This article perfectly bookends my abandoned physics degree.
1. This reminds me a bit of the delayed-choice quantum eraser, which is one of the weirdest scientific outcomes and is the sort of thing that inspired me to pursue a physics degree. It implies a certain kind of time travel is possible, in the sense that in the present moment we can cause some past moments to collapse.
2. As my TA, Frank Wilczek successfully scared me off that physics degree by simply being so smart and having complicated things come so easily to him. Being confronted with the kind of horsepower needed to be successful in academic physics was eye-opening.
Speaking of causality, Wilczek had been a professor for 4 years before the first delayed choice experiment was proposed (1974 vs. 1978), which would normally disqualify him from being a TA/AI. Not doubting your experience, but I don't understand the timeline here. Were you using "delayed choice" to more broadly mean "which way" experiments?
As an outsider who enjoys a certain flavor of conspiracy theories, your confusion about a timeline involving a professor investigating delayed choice experiments tickles me.
He was my recitation instructor at MIT circa 2002/2003. It was very confusing to have a recitation instructor win a Nobel prize a couple years later, I had no idea who he was until 2004.
Thinking back, he was probably just running recitations for fun and to find future phd's, not grading assignments.
Haha, I very much doubt his behavior changed in the slightest. He knew how the universe works at a deep level, and was so excited to have others learn about it too.
Also note that he has become very involved in research into physics (and stem) education in the later parts of his career (and has done some interesting stuff in this space as well).
So it basically reinforces the many-world interpretation, which makes perfect sense, and it’s the most mathematically minimal of all too.
Resorting to some kimd of retro-causality mechanism really shows how many people are uncomfortable with many-worlds.
And many-worlds (though likely only scratching the surface of reality) is pretty much in the vein of panpsychism as it mirors the branching-out biology does with life/consciousness. That’s what I call a tasty correspondence of the universe
We need a new mathematical framework that goes beyond spacetime and amplituhedron https://en.m.wikipedia.org/wiki/Amplituhedron (from which more re-interpretations can happen, especially ones that can encapsulate consciousness more than just “an observer” (or worst leading to absurdity like the quantum suicide experiment https://en.m.wikipedia.org/wiki/Quantum_suicide_and_immortal... which definitely played a role in affecting Hugh Everett’s self-abusive lifestyle leading to his very early death at 51, as well as the suicide of his young daughter
> Everett's daughter, Elizabeth, died by suicide in 1996 (saying in her suicide note that she wished her ashes to be thrown out with the garbage so that she might "end up in the correct parallel universe to meet up w[ith] Daddy"),
There is no retrocausality exactly because there is time resolution: causality with sort itself out whatever the cost, is what the quantum erasure experiment showed.
Thanks for clarifying this! The best way I've been able to intuitively understand it is that all worlds are internally consistent and causal, but the observation that causes us to split away from some worlds can be after the fact. That doesn't make it possible to come up with a superposition of worlds that breaks causality.
When one of my physics class mates told me he was reading topology at the age of 7, I knew I would never make it with my mere hard work. I still love physics but I’m glad I never tried academia. I would have been chewed up
How does one end up reading topology at age 7? Were your parents math professors or something? Or were you just a very mathematically curious 7 year old?
I learnt to use a computer very early and I had few friends, so I would spend my days reading Wikipedia. The maths and physics articles for some reason drew me in particularly, and some times I'd also look at other sources. But really, I didn't understand most of it.
Not same commenter, but we just went to the library as a family every 3 weeks. Around that age I was bored with the childrens section, so I tended to pick books on computing and quantum field theories :)
I ditched the math side soon for the computing section though.
> This reminds me a bit of the delayed-choice quantum eraser, which is one of the weirdest scientific outcomes and is the sort of thing that inspired me to pursue a physics degree. It implies a certain kind of time travel is possible, in the sense that in the present moment we can cause some past moments to collapse.
