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Yale physicists find signs of a time crystal (yale.edu)
426 points by anigbrowl on May 4, 2018 | hide | past | favorite | 102 comments

Glad to see Sean make such a noteworthy discovery. I worked in the lab next door and remember him being the happiest and kindest person in the building. Kudos!

The "small world" effect of HN never ceases to astound me. It's always so cool to have somebody chime in with an anecdote about (what appears to an outsider as) something totally niche and out-there.

Sean was just Ok.

Sean is the kind of advisor that makes being a graduate student both exciting and sustainable. He's always upbeat, supports us professionally, etc., so it's always particularly sad for me to hear from students who have had bad experiences with their advisors.

It's nice to see that he has found the time to really keep your minds ticking.

It's the way he explains things that makes them crystal clear - it builds a strong bond with his students. None of them are ambi-valent about it.

Sounds like a keeper. The first PI I worked for as a research assistant was similar.

Yes! He's one of the warmest, nicest people. I did undergrad research in the lab next door to Prof Barrett's when he was Director of Undergraduate Studies. He always took time out to mentor me even though I wasn't his student.

First author here -- happy to take any questions!

There are a few questions about an "overview," so I'll give that a shot here. This is some imagery I've been using recently, about how our observed signatures are related to crystals.

Sometimes physicists think of phase transitions in terms of "symmetry breaking." Imagine zooming in very close on the molecules in a glass of liquid water, all tumbling quickly into and out of your field of view. The situation is highly "symmetric": if you closed your eyes and I shifted the field of view slightly to the left, you wouldn't know what I'd done when you opened your eyes again.

Now suppose the water freezes into a crystal of ice, so that the molecules are arranged on a regular lattice. If I repeat my "shift-slightly-to-the-left" experiment, you'd be able to tell I moved things. That is, somehow the molecules chose a particular location for the lattice, even though any other location of the lattice could have done just as well. In jargon, we say the water "spontaneously broke the continuous translational symmetry": the defining equations of motion are agnostic about the particular location in space, but the state of the system chose a location anyways.

In our experiment, we do something similar in time rather than space. We drive the system with pulses once every time period "T", so the equations of motion are identical under this "discrete" shift in time. However, the state of the system (in our case, the direction of the nuclear magnetization) only goes back to itself every time 2T, and so "breaks discrete time translational symmetry."

There is one more important feature of the observed signature in this analogy: if you nudge an atom that is in a crystal lattice, it will want to return to its original position. Similarly, the period of the magnetization's direction-reversal is robust to our pulse imperfections, if we allow the quantum interactions long enough to act. So, the "region" of parameter space where you can observe this effect is not confined to perfectly ideal pulses, but is instead robust to our pulse imperfections -- the "robustness" depends on the amount of time we allow the nuclear spin interactions to take place.


I hope this helps. I recommend the synopses available at prl.aps.org, and searching for the PDF preprints on the Arxiv (not yet quite as good as the published versions), if you don't have Physical Review access.


[Edit for links]

[2012 overview] https://physics.aps.org/articles/v5/116

[2013 overview] https://physics.aps.org/articles/v6/31

[2013 quanta mag.] https://www.quantamagazine.org/perpetual-motion-test-could-a...

[2017 overviews: "recipe" and first two results]



[2018 announcement] https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.120...

[A different background by (the great) Natalie Wolchover of Quanta Mag., which provides context for the original thrust of one branch of this research. Our first significant involvement was after a talk about "Time Translational Symmetry Breaking" by Chetan Nayak of Microsoft's Station Q.]


Is there any relationship between this kind of lossless vibration, and other lossless processes like superconductivity or superfluidity?

I'm not confident that what we're observing are "lossless vibrations," but it is the case that there is something that is "lossless" about what we call "unitary evolution." The signal we start with decays to zero after a while, but we are able to show that this signal can be (in large part) restored, demonstrating that much of what initially looked like irretrievable loss is actually what we think of as "evolution towards a complicated but coherent state."

I'm more confused, now. Some of the articles you linked to talk about time crystals as a type of perpetual motion machine, albeit one that is "exactly unity" instead of "over unity" as the crackpots would say.

