Mongolia, Stochastic Quantum Mechanics, and Spacetime Curvature

One of the arguments in the book was that quantum mechanics can describe velocity-dependent distortions in spacetime associated with the motion of a massed particle with respect to its surroundings.

It's a simple enough idea:
For a fundamental particle, QM says that the particle's effective position has a degree of uncertainty to it. It ought to be smeared out over the surrounding region of spacetime as a probability field. Its energy and momentum are smudged. Although any attempts to sample that energy and momentum are going to give quantised results that jump about a lot, if we average the results of a large number of similar possible measurements to produce a smoothed, idealised map of the probability-field for the particle's distribution of massenergy, we end up with a density-field surrounding the particle's notional position that expresses the distribution of massenergy through space that – functionally and definitionally – would appear to have the properties of a gravitational field (because that's effectively what a massenergy field is). The momentum is similarly smudged, giving us a polarised field-distortion component that expresses the particle's state of motion. The shape of the field tells us the probability-weightings for the likelihood of our being able to make certain measurements at given locations.

One interpretation might be that the underlying stochastic processes are truly random, and that the shape and dimensionality of classical physics appears as an emergent feature.
Another might be that the shape represents classical physics principles operating below the quantum threshold, but being drowned out by signal and sampling noise (until we average out the noise to reveal the underlying structure).

Trouble is, if we take these QM averaged-field descriptions seriously, they imply that the correct classical geometrical model for particle interactions isn't flat spacetime – the existence and state of motion of a particle corresponds to a deviation from flat spacetime, and the greater the relative velocity between particles, the more significant the associated gravitomagnetic curvature effects become.

With this approach to quantum mechanics, observer-dependence doesn't have to be some "spooky" effect where the same experiment has physically-diverging results depending on how the observer looks at it, due to reality having an odd, probablistic multiple-personality disorder ... we get different predictions when we change the position and speed of our observers because the presence and properties of those observers physically alters the shape of the experiment, in ways that can cause quantised measurements of the geometry to come out differently. It's a non-Euclidean, nonlinear problem. At those scales there's no such thing as a perfect observer, so to describe how the experiment should play out in isolation, and then to repeat it with different embedded observers charging across the playing-field, is to carry out different experiments.

It's not a difficult argument, but "particle physics" people have a tendency to argue in favour of special relativity by saying that we know for a fact that curvature plays no measurable role in high-energy physics, and mathematicians have a habit of trusting physicists when they say what their experiments show ... so I didn't know of any examples of QM people discussing velocity-dependent curvature when I wrote the book.


Anyhow, earlier this year I stumbled across one. Funny story: I was looking at my Google Analytics statistics, and obsessing about how nobody from Mongolia seemed to have been visiting my website, and then I happened to visit a "citation statistics" site that included a world-map, so naturally I zoomed in to find out what fundamental theoretical research had been coming out of Mongolia. As one does. The search only gave one result, so I clicked on it.

And then I choked into my coffee as this thing came up:
"Space-time structure near particles and its influence on particle behavior"
International Journal of Theoretical Physics [23] 1031-1041 (1984)
Kh. Namsrai, Institute of Physics and Technology, Academy of Sciences, Mongolian People's Republic, Ulan-Bator, Mongolia

Abstract: "An interrelation between the properties of the space-time structure near moving particles and their dynamics is discussed. It is suggested that the space-time metric near particles becomes a curved one ... "

DOI 10.1007/BF02213415

The paper also appears as a chapter towards the end of Namsrai's rather expensive book, Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics (Springer, 1985)

11.8.2:

" ... Physically this relationship means that by knowing the space-time structure near the particle we can calculate its velocity (generalized) and, on the contrary, by the value of the particle velocity one can try to build the space-time structure near the moving particle. Thus, it seems, there exists a profound connection between these two concepts and they enter as a single inseparable entity into our scheme. "

The "stochastic" approach looks at QM from a "shotgun" perspective, superimposes the result of a large number of potential measurements ... and arguably generates a spacetime that's "curved" in the vicinity of a "moving" particle in such a way as to describe the particle's velocity. The curvature generates the velocity, and the velocity generates the curvature. Which was kinda what I'd been saying. But with a lot more advanced math to back it up.

Of course, the irony here is that Namsrai's paper and book describe the emergent classical properties of apparently random processes ... and I only found the piece (which is exactly what I needed to find), by using an apparently random method.

Spooky! ;)

Google Analytics, and World Domination

Every mad scientist should have a big world map on the rear wall or their Secret Lair, with pins or lights on it. It's traditional, and I always had a nagging feeling that I was somehow letting the side down by not doing it.

Google to the rescue! They have a thing called Google Analytics, that generates code that you then embed in all of the web-pages that you want tracked. Google get to sneakily snoop on your site's traffic, and in return, you get to call up breakdowns of traffic sources and search terms and so on for your site(s). And one of the features is the Big World Map, automatically coloured in according to the number of visitors. Bwa ha ha!

Unfortunately, like most online real-time statistics, it gets a bit addictive. Why has nobody from "Serbia and Montenegro" visited my website in the last three months? Everywhere else in mainland Europe has visited, so why not them? It's a little white void in an otherwise green chunk of map. Noth Dakota was another holdout that was bugging me a few months ago, but someone's finally visited, so this quarter's stats have the US totally coloured in (yaay!). Greenland not visiting I can forgive (almost nobody lives there), but what about Iceland? I seem to be missing six Central and South American states this quarter, including Bolivia, Paraguay and Venezuela - the Dominican Republic visited, but not Cuba. Are Cuba's visits logged? African coverage is a bit patchy, but improving around the edges. Iran's dropped off the map this quarter, but Iraq's still hanging on in there.

In the Far East, the last quarter's stats are missing Cambodia, Papua New Guinea, North Korea and Myanmar, and slightly to the West, I have a gap comprising Turkmenistan and the surrounding countries (including Iran). Nobody's visited from Madagascar this year. And Antarctica doesn't appear on the map. Other than that, just about everyone's visited in the last quarter, apart from Mongolia.

Mongolia in particular is beginning to bug me. It's a big white splodge on the map between Russia and China, and it sticks out something rotten. Clearly not enough people in Mongolia feel that my site is worth visiting. I am trying to not feel the wound too deeply ... perhaps I have not paid enough attention to the needs of the Mongolian theoretical physics community. Mongolia, I shall endeavour to do better. Thou shalt be mine!