That’s weird to me. I’m from the 1950s and can measure my life in scores of years (three-and-mumble). I was an avid science fiction reader by the 1960s, so recall an era where we wondered if the year 1984, let alone 2001, would be anything like the famous book.
As it turned out, in both cases: No. Respectively fortunate and unfortunate. The future turned out less extreme (but no less “interesting”). Both demonstrate the difficulty of prediction, a problem science fiction illustrates more often than not.
That said, the other face of Janus looks forward…
The look back in the previous post ran longer than I expected, so there was no room for a look forward. Same thing happened last year: one post to look back; one to look forward. Two faces, two posts, seems apt.
Speaking of running longer, that’s a bridge between the backward and forward views. My average word count per post has certainly increased over the years:
A significant jump after a year off, and something of an upward trend since. The posts per year numbers echo the words per post data with notable exceptions in 2018 and 2021:
Just wasn’t cranking them out last year, but I was more verbose than ever.
That does reflect a conscious loosening of the count leash. I used to see 1200–1500 as a negotiable ceiling, but lately I’ve been feeling very comfortable up to 1700. The lid floats around 1800–2000. Some run longer. Very rarely I’ll break 2500.
I may try for more brevity by not combining multiple TV or movies reviews into a single post. That makes sense if I don’t have much to say about any of them and they’re related by some theme (even as broad as “anime”), but I’ve had too many of those end up with high word counts. Doing shorter single posts would doubly reduce the average by increasing the number of posts while reducing the number of words in those posts.
That said, a lot of the other posts I’m thinking about are technical enough to end up with lots of words in them. Such posts account, in part, for the upward trend.
I’m not gonna give it a lot of thought. It is what it is.
§ §
Jumping into increasingly distant space, I read that, on Saturday the James Webb Space Telescope (JWST) successfully deployed its sunshield. If you’re aware of the incredible effort it took to get to this point, this is awesome news. A gem to start the new year.
A full-scale model of the JWST at Goddard Space Flight Center and the team that worked on it there (mid-September 2005). [photo NASA]
The telescope is optimized for seeing in the near- and mid-infrared, which allows it to search for highly red-shifted ancient galaxies. That’s exciting because observing large ancient galaxies might tip the dark matter question in favor of MOND theories.
Infrared is radiant heat, so telescopes must be as cold as possible. Otherwise the heat of the telescope obscures the image like a light leak in a camera. The JWST will orbit in Earth’s L2 Lagrange point — one-and-a-half million kilometers away from Earth on the opposite side from the Sun. (In comparison, the Moon orbits a bit over one-third of a million km away.)
The point is, the telescope is roughly as far from the Sun as the Earth is — hardly the chill of the outer Solar system, let alone deep space. That means the ‘scope needs a sunshield. A very large and effective sunshield. More to the point, a sunshield much too large to fit in a rocket.
As I mentioned above, 2001 was wrong, we’re still not to the point of serious construction in space, so the large sunshield had to be a 344-step origami trick performed after launch.
Blueprint of the JWST [image NASA]
Twenty-five years of development and the efforts of tens of thousands of people and billions of tax-payer dollars down to 344 sequential steps, any one of which, should it fail, dooms the ‘scope.
And it went perfectly. Must have been one hell of a New Year’s party.
A huge thank you and congratulations to all involved!
§ §
Crossing space from science to science fiction, last year I finally got around to reading Octavia Butler. Long overdue and regrets for not doing it sooner. She more than deserves the acclaim I too long ignored.
This year, already, I finally got around to another author who has been on my radar for a while. Not for as long as with Butler, nor with the same degree of acclaim, but with a strong sense he might be my sort of hard SF author. I’m speaking of Alastair Reynolds.
Born in the mid-1960s, he’s a contemporary writer — one with a Ph.D. in astrophysics and former career as a research astronomer for the ESA. Attractive credentials for a hard SF author. That kind of background is what attracts me to authors such as Greg Egan, Robert L. Forward, Rudy Rucker, and, of course, Isaac Asimov.
As with Butler, I’m sure I’ve encountered his short stories in various collections, but few and far between enough that any sense of his was lost in the general clamor of short story authors. Now I’ve read two of his novels, and I liked them a lot. Definitely my sort of hard SF author.
Reynolds writes (at least in these) of the far future. In one case, the standalone novel House of Suns (2008), many millions of years from now. I also read the first book of his Revelation Space series, Revelation Space (2000), which is set in the 2500s — merely five-hundred years from now.
And while he is not without his indistinguishable-from-magic technology, both books take place in Einstein’s universe — no FTL, no magic warp drive. I have a major soft spot for science fiction that respects the speed of light.
Warp drive is a necessary gimme to tell the kind of story that makes the galaxy (or universe) more an analogue for Earth. But the same bent I have towards hard SF also inclines me towards an appreciation for a galaxy-sized story told in the framework of special relativity.
[Which I remind you says: (1) causality; (2) special relativity; (3) FTL. Pick two.]
So, I’m liking Reynolds a lot and looking forward to reading more. I’m currently waiting for my turn with the next book in the Revelation Space series. Free library books are great, but sometimes you wait.
§ §
Switching back to science, but from the vast to the tiny, at some point last year I got a little overloaded by how much more there is to learn about the mathematics of quantum mechanics. Looking back, I’ve learned a lot, but I’m still in the foothills in some regards. I needed a break from looking up at the mountain.
It’s not that the math is actually that hard, at least in the basics. There are things incredibly tedious to calculate (fortunately, computers are fast, accurate, and don’t get bored), and some things are intractable to normal computation (quantum computers will help). The math used, however, isn’t that tough. It’s mostly just calculus. My problem is that my calculus skills (such as they even are) fade out between derivatives and integrals.
The actual hard part is breaking away from physical intuition about how reality works and wrapping one’s head around what the mathematics says.
[A major puzzle in QM involves the ontology behind the math. Because it’s an abstraction and description of reality, all math is epistemic. But as a parabola abstracts and describes the arc of a physical baseball’s motion, the quantum mechanics math must be derived from something physical and real. If only we knew what it was.]
In any event, after a breather and letting things settle into shape, I’m ready to start climbing again. If I watch that MIT YouTube course again, my guess is I’ll get a lot more out of it.
§ §
I’ve long heard the complaint about older men wearing old clothes and resisting the efforts of family and friends to “throw that old shit away!” And rightfully so; holes and threadbare aren’t a great look no matter how comfortable and memory rich. My dad was certainly guilty — that old red flannel shirt — and guess who has his own red flannel shirt he really ought to just toss.
Hence the new forward looking rule about, after wearing the clean socks, underwear, tee-shirts, or sweaters, one last time, seriously consider, and lean strongly towards, just throwing that shit away. It’s not like I don’t have plenty and aren’t an Amazon Prime order away from more.
The purge has begun!
Now,… speaking of word count (which is under 1500), nuf sed.
Stay telescopic, my friends! Go forth and spread beauty and light.
∇
Logos con carne 
January 9th, 2022 at 5:06 pm
There is a link in the post, but here’s the unfolding video:
January 25th, 2022 at 9:37 am
The JWST has arrived at the L2 point and inserted itself into its orbit there. The mirrors are all deployed, and the next bit step is first light.
Here’s a NASA animation of the telescope’s orbit:
February 5th, 2022 at 8:58 am
Yay! The JWST has captured its first photons from a distant star. The telescope controllers have powered up the cameras enough to look at a star for purposes of mirror calibration. The star, HD 84406, is 241 LY away in the Big Dipper constellation.
What they captured were 18 blurry images. After calibration (and final cool down) there will be one sharp image.
But we won’t see “first light” images — real science images — for six months. It will take that long for calibration and cool down.
February 17th, 2022 at 8:44 am
Here’s a video from the JWST team about receiving the first photons (see above comment):
February 19th, 2022 at 2:50 pm
Here’s a good video from Sabine Hossenfelder about the JWST and what advances it might bring science:
March 18th, 2022 at 7:44 pm
NASA is close to completing the Fine Phasing step. Here’s a nice video about where they are and what they’ve been doing:
January 9th, 2022 at 7:15 pm
Speaking of quantum mechanics, Anil Ananthaswamy has an article in the January Scientific American about a possible test for Bohmian mechanics. Briefly, at extremely short distances, the prediction curves for particle time of flight (a curve that varies due to Uncertainty) differ between Bohmian and Copenhagen formulations of QM. At longer (thus far testable) distances, the two are indistinguishable.
It has, in part, to do with the separation of time from other observable quantum properties. There is no time operator the same way there is a position (or momentum or spin) operator. One version of the Schrödinger equation is even time-independent. The version that evolves over time assumes a t=0 state and a current t as input.
