The Quantum Theory That Peels Away the Mystery of Measurement

A recent test has confirmed the predictions of quantum trajectory theory, which describes what happens during the long-mysterious “collapse” of a quantum system.

Imagine if all our scientific theories and models told us only about averages: if the best weather forecasts could only give you the average daily amount of rain expected over the next month, or if astronomers could only predict the average time between solar eclipses.

In the early days of quantum mechanics, that seemed to be its inevitable limitation: It was a probabilistic theory, telling us only what we will observe on average if we collect records for many events or particles. To Erwin Schrödinger, whose eponymous equation prescribes how quantum objects behave, it was utterly meaningless to think about specific atoms or electrons doing things in real time. “It is fair to state,” he wrote in 1952, “that we are not experimenting with single particles. … We are scrutinizing records of events long after they have happened.” In other words, quantum mechanics seemed to work only for “ensembles” of many particles. “When the ensemble is large enough, it’s possible to acquire sufficient statistics to check if the predictions are correct or not,” said Michel Devoret, a physicist at Yale University.

But there’s another way to formulate quantum mechanics so that it can speak about single events happening in individual quantum systems. It is called quantum trajectory theory (QTT), and it’s perfectly compatible with the standard formalism of quantum mechanics — it’s really just a more detailed view of quantum behavior. The standard description is recovered over long timescales after the average of many events is computed.

In a direct challenge to Schrödinger’s pessimistic view, “QTT deals precisely with single particles and with events right as they are happening,” said Zlatko Minev, who completed his doctorate in Devoret’s lab at Yale. By applying QTT to an experiment on a quantum circuit, Minev and his co-workers were recently able to capture a “quantum leap” — a switch between two quantum energy states — as it unfolded over time. They were also to achieve the remarkable feat of catching such a jump in midflight and reversing it.

“Quantum trajectory theory makes predictions that are impossible to make with the standard formulation,” Devoret said. In particular, it can predict how individual quantum objects such as particles will behave when they are observed — that’s to say, when measurements are made on them.

Schrödinger’s equation can’t do that. It predicts perfectly how an object will evolve over time if we don’t measure it. But add in measurement and all you can get from the Schrödinger equation is a prediction of what you’ll see on average over many measurements, not what any individual system will do. It won’t tell you what to expect from a lone quantum jump, for example.

Measurement derails the Schrödinger equation because of a peculiar phenomenon called quantum back-action. A quantum measurement influences the system being observed: The act of observation injects a kind of random noise into the system. This is ultimately the source of Heisenberg’s famous uncertainty principle. The uncertainty in a measurement is not, as Heisenberg initially thought, an effect of clumsy intervention in a delicate quantum system — a photon striking a particle and pushing it off course, say. Rather, it’s an unavoidable outcome of the intrinsically randomizing effect of observation itself. The Schrödinger equation does just fine at predicting how a quantum system evolves — unless you measure it, in which case the result is unpredictable.

Abstractions navigates promising ideas in science and mathematics. Journey with us and join the conversation. See all Abstractions blog Quantum back-action can be thought of as an imperfect alignment between the system and the measuring apparatus, Devoret said, because you don’t know what the system is like until you look. He compares it to an observation of a planet using a telescope. If the planet isn’t quite in the center of the telescope’s frame, the image will be fuzzy.

QTT, however, can take back-action into account. The catch is that, to apply QTT, you need to have nearly complete knowledge about the behavior of the system you’re observing. Normally, an observation of a quantum system overlooks a lot of potentially available information: Some emitted photons get lost in their environment, say. But if pretty much everything is measured and known about the system — including the random consequences of the back-action — then you can build feedback into the measurement apparatus that will make continuous adjustments to compensate for the back-action. It’s equivalent to adjusting the telescope’s orientation to keep the planet in the center.

For this to work, the measurement apparatus has to collect data faster than the rate at which the system undergoes significant change, and it has to do so with nearly perfect efficiency. “Essentially all the information leaving the system and being absorbed by the environment must pass through the measurement apparatus and be recorded,” Devoret said. In the astronomical analogy, the planet would have to be illuminated only by light coming from the observatory, which would somehow also collect all the light that’s reemitted.

Achieving this degree of control and information capture is very challenging. That’s why, although QTT has been around for a couple decades, “it is only within the past five years that we can experimentally test it,” said William Oliver of the Massachusetts Institute of Technology. Minev developed innovations to ensure quantum-measurement efficiencies of up to 91%, and “this key technological development is what allowed us to turn the prediction into a verifiable, implementable experiment,” he said.