If you have to hit the system with an impulse every once in a while to keep it toggling, how is it different than any other kind of resonant oscillating system? Is it that the cycle goes through states like:

* disorganized

* organized, directional

* disorganized

* organized, opposite direction

I still feel like the part of this system that is special and interesting is getting lost in the translation to lay language :(

This is a good question. The "directions" you mention would, in our system, typically be considered to depend on the nature of the drive. For instance, if you repeatedly rotate the magnetization by 180 degrees, you can imagine the magnetization going up-down-up-down-... repeatedly, whereas if you instead used rotations of 181 degrees, it would take a long time for the state to come back around to pointing along its exact original orientation.

The proposed signature of a "discrete time crystal" was to observe the magnetization point up-down-up-down-... even when you used e.g. 181 degree rotations, if you allow dipole-dipole interactions to act for long enough between rotations. This is what we observe: "wrapped" magnetization when we use imperfect rotations with short nuclear spin interaction times, then locked up-down-up-down-... magnetization when we use imperfect rotations with longer nuclear spin interaction times.

A last subtelty when comparing to traditional oscillating systems is that the response is not at the same frequency as the drive, but will have a period determined by both the drive period T and the symmetry of the dipole interactions. Our system's interactions have 2 symmetric states, so the response period is at 2T. Other systems have other symmetries; for instance, the research team at Harvard showed oscillations at 3T using a spin system with different interaction symmetries.

(HN doesn't do private messages, or this would be sent privately)

Thanks for coming out here and fielding our totally ignorant questions. Its an amazing and beautiful world out there, thank you for sharing your discoveries about it.

Thanks for the kind words. I've focused a good deal in the past few years on teaching/communication (see my profile for a link to some of my basic-physics lectures for student taking the MCAT), and I'm very grateful for the opportunity to discuss our work with this community. Thanks for your interest and great questions!

Actually, HN does do /almost/ private messages, if you hellban your account, and the recipient of your reply comment has “show dead” turned on.

(of course, anybody can activate the “show dead” option, but, in reality, there’s no such thing as privacy on a web server, since there’s always a system administrator noticing unhashed passwords scroll through the log stream)

That's a great insight. That's probably why it's 2X slower in changing spin direction.

This may be a stupid question, but, is there any possibility to store data with this?

Also, what is the size of the crystal that you're looking at in these experiments (sorry if I missed that)

Based on what you describe, it seems to me that a macroscopic example of "symmetry breaking" in the time domain would be the piston of any internal combustion engine. The linear back-and-forth motion of the piston is converted to rotational motion, but in theory the rotation could equally well be in either direction. So when the piston starts moving and picks one or the other direction for the rotation, symmetry is broken. (Obviously real ICE pistons have some way to ensure that the rotation always happens in the same direction.) Have I got that right?

With all fairness don't you think this is not really time-crystal formation in the strict sense (those have been shown to be impossible), but rather an analogue to a "forced" crystal formation? I.e. the direct analogue would be setting up some spatially periodic potential and trapping some atoms in it then finding out it took every second spot. I admit that the doubling appears a bit mysterious from a condensed-matter point of view, but on the other hand period doubling is a well known phenomena in classical physics. I'm a physicist, though not working on time-crystals - some of my friends do.

This overview helps. Thanks much. More to think about...

I'm a software developer with absolutely 0% experience in physics, so if this is a basic/silly question then mea culpa.

If the atoms "flip" when exposed to an electromagnetic pulse, it seems like this could be used to represent state at the atomic level, so highly relevant for computing.

Is there any current indication of how "stable" this flipped/non-flipped state is?

The state of the nuclear spin (up or down, or superposition) is definitely something that has been proposed as a quantum bit ("q-bit"), and many quantum computer proposals have used the nuclear spin as their proposed q-bit. The tricky thing is that these nuclear spins are all interacting with each other, and exercising control of the full state in the presence of those interactions is very tricky.

Just wanted to share since I didn't know what it meant and googled it. It's "mea culpa". I love when people use these old Latin phrases. Never got (or taken) the chance to learn about it and it's always a very quick history lesson alongside learning a new phrase!

>In about 1220, the rite of public penance in Siena for those who had committed murder required the penitent to throw himself on the ground three times, saying: Mea culpa; peccavi; Domine miserere mei ("Through my fault. I have sinned. Lord, have mercy on me").