But even in Relativity time is distinct from space. Its signature is different in the spacetime interval, either (+,+,+,-) or (-,-,-,+), depending on whether one prefers positive or negative space-like intervals (respectively).
January 10th, 2022 at 3:33 am
I’m often amazed at how much larger space probes or rovers are than I envisage them to be (when most images are of them in space or within a landscape with no point of reference); that image of the full-scale model of JWST with the crowd of people provides such a perspective – I’m staggered; it’s twice as large as I thought it was!
The amount of money that gets spent on such things is also vast and barely comprehendible; I recently read David Whitehouses’ account of such things in his book Space 2069.
January 10th, 2022 at 10:30 am
I spent quite a bit of time pondering which images of the JWST to use. I really loved the blueprint, because I love blueprints and maps (and if you click through to the source and look at a big image, the text is in Latin). But of all the assembly pictures and artist renderings, that full-sized model with all those people is the one I kept coming back to. For exactly that reason. “Holy shit! That thing is huge!!”
Yeah, the money is beyond imagining to us. The flow through governments and huge corporations; those numbers just don’t have meaning to someone who cares about a paycheck (or pension). The planning and the need to get so many people on one page for so long is mind-blowing, too.
The length of time this stuff takes, I believe, is a huge impediment for our space exploration chances. It takes so much time to explore space, even with robots that can take high G. We need very long-term commitment, decades, if not hundreds of years. Fully exploring the galaxy would take millions. But democracy pulls the pendulum in both directions, sometimes to extremes, so committing to four more years is a challenge. Committing to a hundred-year project? Hard to imagine us pulling that off.
January 10th, 2022 at 9:42 am
On word counts, I’ve discovered that somewhere around 750 words appears to be my natural spot when I post on one particular topic. Getting shorter seems to take a lot of work, although when I try I can usually get it down to 600 or so. Of course, if I let the post sit in drafts, more points always occur to me and it tends to grow.
I’ve actually been thinking the same thing about entertainment posts. I’ve experimented lately with putting multiple things together, and it helps when I only have a few tidbits about each show. On the other hand, those could be short posts and they’d be easier to find and link to.
Good point about needing warp drive to make the galaxy more like the contemporary world. Interestingly, there are other ways to do it, like what Cowboy Bebop and the Gundam franchise do; just have a bunch of space colonies allowing the same range of polities and cultures. But I can also see why a lot of writers these days just opt for a fantasy world, like a steampunk one. It allows for the same commentary about modern day but with a similar distance to get around people’s partisan reflexes.
Have to admit I’m pretty bad about wearing clothes until they’re ready to give up the ghost. New clothes are just so uncomfortable. It seems like I have to go through multiple instances before finding one that will be a keeper.
That Scientific American article sounds interesting. Hope they put it on their site. (Although I rarely check them anymore. Too much paywalling and low quality content.)
January 10th, 2022 at 12:08 pm
Now you’ve gotten me thinking about looking at my word count numbers more closely. In the WP data, the finest granularity I have is posts and words per month. I do load the XML export file into an SQLite database, so I do have a way to scan individual posts… Hmmm… I have code that scans words in posts already. It creates a vocabulary index. It should be easy to adapt to giving me individual post word counts. Might end up being today’s little project… 🙂
You’re right about individual posts being easier to find. That runs through my mind in those collective posts. In some cases, the first one is the one I care about most, but I do worry about the ones getting second billing. I think I’ll try to stick to single reviews of shows I either really liked or disliked. Shows that give me a strong reason to write about them. The blog is meant to have an autobiographical aspect, but I think I’ll try to be more selective.
The size of space is a real challenge! Cowboy Bebop has inter-system gates, and The Expanse has quasi-magical (“very effective”) drives. The JWST needs 30 days to reach the L2 point. (“And that’s just peanuts compared to space.”) Even the transporters on Star Trek shrunk space down to manageable size. Come to think of it, we do the same thing on Earth sometimes: edit out travel time by horse, car, foot, etc. I suppose it ties into the dream-like thing where distance doesn’t matter.
I’ve bought a lot of clothes at places like Target, and I’ve learned that when I find something I like, be it tee-shirts or whatever, it’s best to buy a number of them at once. Target, especially, changes styles regularly, and items I’ve liked have vanished forever. Buying a bunch means they don’t wear out as quickly either and you can have different color options.
I am so not a fan of SciAm. I used to be. It used to be my favorite magazine. I subscribed to the hard copy starting in the late 1960s and kept that subscription until the 2000s when I finally let it lapse. They’ve gotten worse since for exactly the reasons you mention. I’m paying $9.99/mo for Apple News, which gives me an ad-free newsfeed and access to a lot of e-magazines, SciAm among them. So far it’s been worth the ten bucks a month.
Be pretty weird of Bohmian mechanics turned out right!
Which reminds me, I was thinking about The Absence in House of Suns. I don’t know if it’s what Reynolds had in mind for it, but it occurs to me it could be the result of the wormhole needing to prevent any shift in relative simultaneity. As you know, even low-velocity motion here results in a large shift of our “now” in Andromeda. If a wormhole connects our “now” with some “now” there, which moment in time is that there? It potentially could be any moment there not in our current light cone (because that’s the range in which simultaneity is relative and can be shifted). That’s a range of +/- 2.5 million years.
Now I don’t see why blocking light would matter, the light comes from within our light cone, but locking the wormhole to a specific “now” there might have a side effect of making Andromeda hidden from here. Maybe The Absence is more of a consequence than an intended effect?
January 10th, 2022 at 3:12 pm
I’m with you on thinking you’ll do certain things on the blog. I used to make predictions about what I would write about and how I’d do it, but I stopped doing those years ago. My miss rate was just too high.
Your points about “peanuts compared to space” reminds me of a blog post Linda Nagata did a while back, contrasting her stories with typical space opera. She noted how space opera usually trivializes the vastness of space with warp drive, hyperspace, etc, while she prefers to celebrate it. Reynolds, when recommending her book, Vast, cited her as an influence. (Although the earliest short stories in his Revelation Space universe predate her books, so the influence must have been subtle.)
Yeah, I’ve done the, “This is comfortable. Let me buy half a dozen of them,” thing myself. Unfortunately, I don’t always remember to do that, and clothing manufacturing variances being what they are, often not all of them are as good.
I did find that article on SciAm’s site, but paywalled. I’ll wait. If it turns out to be significant, one of the other sites I follow will cover it.
Definitely it would be weird if pilot-wave turned out to be reality. That was the first interpretation I gravitated toward. It seemed like common sense. Until I learned about its issues. It would mean explicit non-locality. No hiding behind epistemic veils. And rethinking quantum field theory. Maybe, since most physicists don’t currently take it that seriously, it would shake things up for quantum gravity. Given how stubbornly successful QM and QFT have been, I’m not holding my breath, but the universe might surprise us.
Yeah, I don’t know the details of what Reynolds had in mind with The Absence. Given his background, I wonder if he thought it out. (It’s not a given. He had some physics in Terminal World that seemed dubious, although still a fun story.) I do think in the story that it was a consequence, not a designed effect.
What I wondered was, what happens to the light that passes through Andromeda before reaching the Milky Way? Is everything in that direction of the universe now missing? And would the effect spread as the causal effects from both galaxies spread out? What does an observer in a third galaxy see?
January 10th, 2022 at 4:45 pm
That’s a good question. How much light from behind Andromeda reaches us as it is? If we subtracted Andromeda’s light, would any remain?
The kind of non-locality found in QM, which can’t be used to communicate information, never bothered me. It seems a necessary part of wavefunction collapse, which is a big mystery anyway. (As you likely know, I’ve got my eye on interference, superposition, and entanglement, as the potential keys to the puzzle.)
I was reminded recently (by Sabine Hossenfelder) how different “collapse” is mathematically from physically. It’s part of why I think the Schrödinger Equation might not be the whole story. Mathematically, collapse is the projection of the current wavefunction state vector onto some measurement eigenvector. This has two results; it’s the second one Hossenfelder reminded me of. Firstly, of course, the state vector suddenly aligns with the measurement eigenvector. That’s what most think of with (mathematical) collapse. But secondly, the projection, which is the probability density, doesn’t have a length of one. The non-linear adjustment collapse requires moving the vector and resizing it back to one. It’s a double whammy on the math side.
On the physical side, there’s this wave-thing. Interference tells us something wave-like is there. It apparently instantly vanishes if the particle interacts at a point location with something else that thereafter will be seen as a wave (until it’s localized by an interaction). One can sure see the attraction of the Bohmian idea that the wave-thing is some sort of non-local magic that guides the “real” particle.
