many of 'me', each observing a different universe, and with every irreversible thermodynamic event, more universes and instances of 'me' were being created.
This post blew my mind.
@Julian "Whence comes the present moment?" Now I understand that "I" am not a consciousness traveling through time. Instead, my consciousness is represen...
Manon de Gaillande asked "Where does this configuration come from?" Seeing no answer yet, I'm also intrigued by this. Does it even make sense to ask it? If it doesn't, please help Manon and I dissolve the question.
It doesn't make sense in the strict sense, in that barring the sudden arrival of sufficiently compelling evidence, you aren't going to be able to answer it with anything but metaphysical speculation. You aren't going to come out less confused about anything on the other side of contemplating the question.
Furthermore, no answer changes ...
Furthermore, no answer changes any of our expectations -- whether or not we're a naturally occurring phenomenon or a higher-dimensional grad student's Comp Sci thesis has no effect on any of our experiences within this universe.
You're not imaginative enough. If the latter is true, we're a lot more likely to see messages from outside the Matrix sometime. ("Sorry, guys, I ran out of supercomputer time.")
You're not imaginative enough. If the latter is true, we're a lot more likely to see messages from outside the Matrix sometime. ("Sorry, guys, I ran out of supercomputer time.")
For various values of "a lot", I suppose. If something is simulating something the size of the universe, chances are it's not even going to notice us (unless we turn everything into paper clips, I suppose). Just because the universe could be a simulation doesn't mean that we're the point of the simulation.
@Eliezer: You say If you took one world and extrapolated backward, you'd get many pasts. If you take the many worlds and extrapolate backward, all but one of the resulting pasts will cancel out!
If this is true, then why do we calculate forward based only on our current configuration? If we took all the many worlds in our possible pasts and extrapolated forward, would they cancel out all but a single future?
If everything we know is but a simulation being run in a much larger world, then "everything we know" isn't a universe.
If you can receive messages from outside of the Matrix, inside, the Matrix isn't a universe either.
There is no outside to the universe. There's isn't anything there. There isn't even nothing there. There isn't even a there there. You've gone beyond the bounds of existence and nonexistence once you've left the universe behind.
If everything we know is but a simulation being run in a much larger world, then "everything we know" isn't a universe.
The question wasn't "what's outside the universe?", it was "where did the configuration that we are a part of come from?"
I don't think you can necessarily equate "configuration" (the mathematical entity that we are implicitly represented within), with "universe" (everything that exists).
Viewing the universe as a timeless four-dimensional object - rather than the temporal evolution of a three-dimensional one - does not really buy you any "simplicity" - because then you need an additional explanation of why the four-dimensional object is structured in the way that it is.
I don't understand "perfectly local or perfectly global". My intuition of the Schroedinger equation is that it gives an approximation of the probability amplitude for a system, and that approximation is accurate to the extent that the system is isolated from the rest of the universe. The degree to which it is not accurate is the degree to which it is not isolated. An unentangled hydrogen atom in intergalactic space is fairly isolated; a hydrogen atom participating in an H2 molecule is not; but I argue that there are intermediate - "imperf...
"where did the configuration that we are a part of come from?"
That IS speculating about what is beyond the universe. Your question is unanswerable.
If I understand this model correctly, it has the consequence that from a typical point in the configuration space there are not only many futures (i.e. paths starting at this point, along which entropy is strictly increasing), but many pasts (i.e. paths starting at this point, along which entropy is strictly decreasing). Does this sound correct?
Question:
Doesn't the multi-worlds interpretation of quantum mechanics define an arrow of time?
Imagine we have a random number generator which randomly adds or subtracts 1 from a given number, each with equal probability. Say our initial number is zero. After the first iteration, the space of possible values consists of {-1,1}. After two iterations, it expands to {-2,-1,0,1,2}. It seems clear that progressively larger iterations monotonically increase the space of possible outcomes. Doesn't this defines an arrow of time in the forward direction?
Likewis...
Years after first reading this, I think I've internalized its central point in a clear-to-me way, and I'd like to post it here in case it's useful to someone else with a similar bent to their thinking.
