[HN Gopher] Strange new phase of matter acts like it has two tim... ___________________________________________________________________ Strange new phase of matter acts like it has two time dimensions Author : wjSgoWPm5bWAhXB Score : 210 points Date : 2022-07-21 08:59 UTC (1 days ago) (HTM) web link (phys.org) (TXT) w3m dump (phys.org) | Optimal_Persona wrote: | Says Dumitrescu, "I've been working on these theory ideas for | over five years, and seeing them come actually to be realized in | experiments is exciting." Wait, he only specified one of the time | dimensions he's been working in...j/k, any experiment showing | unexpected temporal properties is fascinating! | andsoitis wrote: | "The best way to understand their approach is by considering | something else ordered yet non-repeating: "quasicrystals." A | typical crystal has a regular, repeating structure, like the | hexagons in a honeycomb. A quasicrystal still has order, but its | patterns never repeat. (Penrose tiling is one example of this.) | Even more mind-boggling is that quasicrystals are crystals from | higher dimensions projected, or squished down, into lower | dimensions. Those higher dimensions can even be beyond physical | space's three dimensions: A 2D Penrose tiling, for instance, is a | projected slice of a 5-D lattice. | | For the qubits, Dumitrescu, Vasseur and Potter proposed in 2018 | the creation of a quasicrystal in time rather than space. Whereas | a periodic laser pulse would alternate (A, B, A, B, A, B, etc.), | the researchers created a quasi-periodic laser-pulse regimen | based on the Fibonacci sequence. In such a sequence, each part of | the sequence is the sum of the two previous parts (A, AB, ABA, | ABAAB, ABAABABA, etc.). This arrangement, just like a | quasicrystal, is ordered without repeating. And, akin to a | quasicrystal, it's a 2D pattern squashed into a single dimension. | That dimensional flattening theoretically results in two time | symmetries instead of just one: The system essentially gets a | bonus symmetry from a nonexistent extra time dimension." | ttpphd wrote: | Feeling resigned to just not understanding this one as a lay | person. Oh well, hope it leads to more cool things! | im3w1l wrote: | It's wrong to say that a quasi-crystal _is_ crystal from a | higher dimension. You apparently get a quasi-crystal if you | project a higher dimensional crystal, which I guess is neat. | But really they are just trying to hype up their own results. | xkcd-sucks wrote: | If you look at the graphic at the top of the article (Penrose | tiling) you'll notice there are a bunch of points that are | centers of rotational symmetry (you can rotate it 2pi/N and | get the same thing) and lines of reflection symmetry (you can | mirror it over that line and get the same thing) but there is | no translational symmetry (you can't slide it over in any | direction and overlap with the original), this is a | "quasicrystal" (in 2d) | | Compare to e.g. a grid of squares that has reflection and | rotation symmetry but also has translational symmetry, this | is a true "crystal" (in 2d) | | This article is treating a train of laser pulses as a "1d | crystal" and if long/short pulses resemble a Fibonacci | sequence treating it as a "1d quasicrystal". This seems to be | noteworthy in that using such a structured pulse train | provides some improvements in quantum computing when it's | used to read / write (i.e. shine on) information (i.e. | electron configuration) from atoms / small molecules (i.e. | qubits) | | Edit: And the "2 time dimensions" thing is basically that a | N-d "quasicrystal" is usually a pretty close approximation of | an [N+M]-d "true crystal" projected down into N dimensions so | the considering the higher dimension structure might make | things easier by getting rid of transcendental numbers etc. | jerf wrote: | "Feeling resigned to just not understanding this one as a lay | person." | | The biggest and most important step is to make sure you drop | any mysticism about what a "dimension" is. It's just a | necessary component of identifying the location of something | in some way. More than three "dimensions" is not just common | but _super_ common, to the point of mundanity. The location | and orientation of a rigid object, a completely boring | quantity, is six dimensional: three for space, three for the | rotation. Add velocity in and it becomes 12 dimensional; the | six previous and three each now for linear and rotational | velocity. To understand "dimensions" you must purge _ALL_ | science fiction understanding and understand them not as | exotic, but _painfully_ mundane and boring. (They may measure | something interesting, but that "interestingness" should be | accounted to the thing being measured, not the "dimension". | "Dimensions" are as boring as "inches" or "gallons".) | | Next up, there is a very easy metaphor for us in the | computing realm for the latest in QM and especially materials | science. In our world, there is a certain way in which a | "virtual machine" and a "machine" are hard to tell apart. A | lot of things in the latest QM and materials science is | building little virtual things that combine