[My own WAG isn’t very different. A particle in flight is just the wave, which is a diffuse coherent pattern in the appropriate quantum field. There is no particle, just energy spread out over the wave. The non-local magic is when that wave interacts with another wave at a (random? chosen by some subtle balance?) spacetime point. The energy transfer from one quantum field to the other is instant.]
January 10th, 2022 at 7:20 pm
You’ve been talking lately about “an interaction” causing the collapse. I wonder what you mean by that. Interaction with another particle? It seems to be implied by what you said about the wave interacting with another wave. If so, how would that square with qubits interacting with other qubits and only entangling rather than collapsing? Are we talking about a particular type of interaction? Or by an interaction, do you mean the enormous number of interactions involved with decoherence?
A single interaction does work in Rovelli’s RQM, but that’s because its collapses are only relative to the interacting entities. So the qubits, when they interact, collapse relative to each other, but not relative to an external measuring device. When the measuring device interacts with the circuit of qubits, then, for the measuring device, the entire circuit collapses. (Technically it’s collapsing relative to every particle in the measuring device, and eventually every particle in the surrounding environment.)
Is there another sense of interaction I’m missing?
January 10th, 2022 at 11:21 pm
An interaction with another “particle” (keeping in mind “particle” always means a wave-like object). For instance, a photon is absorbed by an electron, which raises the energy level of the electron. Later that electron might drop in energy and emit a photon. Both absorbing and emitting are interactions between the electron “particle” (which is a single-quanta wavelet in the electron quantum field) and the photon “particle” (a wavelet in the EMF field). In these interaction examples, the electron persists, but the photon is destroyed or created. There are many other kinds. Any valid Feynman diagram, essentially. They all describe “particle” interactions.
The thing is, when the “particle” is in flight, not interacting at that moment, it’s a spread-out wave. Feynman diagrams are misleading in giving a sense of particle trajectories. The lines should be taken as abstractions only — just inputs, outputs, and interactions.
Entanglement, one of my three suspected keys, is the result of a special kind of interaction. For example, a spin-0 “particle” might decay into a pair of spin-1/2 “particles” — the spins of which would be fully entangled to conserve the original spin-0. Splitting a photon into two lower-frequency photons can likewise entangle their spins (polarizations).
Decoherence is likewise the result of interactions, but in kind of the opposite direction. It’s what happens as the result of lots of interactions with other quantum states. It’s the high-entropy attractor. Entanglement is a fragile low-entropy state.
Interference is easily explained because the vibration of the quantum fields really is there and really does interfere with itself when multiple paths combine.
The big mystery in this view (even accepting QM non-locality) is what selects a particular point for interaction, and how does the spread-out quantum field vibration instantly transfer to another field and shape? Einstein’s spooky action example was a photon released inside a hollow sphere with a one-foot radius. One nanosecond later the photon impacts the wall of the sphere and is absorbed by an electron in one of the atoms. But nothing in QM says where it lands, which electron absorbs it. Interference patterns tell us something extends to and touches all points of the inner wall. Something that uses complex number math. It’s what physically “collapses” — suddenly vanishes — when the wave interacts with another wave.
It’s clearly non-local. Maybe the geometry of space is weirder than we think. There are reasons people keep saying “everything is connected.” Time seems fundamental, but space could be emergent.
January 11th, 2022 at 8:32 am
Thanks. I think I see where you’re coming from. But now I’m wondering what you see distinguishing interactions that lead to collapse vs interactions that only lead to entanglement. Or vs interactions that don’t appear to lead to either, such as a photon reflecting off a mirror in a quantum experiment.
The conventional answer appears to be that “which way” information has to propagate into the environment. I’m wondering if your answer here is different. Maybe another way to ask this is, can collapse happen without decoherence, in the sense of the system becoming entangled with its environment?
Definitely if there is an instantaneous physical collapse, then that’s pretty much non-local dynamics, by definition.
January 11th, 2022 at 2:24 pm
Well, depending on what we mean by “collapse”, all interactions cause it. They all result in a sudden change to the wavefunctions of the “particles” involved. In many cases, those “particles” are destroyed or created — a more physical collapse. Those are the interactions behind what most mean by “measurement” — a “particle” is absorbed and detected. Its wavefunction not only collapses, it vanishes. (The Schrödinger equation, in fact, can’t handle particle creation and destruction; it’s about particle evolution. That’s the purview of QFT.)
There are specific types of (generally carefully managed) interactions that entangle wavefunctions. To the extent it happens naturally all around us, it almost instantly vanishes due to decoherence — due to interaction with multiple other wavefunctions. But where we can preserve it, we get non-local observations (unless one clings to the superdetermination loophole). My take is that non-locality is experimentally validated and must be, at least provisionally, accepted as fact. Given that conclusion, similar non-locality in other aspects isn’t a problem for me. I accept a non-local universe — one subject to the no-communications theorem. It does respect causality.
I’m not sure what “which way” information is exactly, so let me state it this way: A coherent system is one that preserves its phase information — the phase always evolves according to what the wavefunction says — it’s not affected (decohered) by phase information from other wavefunctions.
On its own, phase isn’t something we can detect. The global phase of a quantum system has no physical meaning. It’s when the wavefunction interacts with another wavefunction (or itself) in a superposition that the relative phase between the parts of the superposition interact. The two-slit result, of course, comes from such a superposition.
When two wavefunctions interact such that their wavefunctions merge into a single inseparable wavefunction — one that cannot be separated into two separate wavefunctions in superposition — then the two systems are entangled. They have global and relative phase. Interaction with other wavefunctions will “collapse” (i.e. change) the entanglement, in most cases destroy it.
In all cases, decoherence is the loss of phase information. It’s very much like entropy in being strongly one-way. A small system takes on the phase influences of all surrounding systems. It’s the sound of a huge crowd of voices; it completely swamps individual voices. Keeping a system coherent is really hard. You need to kick both Kelvin and Maxwell out the door.
But anyway, yeah, “collapse” (in the sense of sudden wavefunction change) can definitely happen without decoherence. One example is multiple spin measurements on the same particle. We would label the “particle” wavefunction as unknown before the first measurement, but (assuming a Z-axis measurement) is “collapsed” to either Z+ or Z- after. If, say, the Z+ “particles” go through a Y-axis measurement, the wavefunction changes to either Y+ or Y- (and is now a 50/50 superposition of the Z-axis). A third measurement station would again “collapse” the wavefunction. But the particle remains “coherent” until its actually detected. Only then does it “collapse” in the sense usually meant, and that interaction is often also the end of the particle. At the least, it localizes it.
Note that some say the particle is entangled with the spin magnets because, after passing through the field, the particle’s flight carries information about the field (strength, direction). This seems a more generic use of the term “entangled” than the mathematical one where it’s the tensor product (rather than superposition) of two wavefunctions.
January 11th, 2022 at 2:05 pm
Sabine Hossenfelder retweeted this. It quickly gets over my head, but I thought you might find it interesting.
January 11th, 2022 at 2:53 pm
That’s kind of an exciting paper; I saved the PDF for later. In testing the micro-regime where theories deviate in their predictions, it’s a similar approach to the one Ananthaswamy wrote about. I’ve hope they turn up something new; I’ve wanted to see progress in QM for a long time.
(I think I read that the muon weirdness seen at CERN evaporated into the test data, but I still have some hopes for the muon weirdness in Chicago. The thing about the g-2 experiment, though, is that calculation approximation error is still a strong contender. We might be getting so good with experimental data that we’ve bumped into our ability to calculate experimental predictions.)
January 11th, 2022 at 5:47 pm
I think I’m still confused about all interactions causing collapse. It keeps sounding RQMish to me, but I know you’re not an RQMer. And I’m not clear how the subsequent discussion about interacting wave functions and entanglement (which matches my understanding) fits. (It’s also the end of the day and I’m fried, so it might totally be me.)
I agree that non-locality in terms of non-separability has to be accepted (unless the universe does surprise us with actual superdeterminism). But non-local dynamics, as I understand it, are tied to an objective collapse, except in Bohmian mechanics.
“Which way” was just a sloppy shorthand for referring to information like which path the particle took, or whatever is being measured. I’m still thinking about those mirrors in quantum experiments. It seems like the photon gets absorbed and then reemitted by the electrons in the mirror, but due to the properties of the material, no “which way” information get left in the mirror (or only does so very minimally).
On the spin example, do you have a link to the details of that experiment? Or remember what it was called? I remember the setup in that class, but it was a while back and the details are hazy.
On particles being entangled with magnets, something like that is usually described in a non-collapse interpretation where the entanglement never gets destroyed. Decoherence is often described as the measured system becoming entangled with the environment. My understanding is that it’s the same as entanglement between a couple of particles, but on a much larger scale, and obviously far more complex.