Without worrying about the specific nature of the Schrodinger equation, we can say the universe is governed by a set of equations of form x[i] = fi, where each x[i] is some variable in the universe's configuration space, each f[i] is some continuous function, and t is a parameter representing time. This would be true even in a classical universe---the configu...
Do the classical equations, using ψ(r, t), assume that you'll get a different outcome from ψ(r, n)? That is, if the system is in the exact same configuration, but at a "different time", would the classical equations suggest a different outcome?
(Mostly, this struck me as another approach for demonstrating that this 't' thing is extraneous.)
This post inpires wtf moments in my brain. Anyone here read Greg Egan's Permutation City?
Now I find myself asking "What is going on where I feel like there is this quantity time?" instead of "What is time?"
Zero background in physics here. But these essays (or what little I understand of them) are blowing my mind. Here I'm going to ramble and ask questions. I would be so happy if somebody could enlighten me in some way.
I believe I understand the concept of configuration space (the pyramid diagram). But what does it means for an unchanging "quantum mist" to be distributed across this space? Is the mist denser in some areas than in others? Are the denser areas more probable configurations of matter? Are there some points within the space that t...
Previously in series: Relative Configuration Space
I shall begin by asking a incredibly deep question:
What time is it?
If you have the excellent habit of giving obvious answers to obvious questions, you will answer, "It is now 7:30pm [or whatever]."
How do you know?
"I know because I looked at the clock on my computer monitor."
Well, suppose I hacked into your computer and changed the clock. Would it then be a different time?
"No," you reply.
How do you know?
"Because I once used the 'Set Date and Time' facility on my computer to try and make it be the 22nd century, but it didn't work."
Ah. And how do you know that it didn't work?
"Because," you say, "I looked outside, and the buildings were still made of brick and wood and steel, rather than having been replaced by the gleaming crystal of diamondoid nanotechnological constructions; and gasoline was still only $4/gallon."
You have... interesting... expectations for the 22nd century; but let's not go into that. Suppose I replaced the buildings outside your home with confections of crystal, and raised the price of gas; then would it be 100 years later?
"No," you say, "I could look up at the night sky, and see the planets in roughly the same position as yesterday's night; with a powerful telescope I could measure the positions of the stars as they very slowly drift, relative to the Sun, and observe the rotation of distant galaxies. In these ways I would know exactly how much time had passed, no matter what you did here on Earth."
Ah. And suppose I snapped my fingers and caused all the stars and galaxies to move into the appropriate positions for 2108?
"You'd be arrested for violating the laws of physics."
But suppose I did it anyway.
"Then, still, 100 years would not have passed."
How would you know they had not passed?
"Because I would remember that, one night before, it had still been 2008. Though, realistically speaking, I would think it more likely that it was my memory at fault, not the galaxies."
Now suppose I snapped my fingers, and caused all the atoms in the universe to move into positions that would be appropriate for (one probable quantum branch) of 2108. Even the atoms in your brain.
Think carefully before you say, "It would still really be 2008." For does this belief of yours, have any observable consequences left? Or is it an epiphenomenon of your model of physics? Where is stored the fact that it is 'still 2008'? Can I snap my fingers one last time, and alter this last variable, and cause it to really be 2108?
Is it possible that Cthulhu could snap Its tentacles, and cause time for the whole universe to be suspended for exactly 10 million years, and then resume? How would anyone ever detect what had just happened?
A global suspension of time may seem imaginable, in the same way that it seems imaginable that you could "move all the matter in the whole universe ten meters to the left". To visualize the universe moving ten meters to the left, you imagine a little swirling ball of galaxies, and then it jerks leftward. Similarly, to imagine time stopping, you visualize a swirling ball of galaxies, and then it stops swirling, and hangs motionless for a while, and then starts up again.
But the sensation of passing time, in your visualization, is provided by your own mind's eye outside the system. You go on thinking, your brain's neurons firing, while, in your imagination, the swirling ball of galaxies stays motionless.
When you imagine the universe moving ten meters to the left, you are imagining motion relative to your mind's eye outside the universe. In the same way, when you imagine time stopping, you are imagining a motionless universe, frozen relative to a still-moving clock hidden outside: your own mind, counting the seconds of the freeze.
