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What Is Quantum Trajectory Theory?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

Quantum Trajectory Theory

Any chance we can get to bring enlightenment to quantum mechanics is a cause for celebration. Seriously, just ask any two experts on quantum mechanics and you are likely to get different interpretations of what it means. So why would another one be worthwhile in the sea of possible theories? Because this one doesn’t replace but enhances, and in an area of frequent confusion: what an individual particle is up to.

Trajectories laid out for a SG magnet.

Trajectories laid out for a SG magnet.

Collapsing Ideals

When we say a particle is in a specific location, we are making a claim that the wave function used to describe it has collapsed into a single, determined state based on how we have measured the particle. Von Neumann proposed this to explain how we get a solution from the Schrodinger wave equation, and it seems logical. The issue? Von Neumann offered this without justification for why that has to be the case.

Schrodinger contended that quantum mechanics wasn’t about individual objects but collective wholes and how you only have probabilities of things being located somewhere. Nowhere does he state any definite. Plus, doesn’t how we gather data impact the state something is in (Ball 35, Ball “The”)?

You betcha, because once you measure something then a quantum interaction has taken place. It's much like stopping a rolling object. You could ram it into a wall or slowly apply the brakes, and each outcome gets you to a different condition.

But the trouble with the quantum world is we could end up using any method and measure something entirely different, thanks to the random, probabilistic nature of the wave function. By our action of measuring, we are altering the initial quantum system via back-action and so detailing that is challenging (Ibid).

Enter quantum trajectory theory (QTT), developed by Michel Devoret and Howard Carmichael. It is a way to track a particle across all the possible paths it can take at any given moment a measurement is made. It isn’t invalidating anything that quantum mechanics has established thus far but instead offers a way to see what is happening to the routes our particle can take, and it can do it without the Schrodinger equation.

That certainly got my attention too. QTT instead maps out the interactions a particle makes with its environment via quantum systems, then notes the decoherence of the system followed by the back-action our measurement caused (Ball 36, Ball “The”).

It all sounds so nice, so why isn’t QTT more popular? Well, there is one small but important catch: You can only apply QTT if you know everything about the system. At all times. Obviously, a tall task, but the smaller and smaller the time scale we examine the system at, then the fewer details I have to know initially.

It’s just been a matter of our technology being able to achieve the time scales necessary for testing QTT out. Also, averaging out an experiment many times over reveals the behavior of the back-action, allowing you to adjust how you are measuring to minimize its aftereffects (Ibid).

Artificial atom.

Artificial atom.

Testing This Out

Zlatko Minev and his team along with Devoret and Carmichael developed an experiment to help pinpoint quantum measurements to new degrees of accuracy in an effort to test QTT. It involved superconducting quantum bits to create an artificial atom using an aluminum circuit on sapphire.

This was done so that the energy jumps from one state to another could be controlled via microwaves and at time scales that would allow a careful analysis of the back-action at play. By carefully tweaking the variables of the system, scientists were able to get the atom to jump to a state but the back-action of measuring it would force the atom back to the ground state (Ball 36-7, Ball “The”).

Standard quantum physics says the transition should be a sudden jump, but the experiment makes it look much smoother than originally anticipated. And that happens because of the back-action itself. The sudden collapse of our randomly determined atom was real, but the back-action of the measurement itself caused the transition to be smoother than a purely random transition.

This further implies that we could prevent collapses through our back-actions! We can gather the data and once we know exactly the amount of feedback the back-action provides, we can minimize it and prevent a collapse from ever happening while still measuring the state (Ibid).

Folks, that would be a big deal. The idea of collapsing into a state would forever change and instead be more about exploring unaltered quantum states, as they actually exist independent of us. QTT may allow us to delve into previously unknown quantum states of existence. And that is enough to get all quantum scientists excited (Ibid).

Works Cited

Ball, Phillip. “Reality in the Making.” New Scientist. New Scientist Ltd, 28 Mar. 2020. Print. 35-7

---. “The Quantum Theory That Peels Away the Mystery of Measurement.” Quanta, 03 Jul. 2019. Web. 26 Jan. 2021.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2021 Leonard Kelley