Hope they’re able to do that experiment sometime soon. Seems like a lot of people are probing that boundary.
January 11th, 2022 at 8:04 pm
Well, I don’t want to pile on if it’s been a long day! We can pick it up tomorrow. Or never, if you don’t want to pursue it. For now I’ll try to be super brief. (I said I’ll try…)
First, I posted about the spin example a while back. Quantized spin was discovered in the Stern-Gerlach experiment with silver atoms, but it can be demonstrated with light and polarized filters. This post has more about it.
I suppose we could call decoherence entanglement with the environment. That is what’s happening. It’s not a very helpful entanglement, though. That crowd of tens of thousands of voices. You go from having a coherent conversation with the person you walked in with, to having hundreds of simultaneous conversations with hundreds of people around you. Helpful entanglement involves that original conversation between the two of you. (Non-locality being like having cell phones!)
Question: What do you mean by “non-local dynamics“?
January 12th, 2022 at 7:14 am
Thanks for the spin links. I also dug up the class notes for that Allan Adams lecture. https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-notes/MIT8_04S13_Lec01.pdf
This goes to show how imprecise words like “measure” and “collapse” are. Notably, the intermediate sorting between different spins. His example (page 7) includes recombining the pathways, leading to the indeterminate state returning. But that only works if we haven’t done anything to find out which path the particle took before it reaches the combiner. That, to me, seems to indicate we don’t dispense with wave mechanics until the end of the experiment, when information about the spin states propagate out into the environment, which involves decoherence. (At least that’s my current conclusion. Might be different later.)
The term “non-local dynamics” refers to action at a distance. We get that with a physical collapse interpretation. We also get it with Bohmian mechanics. We don’t get it with many-worlds, RQM, or (reportedly) consistent histories. The epistemic collapse interpretations also often claim to avoid it since they’re only talking about our local measurements, if you accept that move.
January 12th, 2022 at 10:35 am
Ah, excellent! That MIT 8.04 course, with Allan Adams, is the first one I watched. He’s a really fun teacher. And of all the other lecture series I’ve found, I still think it’s my favorite. The MIT 8.05 course that follows, with Barton Zwiebach, is just as good. (I watched the 2013 MIT 8.04 course Adams taught. There is also a 2016 version of MIT 8.04 taught by Zwiebach. I’ve been meaning to watch that one.)
So, you’re most excellently on the same page, dude! His Figure 5, on page 4, is exactly the three-stage experiment I’ve been referring to. (As well as what I was talking about in those QM-101 posts I linked to.) And all the experiments that follow are versions of where I’ve been taking my explanation about interaction and wavefunction “collapse” (and “measurement” or “observation”).
Many lectures later, when Adams returns to spin (using spin-1/2 particles; electrons), he tells his students that “hardness” and “color” were actually vertical and horizontal electron spin, and the boxes were essentially Stern–Gerlach devices. Similar experiments use photons as the particle and polarizers as the interaction device. They demonstrate the same phenomenon.
What’s happening on page 7 (and onto page 8) is easy to explain in terms of wavefunction interaction. The hardness box is an interaction that leaves (“collapses”) the electron’s wavefunction to a known eigenbasis. Note that the hardness eigenbasis has two eigenvectors, Hard and Soft. If we detected the electron now, it could only be in one of those two states. But so long as we can (completely) describe the electron as a superposition of these, we preserve the original quantum state.
So, on page 7, in the first case we get 50/50 and in the second only White electrons. The combine box makes the superposed states into a single state, the input state. On page 8, blocking one path destroys half the superposition “collapsing” to a Hard or Soft eigenvector. Since hardness and color are orthogonal, collapsing to a hardness eigenvector means losing all information about color.
The multi-stage experiments I’ve been discussing (as illustrated by Figure 5 on page 4) are extensions of this. The bottom line is that interactions “collapse” the wavefunction — update it in a non-linear way — but can still leave it coherent and in superposition of possible states. What we might call “ultimate collapse” comes when we localize or detect the particle. Depending on how it’s viewed, that seems to involve “spooky action at a distance.”
[A simple home experiment demonstrating quantum mechanics: Position two polarizing filters at 90° to each other so they block all the light that tries to pass through both. Note that, if positioned 0° to each other, they allow most of the light through (minus any tinting), and, if positioned 45° or other intermediate angle, they allow varying degrees of light through. Now, with two set in the 90° position and blocking all the light, insert a third filter between them angled at 45° — suddenly, where light was blocked, an additional filter allows considerable light to pass.]
January 12th, 2022 at 7:17 pm
BTW: I don’t know if you saw (or if you did, if you care about) the more detailed discussion below. I got into it last night, got carried away, more like, so I’m not sure I’ll continue it unless there’s an interest.
January 12th, 2022 at 8:30 pm
I actually had missed it. Looks like you’re thinking on the page. Which I do myself at times, so I totally understand the impetus. But I’m afraid it’s too far over my head for me to provide any intelligent input.
January 12th, 2022 at 9:06 pm
Ha! I was actually in teaching (or mansplaining) mode. This stuff is freshman QM and doesn’t take much thinking. It’s just a detailed explanation of these experiments. The impromptu sense, I’m sure, comes from writing it off the top of my head, as if we were hanging out in a bar. 🙂
I’m sure you’d find it not over your head at all, but it does take the interest and desire to get down into the weeds. Much of what’s here channels that first lecture Adams gives. These are like the two-slit interference experiments in showing us something important about the QM world.
January 15th, 2022 at 12:17 pm
I’ll leave off on further elaboration below. I took it up through the three-stage experiment that can be replicated at home with three polarizing filters. It’s a cool demonstration that shows we can experience quantum effects in our classical world.
More importantly, to wrap this up, hopefully you see what I mean by “interaction” — an umbrella term for many kinds of wavefunction changes (“collapses” or “non-linear updates”). That part is all QM 101. The speculation on my part is that what you term “dynamic collapse” — the kind involving localizing the “particle” — isn’t that much different from the shifts due to magnetic or polarizing interactions. Both involve non-linear wavefunction updates, but it’s only when we localize or “measure” the “particle” the wavefunction represents that things get “spooky.”
I further speculate that vibrations in the quantum field — Bohm’s guiding waves — are the thing. They don’t guide a particle, they are the “particle” — its energy is spread out in that wave. That much is what QFT basically says. The speculative part is the non-local way the energy of that spread-out wave instantly transfers to a spread-out wave in a different quantum field. The vibration in the EMF field that’s the “photon” suddenly, at a certain point, becomes a vibration in the electron field that’s the “electron.” That’s definitely spooky and I have no explanation at this time.
But! 🙂 It does solve the measurement problem.
January 15th, 2022 at 2:25 pm
I couldn’t resist one more. I meant to explore that Allan Adams experiment in terms of wavefunction interaction. I’ve done so below.
January 11th, 2022 at 9:03 pm
Writing a detailed explanation helps solidify things in my own mind, so this can be seen as an exercise for my own sake. Feel free to join in, or not, when and if you like.
“I think I’m still confused about all interactions causing collapse.”
By which I mean that all interactions cause a non-linear change to the wavefunctions of the respective “particles” (there may be some exceptions, but I think I’m safe saying that’s the rule).
Specifically, the wavefunction state vector “collapses” to some eigenbasis according to the projections onto that eigenbasis (the length of each projection determines the probability of getting that measurement; their squares must sum to 1.00). For the wavefunction to continue to be valid, an interaction (“measurement”) involves two non-linear updates to the wavefunction. Firstly, update the state vector to the eigenvector actually measured — in other words, select that projection. Secondly, since the projections usually have lengths less than 1.0, the selected one is updated to a length of 1.0. These non-linear updates are what some see as a problem single-world non-collapse interpretations.
There are certain cases where this also involves the “collapse” of that magical quantum field that can interfere with itself and other quantum systems. And since that field seems to be real, that it suddenly vanishes is very vexing. Updating a vector is mathematical and can be dismissed as epistemic, but whatever is going on here is hard to understand. A related question is why a photon lands here and not there.
The first thing to be clear about is that localizing a “particle” — measuring its location — is a QM operation that “collapses” its wavefunction in terms of position and momentum (but may leave other quantum properties untouched). But how we localize a particle may affect them. If we absorb a photon to energize an electron on a screen, we know where that photon is. Or was. The electron has inherited its quantum properties (energy, being about it; photons are spin-0 and have no charge, so there’s nothing for the electron to conserve).
Let’s use photons and polarizing filters. The basic setup is that one photon sequentially interacts with three polarizing filters, each set at its own angle. Schematically, it looks like:
With photon, gamma (γ), going through three polarizing filters a, b, and c. After passing through any filter, the photon’s wavefunction has made the non-linear change — mathematical “collapse.”