Only if you assert the copenhagen interpretation. If you instead assert that the experimenter merely becomes entangled with one part of a superposition on measurement, causality is just fine.
I think you’ve got to call the bluff and try to level up. Progress through Physics isn’t monotonic and a bit like the speeding cars of the freeway, you’ll probably meet those going faster at the traffic lights due to the throughout bottleneck of your environment.
Grinding is a separate super power — few can grind at an elite level.
2. Seems sad to me, his job was to make sure you are inspired, or at least informed to make a wise choice, but not scared off. But maybe he didn't know.
He definitely didn't know (he was just excited about showing us Einstein summation notation), and he definitely informed me to make a wise choice. Not every degree program is about ensuring the best median performance, some are only concerned with picking out the world-changers. And that's okay.
As a disillusioned phd I appreciate your response here. For years I’ve beaten myself up for not doing noteworthy science. For some reason your words have washed away a lot of guilt.
Glad it helped! It was a bit crushing at the time (and TBH I am still working through residual shame here and there), but it was kind of like washing out of Navy SEAL training. There's no shame in not hitting the very top of the mountain. Hardly anyone does.
Sounds like “informed to make a wise choice” still applies? I had a similar experience with mathematics, having been “good at maths” in high school and then making friends in university with people who are ACTUALLY good at maths.
"delayed-choice quantum eraser" is so mind-boggling that I don't see any comprehensible explanations to me, a beautiful enigma that locks one of deepest secrets of our universe. And my brain simply refuses to accept any violation of causality - I consider causality possibly the most fundamental rules of physics, if it conflicts with others, I can only consider other rules to not hold.
Reading about these kinds of experiments always fills me with lots of little questions like "well what if we did THIS" or "what if we tweaked THAT slightly". I have the urge to try and "catch reality out", to expose the trick.
Makes me wish you could do these experiments with a laser pointer and a piece of paper instead of needing lots of very expensive machinery and a research grant. Everyone should have the chance to play around with quantum weirdness.
It certainly seems like a mind blower - Perhaps causality is not violated if the concept of causality is actually orthogonal to the concept of time. We perceive causality to be time-dependent, but could this be an illusory constraint from our frame of consciousness?
My feeling is that ultimately causality will turn out to be the same as “absence of contradiction”, and that time is just an emergent phenomenon in the causal network of all possibilities.
As is usually the case with any advanced physics / astrophysics article I read, I can't get into the article because I'm stuck mulling over a premise. Article states:
> The laws of physics are symmetric through space ... But in a crystal, this gorgeous symmetry gets broken. The molecules of a crystal arrange themselves in a preferred direction, creating a repeating spatial structure. In the jargon of physicists, a crystal is a perfect example of "spontaneous symmetry breaking" — the fundamental laws of physics remain symmetric, but the arrangement of the molecules is not.
I don't understand how crystals break spatial symmetry. Are we talking about some absolute spatial directional bias? If it's just relative the crystal lattice itself I can't see how that breaks symmetry.
There's two things that can have symmetry here: The laws of physics themselves, and the system under investigation. The symmetries of the laws of physics don't get broken, but those of the system do. Compare a crystal to a gas: In a gas, the atoms are all bouncing around pretty randomly, so at any given point in space, there's roughly the same chance of finding an atom. Shift the gas to the left by distance x, and the local probability distribution of atom positions looks pretty much the same. In a crystal on the other hand, the atoms are still moving around and vibrating (so there's still some uncertainty in the positions of the atoms), but they tend to stay pretty close to their proper position in the crystal lattice. So the atoms are more likely to be in positions that line up with the rest of the crystal lattice than anywhere else. This breaks the symmetry. Shift by distance x and the peaks of that probability distribution no longer line up. The exception to this is if x is a multiple of the spacing of atoms in the crystal. Then you're shifting the peaks by exactly the right amount that they line up again when you're done. So a crystal doesn't completely break the symmetry of space, but it reduces it from a continuous symmetry (you can translate by any amount in any direction) to a much weaker discrete symmetry (only certain translations of space will preserve the symmetry).