the existing | simple QM primitives to build new systems. The simplest | example of this sort of thing is a "hole". Holes do not | "exist". They are where an electron is missing. But you can | treat them as a virtual thing, and it can be difficult to | tell whether or not that virtual thing is "real" or not, | because it acts exactly like the "virtual" thing would if it | were "real". | | In this case, this system may mathematically behave like | there is a second time dimension, and that's _interesting_ , | but it "just" "simulating" it. It creates a larger system out | of smaller parts that happens to match that behavior, but it | doesn't mean there's "really" a second time dimension. | | The weird and whacky things you hear coming out of QM and | materials science are composite things being assembled out of | normal mundane components in ways that allow them to | "simulate" being some other interesting system, except when | you're "simulating" at this low, basic level it essentially | _is_ just the thing being "simulated". But there's not | necessarily anything new going on; it's still electrons and | protons and neutrons and such, just arranged in interesting | ways, just as, in the end, Quake or Tetris is "just" an | interesting arrangement of NAND gates. There's no upper limit | to how "interestingly" things can be arranged, but there's | less "new" than meets the eye. | | Unfortunately, trying to understand this through science | articles, which are still as addicted as ever to "woo woo" | with the word dimensions and leaning in to the weirdness of | QM and basically deliberately _trying_ to instill mysticism | at the incorrect level of the problem. (Personally, I still | feel a _lot_ of wonder about the world and enjoy learning | more... but woo woo about what a "dimension" is is not the | place for that.) | deanCommie wrote: | This may be the most eye-opening and clarifying thing I've | read about this domain in literally years. Thank you. | | The connection back to the complexity chasm that exists | between NAND gates and Quake is also fantastic because as a | "traditional" software engineer, it makes perfect sense. | | It's also good remembering that most of the "academic | science" that underlies computers was established almost | 100 years ago. But it took this long for us to get GTA | Online. | | Whatever advances arrive from these developments in Quantum | computing may not see practical groundbreaking applications | until we're all very old and decrepit. | | It's still incredible to hear about. The fact that our | modern "wireless" world exists on fundamentally the same | physical primitives as a radio wave pulsing morse code | bouncing it off the ionosphere 100 years ago is | mindboggling. | lucasgw wrote: | This is a really wonderful explanation that removes the woo | from QM. As a non-scientist, I've spent a lot of time | reading about QM and trying to understand stuff, and | eventually get lost in hand-waviness about dimensions and | vague references to Schrodinger and his boxes of semi-cats. | Thanks!! | phkahler wrote: | They could have just said "aperiodic laser pulses" are | used. No need to introduce fantastical sounding terminology | about multiple time dimensions, which seems to have been | done quite deliberately. | philipswood wrote: | Yeah, extra spatial dimensions might be common as grass in | visualisations, but extra TIME dimensions... those are | pretty unusual. | [deleted] | kmeisthax wrote: | Ok, so let's cut through the woo: | | A crystal is a repeating pattern of elements in space. For | example, a diamond is carbon atoms - the same thing in | ordinary coal - arranged in a particular shape of grid. | | You can have patterns that are made in time rather than | space, such as by hitting a drum with a stick in time with | music. Of course, this isn't really very crystal-like, | because the drum doesn't try to resist you hitting it off- | time. However, there _are_ certain atomic-scale materials | that _do_ resist your horrible off-beat drumming, and you | "hit" them with a laser rather than a drumstick. _These_ | systems are time crystals[0]. | | You can also have crystal patterns that _don 't_ repeat, | which are called quasicrystals. For every quasicrystal, | there's a higher-dimension crystal that it is a shadow of. | You could imagine, say, a 3D grid or lattice that you can | shine a light through onto a piece of paper to get an | irregular 2D pattern, which would be your quasicrystal. The | two structures are related to one another, but that doesn't | necessarily mean that the flatlanders living in it have proof | of the existence of a third dimension. | | The new development is time _quasi_ crystals: i.e. a drum | that you can bang with some non-repeating pattern and it will | also keep in time with the pattern even if you are off. The | stuff about "acting like it has two time dimensions" is more | woo; there _is_ a 2D time relation to the 1D time | quasicrystal, but there is no actual 2D time shenanigans | going on. The non-repeating pattern apparently also makes the | time crystal better at "keeping time" which _may_ help build | more stable qubits for quantum