But what would it mean for 10 million "years" to pass, if motion everywhere had been suspended?
Does it make sense to say that the global rate of motion could slow down, or speed up, over the whole universe at once—so that all the particles arrive at the same final configuration, in twice as much time, or half as much time? You couldn't measure it with any clock, because the ticking of the clock would slow down too.
Do not say, "I could not detect it; therefore, who knows, it might happen every day."
Say rather, "I could not detect it, nor could anyone detect it even in principle, nor would any physical relation be affected except this one thing called 'the global rate of motion'. Therefore, I wonder what the phrase 'global rate of motion' really means."
All of that was a line of argument of Julian Barbour's, more or less, Let us pause here, and consider a second line of argument, this one my own. That is, I don't think it was in Barbour's The End of Time. (If I recall correctly, I reasoned thus even before I read Barbour, while I was coming up with my unpublished general decision theory of Newcomblike problems. Of course that does not mean the argument is novel; I have no idea whether it is novel. But if my argument is wrong, I do not want it blamed on an innocent bystander.) So:
A fine sentiment; but what does it mean to change the future?
Suppose I have a lamp, with an old-style compact fluorescent bulb that takes a few seconds to warm up. At 7:00am, the lamp is off. At 7:01am, I flip the switch; the lamp flickers for a few moments, then begins to warm up. At 7:02am, the lamp is fully bright. Between 7:00am and 7:02am, the lamp changed from OFF to ON. This, certainly, is a change; but it is a change over time.
Change implies difference; difference implies comparison. Here, the two values being compared are (1) the state of "the lamp at 7:00am", which is OFF, and (2) the state of "the lamp at 7:02am", which is ON. So we say "the lamp" has changed from one time to another. At 7:00am, you wander by, and see the lamp is OFF; at 7:02am, you wander by, and see the lamp is ON.
But have you ever seen the future change from one time to another? Have you wandered by a lamp at exactly 7:02am, and seen that it is OFF; then, a bit later, looked in again on the "the lamp at exactly 7:02am", and discovered that it is now ON?
Naturally, we often feel like we are "changing the future". Logging on to your online bank account, you discover that your credit card bill comes due tomorrow, and, for some reason, has not been paid automatically. Imagining the future-by-default—extrapolating out the world as it would be without any further actions—you see that the bill not being paid, and interest charges accruing on your credit card. So you pay the bill online. And now, imagining tomorrow, it seems to you that the interest charges will not occur. So at 1:00pm, you imagined a future in which your credit card accrued interest charges, and at 1:02pm, you imagined a future in which it did not. And so your imagination of the future changed, from one time to another.
As I remarked previously: The way a belief feels from inside, is that you seem to be looking straight at reality. When it actually seems that you're looking at a belief, as such, you are really experiencing a belief about your beliefs.
When your extrapolation of the future changes, from one time to another, it feels like the future itself is changing. Yet you have never seen the future change. When you actually get to the future, you only ever see one outcome.
How could a single moment of time, change from one time to another?
I am not going to go into "free will" in today's blog post. Except to remark that if you have been reading Overcoming Bias all this time, and you are currently agonizing about whether or not you really have free will, instead of trying to understand where your own mind has become confused and generated an impossible question, you should probably go back and read it all again. For anyone who is just now joining us... perhaps I shall discuss the issue tomorrow.
Just remember Egan's Law: It all adds up to normality. Apples didn't stop falling when Einstein disproved Newton's theory of gravity, and anyone who jumped off a cliff would still go splat. Perhaps Time turns out to work differently than you thought; but tomorrow still lies ahead of you, and your choices, and their consequences. I wouldn't advise reworking your moral philosophy based on confusing arguments and strange-seeming physics, until the physics stops appearing strange and the arguments no longer seem confusing.
Now to physics we turn; and here I resume drawing my ideas from Julian Barbour.
For the benefit of anyone who hasn't followed the series on quantum mechanics, a very very quick summary:
Above is a diagram that shows what a configuration space might look like for three particles, A, B, and C. ABC form a triangle in two-dimensional space. Every individual point in the configuration space corresponds to a simultaneous position of all the particles—above we see points that correspond to particular triangles i.e. joint positions of A, B, and C. (Classical Configuration Spaces; The Quantum Arena.)