A time crystal is similar to an ordinary crystal except that instead of reducing symmetry of translations in space from a continuous symmetry to a discrete symmetry, it reduces symmetry of translations in time from a continuous symmetry to a discrete symmetry.
EDIT: It's a little ironic that if you ask most people, they would say that a crystal is more symmetric that a gas, since a gas will look completely random and asymmetric if you take a snapshot of the positions of all the atoms at a single time. But since physicists care about the probability distribution of atom positions, they say that the gas is more symmetric than the crystal.
I feel like there must be more to it that this. Wouldn't any physical structure that's not homogeneous and isotropic also break symmetry in the same way. Does the room I'm in break symmetry as there's a different likelihood of hitting a wall depending on the direction I travel?
The x in "distance x" (grandparent comment) is very small.
"Very small" in this context is less than the lattice spacings, which for a typical crystal can be on the order of the wavelength of an X-ray (i.e., there's ~ 0.1-100 ångströms between the crystal's diffracting planes, so "distance x" must be a fraction of that length).
A typical room is effectively a <https://en.wikipedia.org/wiki/Gas_in_a_box>. If the walls of your box are good X-ray detectors then an isotropically-radiating X-ray source somewhere near the middle of the room will evidence an essentially uniform energy loss at the detectors, and and weak reflection from air molecules back towards the source. However, if you substituted the air in the room with a crystal lattice, the energy loss would be much stronger at detectors in some directions, and there would be strong reflections back towards the source along some directions. See <https://physicsopenlab.org/2018/01/18/bragg-diffraction/> for some details.
Symmetry breaking is very important to the study of condensed matter physics, including solid matter, and arguably it’s the reason your room exists at all.
> Wouldn't any physical structure that's not homogeneous and isotropic also break symmetry in the same way. Does the room I'm in break symmetry as there's a different likelihood of hitting a wall depending on the direction I travel?
> continuous symmetry (you can translate by any amount in any direction)
Thanks for the definition. That is close to the math idea of automophic, that is, can map onto itself. So, what physics means is that translations are essentially automorphisms. Simple now that we have a clear definition!
It's about being periodic in a lowest-energy configuration.
A spatial crystal freezes into a spatially-periodic configuration at its lowest energy: you don't need to add energy to keep a crystalline solid's microscopic components arranged in lattice-like form.
A time crystal freezes into a periodic configuration at its lowest energy: you don't need to add energy to keep a time crystal arranged in its temporally periodic arrangement. If at t_0 we have one spatial configuration, at t_1 another spatial configuration, ... at t_n-1 we have yet another spatial configuration, and at t_n we have the same spatial configuration as at t_0, and we have no net flow of energy into the spatial configuration at any t_x, we have a time crystal. The spatial configurations at any t_x need not be crystalline, they just have to differ at different points in their cycle.
An analogue clock is not a time crystal because even though the configuration of the hands at 12:00->12:01->...->11:59->12:00 is temporally periodic, you have to wind a clock (or power it in some other way) or it gets stuck at some arbitrary configuration -- it stops cycling unless "disturbed" with added energy. The clock's lowest-energy configuration has its hands always pointing to one hh:mm time, and no different time is shown over the course of a day.
A time crystal, being in its lowest-energy state, cycles through all its configurations endlessly until energy is added.
Does this mean you could use a time crystal to efficiently measure time accurately, by counting the number of cycles? I know we do that with quartz oscillators but those need energy input to keep oscillating.
Good question. I was about to edit this into my comment, but now it works better as a reply.
The act of "reading" the configuration of a time crystal disturbs the time crystal. So you either a set of maximally-similar time crystals that you read at various times during a day, or you need to re-freeze your single disturbed time-crystal each time you read it.