Mea culpa is pretty common and translate similarly in Brazil (minha culpa), after all, portuguese is a language that has latin as an ancestor, but my favorite and the one that confused me the most the first time I saw is "Quod erat demonstrandum", almost all mathematical proofs that I did in college had Q.E.D. instead of the portuguese C.Q.D. at the end to indicate that that was the point where the proof was finished.

Goddamnit, I always misspell it. Interesting; had never read about the origin of the term.

If it helps for the future, it's pronounced "mayuh coolpuh", so the e makes the "ay" sound.

The IPA is /me.a kul.pa/.

So that's a reasonable approximation. The vowels are off. If you know Spanish pronunciation, it's exactly the same for this word.

Specifically, The E sound is actually the single-vowel /e/, not the diphthong /aɪ/. The "uh" in both words is closer to "ah".

I fixed it for you. If you want it changed back, let me know.

Ut desint vires, tamen est laudanda voluntas.

The latin way to say "my bad"

miserere does sound much closer to misery than mercy. In English, it also "A medieval dagger, used for the mercy stroke to a wounded foe" ... That seems more like it.


What's the layman's 2-minute definition of a time crystal?

The name makes it sound very sci-fi, like it might have the ability to travel through time (!)

Crystal has repeatable structure over space. Its lattice is the same shape over and over again.

Time crystal is a kind of crystal that has repeatable structure over time. It just means it changes its "shape" in a repeated fashion over time. Usually an external force is required to force a crystal to change its shape over time such as with the piezoelectric effect. Time crystal is supposed to just keep changing its "shape" over time by itself. In the Yale case, the changing of "shape" is the flipping of the nuclear-spin magnetization periodically.

That's a great illustration of repeated structural change over time; admittedly that requires an external power to spin it initially.

So could a time crystal be viewed as a source for time information in a system?

The original idea of time crystal is a material that has periodic structures in time, at the lowest energy state [1]. That means it can have repeated structural change over time by itself at rest. In that case, the crystal itself has an intrinsic periodicity in motion, and can be used as a source of time information.

However, now it seems to be changed to that an external energy source is driving the frequency of the structural change of the crystal over time. Like in the Yale experiment, an external pulsing light shines at the system at certain pulsing frequency and they found the system reverses its nuclear spin at twice as slow as the light's pulsing frequency. There's no intrinsic timing property shown in the crystal, so it cannot be used as a source of time information. I've asked the same question. [2]

[1] https://physics.aps.org/articles/v5/116

[2] https://news.ycombinator.com/reply?id=16997756

Let me know if my attempted synopsis above is helpful or not... I think I can confidently say that the crystal does not travel backwards in time (or forwards in time any faster than the normal rate, as has been pointed out).

However, it is a seemingly miraculous trick of spin systems that we are able to use pulses to effectively reverse the time evolution of the system and produce echoes. When looking at one new pulse sequence which had many pulses, the discoverer of the spin echo (Erwin Hahn) said "With that many pulses I could bring back the Messiah!" [1].

[1, PDF] https://pines.berkeley.edu/sites/default/files/publications/...

Totally out of my element here, I read: "Ordinary crystals such as salt or quartz are examples of three-dimensional, ordered spatial crystals. Their atoms are arranged in a repeating system, something scientists have known for a century." Do we know why "time crystals" are structured differently? Does this structure have any implications for our understanding of how atoms can be arranged or is this already well documented? I see in the article the potential applications of this in "clocks, gyroscopes, and magnetometers" but I'm wondering if there are further implications just in our understanding of the universe.

(Sorry that may be a bit vague)

As far as I know, there are no implications for how physical structures are organized in space (e.g. spatial crystal lattices). The signatures we've observed were in a crystal with a very well-characterized lattice structure, and could be observed in systems with different geometries as well (i.e., we didn't have to go out of our way to find a "special" crystal lattice).

Ah, that makes sense. Given that the term "time crystal" seems to conjure up images of physical objects that exhibit supernatural characteristics, is there a more specific term you'd think would be more accurate for describing what it is you're observing?

You're right that the terminology has been tricky to contend with, although it's hard to say what a 'least-confusing' name would be. Other names for the phenomenon include "Pi spin glass" and "Floquet time crystal," neither of which seem to definitely avoid any confusion. The accounts of these phenomena are becoming more clear over time, which will help, but given the name and the images often used in the press, I understand why it can come across as fantastical.

