* Background*:

At the scale of the electron, we know temporal units and scales must be unimaginably small. Consider just a measurement made
to determine the *instantaneous
position of an electron* by means of a hypothetical ("Heisenberg") microscope as shown in the graphic. In such a measurement the
electron must be illuminated, because it is actually the light quanta (photon)
*scattered by the electron* that the observer sees. The
resolving power of the microscope determines the ultimate accuracy with which
the electron can be located. This
resolving power is known to be approximately:

l/ 2 sin q

Where l is the wavelength of the scattered light and q is the half-angle subtended by the objective lens of the microscope. Then the uncertainty Δx in position is :

Δx = l/ 2 sin q

In order to be collected by the lens, the photon must be scattered through any range of angle from -q to q. In effect, the electron’s momentum values range from: h sin q/ l to - h sin q/ l

Then the uncertainty in the electron momentum is given by:

D p_{x } = 2 h sin q/ l

As for timing the electron's motion, that is impossible given it lacks a defined particle nature. Hence, electron locations can’t be computed from Newtonian mechanics but only relatively assessed from probability computations using quantum mechanics.

Thus we are relegated to using probabilistic regions for electron occurrence only. In the diagram below, for example, we see the n=1 electron orbital for the hydrogen atom:

This
diagram more than any other dispenses with the notion that the hydrogen electron
occupies a definite position. Instead, it’s confined someplace within a “cloud”
or probability (b) but that probability can be computed as a function of the
Bohr radius (a_{o} = 0.0529 nm).
The probability P_{1s} for the 1s orbital is itself a result of
squaring the “*wave function*” for the orbital. If the wave function is defined y (1s) = 1/Öp (Z/ a_{o}) exp
(-Zr/ a_{o}), and the probability function is expressed:

P
= ½y (1s) y (1s) *½

Where y (1s) * is the complex conjugate, then the graph shown in the figure is obtained. Inspection shows the probability of finding the electron at the Bohr radius is the greatest, but it can also be found at distances less than or greater than 0.0529 nm. In the case of the hydrogen electron the first three cloud-wave regions are shown below:

These in turn, defined by the quantum numbers n and ℓ lead to electron density computations leading to "probability lobes" for finding an electron in a defined space, e.g.

**In the case shown one must also visualize a symmetrical lobe "mirroring" on the other side (making the whole orbital resemble a dumbbell) to make it complete. As one alters the set of quantum numbers the electron densities change and so do the probabilities associated with the orbit.**

Given these complexities, imagine now the feat of trying to time the electron say from one region of an atom like hydrogen to another. Why indeed would anyone do such a thing as opposed to just settling for orbitals and probability densities of electrons? Well, because it opens a totally new time dimension, ruled by * attoseconds*. The basic unit needed to time an electron's motion - if motion is even the right word to use.

According to its basic physics definition: an attosecond is:

A billionth of a billionth of a second.

To fix ideas, there are around as many
attoseconds *in a single second* as there have been seconds in the 13.8-billion
year history of the universe. Think about that if you can, and let it blow your mind.

Well, on Tuesday we in the physics community celebrated the 2023 Physics Nobel Prize to French-Swedish physicist Anne L'Huillier, French scientist Pierre Agostini and Hungarian-born Ferenc Krausz for their work which explored the behavior of electrons at the time scale of attoseconds. In effect, the three Nobel laureates’ work has enabled the investigation of processes at this time scale, which are so rapid that they were previously impossible to follow, according to the committee. In the words of Eva Olsson, chair of the Nobel committee for physics:

“We can now open the door to the world of electrons"''You can see whether it's on the one side of a molecule or on the other. 'It's still very blurry. The electrons are much more like waves, like water waves, than particles and what we try to measure with our technique is the position of the crest of the waves."

This is, of course, why the de Broglie wave l_{D }= h/ p has generally been applied to electrons (as well as protons) and why the probabilistic (wave-cloud) treatment has endured so long, superseding all attempts to apply Newtonian motion standards. Should that deter these specialists? Not on your life. According to Ferenc Krausz, the Hungarian laureate:

Attosecond
pulses of electrons might also be used in medical diagnostics, he added, including
one day assisting with diagnosing early-stage cancer for improved treatment.

According to Peter Armitage, a professor of physics and astronomy at Johns Hopkins University who wasn’t involved in the research:

“*I see this as kind of the
latest in what is a long and remarkable saga of human beings trying to develop
ways of timing events to shorter and shorter time scales*,”

Adding:

"*This is the
time scale you want to look at to understand how atoms form molecules, how
electrons around atoms behave and the physical processes that are happening in
any chemical reaction*."

The committee chose to award work in this field of research because it opens up entire new areas of study, according to Robert Rosner, president of the American Physical Society and professor of astronomy, astrophysics and physics at the University of Chicago, noting:

“*They’ve
basically created a tool that allows you to look at phenomena and time scales
that we’ve never been able to explore before*.”

Let us in passing just hope the research is applied to more positive and constructive purposes - than to developing new (e.g. high power electron beam) weapons.

**See Also**:

Physicists Who Explored Tiny Glimpses of Time Win Nobel Prize | Quanta Magazine

**And:**

Physicists who built ultrafast ‘attosecond’ lasers win Nobel Prize (nature.com)

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