There are ordinary crystals which literally melt out of their crystalline state when handled / measured-by-bright-light. The organized pattern is broken with the additional energy. Time crystals are patterened over time, and that pattern breaks when they are handled / measured-by-bright-light.
You could think of it as having to shine a flashlight (or laser) through the time crystal to figure out which way it twists the light at a given time t_x. If you know the temporally-periodic structure, you can predict the different twisting when you turn on the light at t_x versus t_x+1 or t_x-1. But lighting up the crystal breaks the lowest-energy condition of the time crystal -- it's melted by the light it twists -- so you have to re-freeze it back into its predictable periodic structure, otherwise you might get the same twisting (or none) at t_{measured}+1, t_{measured}+2, ..., t_{measured}+n.
(It is fairly literally re-freezing: you have to do laser cooling or the like. And it takes energy to run the cooler, which removes energy from the not-lowest-energy-state broken time crystal, so thermodynamics isn't violated.)
That's a very good question. I started but abandoned a fairly deep answer, mostly because this is an area far from my expertise and in which it is easy to be howlingly wrong. (To be fair to me, subject matter experts have been arguing about this in the literature for some twenty years.)
I don't get why it's surprising. Any regular structure has resonance modes: struck a bridge or a violin and it will keep vibrating in a time-periodic fashion. Most structures are leaky and lose that initial energy quickly. Crystals are super-regular, nearly perfect macroscopic structures, so they lose energy slowly, and if the periodic motion only involves electrons in the crystal, the motion will conserve energy almost perfectly and may keep going for billions of years.
Practically speaking, this means we couldn't use the cyclic process to do work, because that would require it to have excess energy it could transfer. If a time crystal's periodic behavior were to spin, you couldn't use the rotation to push something. Right?
Right. Lowest-energy means that you can't pull energy out of a time crystal; there's no excess. Anything you try to attach to a time crystal will transfer energy into the crystal.
Practically all we can do with a time crystal is to measure it with the lightest possible touch and hope it doesn't break the periodicity. (So far, afaik, the periodicity has always been broken by the measurement process's energy input).
I don't know what we could do with large numbers of time crystals, though. One can't pick up a snowflake in one's bare hands and use it like a buzz saw to cut a sheet of paper (the snowflake melts on contact), but an avalanche of snowflakes can snap trees. Maybe for time crystals that rotate light a predictable amount at a given time t_x, we could create some sort of interesting lens from a large cloud of such time crystals arranged at different distances from a bright light source -- a sort of "anti-fog".
If the periodicity is broken by any measurement we have been able to make so far then how do we know the periodicity is there in the first place? Just theory? If it’s not too much of a burden could you outline the proof of the existence of time crystals?
> how do we know the periodicity is there ... Just theory?
Theory guides us, but experimentally you can for example make a whole bunch of time crystals (especially straightfoward for driven time crystals, which have a period that's an integer multiple of the driver, the driving force being laser light or microwaves) with an expected set of states it cycles through, and you can test those states once per time crystal. If you reliably get the states theory predicts, that's good evidence.
> I don't understand how crystals break spatial symmetry.
Imagine doing some experiment in a vacuum. It will work the same no matter which direction you orient the experiment or where in space you put it.
Now imagine doing the same experiment inside a crystal. Now it won't work the same no matter which direction you orient the experiment (because some directions will cause something in the experiment to hit one of the atoms of the crystal, and other directions won't) or where in space you put it (because there are crystal atoms in some places but not in others).
A minor addition to clarify: if one did the same experiment inside an ideal gas, rather than a crystal, there are still atoms in the way (compared to vacuum) but there is no preferred direction through the atoms. Crystalline structure gives a preferred direction along the principal axes. This might mean there is less optical extinction along the principal axes from deep inside the crystal, for example, whereas from deep inside the ideal gas optical extinction is the same in every direction.