>You're right that the terminology has been tricky to contend with, although it's hard to say what a 'least-confusing' name would be.

"Chrystal with periodically re-arranged structure"?

Chronocrystal? Chronal?

Since it moves: something with warp, then you put the warp ice in the warp drive.

How is one of these different from an ordinary piezoelectric crystal oscillator?

I notice a lot of questions here about piezoelectric oscillators, which I realize now makes sense given this community. A key difference to understand here is that the phrase "time crystal" is referring to a state of a particular "driven" system. So, the signatures we've observed are properties of not only the nuclear spins, but of their response to our driving pulses. So I could not for example "make an equilibrium time crystal and send it to you." Rather, to duplicate our particular results, you would need a clean MAP crystal, which you would then need to "drive" in a particular way, with energy input.

However, for applications, one could imagine a packaged system+driving apparatus with potentially useful properties... but that is just speculation on my part.

"..."time crystal" is referring to a state of a particular "driven" system"

eli5 please

They drive a pulse of electro magnetic radiation (e.g. light) through it, and it takes a very long time to go through, perhaps the signal is altered and ideally it isn't emitted from the system until made to. That's more or less the same explanation as for magnetic and electronic memories, too. Explained like I was five.

Can you supply a link to an author's copy of the article -- or shoot me an email (see profile)? I don't have a subscription to those journals.

Here are Arxiv pre-prints, which are still a bit different from the published versions:



So is the idea of a "time crystal is supposed to have periodic structure at the lowest energy state" out of the window?

If an external periodic pulse is required to drive the crystal to change its structure periodically, the time aspect is coming from the external pulse. The crystal itself doesn't have an intrinsic structural periodicity. The periodicity comes from the external pulsing. Is it still qualified to be called a "time crystal"?

The 2X slower reversing rate does show it has a time magnifying aspect, which can be huge.

See my response here, about the way in which the response frequency depends on both the nature of the drive and the nature of the internal interactions in the system:


The idea of a ground state time crystal was shown to be impossible, which led to the proposals for a non-equilibrium time crystal, connecting the idea (serendipitously) to the research that was already taking place in non-equilibrium systems by condensed matter physicists.

While we do think that each of the 4 existing experiments on discrete time crystals are showing the same effect, we're not yet sure how these observed "signatures of DTC order" will be eventually interpreted relative to the original idea of the time crystal (hence our conservatively named papers/descriptions). Sean's lab used subtleties of complex pulse systems to enable high-resolution MRI imaging in solids like bone (!), and we're pretty sure (not certain) that there's a connection between some of the effects related to those pulse sequences, and what we're now observing in these "DTC signatures"... that's what got us looking at these non-equilibrium ideas originally, and we're pursuing the possible connection.

Thanks for the detail explanation. Good work in expanding our knowledge of new material.

Do time crystal exist in higher dimensions than 3d since it has quantum properties? How would time crystals behave in those higher dimensions?

I think it's fair to say that regular crystals exist in higher dimensions if they have more than 3 planes or axes of symmetry.

This is definitely not true.

Here's the point group (rotational symmetries around a lattice point) for a typical cubic lattice found in many metals: http://materials.cmu.edu/degraef/pg/pg_mbar3m.gif

Here's the space group (rotational symmetries combined with lattice/translational symmetries): http://img.chem.ucl.ac.uk/sgp/large/225az1.htm This is for face-centered cubic crystals. That's 48 symmetry operations, for one of the most common crystal systems used. However, they don't exist in higher dimensions because they're not fully independent. You can construct the full symmetry from just a handful of operators.

Can you elaborate on how this is different from how a quartz crystal works. I assume it's related to the following.

>That’s the “ticking.” In addition, the ticking in a time crystal is locked at a particular frequency, even when the pulse flips are imperfect.

I assume this is not true for quartz?

I'm not an expert in quartz, but I'd assume there are physical "mechanical" oscillations with a hopefully-small distribution of frequencies around a given frequency, which is known to some particular degree of accuracy.

The "ticking" in our system is a periodically flipping nuclear-spin magnetization (rather than mechanical oscillations) whose period is definitely centered at twice the input drive period.