Note that we never localize the photon — its position is never measured. It could pass through a fourth device and its wavefunction would change again. The analysis is about how its wavefunction changes due to interacting with the filters.
A key point is that the four wavefunction states (γ0–3) are all superpositions.
At first, γ0, polarization is completely unknown, so we can describe it as an equal superposition of any eigenbasis. The canonical form uses the {|0⟩,|1⟩} eigenbasis:
But it’s just as valid to say:
Or:
Or any other eigenbasis you care to come up with. In all cases, we’re saying there is a 50/50 chance — if we measure — of finding the polarization at any given angle. All angles, 50/50 shot the photon passes the filter.
To try to keep this from being obscenely long, I’ll stop here. That will also allow for questions or discussion about the framework and setup.
January 11th, 2022 at 9:15 pm
Oops. The three superpositions are how we’d write it for spin-1/2 particles. It’s the same basic thing with photons but written a bit differently, like this:
Same thing, different spelling. The Bloch Sphere applies in both cases.
January 11th, 2022 at 10:21 pm
Part Two…
So, given the setup:
And the initial superposition:
After passing through Filter-A (if it passed through), we’ll assume the filter angle is vertical, the wavefunction collapses:
The wavefunction vector is updated to the |V⟩ eigenvector (as described previously). Note that, because of this double update, the photon passes through additional filters with the same setting with 100% probability. And fails to pass an orthogonal filter with the same certainty.
The polarization state has collapsed, but note that the photon is coherent, and we can validly describe it as a superposition of a different eigenbasis:
Because this eigenbasis is orthogonal to the {|V⟩,|H⟩} eigenbasis, we know there are 50/50 odds, but that’s actually a special case. Non-orthogonal angles work, but deliver different odds because we know the polarization is vertical. The general case is:
Where theta (θ) is the angle of the filter from the vertical. The probability of either result is the square of the cosine of the angle. In the case of the {|D⟩,|A⟩} eigenbasis, we know that the relative angle is 45°, so
Which is how we got the one above. The original {|V⟩,|H⟩} eigenbasis has a zero angle to the vertical, which is why:
Where things get interesting is after the second filter. That’s enough for this one. More later.
January 12th, 2022 at 8:11 pm
Part Three…
In case it’s not clear, in this representation:
The photon (gamma, γ) goes through (arrow) a filter (circle labeled a—c). The slash signifies the filter has an angle, which is indicated in a superscript. The colon signifies the result or output, the photon (γ) in a new state (labeled 0–4).
Initially, we have:
Or any other eigenbasis. We don’t know anything about the initial polarization, so there’s a 50/50 chance the photon will pass a filter at any given angle. In this case, the first filter is set to an angle of 0° and now (assuming the photon passes — 50% of them will) the wavefunction is:
The last version shows the general case. The key point is that the photon is still described by a superposition. The interaction with the first filter “collapses” the state vector to the |V⟩ eigenvector, but it’s still a superposition of other eigenbases. (As shown previously, it’s even still a superposition of the {|V⟩,|H⟩} eigenbasis with coefficients of 1.0 and 0.0, respectively.)
So now suppose it goes through the second filter, which we’ll say is set to 45°. This gives us the third state of the photon. If it passes the filter — the probability is:
Note: This assumes the 45° angle is the same as the |D⟩ (diagonal) eigenvector. A 135° angle would match the |A⟩ (anti-diagonal) eigenvector.
The photon state is now:
The state vector has “collapsed” again, this time to the |D⟩ eigenvector. As before, it still can be described as a superposition, but that superposition is now relative to the |D⟩ eigenvector, not the |V⟩ one.
A key point is that we’ve lost the previous information about the |V⟩ value of γ1. If we measure the vertical axis, our results are again 50/50.
Likewise, if we measure the horizontal axis. After the first filter, there was a zero chance of γ1 passing a horizontal filter. But γ2 has a different wavefunction, one oriented at the |D⟩ eigenvector, which is 45° from the horizontal. That means, as before, the photon (γ2) now has a 50% chance of passing a horizontal filter.
Assuming it does, we have:
Going through the second filter gives the photon a (50%) chance of passing the third filter whereas, without the second filter, it has a 0% chance. That’s a distinctly QM result, and it can be demonstrated with three polarizing filters. And note that, once again, we’ve lost information about the diagonal and other axes.
It’s actually kind of mind-blowing. 🙂
January 15th, 2022 at 2:21 pm
I meant to go over the experiment Allan Adams describes in his MIT 8.04 (Spring 2013) lecture notes, specifically what happens with the cases described on page 7 and page 8. I’ll try to be as succinct at possible.
Starting with Figure 9 and Figure 10 on page 7, note similar experiments but different input preparations. The first case uses Hard electrons, the second uses White ones. We obtain these starting conditions through off-stage boxes, Hardness and Color ones, respectively. Prior to that, the electrons are in an unknown “random” state (for all we know, truly random). We describe that as:
Unknown electrons are a (50/50) superposition of any orthogonal basis we like. Here we have two:
An important point: Each basis is orthogonal; its components are mutually exclusive. However, the two bases are orthogonal to each other. A measurement is either Hard or Soft (or White or Black) but measuring one or the other is also orthogonal. A key thing the experiment demonstrates is that orthogonality.
So the superposition above could be in terms of either of those. In Figure 9, the off-stage box is a Hardness box, and the experiment uses only the ones that emerge from the Hard port. So, we update the wavefunction:
It’s important to understand that, although the wavefunction has “collapsed” to Hard, it’s still also a superposition of White and Black. Likewise, in Figure 10, we have:
And that superposition is important to understanding what happens in the experiment.
In both cases, the first stage is a Hardness box. In the first case, if we measured the electron, we’d find only Hard ones, no Soft ones. That’s because the wavefunction is already collapsed to Hard. In the second case, if we measured, we’d find a 50/50 mix of Hard/Soft, because the input state there was a superposition of those states.
When we combine the output of the first stage (the Hardness box), we regain the input state. The Color box is presented with, in the first case, Hard electrons, and in the second case, White electrons. The results are exactly what we’d expect.
The kicker comes from blocking a path before the Combine stage in the Figure 10 experiment (as shown in Figure 11 on page 8). But it’s simple to understand because after the first Hardness box we have:
The path1 and path2 superpositions mathematically combine to result in a |White⟩ state vector (that has to be renormalized). But if either are blocked, we’re left with a superposition that the Color box splits into 50/50. Note that it’s the phase difference between the two |Black⟩ states that cancels them out. The two |White⟩ states have the same phase and reenforce (hence the need to renormalize the vector).
Bottom line, the experiment results are easily understood in terms of what the wavefunction is doing — how it evolves as the result of interacting with the boxes.
January 15th, 2022 at 2:46 pm
I should maybe add that, if we fed Black electrons into the Hardness box, the two paths would have the |White⟩ state as out of phase and canceling and the |Black⟩ state as in phase and reenforcing.
January 15th, 2022 at 4:43 pm
Right. For me, the key thing here is that since the particle wave packet can be recombined afterward, it seems like the sorting inside the boxes, by themselves, don’t cause collapse. It’s what happens afterward. It’s only when information about the property being measured gets out, when its causal effects propagate into the environment, that we get the irreversible collapse, or at least the phenomenology of collapse. (Which fits with most of what I’ve read.)
January 15th, 2022 at 7:56 pm
Perhaps a way to distinguish it is that there is an unrecoverable form of collapse when we localize the wave, an action that involves transferring some or all of that wave to another wave. Keep in mind that, physically, this usually involves absorbing the particle. Photons disappear (it’s more complicated with electrons).
But the same way the two-slit experiment demonstrates the reality of interference, these filter experiments demonstrate the reality of wavefunction change. In many regards they’re the same thing. The two parts interfere or reenforce. What’s going on there is as real as what’s going on two-slit experiments.
😀 As I’ve said, I’ve come to see superposition, interference, and entanglement, as the key mysteries. My guess is that solving those solves the package. (Note what’s not on that list: decoherence and measurement. We’re making progress on the former, and I think the latter depends on the big three.)
January 23rd, 2022 at 5:56 pm
It’s my night for stupid questions, Wyrd, so bear with me. I’ve been thinking about MWI a bit, based on Mike’s latest post, and what it caused me (unexpectedly) to ponder. And I’ve got a question maybe you can answer…
But it will force you to think like an MWI advocate for a moment or two, if you’re willing. Haha.
As I understand MWI, we could come up with an experiment to measure the up/down spin of a particle. And if MWI is correct, assuming there are only two outcomes to this experiment, the universe would split into two branches. In one branch, the value would be “up” and in the other branch it would be “down.”