That is, the view varies depending on direction one looks within a crystal. "Symmetrical" means that the view should not vary that way. If we freeze our gas into a crystal lattice, we break this symmetry.
Symmetry becomes much more easy to grasp if you think of it only in terms of transformations - in this case coordinate transformations. If you for example rotate your system by a few degrees, does it look the same if you were to overlay it with the initial state (imagine the crystal as an infinite lattice). If yes, you have found a symmetry. For a crystal structure, you usually only have some discrete symmetries, i.e. you can maybe rotate by multiples of 90 degrees or shift axes by multiples of a certain length, but apart from these things the "inherent" rotational and translational symmetry of empty space is gone. What they're calling "spontaneous symmetry breaking" here is technically correct, but in this context it's a pretty trivial observation (I mean, yeah, it is a lattice after all) without any deep insight, as opposed to the Higgs mechanism for example.
It’s counterintuitive because most people are more familiar with the mathematical concept of symmetry whereby a lattice has more symmetry than a random set of points (which almost certainly has no symmetry at all). However from the physics point of view, the random set of points is more symmetrical than the lattice because there’s no way of telling which way a random set of points is oriented.
Symmetry in physics is not just about orientations in space. This notion rather comes from the fact that large systems of discrete points are often described using continuum mechanics or field theory, which naturally has a lot more symmetries. But even a set of randomly distributed point-like particles can have symmetries. If the set was made up of identical bosons for example, it would have a wave function symmetry under particle permutations. And real particles would also exhibit a whole lot of other discrete symmetries, like CPT symmetry at the very least.
Your question reminded me of this video about "Homochirality: Why Nature Never Makes Mirror Molecules"[1] - even though it's not directly related I think it may be interesting to you.
If you imagine every molecule in the crystal can be oriented randomly, then there is a very large number of possible global configurations that are equally likely and we say the crystal is "symmetric" with respect to these outcomes. If the orientations become ordered in some fashion as the article is saying we say the symmetry is broken.
Yes, I went to grad school in math. The first test was a pop quiz in real analysis and was about the little axiomatic set theory the prof had started the course with.
When the prof handed back the papers, he'd given me a zero. At the end of class, he asked that I stay. We went over my test paper: I had used little omega as the first infinite ordinal, essentially the same as the set of natural numbers. In an NSF course in axiomatic set theory the previous summer, that notation was standard. I'd thought of my proof, that is, my solution on the test, only at the last moment so just used little omega without defining it. When I gave the prof the definition, he saw that my solution was correct and, indeed, one step shorter than his. So, I got credit on the test.
Then I asked the prof why he had wanted to see me, and he smiled and said that he no longer did.
It was a class of 20+ students, and I doubt that all the other students got a good proof. So, why was the prof picking on me?????
He was regarded as a bright prof. In later years, he did have some fame.
So much for such a bright math prof. I smelled I was being dumped on. I didn't know that prof at all.
His lectures were not very clear. The book he had selected was just in typing which is awful for the math of real analysis -- he could have used, say, Royden. And he'd just tried to dump on me for no good reason. Also, I was correct and he hadn't known that -- my meaning for little omega is and was standard.
At times I'd been dumped on in grades 1-12. I did well on standardized tests in math and physics, and that saved me. I was well out of patience being dumped on so walked out of the course and never saw that prof again.
In high school plane geometry the teacher believed that I refused to do any homework. Well, I didn't bother with her homework assignments -- they were too easy. Instead in the back of the book there were lots of more difficult exercises, and I made sure I worked 100% of those, never missed even one. One of those took me the weekend, and when I mentioned it in class on Monday, my first and last class participation, 20 minutes later the teacher was close to screaming exhorting the class to "think". Not wanting to be accused of ruining the class, as I started to give the steps to a solution, the teacher cut me off and screamed "You knew how to do it all along." Guilty as charged! Gee, she was not interested in getting the solution from me!
