Its getting very difficult to explain things without math..I just realized particles lock into a fixed position with bits every global tick and it makes the uncertainty principle solvable. And i decided that quantum probabilities could be distance from a bit in the bit lattice or from an eigenvalue and its frequency. I said that to myself a couple days ago and then asked chatgpt to do that chain rule the way it defined it just now. I saw lighting in the sky a few nights ago. I imagined that its zig zagging is because of the allowed paths through a bit lattice. Like cardinak directions, but with more directions. And the lighting is a bundle proportional to it's field strength..thats off the top of my head as well. Ill leave it as a prediction. Oh yeah..I was trying to model mass in my head and i saw bits can sit in between particles that are entangled to an object. I smiled at the partial derivative of Epsilon with respect to N and "spectral/informational geometry". I think I really need to let go of this now..im not thinking about it. I want to sleep and study more calculus..
Its getting very difficult to explain things without math..I just realized particles lock into a fixed position with bits every global tick and it makes the uncertainty principle solvable. And i decided that quantum probabilities could be distance from a bit in the bit lattice or from an eigenvalue and its frequency. I said that to myself a couple days ago and then asked chatgpt to do that chain rule the way it defined it just now. I saw lighting in the sky a few nights ago. I imagined that its zig zagging is because of the allowed paths through a bit lattice. Like cardinak directions, but with more directions. And the lighting is a bundle proportional to it's field strength..thats off the top of my head as well. Ill leave it as a prediction. Oh yeah..I was trying to model mass in my head and i saw bits can sit in between particles that are entangled to an object. I smiled at the partial derivative of Epsilon with respect to N and "spectral/informational geometry". I think I really need to let go of this now..im not thinking about it. I want to sleep and study more calculus..
Born's reaction In his reminiscences, Born recounted his memories of these exciting days (Born, 1978): ‘Meanwhile Heisenberg pursued some work of his own, keeping its idea and purpose somewhat dark and mysterious. Towards the end of the summer semester, in the first days of July 1925, he came to me with a manuscript and asked me to read it and decide whether it was worth publishing … He added that though he had tried hard, he could not make any progress beyond the simple considerations contained in his paper, and he asked me to try myself, which I promised … His most audacious step consists in the suggestion of introducing the transition amplitudes of the coordinates q and momenta p in the formulae of mechanics … I was most impressed by Heisenberg's considerations, which were a great step forward in the programme which we had pursued … After having sent Heisenberg's paper to Zeitschrift für Physik for publication, I began to ponder about his symbolic multiplication, and was soon so involved in it that I thought the whole day and could hardly sleep at night. For there was something fundamental behind it … And one morning … I suddenly saw the light: Heisenberg's symbolic multiplication was nothing but matrix calculus, well known to me since my student days from the lectures of Rosanes at Breslau.’
The Schrödinger free particle equation in 1+1 dimension describes second-order effects in ensembles of lattice random walks, in addition to its role in quantum mechanics, and its solutions represent the continuous limit of a property of ensembles of Brownian particles. In the present paper, the classical Schrödinger and Dirac equations have been derived from the Brownian motions of a particle, and it has been shown that the classical Schrödinger equation can be transformed into the usual Schrödinger quantum equation on applying the Heisenberg uncertainty principle between position and momentum, while the Dirac quantum equation follows from its classical counterpart on applying the Heisenberg uncertainty principle between energy and time, without applying any analytical continuation.
Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem. I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that “If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be ‘Shut up and calculate!’” In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago. Given my capacity for intellectual development (“inconsistency,” in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue. This amnesia, combined with the evolution in my thinking that had distanced me from my long-forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as “the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics.” I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics.
Based on the hypothesis that the position-representation of a physical state <x|α> is the Fourier transform of its momentum-representation <P|α> and that the time-representation <t|α> is the inverse Fourier transform of its energy-representation <E|α>, we are able to find the Planck relation E = hv, the de Broglie relation P = λh. Afterward, utilizing the Dirac delta function δ(x) and the property FTxf(x) = -iℏ∂, pFTxf(x) = -iℏ∂, pF(p) we obtain the links between operators in ordinary and Hilbert spaces leading to the Dirac fundamental commutation relation [p^,x^] = -iℏI^, the Schrödinger equations, the Heisenberg uncertainty principle in quantum mechanics, the annihilation & creation of a photon from excitation & de-excitation of an atom according to Bohr.
Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.
Particle paths are skewed by a sea of gravitational waves. I snuck in lambda into this because I remembered reading about that theory a long time ago. And I enjoy pilot wave theory as well, I dont like quantum spookiness like Einstein. The physics is more straightforward in my head. The partial derivative of x with respect to y is the tradeoff between predictability of an object's path and size of an object. And I built some aspects of particle motion/interaction around it. I dont want to say more for fun.