Strange new phase of matter acts like it has two time dimensions
phys.org
phys.org
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."
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 quasicrystals: 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.
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?
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.
> 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?
If you wanted to really convince yourself, add multiple windows such that the shadow is affected by the 'swiss cheese' effect of the holes of all the windows lining up relative to the sun.
This is the relationship between a 2d lattice and this sequence that wikipedia told me. Calling it a projection seems a bit much to me. Expanding on this, I would expect the Penrose tilings to be a similar slice through a regular high-dimensonal 'crystal'. The key being that irrationally of the slope means no periodicity of the intersections.
This picture I stole from some blog shows this projection: https://grahamshawcross.files.wordpress.com/2012/04/spots.jp...
--
A 2D square lattice is defined by two perpendicular basis vectors denoting nearest-neighbor distances. Lets put a grid point at the origin at define position as (a,b), where a and b are in units of the basis vectors. That is every integer (a,b) is a grid point that is a hops to the right and b hops up from the origin. Lets also define directions [a,b], where this is the vector from the origin (0,0) to point (a,b).
Consider the following operation: we draw an arbitrary line on the lattice then take all the points within some distance of that line and project them onto the line.
If you draw the line parallel to either basis vector, i.e. [1,0] or [0,1], you will get a 1D sequence where every point is identical: a 1D grid. This is actually independent of the size of the neighborhood around the line we consider as long as it is large enough to include any points; the projections of more distant points align with closer points due to the symmetry of the lattice. A line at 45 degrees (i.e. [1,1]) produces a similar result.
What about some other integer vector? If we draw a line along [5,7], the projected points will no longer be as tidy, but after some distance along the line, we will reach a point equivalent to where we stared: the grid point (5,7). And then (10,14) and (15,21) so on. Every time we hit a new grid point, the pattern of the projection will repeat. The specific pattern between grid points may vary as we change the size of the neighborhood around the line we consider for the projection, but it will always retain the same periodicity. Like the previous cases, as we increase neighborhood size, the projection will stop changing after some critical value as all new points in the neighborhood will line up with previous points. You can see this properties by playing with a piece of graph paper. All rational vectors have parallel integer vectors, and so will have some underlying periodicity.
What about an irrational vector, say [e,pi]? After leaving the origin travelling on this path your will ~never~ hit another grid point. Therefore the projections of grid points will be aperiodic. Not only that, as we increase the neighborhood size, the pattern constantly changes: each new point always has a new spot on the projection. However despite being aperiodic, the system is still ordered: you can know where the next point will show up every time.
It turns out, if you draw a line along the vector [phi,1], where phi is the golden ratio, and use a neighborhood size of sqrt(2), the projection of the points has another interesting property: there are only two possible distances between projected points on the line, lets call them long (L) and short (S), themselves related by the golden ratio. The pattern of Ls and Ss is itself ordered and aperiodic. Not only that, but a simple substituion relation L->LS and S->L produces a longer sequence that includes the original. This just happens to be the substitution relation for finding subsequent terms in the binary fibbonaci sequence.
---
I am sorry for this long-winded explanaton, but I am hoping it helps with visualization without pictures. Perhaps I should write a short blog post with some pictures. The key points are: starting from the origin a rational vector on a grid will always hit another grid point (and then infinite additonal points), which will define periodic relationships will all other grid points to the line. An irrational vector will never hit another grid point, so the relationships are always aperiodic. For a specific choice of projection and vector, you can recover the binary fibbonacci sequence.
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?
If you have a repeating three-dimensional crystal lattice, and a ray of light that is following an irrational slope, then it is guaranteed to intersect one of the cell units or vertices in that lattice.
If it did not intersect any nodes, then you would be able to express that slope rationally just by counting the number of vertical nodes over the number of horizontal nodes!
I’m assuming an infinite lattice here. For finite ones an irrational slope could still “sneak through”
The function n -> sin(n) might be called a "shadow" of t -> sin(t), where k is an integer and t is a real number: namely, it's not periodic, but it's a shadow (projection from reals to integers) of something periodic.
Maybe someone can confirm if the analogy is correct here?
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.
whoa.
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.
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.)
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.
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).
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.
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
Why is time "constrained" as a dimension, that is, you can only move one direction through time, why?
So thinking about how to constrain a dimension, I thought of black holes, once you pass the event horizon they remove half a dimension,
This then makes me think of the big bang and why is it not a black hole? the entire mass of the universe in one place... suspicious, then I think... what if it is a black hole(ish) and we(and the entire known universe) are in the event . horizon and the dimension constrained we perceive as time. and each layer of event horizon constrains another dimension.
At which point I usually fall asleep.
The way I think about time (also probably wrong and not nuanced enough) is through the energy of a system (entropy?). Essentially if the whole universe operates on a tick based update system, then moving from one state to the next is all about how various particles interact with each other. And this in general would be particles moving from a higher entropy state to a lower entropy state. So effectively to go back in time you'd need a lot of energy to undo all the chemical reactions / potential to kinetic energy conversions etc. that caused us to go from one state to the next. So even if it was possible to undo the appropriate state changes using some magic machine, there wouldn't be energy to do it
Now what's really mind blowing is that if such a machine was operating on you, you might still be conscious in a potentially horrifying way. The conclusions of your thoughts come before the thoughs that triggered them, and then they melt away into the thoughts that will trigger them...
Whenever I see something may be periodic, it makes me think it just lives in the Complex plane - maybe time is imaginary :headexplode:
"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.
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.
But the part about starting to predict these patterns in our minds, and the connection to the underlying structures of geometric nature in our cells and for example the visual cortex, makes the process really interesting, it somehow can to my experiences help us in best cases connect to those structures in a deep way, and also the structures that are all around us in nature.
Thanks for sharing, this prediction aspect gave me some thoughts to think about more.
The ability of our minds and brains to create these forms by themselves and also there being a logical, game like mechanic when you use our software might explain parts of why it feels so good to continue doing, and why these acts permeate into the mind even not when doing it.
Also the fact that you can easily spend hours working on these patterns, when you have a tool that enables that easily enough, it supports the thinking that our minds start to replicate and predict these patterns, as mentioned by one poster above this.
(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.)
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...
Also, in math, lots of things are projections of higher order objects into lower order spaces!
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.
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.
Propagating along a 1D trajectory (ie flow of time) would then be along a 2D "trajectory" through which I would experience indefinitively many events at once, unclear which one impacts on which others. But clearly I perceive me writing this post "right now", and am about to push the send button..
A photon moves at the speed of light, it does not experience the flow of time because of that, its whole lifetime is an instant from its point of view, and it "sees" the universe in the superposition of the states the universe goes through.
Similarly, the indefinite number of states of the particle could be observing a development in a time dimension in which the time does not flow for the observer.
They say, one man's instant, another man's eternity...
I have no idea how 2D time would work, though.
> However, if the events are causally connected, precedence order is preserved in all frames of reference.
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?