The state of a quantum system is not a single point in this space; it is a distribution over this space. You could imagine it as a cloud, or a blob, or a colored mist within the space.
Here we see a relative configuration space, in which each axis is the distance between a pair of particles. This has some advantages I'm not going to recapitulate (it was covered in a previous post), so if you're dropping into the middle of the series, just pretend it's a regular configuration space.
We've just chopped up the pyramidal space you saw before, into a series of slices. In this configuration space, the slices near the bottom show all the particles close together (tiny triangles). As we rise up, the particles get further apart (larger triangles).
At the very bottom of the configuration space is a configuration where all the particles occupy the same position.
(But remember, it's nonsense to talk about an individual particle being anywhere in a configuration space—each point in the configuration space corresponds to a position of all the particles. Configuration space is not the 3D space you know. It's not that there are a bunch of particles resting in the same place at the bottom. The single bottom point corresponds to all the particles being in the same place in 3D space.)
Here we take a closer look at one of the slices of configuration space, and see a cloud of blue and red mist covering some of it. (Why am I only showing the cloud covering a sixth (exactly a sixth) of the triangle? This has to do with a symmetry in the space—exchanges of identical particles—which is not important to the present discussion.)
But there is your glimpse of some quantum mist—in two colors, because amplitudes are complex numbers with a real and imaginary part. An amplitude distribution or "wavefunction" assigns a complex number to every point in the continuous configuration space—a complex number to every possible configuration of all the particles.
Yesterday, I finished by asking how the state of a quantum system might evolve over time.
You might be tempted to visualize the mist churning and changing colors, as quantum amplitude flows within the configuration space.
And this is indeed the way that you would visualize standard physics.
Behold the standard Schrödinger Equation:
Here ψ(r, t) is the amplitude distribution over configuration space (r) and time (t). The left-hand side of the Schrödinger Equation is the change over time of the wavefunction ψ, and the right-hand-side shows how to calculate this change as the sum of two terms: The gradient of the wavefunction over configuration space (at that time), and the potential energy of each configuration.
Which is to say, the derivative in time of the wavefunction—the instantaneous rate of change—can be in terms of the wavefunction's derivative in space, plus a term for the potential energy.
If you tried to visualize Schrödinger's Equation—doesn't look too hard, right?—you'd see a blob of churning, complex mist in configuration space, with little blobs racing around and splitting into smaller blobs as waves propagated.
If you tried to calculate the quantum state of a single hydrogen atom over time, apart from the rest of the universe—which you can only really do if the hydrogen atom isn't entangled with anything—the atom's quantum state would evolve over time; the mist would churn.
But suppose you think about the whole universe at once, including yourself, of course. Because—even in the standard model of quantum physics!—that is exactly the arena in which quantum physics takes place: A wavefunction over all the particles, everywhere.
If you can sensibly talk about the quantum state of some particular hydrogen atom, it's only because the wavefunction happens to neatly factor into (hydrogen atom) * (rest of world).
Even if the hydrogen atom is behaving in a very regular way, the joint wavefunction for (hydrogen atom * rest of world) may not be so regular. Stars move into new positions, people are born and people die, digital watches tick, and the cosmos expands: The universe is non-recurrent.
Think of how the universal wavefunction ψ(r, t) might behave when r is the position of all the particles in the universe.
Let's call 9:00am the time t=0, measured in seconds.
At ψ(r, t=0), then, you are wondering what time it is: The particles making up the neurons in your brain, are in positions ryou that correspond to neurons firing in the thought-pattern "What time is it?" And the Earth, and the Sun, and the rest of the universe, have their own particles in the appropriate rrest-of-universe. Where the complete r roughly factorizes as the product (ryou * rrest-of-universe).
Over the next second, the joint wavefunction of the entire universe evolves into ψ(r, t=1). All the stars in the sky have moved a little bit onward, in whatever direction they're heading; the Sun has burned up a little more of its hydrogen; on Earth, an average of 1.8 people have died; and you've just glanced down at your watch.