Quartz crystal vibrates due to the piezoelectric effect. External electric current is applied to the quartz to force it to physically bend. When it bends, it triggers the circuit to shut off the external electric current. With no external electricity applied, the bent quartz reverses back to its original shape and its piezoelectric property generates a small electric current in the unbending process. That current triggers the circuit to open the external electric current again, bending the quartz again. This bending and unbending creates the vibration.

Time crystal I gather just vibrates (ticking) by itself with no external power, which is amazing. In this case, it's at the sub-atomic level rather than at the crystal lattice level of the quartz.

Interesting, I only knew the piezo diaphragms that need a frequent pulse drive to vibrate, probably because the energy need and loss in the process is much bigger for the amplitudes needed by audible vibration.

Piezoelectric effect can be applied differently to have different applications. In the piezo diaphragm case, the electric pulse is the frequency driver. If the electric pulse runs at once per second, the diaphragm is moved once per second (bending and unbending once per second). If the pulse runs at 1000/sec, the diaphragm is moved at 1000/sec (1kHz), producing a different pitch of sound. With different frequencies of electric pulse, you can produce different frequencies of diaphragm movement and different pitches of sound.

What was Blum was referring to when he mentioned trying an 'echo'?

Duplicating my reply from here: https://news.ycombinator.com/item?id=16996428

See also the reply here: https://news.ycombinator.com/item?id=16996766

It was shown after the original proposal in 2012 that these signatures can only be observed in "non-equilibrium" systems, so we are actually supplying the pulses, which drive the ticking. The quantum basis for the robust frequency of the ticking relies on dipole-dipole interactions among the nuclear spins.

It is very difficult to understand the complex state of the system after many of these interactions, but in our papers we explore how "coherent" the interactions are by "resurrecting" the signal in what are called spin echoes [1]. Simply speaking, after many interactions the "order" of the system lies not in the nuclear spins individually, but in a complex network of interactions among the spins -- this complex order is not observable (and so the signal appears to "decay away" over time).

Using techniques developed in nuclear magnetic resonance (NMR), we are able to put this "order" back into an observable state, and watch it return. It feels like reversing time, I never get used to it!

[1] https://en.wikipedia.org/wiki/Spin_echo

Interesting work. Can you elaborate on how the ticking actually occurs? What is the quantum basis for the effect?

It was shown after the original proposal in 2012 that these signatures can only be observed in "non-equilibrium" systems, so we are actually supplying the pulses, which drive the ticking. The quantum basis for the robust frequency of the ticking relies on dipole-dipole interactions among the nuclear spins.

It is very difficult to understand the complex state of the system after many of these interactions, but in our papers we explore how "coherent" the interactions are by "resurrecting" the signal in what are called spin echoes [1]. Simply speaking, after many interactions the "order" of the system lies not in the nuclear spins individually, but in a complex network of interactions among the spins -- this complex order is not observable (and so the signal appears to "decay away" over time).

Using techniques developed in nuclear magnetic resonance (NMR), we are able to put this "order" back into an observable state, and watch it return. It feels like reversing time, I never get used to it!

[1] https://en.wikipedia.org/wiki/Spin_echo

Would it be possible to use this as phenomenon in a clock?

That is the kind of thing we are working on understanding right now, and research proposals into this (so-called "quantum metrology") are underway. Is it definitely the case that radio-frequency pulse sequences (related to those used in our work) have been used for extending quantum coherence and making measurements, for instance in MRI. (In fact, that's the kind of work that got me into this!)

As someone with a high energy theory background but has only read titles/headlines about this time crystal business, can you give a precise TL;DR on what a time crystal is?

Let me know if my synopsis above helps, or if you have any specific questions from a high-energy theory point of view. Given your background, you might appreciate that we ran many simulations, to characterize the sample, understand our early results, and build our echo sequence.

> a time crystal — a form of matter that “ticks” when exposed to an electromagnetic pulse

what a fancy name.

We would have called that an "oscillator" or a "resonator" or so back in the days :)

Out of curiosity, how is this different from the crystals used for timing in a small electronic device like an arduino? Is this an effect different from the piezoelectric effect?

instead of readily usable voltage/current changes, you get (so far) useless, probably cased by the measurements, electron spin in one direction or another flipping over time.

Most of this stuff goes way above my head, but I remember that creating time crystals used to be a thing last year? [0]

What's so special about these Yale time crystals, are they of a different type then these previous ones? This all feels a bit weird like there's some kind of secretive time crystal production going on, by people initiated into the dark arts of metaphysics.