computers. | | [0] Note that you can't have _spacetime_ crystals in the same | material. You can either have atoms that link to one another | with chemical bonds to form a pattern, or atoms that trade | their bonds in rhythmic patterns, but not both. | function_seven wrote: | > _You could imagine, say, a 3D grid or lattice that you | can shine a light through onto a piece of paper to get an | irregular 2D pattern, which would be your quasicrystal._ | | This is where I lose it. I actually can't imagine such a | thing. Every regular 3D crystal I imagine has a repeating | pattern in its shadow. For every ray of light passing | through one part of the 3D lattice, I can locate parallel | rays that produce the same result in other parts of the | lattice. | | What am I missing here? Just not imagining the right | lattice types? Or are we assuming a point-source of light | so that no 2 rays are parallel? | mensetmanusman wrote: | If you angle the 3D lattice at an irrational angle | relative to the 2D plane the points will not be perfectly | periodic in the plane. | boppo1 wrote: | What is an irrational angle? Is this something I can | actually do physically, or is it more of a theoretical | math thing? For example, if I'm holding a toy that is a | lattice showing the 3d structure of carbon between my | dining room table and ceiling lamp, how do I rotate it | such that it is irrational relative to my table? | tiler2915072 wrote: | this might help a little: | https://math.stackexchange.com/questions/791848/penrose- | tili... which is just a watered down explanation of the | excellent https://tilings.math.uni- | bielefeld.de/substitution/fibonacci... | McBeige wrote: | I'm guessing it's irrational as in rational vs irrational | numbers. Rational means a fraction of whole numbers, so | irrational numbers are those which cannot be represented | as such a fraction. A 1/4 turn is rational, a 1/pi turn | is irrational. | | I feel like the light has to be parallel for it to work, | so sunlight is a better example than a table lamp. | Although I can't imagine any rotation of a simple 3D | lattice having a nonrepeating shadow. Perhaps a more | complex 3D crystal is necessary? | mcswell wrote: | Rational/ irrational here depends on the unit of | measurement. A full circle (360 degrees) is rational if | you measure it in degrees, but irrational if you measure | it in radians (it's 2 pi radians). | cercatrova wrote: | Look at this image: https://i.pinimg.com/736x/54/1b/1a/54 | 1b1afd4a72564f808825b3e... | | The window is the lattice, which is regularly ordered. | The _shadow_ , however, is distorted, ie each light beam | is not the same size as the one next to it. | abeppu wrote: | ... but that window is a 2D lattice, with a 2D shadow. | | > For every quasicrystal, there's a higher-dimension | crystal that it is a shadow of. | | So what's the 3d crystal whose shadow is the Penrose | tiling? The article says it's a "projected slice of a 5D | lattice", which I really struggle to visualize. | | Or perhaps easier, what's the regular 2D pattern of which | the Fibonacci sequence is a projection? | mcswell wrote: | You're struggling to visualize this? "You're just not | thinking fourth dimensionally." --Doc Emmet Brown | (https://www.youtube.com/watch?v=CUcNM7OsdsY) | [deleted] | rocqua wrote: | My guess is that it has to do with projections at an | 'irrational' slope. That would prevent repetition, though | I believe it would cause a dense set of points if you | project the infinite lattice to a lower dimension. | vez- wrote: | This video gives a very concrete example of a non- | repeating pattern (Penrose tiling) | https://www.youtube.com/watch?v=48sCx-wBs34 | function_seven wrote: | I understand the non-repeating patterns. I just don't see | how a regular 3D lattice can produce such a pattern. | Unless the light source creating this shadow is a point- | source rather than a parallel one? | | I guess I'm just looking for confirmation on this | thought: _A parallel light shone through a repeating 3D | lattice will always produce a repeating 2D lattice._ | yazanobeidi wrote: | Try projecting it on a surface with curvature. The | projected grid spacing will be irregular and follow the | curvature. | wnolens wrote: | > there are certain atomic-scale materials that do resist | your horrible off-beat drumming | | whoa. | clord wrote: | Does this then count as a sort of "holographic time"? Encoding | two dimensions on a single stream of time. | Izkata wrote: | ..and can two of them create a Time Cube? | | https://knowyourmeme.com/memes/the-time-cube | Tao3300 wrote: | 4-day confirmed. We're all educated stupid now. | AnimalMuppet wrote: | But that's saying that if you have something repeating in the | same way along the X axis, you have two spacial dimensions. | That's not the way most of us use "dimensions". (The math may | work out for their usage to not be nonsense, but it's | considerably less than a "real" extra time dimension.) | elil17 wrote: | So essentially this is somehow akin to a network with hypercube | topology - it's got a mathematical relationship to an extra | dimension but there's no physical extra dimension. | philosopher1234 