With these innovations, “it’s possible to know at all times where the system is, given its recent past history, even if some features of the motion are rendered unpredictable in the long term,” Devoret said. What’s more, this near-complete knowledge of how the system changes smoothly over time allows researchers to “rewind the tape” and avoid the apparently irreversible “wave function collapse” of the standard quantum formalism. That’s how the researchers were able to reverse a quantum jump in midflight.

RELATED: Quantum Leaps, Long Assumed to Be Instantaneous, Take Time Mysterious Quantum Rule Reconstructed From Scratch Real-Life Schrödinger’s Cats Probe the Boundary of the Quantum World The excellent agreement between the predictions of QTT and the experimental results suggests something deeper than the mere fact that the theory works for single quantum systems. It means that the highly abstract “quantum trajectory” that the theory refers to (a term coined in the 1990s by physicist Howard Carmichael, a coauthor of the Yale paper) is a meaningful entity — in Minev’s words, it “can be ascribed a degree of reality.” This contrasts with the common view when QTT was first introduced, which held that it was just a mathematical tool with no clear physical significance.

But what exactly is this trajectory? One thing is clear: It’s not like a classical trajectory, meaning a path taken in space. It’s more like the path taken through the abstract space of possible states the system might have, which is called Hilbert space. In traditional quantum theory, that path is described by the wave function of the Schrödinger equation. But crucially, QTT can also address how measurements affect that path, which the Schrödinger equation can’t do. In effect, the theory uses careful and complete observations of the way the system has behaved so far to predict what it will do in the future.

You might loosely compare this to forecasting the trajectory of a single air molecule. The Schrödinger equation plays a role a bit like the classical diffusion equation, which predicts how far on average such a particle travels over time as it undergoes collisions. But QTT predicts where a specific particle will go, basing its forecast on detailed information about the collisions the particle has experienced already. Randomness is still at play: You can’t perfectly predict a trajectory in either case. But QTT will give you the story of an individual particle — and the ability to see where it might be headed next.

The twirling lady is a good demonstrator of cognitive bias.

Mysteries of the universe are a matter of perception and perspective. :)

Like with pi,

because either way you look at it, forward or reverse, it's the same...

the inverse of pi

It's like what Ben He He famously said:

"Ben He He said, 'according to the labor is the reward.'" (Pirkei Avot 5:23)

Hehe, that quote, because it's:

לְפוּם צַעֲרָא אַגְרָא

722, the same as

"shmo Esav" [שמו עשו], meaning "his name is Esav"

Esav *IS* the laborer of the family -- that's the meaning of his name, the do-er. "His name is Esav" is 722, the inverse of pi -- 7/22, whereas pi is 22/7.

According to the labor is the reward:

*The Quantum Theory That Peels Away the Mystery of Measurement*

LUV it. Simple. And fun. People don't want simple. Discover the unknown because it is the joy of discovery. Unlike at Disneyland, there are no crowds.

The magic Kingdom truly is the happiest place on earth.

Gotta laugh..

Altering the cat’s pre conditions and preparatory box activities may improve the cat’s chances of remaining alive.... but it doesn’t alter the basic question....the cat might be a live or it might be dead...
….just as altering conditions that affect sub particle spins might affect the calculus and conclusions of certain experiments and bring about a desired positive result but the desired result still might not happen.

We might have seen that result happen during the 2016 election. They were so sure they had Clinton elected that when she was defeated, I think some seriously thought there was interference from some source. That tells me that there was a lot of planned secret sauce cheating going on somewhere but Trump got unplanned support from voters in places that they had not planned for and it spoiled their strategy. Hence the extreme anger of the Dem’s against the Electoral college and their disparaging of small town folks and the out of the way voting districts that they couldn’t get their cheating hooks into.(The main cheating seems to be repeat counting of ballots such as 51 voters came in that day in one district in Detroit with 50 voting for Hillary and 1 vote for Trump. The ballots were recast 6 times so that Hillary got 300 votes and trump got 6 votes. The ballot lock box read 306 votes but when the Michigan recount began they found that the box only had 51 ballots in it and only 51 persons had come into the voting precinct that day. Talk about prepping the “cat’s box”!)

“just as altering conditions that affect sub particle spins might affect the calculus and conclusions of certain experiments and bring about a desired positive result but the desired result still might not happen.”

It’s not altering, but knowing the actual state and conditions.

The whole point of this article is that the better you know a priori the state of the particle the better you can predict what it’s going to be and even control it. DUH!