[0] https://news.ycombinator.com/item?id=13505287

There are a few key differences in our work. First, it's a very different system; the prior experiments were done using trapped ions, and "defects" (nitrogen-vacancy centers) in diamond, while our system used nuclear spins. The more important difference is that our system is very ordered, since it took place on an actual crystal lattice with a high degree of symmetry (this matters because some theories proposed the need for this disorder to observe the effect -- the trapped ion experiment even purposely included disorder). This is the reason for our use of the word "ordered" in the title of the paper.

Other differences include our further work to clarify the phemomenon, including the creation of "echoes" to explore the coherence of the system (see my other comments) among other new contributions about the parameter space and behavior of the effect. Finally, it's just surprising to have observed this effect across so many systems which are all so different from each other (very different Hamiltonians).

Naively I’m imagining the flips are triggered via incoming particles - photons? If so, what are the characteristics required of the inputs and how does that affect the particles in/out of the system?

I’m wondering about possible applications for time crystals?

Anyway this is really intriguing! When I first read of time crystals they really seemed unlikely to ever be observed. But if they’re in human made crystals they just might be either more common or easier to produce than I’d thought.

We use a solenoid to drive magnetic fields in our sample (RF frequencies, near field), but yes, we do often envision an absorption or emission event by a given nuclear spin as it changes its spin state in the presence of an even stronger, static magnetic field. We have to carefully match the frequency of the driving magnetic field to the so-called Larmor frequency of the spins, which allows them to absorb the supplied energy.

We're working on understanding possible applications now, and we also wonder whether this is a more commonly available phenomenon than originally thought. As experimentalists, we're very conservative in our claims -- for instance, we explain our observation of the "DTC signature" specifically proposed by theorists, without making claims as to the final interpretation of the results for the existing theory. Instead, our job is to very clearly explain what we did and what resulted, and then we get to see (and in some ways participate in) how the broader condensed matter community comes to understand the phenomena. It's an exciting position to be in, there are still many interesting unknowns!

Is the timing of the crystal influenced by its size, shape, or composition? Does it just double whatever the input signal is, or do you have to find a particular resonant frequency? If you brought a ticking crystal into contact with one that was not, or was ticking at a different frequency, would there be transfer or loss? If you just charge up a corner of a crystal, does it extend to the rest? Can you look for ticking in crystals you haven't charged, and if so, are they readable long enough to be used for dating or information storage?

Thank you so much for your reply!

I wonder if the time crystal could be reinforced to last a while. Then whether two such crystals could be brought to an entangled state?

Off-topic, but the name "time crystals" just sounds like something straight out of a Doctor Who episode.

So what are the practical applications of a "time crystal"? The name certainly allows the mind to run wild...


Does it have four-corner rotation?


"Scientists say that understanding time crystals may lead to improvements in atomic clocks, gyroscopes, and magnetometers, as well as aid in building potential quantum technologies"

So you are saying that the Time Stone/Gem is real? How exciting!!!!

Can I somehow integrate this with my 1982 DeLorean?

We detached this subthread from https://news.ycombinator.com/item?id=16995305 and marked it off-topic.

Admittedly, if you asked me 20 years ago which one of "time crystal" or "flux capacitor" were actually from a movie called "Back to the Future," I am not confident I would answer correctly.

I hope that's because you were too young to have seen the movie, because 20 years ago was 1998.

Back to the Future was 1985. (And 1989/1990)

If a time crystal could somehow be manipulated to change the moment of inertia, that might be called an oscillation overthruster.

Don't let Thanos get it.

I'm still waiting for researchers to find a Time Cube.

Hold off- we need to find a Time Square first!

"The 4-equidistant Time points can be considered as Time Square imprinted upon the circle of Earth."

I don't think it's this:


You could argue that all crystals travel through time

We detached this subthread from https://news.ycombinator.com/item?id=16995373 and marked it off-topic.

No argument there.

Hello readers from the future!

Hi, you from 8 minutes ago!

He won't see your message :(


Nah, but they used to.

In other news, Timex remains in business and the Marvel Comics Universe will be hiring the most photogenic of the three for "scientific consulting" on the next 3 to 7 MCU films.

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