wrote: | I don't think anything is claimed about the existence or non | existence of a corresponding physical dimension | joenathanone wrote: | "The system essentially gets a bonus symmetry from a | nonexistent extra time dimension." | bordercases wrote: | It's in the last sentence of the GP | aaaaaaaaaaab wrote: | Two time dimensions? So the metric signature is (+,+,-,-)? | Sharlin wrote: | Apparently not in this case. But Greg Egan (of course it's Greg | Egan) has written an entire novel about a civilization of | sentient creatures inhabiting a universe with a (+,+,-,-) | metric - time is still one-dimensional in their universe, but | one of the spatial dimensions is hyperbolic: | https://www.gregegan.net/DICHRONAUTS/DICHRONAUTS.html | jacquesm wrote: | That makes Flatland look tame. | thatcherc wrote: | And in case anyone is new to Greg Egan, there's also the | Orthogonal series (starting with The Clockwork Rocket) where | the metric is (+,+,+,+) - the "time" dimension is just like | the spatial dimensions. Pretty cool read with a bit of | physics background! | fareesh wrote: | Can someone ELI5 | [deleted] | awsrocks wrote: | [deleted] | inDigiNeous wrote: | Interesting article. The part that caught my attention was: | | "Even more mind-boggling is that quasicrystals are crystals from | higher dimensions projected, or squished down, into lower | dimensions. Those higher dimensions can even be beyond physical | space's three dimensions: A 2D Penrose tiling, for instance, is a | projected slice of a 5-D lattice." | | I've been working on creating digital mandala software for the | past 10 years, and have created countless digital fractal mandala | patterns during that time, and I've noticed that something really | interesting can happen when you do that with a tool that enables | quick and recursive creation of this kind of images. | | After creating a pattern for 4-5 hours for example, after that | the patterns would continue be visualized inside my eyelids once | I would close my eyes, evolving into new patterns that I did not | draw on the screen, in a seemingly intelligent way, finding new | shapes and patterns that I could not have created by myself, but | some part of me continues visualizing these shapes into new, | alive feeling forms inside my eyelids. | | Many times these patterns would continue living inside my eyelids | when I go to sleep, and even sometimes continue right away when I | awoke after that night. And this completely sober even. | | This effect can be magnified exponentially when combined with | some mind altering entheogenics, but it works completely sober | also. | | It is hard to describe, but the feeling has been many times that | I am looking at an "2D shadow" of something that lives beyond | this current moment, like I am seeing a slice of time represented | in 2D about a higher dimensional form that is not possible to | visualize with current tools. | | This article would push towards confirming my theories about | forms existing that we only see parts of in slices of time, but | somehow we can connect to those higher dimensional versions | through the act of mandala creation. | | Just wanted to share some thoughts on the subject, it is not | something I claim to understand at all. If you want to test this | out yourself, we have a trial version of our software available | at http://www.OmniGeometry.com :-) | | Would be interesting to hear if you have some thoughts on this | subject. The act of creating mandalas is something many spiritual | traditions also have utilized to connect us to the coherence of | the greater patterns, like the tibetan monks creating sand | mandalas and then wiping them away. | akomtu wrote: | Your software seems similar to iterated function systems (IFS, | e.g. Apophysis) in principle, but it's deterministic. | | On the philosopical side, these shapes are particular kind of | thought-forms, something that mind naturally creates when it's | not distracted by sensory input. The forms hardly have any | profound meaning - they are just art created by bored mind - | but sometimes they represent sonething profound. | ProllyInfamous wrote: | For anybody whom might be interested in "what a 4D cube might | look like..." | | https://youtu.be/1wAaI_6b9JE?t=2360 | | The entire video in mesmerizing -- one of the coolest party | tricks I've learned is the double-twisted morbius strip | dissection. | robocat wrote: | Our brains are general purpose pattern-matching machines, self- | programmed by their environment. | | Intense interest in anything, will eventually train models | within the mind that not only recognise higher order patterns, | but predict them too. | | Those "predictions" come from the intuitive parts of our mind - | they bubble up - seemingly from nowhere. There is a lot of | wonder about this, and it is fun to explore (say making music, | or playing with patterns). The predictions are not part of our | rational (imperative?) step-by-step mind. | | We also create irrational narratives to explain where our | intuitions came from - the successful startup founder | explaining their route - the mystic explaining their source. | It grew out of tasks in which he asked a split-brain person to | explain in words, which uses the left hemisphere, an action | that had been directed to and carried out only by the right | one. "The left hemisphere made up a post hoc answer that fit | the situation." In one of Gazzaniga's favourite examples, he | flashed the word 'smile' to a patient's right hemisphere and | the word 'face' to the left hemisphere, and asked the patient | to draw what he'd seen. "His right hand drew a smiling face," | Gazzaniga recalled. "'Why did you do that?' I asked. He said, | 'What do you want, a sad face? Who wants a sad face around?'