I've come to suspect: Students with some flair for originality and creativity can look different, not the same as the image of a good student -- nose to the grindstone, ear to the ground, shoulder to the wheel, and from that position dot all the i's and cross all the t's -- and less good than desired instead of better.
The other two courses they had me in were close to what I'd already studied carefully in ugrad school. One of these two was from Kelley, General Topology that I had lectured from to a prof.
I did well at my ugrad teaching, started violin, met my wife, and got a Ph.D. in applied math later at another university.
There, too, at times I did work comparable with that of the brilliant profs.
Net, I'm not so impressed by the super brains of so called brilliant profs.
Or I believe in the standard, "Everyone puts pants on one leg at a time."
More generally, my experience is, given the basic context of data and background, a lot of people can work through and find the immediate consequences.
In case anyone else is as confused about time crystals as I was, Physics Girl recently released a video on YouTube that does a decent job of explaining it:
https://www.youtube.com/watch?v=ieDIpgso4no
tl;dw: Crystals are materials which atoms or molecules are aranged in a repeating manner. Time crystals are a material which isn't just repeating in the three dimensions of space but also in the "time dimension". Basically, the quantum spin of the material switches regularly, even though no energy is being applied.
> It wouldn't mean free energy — the motion associated with a time crystal doesn't have kinetic energy in the usual sense, but it could be used for quantum computing.
I'm not smart enough to have anything really insightful to say about the article. But I don't know if it is more amusing or vaguely annoying that a technobabble phrase like "we'll have to pick up more time crystals for the ship's navigation computer to keep functioning" could be realistic in the future. Or, if it isn't realistic, the real show-stopper could just be the lack practical long distance space travel.
One thing I've learned over time is that absurd and even naive-seeming sci-fi premises can and do become reality. I remember watching The Net with Sandra Bullock and laughing at the stupid representation of a website with sound and animation. How naive! And I also remember reading about "online" money that could be stolen like gold and held on a drive. How silly these sci-fi writers were back in the day.
Ha - I came here to post pretty much the same thing. It always makes me wonder which came first. Did sci-fi/literature-at-large start using crystals this way after we started using them for time purposes, or did humans just always think crystals were cool and somehow supernatural and it just turns out we can use crystals to keep time? Probably the latter, given that humans do love shiny rocks, and they've existed much longer than we have.
Apparently (based on the article) these time crystals were thought up in 2012. I'm sure you could find the phrase "time crystal" in sci-fi previously. In fact I bet the person who thought the idea up was extremely pleased that they could get such a cool sci-fi sounding name for their thought experiment.
On the other hand, crystal oscillators (riffing off your "using crystals [...] for time purposes") go way back, and pre-date Star Trek style technobabble I guess.
But the idea of "magical crystals" goes back even further, and the thing that makes them interestingly shiny is tied to their structure. So I guess we knew there was something kind of funky going on there but didn't have the science to describe it really well.
And what's sci-fi anyway? If someone in like 1800 wrote a story about teaching rocks to think, we'd probably call it fantasy. It just so happens that we managed to pull that idea from magic to reality.
Yeah "time crystal" will always make me think of Doctor Who. Not sure if they were ever actually mentioned in any story lines, but it sounds like something their writers would come up with.
It sounds like it's not really a "crystal" as such. I wonder if the person who came up with this term was a scifi fan. It sounds like the kind of thing that would be in Dr Who or Star Trek.
1. This reminds me a bit of the delayed-choice quantum eraser, which is one of the weirdest scientific outcomes and is the sort of thing that inspired me to pursue a physics degree. It implies a certain kind of time travel is possible, in the sense that in the present moment we can cause some past moments to collapse.
2. As my TA, Frank Wilczek successfully scared me off that physics degree by simply being so smart and having complicated things come so easily to him. Being confronted with the kind of horsepower needed to be successful in academic physics was eye-opening.