Now I think what Mike’s most recent post was about was the notion that the split (where I see one result and another version of me sees another) doesn’t happen “everywhere at once” but propagates based on interactions. But I just see a number of paradoxes here so I’m curious how you think about them.
1) Imagine the branches split the entire universe at once. I guess this is something like the Sean Carroll version, though I’m not 100% sure I’ve got that right. But either way, I think there’s a version like this right? In this case my question is, why would one experiment we create split everything when we’ve ignored a trillion, trillion, trillion, etc., other things? I mean how can one actually draw a box around an experiment and the rest of the universe? Seems like insanity really. I can’t comprehend how that might work.
2) Imagine the branches only propagate based on interaction, then could this potentially mean entire swaths of the known universe (those outside of our light cone for instance) simply NO LONGER EXIST FOR US? (Not that they did anyway, I guess.) But we like to think if we launched a projectile into one at close to the speed of light it would eventually get there. But wouldn’t entire sections of the universe be out of phase from us over time due to all this branching? It seems like without defining an absolute phase of wave function branches, we get into trouble. If there was an absolute phase we could bring together two things from opposite ends of the universe and see if they are in phase (real to each other) or not.
Ultimately what I’m getting at is what is a phase and is it something that would or wouldn’t result in some of these awkward situations?
Michael
January 23rd, 2022 at 7:49 pm
It isn’t a stupid question if you don’t know the answer. (It would be worse to not ask and never know!) I don’t know how much advocacy I can raise for the MWI, but I think I understand it enough to have a go at your question…
Yes, assuming you detect the particles, under the MWI reality splits into spin-up and spin-down branches. With all the consequences that entails. 😉
My understanding is that Sean Carroll says one can assume the branch is everywhere instant or that it moves at the speed of light and that it makes no difference either way. I believe our friend Mike goes with the speed of light version because he commits to locality. Splitting everywhere in an instant is hugely non-local. And if the physical universe actually splits, how? There’s a huge energy/mass problem, and since gravity is a function of mass, if mass changed, so should gravity. I find the notion the universe physically splits at all very problematic.
And, yeah, totally, I think a key question is how is it possible a quantum measurement (of say spin up or down) causes a new copy (instantly or otherwise) of the entire universe (or even just the part in our future lightcone). Branching at the speed of light also makes one wonder about all those branching lightcones spreading out from every quantum event. Of course, causality effects do, but new universes?
It isn’t that the universe outside the lightcone doesn’t exist so much as that the spreading split hasn’t reached it yet. The expansion does place a limit on how far it will ever get, but each part it does reach just branches. It supposedly travels at light speed, so any physical probe we launched would never catch it.
The notion of branching in the MWI needs examination, I think. It’s not clear to me how a wavefunction “branches” — it can contain superpositions of other wavefunctions, but I’m not clear on the mathematics of a single wavefunction becoming two. I mentioned on Mike’s most recent post that I know of two formulations that allow “many worlds” in a wavefunction: [1] As in particle tunneling and some electron orbitals, the single Universal wavefunction has multiple “lobes” of probability where the “particle” (world) might be found. Here there is indeed a branching as lobes evolve. there was one cat with two probability lobes. [2] Multiple world wavefunctions superposed in one Universal wavefunction. Here the wavefunctions diverge in how they describe their worlds. There were always two cats. Their lives were identical up to the point they diverged and one died. (The other was really pissed about being in a deadly box.)
Version [1] seems the popular one, but version [2] has no energy problem nor the paradoxes of splitting physical reality (at light speed or instantly). It’s a true parallel worlds theory.
So, bottom line, to hopefully answer your initial question, under [1] I agree there seem a lot of paradoxes with both speed of light changes and instant ones. If that’s how reality actually works, it’s got some ‘splaining to do. Under [2] there’s no problem. I’ll do the phase question separately. It deserves its own space.
January 23rd, 2022 at 8:38 pm
Looking at your comment again, you may have meant phase in a more general sense. As I think you may have meant it, yeah, I think so, too. Not just distant parts, but even locally it seems like all the branching could be a problem.
It sort of does lead to the comment I started typing…
Okay, so phase and decoherence, respectively the magic of quantum and the mantra of the MWI. They’re related, obviously, because the latter is the loss of meaning in the former. I hope you’ll excuse another long one, because decoherence involves one of my key puzzles about the MWI.
Do I understand you to have engineering background? Can I assume you’re read in on complex numbers and a little basic wave mechanics? If I say that “phase” is one of two properties a complex number can have, do you nod thinking, “Well, duh!” If any of it is a “Huh?” we can backspace over it.
Oh! I just thought of a great litmus test:
Which best describes your reaction: “Huh?” … “Wait! What?” … “Duh.” … “Duh. And, by the way, mathematical poetry.” 😀
Anyway, setting the scene, on one level phase is a property of a complex number. A quantum state is a set (vector) of complex numbers, each with phase, and in QM math it’s phase that causes interference effects. Decoherence is when the phase of other wave systems causes shifts in the phase of coherent system. Multiple voices drown out the one. Two coherent systems are no long in step with each other. (Two people having a conversation find it impossible in a crowd of others also talking to them.)
Under the MWI decoherence is said to account for why we don’t see the other branches. It’s why physical matter can coincide, despite the Pauli Exclusion Principle. But I have yet to discover how — or why! — that works. Normally decohered systems are concrete to each other — they can’t coincide. If anything, it would seem coincidence requires coherent systems.
So I really don’t understand the principle that allows physical coincidence in the MWI.
Proponents of the MWI staunchly deny the theory is Tegmarkian, that reality is all just the math. Okay, fine, but that means physical matter physically coincides, which seems to need explaining. Superposition works fine mathematically but until we fully understand what the wavefunction math is modeling, we’re so in the dark. In QM that phase affects probability amplitudes. What does that even mean?
I just mentioned on Mike’s post that I recently heard how relativistic version of the Schrödinger equation (the Dirac equation) looks much like the electrical current flow law (the amount of current flowing into an area matches the amount flowing out). Thus, one can refer to “probability currents” that flow as the wavefunction evolves. All those graphs of wavefunctions showing the probability lobes moving over time show probability current. Cool idea. 🙂
January 24th, 2022 at 6:17 pm
Your second reply was more in line with my question. While I’d have to brush up to remember the exponent(i-Pi) -1 = 0 thing, it’s just from lack of use. I remember doing phasors in introduction to electrical engineering where we dealt with complex numbers. I seem to recall interchanging a number format of [real] + i [imaginary] with a format of [magnitude] [phase]. There was some trig involved to pull this off, etc., etc. In electrical engineering the [magnitude] [phase] could be current or voltage, and in some cases impedance. And there was math to be done combining them, etc.
So that is how I often think of this, and fail to make headway. In electricity, when currents are in phase they play nice and when they’re not they certainly decohere. But they do so in the same world and that’s problematic for real world systems… (A generator out of phase with the grid, when interconnected to the grid suddenly, will likely be destroyed, etc.)
In MWI, it’s kind of the inverse: everything that’s “in-phase” interacts, and when “out of phase” they just don’t interact at all. But here’s the part I can’t follow and think people way smarter than me must understand: what are these phases of? I mean, is it actually something that matters in an absolute sense throughout the universe?
Example: I have a branch phase coherence of a system. It bumps into another particle or there is an experiment with a measurement or whatever. One branch is given a phase of 0, the other of 180-degrees. Does the one with 180-degrees now interact with everything else in the universe that is at that phase?
It seems not… which leaves me at a loss to understand this. Because if there is no absolute physical property of phase, such that systems anywhere in the universe could potentially share such a phase and others not, then the alternative I imagine is an “infinite” number of phases, so that all these millions-billions-quadrillions of branches don’t interact.
See what I mean? Phase of what?
January 25th, 2022 at 3:19 pm
Michael, my most honest answer to your last line is, “Of reading too many multi-dimension comic books and SF stories!” The more I look into the MWI, the more I’m astonished people believe in it. Either I’m missing something huge… or they are. (And, after a lot of self-study, I’ve gotten to the level where I’m mostly understanding physicists, but I’m not understanding this.)
Frankly, until I do, I see physical coincidence as a deal-breaker for the MWI, an effective disproof.
But let’s accept a magic sauce, called “different quantum state,” that we can paint things with. This isn’t unprecedented. It’s very much like whatever magic sauce causes interference in two-slit experiments. As I explained above, we have the math for interference, but no idea what physical mechanism obtains. So let’s say the same magic sauce in play there is in play here. What does that buy us?
