Followup to: Timeless Physics
One of the great surprises of humanity's early study of physics was that there were universal laws, that the heavens were governed by the same order as the Earth: Laws that hold in all times, in all places, without known exception. Sometimes we discover a seeming exception to the old law, like Mercury's precession, but soon it turns out to perfectly obey a still deeper law, that once again is universal as far as the eye can see.
Every known law of fundamental physics is perfectly global. We know no law of fundamental physics that applies on Tuesdays but not Wednesdays, or that applies in the Northern hemisphere but not the Southern.
In classical physics, the laws are universal; but there are also other entities that are neither perfectly global nor perfectly local. Like the case I discussed yesterday, of an entity called "the lamp" where "the lamp" is OFF at 7:00am but ON at 7:02am; the lamp entity extends through time, and has different values at different times. The little billiard balls are like that in classical physics; a classical billiard ball is (alleged to be) a fundamentally existent entity, but it has a world-line, not a world-point.
In timeless physics, everything that exists is either perfectly global or perfectly local. The laws are perfectly global. The configurations are perfectly local—every possible arrangement of particles has a single complex amplitude assigned to it, which never changes from one time to another. Each configuration only affects, and is affected by, its immediate neighbors. Each actually existent thing is perfectly unique, as a mathematical entity.
Newton, first to combine the Heavens and the Earth with a truly universal generalization, saw a clockwork universe of moving billiard balls and their world-lines, governed by perfect exceptionless laws. Newton was the first to look upon a greater beauty than any mere religion had ever dreamed.
But the beauty of classical physics doesn't begin to compare to the beauty of timeless quantum physics.
Timeful quantum physics is pretty, but it's not all that much prettier than classical physics. In timeful physics the "same configuration" can still have different values at different times, its own little world-line, like a lamp switching from OFF to ON. There's that ugly t complicating the equations.
You can see the beauty of timeless quantum physics by noticing how much easier it is to mess up the perfection, if you try to tamper with Platonia.
Consider the collapse interpretation of quantum mechanics. To people raised on timeful quantum physics, "the collapse of the wavefunction" sounds like it might be a plausible physical mechanism.
If you step back and look upon the timeless mist over the entire configuration space, all dynamics manifest in its perfectly local relations, then the "pruning" process of collapse suddenly shows up as a hugely ugly discontinuity in the timeless object. Instead of a continuous mist, we have something that looks like a maimed tree with branches hacked off and sap-bleeding stumps left behind. The perfect locality is ruined, because whole branches are hacked off in one operation. Likewise, collapse destroys the perfect global uniformity of the laws that relate each configuration to its neighborhood; sometimes we have the usual relation of amplitude flow, and then sometimes we have the collapsing-relation instead.
This is the power of beauty: The more beautiful something is, the more obvious it becomes when you mess it up.
I was surprised that many of yesterday's commenters seemed to think that Barbour's timeless physics was nothing new, relative to the older idea of a Block Universe. 3+1D Minkowskian spacetime has no privileged space of simultaneity, which, in its own way, seems to require you to throw out the concept of a global now. From Minkowskian 3+1, I had the idea of "time as a single perfect 4D crystal"—I didn't know the phrase "Block Universe", but seemed evident enough.
Nonetheless, I did not really get timelessness until I read Barbour. Saying that the t coordinate was just another coordinate, didn't have nearly the same impact on me as tossing the t coordinate out the window.
Special Relativity is widely accepted, but that doesn't stop people from talking about "nonlocal collapse" or "retrocausation"—relativistic timeful QM isn't beautiful enough to protect itself from complication.
Shane Legg's reaction is the effect I was looking for:
"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."
I wish I knew whether the unimpressed commenters got what Shane Legg did, just from hearing about Special Relativity; or if they still haven't gotten it yet from reading my brief summary of Barbour.
But in any case, let me talk in principle about why it helps to toss out the t coordinate:
To reduce a thing, you must reduce it to something that does not itself have the property you want to explain.
In old-school Artificial Intelligence, a researcher wonders where the meaning of a word like "apple" comes from. They want to get knowledge about "apples" into their beloved AI system, so they create a LISP token named apple. They realize that if they claim the token is meaningful of itself, they have not really reduced the nature of meaning... So they assert that "the apple token is not meaningful by itself", and then go on to say, "The meaning of the apple token emerges from its network of connections to other tokens." This is not true reductionism. It is wrapping up your confusion in a gift-box.
To reduce time, you must reduce it to something that is not time. It is not enough to take the t coordinate, and say that it is "just another dimension". So long as the t coordinate is there, it acts as a mental sponge that can soak up all the time-ness that you want to explain. If you toss out the t coordinate, you are forced to see time as something else, and not just see time as "time".
Tomorrow (if I can shake today's cold) I'll talk about one of my points of departure from Barbour: Namely, I have no problem with discarding time and keeping causality. The commenters who complained about Barbour grinding up the universe into disconnected slices, may be reassured: On this point, I think Barbour is trying too hard. We can discard t, and still keep causality within r.
I dare to disagree with Barbour, on this point, because it seems plausible that Barbour has not studied Judea Pearl and colleagues' formulation of causality—
—which likewise makes no use of a t coordinate.
Pearl et. al.'s formulation of "causality" would not be anywhere near as enlightening, if they had to put t coordinates on everything for the math to make sense. Even if the authors insisted that t was "just another property" or "just another number"... well, if you've read Pearl, you see my point. It would correspond to a much weaker understanding.
Part of The Quantum Physics Sequence
Next post: "Timeless Causality"
Previous post: "Timeless Physics"