Not sure of the reference but if you wish to criticize at least use big words like Aquila’s use of the term “Duh”!

Proverbs 16:33 is an interesting verse to bring up in discussions of Shrodinger’s Cat and Heisenberg’s uncertainty principle!

It explains a lot about the Dem’s total melt down concerning Trump’s win. They had accounted for all variables and had the cheating game going well....but some how he still won. Something had interfered, many of the uppers I believe were sure of it. Where had the rigging gone wrong(?); they were sure they had us “normals” all sewn up! Yes the theoretically the vote should be unplanned but due to their extreme reactions, it tells one they felt they had the game rigged but everything went awry.

I’ll bet they tried all sorts of combo’s over the years. Interesting though....if diffractions off the edges of the slits themselves affect observable phenomena...changing diameters.

Camera apertures for example are fascinating studies. Depth of focus changes towards infinity(all things in the field of focus) or equal focal sharpness as the apertures get smaller(and more light exposure is needed for a proper picture) but unless the shutter blades are designed for it, there is a point that light rays will glint off the edges of the aperture blades causing diffractions and loss of focus. Obviously when the aperture blades close completely no light hits the sensor...but just at that point with good control of aperture design, all objects beyond minimal focus distance are in infinity focus having equal maximum sharpness.

I just wonder in their ‘slit’ experiments they account for the effects of light diffractions off the inner edges of the “slits”. Yes I’m familiar with what the various slits were supposed to do...a light beam gets split in a way that make it behave as a wave or a particle as the first split is sent through a slit and the twin beam is unaltered but is observed behaving in the same fashion as the altered beam. I’m curious if diffraction effects are also accounted for and if affects are seen in the unaltered beam as well. I guess I’ll never know.

Yes indeed but even if you know and control every variable there is still no way to know the outcome for you never know that a force acting outside of your control might alter expected events.

We are stuck in a kind of Tautology principle; that we have to trust that the cat stays alive as we planned for it to be. Linear cause and effect science and reasoning drops off and we are stuck with faith that things will continue as we have always observed them to continue and dead-end our reasoning and experimentation modelling along that path. Or we continue our searching combining both faith and reason, being open to an ever enlarging expanding universe.

Proverbs 16:33 has much to say concerning this article and one can even derive a kind of principle from it. All structured reality and it’s quantum substructures remain unaltered unless acted upon by an intervening agency.(a kind of quantization of the laws of inertia)

Proverbs 16:33 The dice are thrown, but the Lord determines every outcome!

“All structured reality and it’s quantum substructures remain unaltered unless acted upon by an intervening agency.(a kind of quantization of the laws of inertia)”

I’m coming to appreciate the idea of “random variables” from statistics. When I first studied statistics, it took some effort to grasp the concept. I used to think, like most people, that measured quantities were fixed. My height is X and that’s that. But it isn’t that. Every measurement carries with it a margin of error, even in our macro world, thus my height has an uncertainty, a distribution, thus it is a random variable. We’re in luck that in the macro world these distributions have a fairly small standard deviation, so that any measurement is a good enough approximations for making decisions about most things. But like subatomic particles you really don’t know its “value” until you measure it, and next time you measure it, it may be slightly different, but in the macro world the small difference doesn’t matter.

Variables in the micro world appear to have much larger standard deviations, thus their distributions cannot be ignored when doing calculations, and so quantum mechanics must be done with statistical methods.

One other thing that I find interesting about this article is that it says they are now able to “capture” and manipulate particles between quantum states. One of the hallmark of quantum theory (and where it gets its name) is that particles can only exist in discreet states - quantized states. But if you can now capture and manipulate entities anywhere between two quantum states, does this mean that the most hallowed notion of quantum theory is out the window and that we are now back to a continuous nature?

Also, does this mean that the only reason up to now that scientists took on faith the idea of discrete states was simply ignorance about the conditions of whatever they were looking at? Because, according to the article, if they can get sufficient information about a subatomic entity then they can “catch” it between states. So, in essence, quantization is simply an “ignorance” effect.

I was just saying that at a cocktail part last night.

Nice try Larry, that was our bowling team in the bar after the games.

You really screwed up the celebration when you brought up string theory..We warned you about that before.

As a side note, congratulations on winning the mystery jackpot...........

Glad you enjoyed it.

As an aside, it’s always struck me as odd that atheists have a hard time believing in God, yet they all believe in QM. But you need a hell of a lot of faith to believe some of the weird stuff predicted by QM.

I wonder what has a higher probability, you being able to walk through walls or you rising from the dead?

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