L.D. Edmonds I did not mean to stir things up. I track global sensor networks (the communities of people working together) and many of the “quantum” and “gravitational” and “quark gluon” and “neutrino” groups get rather esoteric in their language and methods. The methods are not too hard, but sorting out what people mean by the simple words and jargon they make up to talk about things can get messy.
Your “Can Schrodinger’s equation be derived from a set of statistical postulates?” is a bit clearer. I am trying to read your several postings to see what you want to do with it, once you get an answer. You seem to have a fragment of an idea that is nagging at you that it is important, but you just don’t know where to get started.
You mention Bell. He was very practical and his “statistical postulates” were not theory so much as a framework for solving real problems. That is what I trying to indicate when I mentioned words like “calibration”. You don’t pile theory on top of theory (ought not to, but many people spend their whole lives doing that). But find real problems in the world and solve them – usually hoping to create new industries and transformations of society at the same time.
I spent several years at UT Austin in the early 1970’s when Ilya Prigogine was there. I followed most of what his group was doing, and tried to help them with problems like chemical oscillators. A bulk solution that changes colors periodically is a wonderful visual wonder.
But among the ideas that were floating around was the ergodic theorem. I use it in a particular way to know that by reading the tiny bits of evidence about anything – if you are patient and careful enough – you can learn the resonances and states of the thing. From passive noise measurements you can extract complete pictures of things, when active methods are not possible, or too costly.
Schrodinger (also Dirac for particle antiparticle bound states) methods are simply mathematics and computing methods. The insight was to apply that to large numbers of things interacting to address each specifically. It is the addressability of quantum states (Schrodinger states if you use that representation for some of the parameters) that make things like super-resolution, atom interferometry, and many practical nanoscale devices possible. How you model and represent things is not that important – if it works, is reasonably teachable, and does not waste too much valuable human time.
You might want to ask: “Can a portion of any random process, measured by practical sensors, use elementary states as the basis for compact representation of that process?” You might be too young to remember the impact that the atomic model had on society. Just that atoms were things you would identify, characterize, measure, move around, build things with, do things with – that was transformative for society.
I have been representing the vacuum as a turbulent fluid that has flow, compressibility, diffusion, a boiling and melting and freezing point. Those things can be represented mathematically and measured. If the vacuum is compressible, then faster than light travel and communication is possible. When I was a child the story of breaking the sound barrier was a constant thing. That was a year before I was born. Now this generation can do the same thing with light. All those gravitational waves can be represented as waves in a compressible vacuum. It is just a change of representation, not a fundamental change in reality. But it makes tackling certain kinds of problems easier.
If you have things you want to build or do, just ask me and I will offer to help. I work 12-18 hours a day, 7 days a week and have most of my life. If I want to see what is happening with “Schrodinger’s equation” “statistical” I google it to get 90,300 results just now and then I read several hundred of them to get a sense of who is working on what. If it seems important, I review it formally and build a framework so it will be organized anytime I want to use that body of knowledge.
There are lots of papers like A model for the stochastic origins of Schrodinger’s equation by Mark P. Davidson at
You probably have not looked at zwitterbewegung lately. All that noise and turbulence in the vacuum comes from somewhere. it is not magical. Most of the gravitational noise is a mixture of many things. Part of the reason I spend so much of my time on global sensor networks, is that many of the correlations of signals from experiments at the nano level are from gravitational noise sources. The gravitational potential itself is grainy, it has flows and turbulence. It is not idealized but very real. Its properties are measurable. And on the earth, you have to check many different noise sources – use time of flight to separate and characterize them – just to determine the likelihood that a fluctuation is “magnetic” or “gravitational”. For many practical things, gravity and electromagnetism merge at low frequencies and large numbers. I am trying to image the interior of the earth, sun and moon. You have to use every sensor network to do that. It is nice to label things neatly, but often it is just signals and noise, correlations and probabilities. And seldom anything as simple as Schrodinger for an incompressible fluid.
Most of the “kT” noise (you mentioned Bell) is thermal radiation connected inside the device. But part of the measured noise is from magnetic and low frequency electromagnetic sources that can be from anywhere. In the atom interferometer gravitational sensors you have to use clusters and arrays of sensors of different types to sort things out. Look at the huge investment LIGO made to suppress the earth based gravitational noise. They would have been better off to study it and develop methods for using it.
I am saying that real problems that change society have practical applications. You can move theories around, but I see tens of millions of papers on the Internet and most of them don’t change much. Nowadays, if you want to have an impact, start a new industry. I suggest something in “gravitational engineering” or “applied gravitational science”.
I wish I could just give you 60 years of ideas and investigations. There have been groups working to record and interact with the human brain most of my life. Just now the cost and sensitivity are in the range of practicality.
Richard Collins, Director, The Internet Foundation