In two-slit experiments, multiple paths, which we might compare with multiple worlds, can interfere such that the probability of the “particle” represented by those waves changes from {equal at all points} to {a pattern of highs and lows}. In two-slit experiments, ultimately the “particle” is detected (alternately just lost) and the magic sauce instantly evaporates (causing great consternation among staunch localists; spooky! they cry). Note this assumes the “particle” remains “coherent” along its paths. (There’s a caveat that gets down in the weeds. Maybe later.)
Now, if the paths were worlds, what is this saying (other than it’s a bad analogy)? The coherent “worlds” interfered creating a pattern but effectively pass through each other as all waves do. In fact, proponents of the MWI often use the superposition of waves as an example of coincidence. (Unfortunately, I don’t think they’ve examined their analogy in sufficient detail.) As they pass through, they amplify or cancel the probability at that location. I don’t know what that’s supposed to mean in terms of the MWI, since it’s their interaction that matters. Without it there is equal probability everywhere.
But this must be a bad analogy, because waves pass through each other whether they’re coherent or not. (We’ll have to get into those weeds a bit.) Coherence is one of those words with multiple meanings (so is entanglement, which I noticed you and Mike discussing). In a laser beam, it refers to all the gazillions of particles having the same wavelength and phase. Photons, being bosons, can bundle together in tight bunches, which can pack a lot of energy in a small space. In QM it refers to the “purity” of a quantum state such that it will create meaningful interference (to obtain a QC result, for instance). Decoherence is when other influences swamp it out (the voices of the crowd).
So, back to the two-slit experiment, imagine that dust particles interacting with the wave along one path but not the other cause a loss of coherence along that path. The phase of the particle is affected by the interactions. For a single particle, once it meets the wave from the other particle, the waves will interfere as they always do. On their own they participate in creating an inference pattern. But with multiple particles, each affected differently, that pattern is slightly different. The sum of them isn’t a pattern at all. This is why “decoherence” along the path ruins the pattern (blurs it into a whole).
If the two paths are supposed to be worlds, then “decoherence” isn’t an issue for individual cases. It doesn’t really exist for individual cases. All that happens is that the interference pattern shifts per the shifted phase. Decoherence certainly matters if you’re trying to build a pattern from lots and lots of particles, but I can’t make any useful analogy between the wave interaction here (or anywhere) with what the MWI folks claim.
There is also that any object with more than a handful of particles doesn’t have a (quantum) phase in any useful sense. (Other than say if an A.C. current passes through it imposing a field phase.) All the particles have their own. It’s the huge crowd with trillions of voices.
Bottom line: I can’t make any comparison between the magic sauce of the two-slit experiments, and I don’t understand what kind of “phase” larger objects, let alone worlds or universes, could have. “Quantum state” is not a magic sauce that comes from a wand, but that’s what seems to be happening here.
I can’t answer your question about the 0° and 180° branches, because it seems based on an entirely nonsensical premise. The only valid answer is Douglas Hofstadter’s mu (μ) (“your question cannot be answered”). You might appreciate that a key word in Buddhism, mu, means “not have; without”. Might be why Hofstadter used it, although IIRC, he associates it with the Greek letter, μ.
So, yeah, totally with you on being very puzzled by this physical coincidence thing. That’s some amazing magic sauce that can paint a whole world or even large parts of it such that it becomes invisible (but still there). It’s like something out of a comic book!
January 25th, 2022 at 7:01 pm
p.s. See this comment below if you want to brush up on the exp() thing.
January 25th, 2022 at 7:03 pm
Thx! Will check it out. I was thinking e^ix could be transformed to a combination of sines and cosines but it’s been too long since I just sat down to do math… I look forward to your refresher!
January 25th, 2022 at 7:10 pm
Read it… good stuff and I enjoyed the history and review of the definitions of these various number types. The part where you got into trig is what I was remembering, but no one ever explained the multiplication by “i” as a quarter rotation and that was a cool insight for me… Thanks for taking the time Wyrd!
January 25th, 2022 at 7:35 pm
With complex numbers, viewing multiplication as rotation makes a number of things much clearer. That whole “wheel” thing is based on it. And I have to say, I’ve been calculating sine waves for many years using sin() and cos(), but using e^iπx to generate them (just incrementing x) kinda blew my mind. Turns out they both come from an underlying symmetry, but, wow, that was an eye-opener. The real part traces out the cosine wave, the imaginary part the sine wave.
There’s a really interesting connection to Fourier transforms that makes them easy to understand. See this post for details.
BTW: In saying the answer to that question is “mu” I don’t mean to disdain the question but what it asks about. I just don’t think there is a creditable answer. (I didn’t want to imply I was rejecting the question!)
January 25th, 2022 at 7:40 pm
On the “mu” thing, I read you five by five Wyrd. Appreciate the clarification but I was picking up what you were laying down there. I still don’t get what you aptly describe as physical coincidence. To me it implies all coherent but non-simultaneously-experienceable “worlds” are in some sense virtual. Like overlaid cable channels… But what is the descrambler?
January 25th, 2022 at 8:43 pm
Where, indeed? Until I find some creditable explanation of physical coincidence, I’m stuck thinking the MWI doesn’t make sense. To me it seems logically falsified. As we often do, assume a given, follow the logic and see if it leads to a contradiction. If it does, the assumption is probably false.
Ironically, mathematically it’s fine. Numbers coincide just fine. I knew a guy back in the 1990s who was committed (in a casual sort of way) to the MWI. His take was mathematical. Polynomials have multiple roots; there’s no problem that x^2=4 has two solutions, x=+2 and x=-2. Higher degree polys have more. Some have infinite roots. This is a Tegmarkian take on the MWI — making the math the base reality — but proponents of the MWI deny that it’s Tegmarkian. They insist it’s all physically real and that all branches have equal reality. All the cable channels are tuned in.
Real enough that at least some consider the question of splitting energy/matter in branches, a problem I believe would reveal itself through changing gravity, it being due to mass, which is the same thing as energy.
As to how millions of worlds coincide, beats me. Magic sauce. Fairy dust.
I noticed you talking about entanglement. I wanted to mention, that’s another word that has multiple meanings. There is a specific meaning in QM that I think sometimes gets confused with more casual meanings. If two particles interact and fly apart, they’re often said to be entangled. Or if a photon bounces off a cat and into my eye, it’s sometimes said we’re entangled. In both cases, information is exchanged, at least in one way (as with reflected photons), but sometimes both (as in particle collisions).
In a similar sense, you and I are entangled. As you mentioned elsepost, your interaction with me is singular (and likewise mine with you). Due to our interaction over time, a fair amount of information has been exchanged, so the entanglement isn’t trivial. It is not, however, entanglement in the quantum sense that we have become an inseparable whole or that actions on one of us directly affect the other (instantly regardless of distance). [As an aside, the curious nature of such quantum entanglements does make me wonder what’s possible with mind. We’ve both experienced connectedness personally.]
I think how “entanglement” is used in the MWI refers to as aspect of the theory I’ve been trying to fully appreciate since I started studying it. Say we have Cat-In-The-Box with a humane sleeping potion device monitoring the radioactive sample and Scientist Person outside watching. Under Copenhagen, an atom decays or doesn’t with some probability. If it does, the wavefunction of the sample “collapses” at that point to a new state, and a new “particle” is emitted. It has its own quantum state and could end up anywhere. But say it ends up interacting with the detector. This “collapses” its wavefunction and triggers the detector (which is in a highly energetic “coiled spring” state awaiting triggering). Everything that happens from then on is entirely classical and involves billions or trillions (or more) particles. That’s Copenhagen.
But a key feature of the MWI is “no collapse” so none of the above happens that way. An atom that decays (creating, I assume, a new branch) releases a particle that “entangles” with the detector (more branches: in most it’s lost elsewhere). Here’s where I get confused. What exactly happens in the detector? We have a particle that may or may not be there — no collapse means it could be, and is, elsewhere. So, some aspect of the detector decides to go with the possibility and act as if it detected the particle. But in all the other branches where the particle went elsewhere, let alone where it never decayed, nothing happens. But some branch decides to be the one that reacts. Things proceed “normally” except that in most branches nothing happens. But in some branches things proceed as if the particle had been detected. This spreads to copies of the cat and eventually to copies of Scientist Person and on to Wigner and his friends. Reality doesn’t proceed because of energy transactions (because those would involve measurements) but because of probability flow. The detector might trigger, so reality has a branch where it does. I just don’t understand how that’s supposed to work.
And, again, it’s not the quantum kind of entanglement where a change to one part affects the whole instantly. It’s more the interaction know about kind (at least from what I can tell).
January 25th, 2022 at 9:14 pm
You wrote, It is not, however, entanglement in the quantum sense that we have become an inseparable whole or that actions on one of us directly affect the other (instantly regardless of distance).