At ψ(r, t=2), the stars have moved a little onward, the galaxies have rotated, the cosmos has expanded a little more (and its expansion has accelerated a little more), your watch has evolved into the state of showing 9:00:02 AM on its screen, and your own mind has evolved into the state of thinking the thought, "Huh, I guess it's nine o' clock."
Ready for the next big simplification in physics?
Here it is:
We don't need the t.
It's redundant.
The r never repeats itself. The universe is expanding, and in every instant, it gets a little bigger. We don't need a separate t to keep things straight. When you're looking at the whole universe, a unique function ψ of (r, t) is pretty much a unique function of r.
And the only way we know in the first place "what time it is", is by looking at clocks. And whether the clock is a wristwatch, or the expansion of the universe, or your own memories, that clock is encoded in the position of particles—in the r. We have never seen a t variable apart from the r.
We can recast the quantum wave equations, specifying the time evolution of ψ(r, t), as specifying relations within a wavefunction ψ(r).
Occam's Razor: Our equations don't need a t in them, so we can banish the t and make our ontology that much simpler.
An unchanging quantum mist hangs over the configuration space, not churning, not flowing.
But the mist has internal structure, internal relations; and these contain time implicitly.
The dynamics of physics—falling apples and rotating galaxies—is now embodied within the unchanging mist in the unchanging configuration space.
This landscape is not frozen like a cryonics patient suspended in liquid nitrogen. It is not motionless as an isolated system while the rest of the universe goes on without it.
The landscape is timeless; time exists only within it. To talk about time, you have to talk about relations inside the configuration space.
Asking "What happened before the Big Bang?" is revealed as a wrong question. There is no "before"; a "before" would be outside the configuration space. There was never a pre-existing emptiness into which our universe exploded. There is just this timeless mathematical object, time existing within it; and the object has a natural boundary at the Big Bang. You cannot ask "When did this mathematical object come into existence?" because there is no t outside it.
So that is Julian Barbour's proposal for the next great simplification project in physics.
(And yes, you can not only fit General Relativity into this paradigm, it actually comes out looking even more elegant than before. For which point I refer you to Julian Barbour's papers.)
Tomorrow, I'll go into some of my own thoughts and reactions to this proposal.
But one point seems worth noting immediately: I have spoken before on the apparently perfect universality of physical laws, that apply everywhere and everywhen. We have just raised this perfection to an even higher pitch: everything that exists is either perfectly global or perfectly local. There are points in configuration space that affect only their immediate neighbors in space and time; governed by universal laws of physics. Perfectly local, perfectly global. If the meaning and sheer beauty of this statement is not immediately obvious, I'll go into it tomorrow.
And a final intuition-pump, in case you haven't yet gotten timelessness on a gut level...
Think of this as a diagram of the many worlds of quantum physics. The branch points could be, say, your observation of a particle that seems to go either "left" or "right".
Looking back from the vantage point of the gold head, you only remember having been the two green heads.
So you seem to remember Time proceeding along a single line. You remember that the particle first went left, and then went right. You ask, "Which way will the particle go this time?"
You only remember one of the two outcomes that occurred on each occasion. So you ask, "When I make my next observation, which of the two possible worlds will I end up in?"
Remembering only a single line as your past, you try to extend that line into the future -
But both branches, both future versions of you, just exist. There is no fact of the matter as to "which branch you go down". Different versions of you experience both branches.
So that is many-worlds.
And to incorporate Barbour, we simply say that all of these heads, all these Nows, just exist. They do not appear and then vanish; they just are. From a global perspective, there is no answer to the question, "What time is it?" There are just different experiences at different Nows.
From any given vantage point, you look back, and remember other times—so that the question, "Why is it this time right now, rather than some other time?" seems to make sense. But there is no answer.
When I came to this understanding, I forgot the meaning that Time had once held for me.
Time has dissolved for me, has been reduced to something simpler that is not itself timeful.
I can no longer conceive that there might really be a universal time, which is somehow "moving" from the past to the future. This now seems like nonsense.
Something like Barbour's timeless physics has to be true, or I'm in trouble: I have forgotten how to imagine a universe that has "real genuine time" in it.
Part of The Quantum Physics Sequence
Next post: "Timeless Beauty"
Previous post: "Relative Configuration Space"