." | The left-brain interpreter, Gazzaniga says, is what everyone | uses to seek explanations for events, triage the barrage of | incoming information and construct narratives that help to make | sense of the world. | | A split-brain guy creating an narrative, rationalising: | https://m.youtube.com/watch?v=Of01gO_fC1M | jacksnipe wrote: | This isn't any sort of crank theory, I think this is basically | what string theory amounts to: we experience a 4-dimensional | projection of an N-dimensional space. | | Also, in math, lots of things are projections of higher order | objects into lower order spaces! | s1artibartfast wrote: | I believe this is a common Phenomenon with a lot of different | manifestations. I think it's scientifically boils down to | hyperactive pattern matching by the brain. Is common with | psychedelics and often manifests as a fractal growth but also | manifest in normal life. A common sober example is seeing | floaters in your vision. Most people have floaters but not all | see them and not all the time. The brain gets a lot of | information and passes it through a filter, and then tries to | pattern fit it. Prolonged exposure to a certain stimulus or a | fixation on it attenuates the filters down and the pattern | fitting up. | | With sufficient attenuation, the brain will simply fit any | noise it sees into the pattern. | | The idea is related to the Nobel prize winning vision cognition | studies of David Hubel and Torsten Wiesel, where animals can be | conditioned to not perceive vertical or horizontal lines. | | https://www.google.com/amp/s/www.psychologytoday.com/intl/bl... | jlokier wrote: | You might enjoy "The Hyperbolic Geometry of DMT Experiences | (@Harvard Science of Psychedelics Club)", | https://www.youtube.com/watch?v=loCBvaj4eSg | colechristensen wrote: | I would classify what you experience as an instance of the | Tetris effect. | | https://en.m.wikipedia.org/wiki/Tetris_effect | purplerabbit wrote: | I've experienced with this with racquetball strangely enough, | and my brother tells me that he regularly experiences this | with playing the piano. | | (This makes me terrified of the degree to which programming | has affected my way of thinking, considering I've spent 100x | as much time doing that as playing racquetball.) | duskwuff wrote: | One part Tetris effect, one part Kluver form constants. | | https://en.wikipedia.org/wiki/Form_constant | Sniffnoy wrote: | Note, the sequence used here is what's normally known as the | Fibonacci word: https://en.wikipedia.org/wiki/Fibonacci_word | [deleted] | roywiggins wrote: | The "encoded" time dimension has a certain "Permutation City" | flavor. | dukeofdoom wrote: | So is the Earth flat or not? That is, are there any | mathematically possible ways the earth could be considered flat | or two dimensional after all. | xwdv wrote: | Can someone attempt to explain what the implications of this | would be on a more macro level? | sedatk wrote: | "Information stored in the phase is far more protected against | errors than with alternative setups currently used in quantum | computers. As a result, the information can exist without | getting garbled for much longer, an important milestone for | making quantum computing viable" | awinter-py wrote: | nature article is paywalled, but looks like this arxiv from last | year is the same? | | https://arxiv.org/abs/2107.09676 Dumitrescu et al | | not my area, but I think they're working with 'floquet systems' | (the same platform used to build a time crystal) and 'mbl | systems' (a kind of quantum system that can be temporarily | protected from thermodynamic entropy). I'm reaching, but I think | both kinds of systems show extended lifetimes when you drive them | externally with a periodic laser. | | I think the Dumitrescu paper is building on work done in Else | 2020 https://arxiv.org/abs/1910.03584 | | The Else paper is using two lasers with non-ratio frequencies to | extend the lifetime of these systems. The new dumitrescu paper is | discretizing that approach by using a fibonacci sequence instead? | and somehow this buys them a few more seconds of system | coherence? | cohomologo wrote: | As far as I understand it, either two incommensurate | frequencies or the Fibonacci sequence ABAAB... approach produce | similar physics. The Fibonacci sequence is easier to simulate | numerically on a (classical) computer because there is a | recursive property to it that allows you to jump forward in | time in large steps, making it nice for theorists even if the | experiments are fairly similar. | ffhhj