This goes to what I was trying to understand out loud at Mike’s place. When you have entanglement and correspondence you have the situation of two particles in a state where the value of one requires a corresponding value of the other, right? Like the Bell tests when spin up on one requires the other particle of the entangled (and corresponding) pair to be spin down. This, I think, and am just realizing, has been truncated to simply being called “entanglement” in a lot of popular descriptions. But there’s entanglement without correspondence, right? Or am I wrong on that. I don’t really know. But if entanglement occurs through every interaction, I was thinking not every interaction produces such a neat set of outcomes as down polarization which yields two photons that must maintain through conservation certain properties of the original electron (is it an electron?).
As to this, Reality doesn’t proceed because of energy transactions (because those would involve measurements) but because of probability flow[,] this description really helped me understand what you meant by probability flow. It just sunk in. I can’t help but think, perhaps as an artifact of my propensities and inclinations, that not all probabilities are actualized and that we’re missing something really important about how a web of possibilities becomes something actualized.
I am inclined to think not all probabilities happen in the same way, meaning they may all “exist” in some form in a probability space, like a palimpsest of possibility, but that somehow there is only one bold line that is “activated” through it as the physical world unfolds. It’s almost like all these exist in a way of “not existing” until they interact with something else. I don’t know much about the Higgs boson (Higgs field) stuff, but kind of like that, which I understand as a field everywhere that interacts with matter in some way to yield mass. You have these particles but they only get mass through interaction with this field. And maybe we have all these possibilities, but the one(s) that are “activated” are the result of a coupling with some other field.
Late night musings, Wyrd… Take ’em or leave ’em my friend!
January 25th, 2022 at 9:59 pm
Yeah, what you’re calling entanglement and correspondence (known as inseparable states) is, strictly speaking, what is formally meant by quantum entanglement. And you’re right without the correspondence, it just means particles interacted and now contain information about each other (or at least one does about the other). In particular, they are not causally connected. Actions on one don’t affect the other.
Bell’s tests often take a fairly high-frequency photon and use a crystal that splits the photon into two photons of half the frequency (because energy is conserved and frequency=energy with photons). Note that this isn’t a superposition as a half-silver mirror creates, but two actual photons. Because spin is also a conserved property, whatever spin one has, the other has to have the opposite. (With photons, spin=polarization.)
I get the sense the more casual use has led to other ways of saying entanglement and correspondence. Scott Aaronson, talking about what distinguishes QM from classical physics in his blog post just today wrote, “Why the complex-valued amplitudes? Why unitary transformations? Why the Born rule? Why the tensor product?” That last phrase refers to entanglement.
You can add quantum states in superposition (because you can add column vectors), but you can’t multiply them (which entanglement requires). That’s mathematically invalid. So you take the tensor product (basically a Cartesian product). That creates a new state that cannot be decomposed into a sum of superposed states — an inseparable state. Such states share a single wavefunction, so any action on one instantly affects the other.
I like the term tensor products. It’s kind of a razor. 😀
January 25th, 2022 at 7:00 pm
“While I’d have to brush up to remember the exponent(i-Pi) -1 = 0 thing,…”
Here’s a brush up reference in a separate comment so you can ignore or not. The exp() thing is pretty important in QM, so this is here if you want it. If you want more detail, I’ve written some posts, and so have many better others. (Gotta love that aspect of the web world.)
What I love is the natural progression that suggests complex numbers have to be taken seriously. As you’ll see, they keep insisting on their existence.
It starts with the need to count things. That leads to the natural numbers. Important fact: The natural numbers are closed for addition and multiplication. That means we can add or multiple any two natural numbers and the result is always another natural numbers. Works great. Hooray, we gots math!
The problem is subtraction. Some of it works, 7-4=3 has a natural number result, but some subtraction broke math: 4-7=??? So, we did what we’re going to be doing quite a few more times: we expand the definition of numbers to include a new type of number. In this case, the integer numbers, which feature negative values. Subtraction now works great (i.e. is closed). Hooray, we gots math!
The problem now is division. Again, some it seems okay, 8/4 and 10/5 have integer answers, but what to do about 1/3 or 4/7? Wash, rinse, repeat. This time we invent the rational numbers. Numbers in the form of a/b or with a repeating decimal, 2.3333… Works great, we cool now?
Well, no. Certain obvious and simple problems (square root of two) have answers that don’t fit. By now we know the tune, this is just another verse. We had the rational numbers, we’ll call these the irrational numbers. Their decimals never repeat, and there is no fraction that expresses them. Since the decimal expression is infinite, their values can never be written out or precisely known. However, there are finite mathematical expressions, polynomials, that can express their value. The square root of two, yet again, is an example:
If a value can be expressed as a polynomial, it is merely irrational.
Further investigation into, again fairly simple obvious number problems (like the ratio of a circle’s diameter and circumference) turn up yet another kind of number, the transcendental numbers. These are a little weird. Not only is there no fraction, there is no finite polynomial that expresses them. We can only write infinite series that converge on an answer to what degree of precision one wants (and has time and space to calculate).
Okay, I hope you’ll excuse the lead-up. It feeds directly into what happens next. Mathematicians came up with what they saw as an iron-clad rule that all polynomals have a root. So, any expression in the form:
Has some value of x that makes it true. Flashback: Works great… much of the time. A trival example:
A trivial counter example that broke math again:
So once again, we need a bigger boat. Ultimately, after a bit of thought and pencil work, it turns out that what we need is something that satisfies:
Which seems in violation of math as we know it. But the tune is familiar now; we just add yet another verse, the complex numbers. (Again, I hope you’ll excuse taking the scenic route, but it’s one of my favorite stories, and I’m fascinated by how each number type demands a seat at tht table.) We can, by fiat, just define i — the imaginary unit — as the square root of minus one and live with it, but there’s a beautiful geometrical logic behind it.
Imagine the real number line familiar from school. Negative numbers extend to the left, positive ones to the right. All the types defined above lie on this line. It includes the naturals, the integers, the rationals, the irrationals, and the transcendentals. It is the canonical X-axis.
Now, if you have a positive number on the line, say +4, and you multiply it by -1, as you recall from school, the result is -4. The number jumps from the right side to the left side. Anything multiplied by -1 flips like this. Even negative numbers flip, -4 × -1 = +4.
But now think of them, not as flipping, but rotating around zero. Think of +4 as an arrow four units long that swings 180° to point the other direction. Likewise -4 is an arrow that swings (counter-clockwise; always counter-clockwise) around to point right. That’s multiplying by -1. What if we only went halfway? Wouldn’t that be multiplying by the square root of -1? If we did it again, swung only 90°, then we’d be at the -4 mark we should.
We can view multiplying by i as rotating the arrow only halfway, 90°, rather than twice that, as with -1 (i × i = -1). This tells us that numbers are two-dimensional. The imaginary unit is the basis of an axis that is orthogonal to the real number line.
Gauss wanted to call them “lateral numbers” for good reason. Having a very clear picture of this two-dimensional setup makes the complex numbers fairly easy to understand and work with. A bit of terminology: the imaginary unit is the square root of -1; the imaginary numbers are numbers that are a factor of the imaginary unit; the complex numbers are compound numbers with a real part and an imaginary part. They have the form we first learned in school: a+bi (They are, in a sense, stuck in this form because the addition can never be performed. We treat them as a single value, often denoted z or c. I favor the former to avoid confusion with the speed of light.)
As you pointed out, they have that real+imaginary form and a magnitude+phase form:
And, indeed, a bit of trig converts between them:
In the last form, eta (η) is the magnitude and theta (θ) is the phase. For wave mechanics, its very handy to have them as distinct numbers. I think of:
As a “wheel” — a vector with a length of one that spins around the origin depending on alpha (α), which, from 0.0 to 1.0, is how far around (counter-clockwise) the arrow moves (1.0=full circle). Thus, if alpha is 1/2 — halfway around the wheel — then we have:
Because halfway around the circle is -1. By throwing the -1 on the other side of the equation:
We have Euler’s beautiful sonnet. The beauty comes from the form. On the right, the two key constants, 1 and 0 (one and none; the only other is many). On the left, three somewhat magical constants, two of them transcendental, one imaginary. The equation has (a single instance) of addition, multiplication, and exponentiation, the key operations, and it contains the most important, the equality. It includes the entire territory I described above, from the natural numbers to the complex, in a single very elegant mathematical poem. I wrote a whole post about it.
So there it is, a “brief” treatise on exp(). I’ll end with a last bit of math, the definition of the exp() function:
Since exp(x) is just ex, and e is transcendental, it can only be expressed as an infinite series. (I’ve posted about this, too, if you want more details.)
January 28th, 2022 at 7:27 am
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