wrote: | 2 dimensions of time would allow supertasks in our reality. A | problem is solved in the perpendicular axis and the result is | returned to our observer axis. No time travel paradoxes. Next | thing after quantum computing. | t_mann wrote: | Dear quantum physicists, when will you stop messing with our | minds? Just when we'd warmed up to superpositions over 2^n qubit | states, you had to introduce extra time dimensions? | | Tbf, the quasi-periodic pulsing explanation is a lot more | understandable than the headline had me think. Sounds like the | second dimension is just a mathematical interpretation, just like | you can reason about which higher-dimensional objects _would_ | give rise to a particular 2D pattern if projected onto a plane - | it doesn 't necessarily mean that the extra dimensions are really | there, it just provides us with a new way of thinking about it | mathematically (although I wouldn't be surprised if some quantum | physicists came round the corner arguing that the second time | dimension is _actually_ there, sigh). | falcor84 wrote: | Yeah, it reminds me that as a student I always felt that it's | "cute" that a hyperbola can be considered as a 2d section of a | double cone, but that this property doesn't really help me in | any way when working with them. | xigency wrote: | I wonder if one of the reasons more advanced physics can be | intractable to understand is because of all of the clever | interpretations. By abstracting raw empirical results into an | analogous interpretation that defies ordinary logic, we are | introducing gates to understanding by some cleverness test. | | I see this for instance in the difference between elementary | quantum explanations and something more like the Standard | Model. One is concerned with indoctrinating some kind of belief | or interpretation of phenomenon, even introducing philosophical | and unfallsifiable elements, and the other is a useful index of | known bits and pieces and their interactions found through | empirical digging. | contravariant wrote: | I blame the string theorists. A single time dimension ought to | be enough for everyone. | JKCalhoun wrote: | Yeah, no, I'm happy in Newton's world thank you very much. | altruios wrote: | I fully expect us to find multiple time dimensions to actually | exist. | | But that is just a selfish hope for free will to exist. | | think about it: | | _taps head_ | | If it's a time 'line' then you don't get to pick your direction | - no choice is no free will, only if a line exists in a plane | does choice come into the picture. /s | t_mann wrote: | Haha, yeah this is missing a _taps head_ meme. But we don 't | even need multiple time dimensions for free will to exist! | I've heard more than one physicist argue that quantum | uncertainty alone is enough to get us free will. | mehphp wrote: | I'd be curious how? | jaynetics wrote: | I'd argue that a certain randomness of choice could indeed | increase freedom of action, though it doesn't grant "free | will" in the common sense. There's no need for quantum | physics in this, though. A deterministic rand() will do | just fine. | [deleted] | brandmeyer wrote: | They just need one more to catch up with the time cube guy. | 19f191ty wrote: | It's still a single flow of time right? So more like two time- | scales than two time dimensions? e.g. day and night cycle plus | monthly cycles happening together on the same time variable. Have | I understood this all wrong? | bufferoverflow wrote: | What you're describing is generally not considered two | dimensions, but just different scales of one dimension. | 19f191ty wrote: | That's what I said too. The article seems to describe scales | rather than dimensions. They specifically say there's just | one flow of time. But as one the comments below says, there | are two time-translation symmetries. Which in certain | contexts can be thought of as multiple scales. It is also | very common in the real world | dclowd9901 wrote: | That's how I read it too. More that they're encoding another | aspect into their pulsing. But "multidimensional time atoms" is | probably a much more appealing headline. | comnetxr wrote: | Yep, this is it. The key is not that there are two time | dimensions but two independent time translation symmetries, | each which translates the system by a different period of | time corresponding to the two frequencies in their pulse. The | two time dimensions is an analogy that's useful for the | theoretical treatment of such a system. | [deleted] | PartiallyTyped wrote: | I am way outside of my field, but what you describe sounds like | Fouerier series. | 19f191ty wrote: | Fourier series is one way of separating out multiple time- | scales, especially when they are regular and periodic. The | example I gave will be amenable to that because the cycles | are very periodic. But the different timescales don't have to | be periodic. They can be quasi periodic, or completely | irregular. They just have to run at different speeds. | PartiallyTyped wrote: | I see, thank you! Very interesting! ___________________________________________________________________ (page generated 2022-07-22 23:00 UTC)