Posted on 01/02/2021 8:54:00 PM PST by BenLurkin
Central to both quantum chemistry and the Schrödinger equation is the wave function – a mathematical object that completely specifies the behavior of the electrons in a molecule. The wave function is a high-dimensional entity, and it is therefore extremely difficult to capture all the nuances that encode how the individual electrons affect each other. Many methods of quantum chemistry in fact give up on expressing the wave function altogether, instead attempting only to determine the energy of a given molecule. This however requires approximations to be made, limiting the prediction quality of such methods.
Other methods represent the wave function with the use of an immense number of simple mathematical building blocks, but such methods are so complex that they are impossible to put into practice for more than a mere handful of atoms. “Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry,” explains Dr. Jan Hermann of Freie Universität Berlin, who designed the key features of the method in the study. “As yet, the most popular such outlier is the extremely cost-effective density functional theory. We believe that deep “Quantum Monte Carlo,” the approach we are proposing, could be equally, if not more successful. It offers unprecedented accuracy at a still acceptable computational cost.”
The deep neural network designed by Professor Noé’s team is a new way of representing the wave functions of electrons. “Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei,”
(Excerpt) Read more at scitechdaily.com ...
Aren’t there some physics folks (maybe very few) who think that viewing decides the outcome?
I don’t know if i even put that right.
I think it’s related to Biocentrism.
Thanks for the reply, btw.
i had the solution all along, but i just wanted to see howl ong it would take someone, or some AI to come up with the answer-
HA! Good one!
...but I imagine I am of the minority...
“If you expose a neural network to enough empirical molecular orbitals, . . . “
But how do you get the data? Measurement is a problem.
As the famous Mathematician, Scientist and Philosopher Rene Descartes pointed out:
And to render this quite clear, I remark, in the first place, the difference that subsists between imagination and pure intellection or conception. For example, when I imagine a triangle I not only conceive (intelligo) that it is a figure comprehended by three lines, but at the same time also I look upon (intueor) these three lines as present by the power and internal application of my mind (acie mentis), and this is what I call imagining. But if I desire to think of a chiliogon, I indeed rightly conceive that it is a figure composed of a thousand sides, as easily as I conceive that a triangle is a figure composed of only three sides; but I cannot imagine the thousand sides of a chiliogon as I do the three sides of a triangle, nor, so to speak, view them as present with the eyes of my mind. And although, in accordance with the habit I have of always imagining something when I think of corporeal things, it may happen that, in conceiving a chiliogon, I confusedly represent some figure to myself, yet it is quite evident that this is not a chiliogon, since it in no wise differs from that which I would represent to myself, if I were to think of a myriogon, or any other figure of many sides; nor would this representation be of any use in discovering and unfolding the properties that constitute the difference between a chiliogon and other polygons. But if the question turns on a pentagon, it is quite true that I can conceive its figure, as well as that of a chiliogon, without the aid of imagination; but I can likewise imagine it by applying the attention of my mind to its five sides, and at the same time to the area which they contain. Thus I observe that a special effort of mind is necessary to the act of imagination, which is not required to conceiving or understanding (ad intelligendum); and this special exertion of mind clearly shows the difference between imagination and pure intellection (imaginatio et intellectio pura).
--From Meditations of First Philsophy, 1641, Rene Descartes, translated by John Veitch in 1901. From the sixth meditation.
In a way, this is inevitable.
“I love reading about quantum physics. I love the “spooky” physics.
I just don’t understand it that well.
2 states at once.”
Yes, I sympathize...
The way I’ve come to understand it, is that the “wave function” is nothing more than what in probability is called a “random variable”. Random variables don’t have single values, rather they have a distribution of values (distribution curve). So that a random variable can take on many different values depending on when or what you sample.
For example, take the random variable “height of people”. There is no single value for that variable - people come in all sort of different heights. It is best described by a distribution curve (similar to a bell curve).
It takes on a distinct value only when you measure the height of a specific person. Similarly the wave function of a particle takes on a specific value - a state - when it is measured.
Another example might be “wind speed” on a gusty day. There is no single value that describes the wind - sometimes it’s calm sometimes it’s strong, so the variable “wind speed” has a range of values. It takes on a specific value when you actually measure it.
So just like Schrödinger’s cat can be either dead or alive, the same wind can be strong or calm.
At least that’s my two cents worth of understanding. I welcome anyone with four cents worth of understanding to correct me if I’m wrong. :)
(BTW the reason sometimes this stuff is hard to grasp is because “the experts” use esoteric terms - like “wave function” instead of the more common and understandable “distribution curve”. Physics is not the only field that obfuscates understanding for the layman, Every specialized field does that. In economics you have “quantitative easing’ which is just an obfuscation of “printing money”. In politics you have “affirmative action” which is an obfuscation of “reverse discrimination” or “racial quota system”. There are many such examples.)
But it is not as smart as people are led to believe. Networks are usually designed to handle a narrow specialized task. Furthermore, they have to be spoon-fed well-digested inputs. That is, humans have to clean up the inputs before feeding them into a network. This cleaning-up process can be very time-consuming chore.
One more additional point...
When they talk about the cat being dead or alive, they are not talking about a specific cat having two simultaneous states - dead and alive. Rather what they’re saying is that in a population (distribution) of cats, a particular cat can be dead or alive (it can also be sick or well, black or white or orange and so on). Until you open your eyes (sample it) and actually see it you don’t know what state (or color) that particular cat is.
Once you’ve seen it (sampled it) that particular cat can no longer be dead or alive or black or white at that instant in time. Later on, on seeing the same cat it may be somewhat different than when you saw it the first time, because it just got run over by a car. Like the human called Bruce Jenner was a good looking man 20 years ago and when you see him today he looks like a delusional ugly woman.
I respectfully beg to differ slightly with your comment, at least with regard to physics. (I agree on the others you list later.) Granted, my physics degree is only a BS, and it's from 1974. Much has changed, and I've forgotten most of what I learned back then anyway because I went into electronics and computers, not physics, as a career. But I do think that it's fair to say that the wave function does indeed have the right name.
I'll let Wikipedia supply the explanation:
The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality. However, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves.So it is a wave, just not the simple "classical mechanics" sort. Are you incorrect to say that it is also a "distribution curve"? No, you are correct at least in part, because it is a probability distribution. But I would add that that attribute does not take away from its "wave" characteristics.
Well, since the act of observation changes the outcome, I would have to suppose the cat is in a perpetual state of limbo between the two. The entirety of Quantum Physics is too bizarre for me to have any sustained interest.
Each time I decide to go back to studying the theories, I throw up my hand in disgust, because the whole of it comes across as insanity. I refuse to believe that the God who created the universe could be so malicious in his design.
I’ll stick with classical physics for what happens in the macro world. The relativistic universe of Albert Einstein is acceptable to me - at least it makes sense, and does not give me a migraine!
So, in half of those states the cat spins his tail clockwise - and in the other half, he spins his tail counterclockwise... BTW, is the cat a male of female? I guess we cannot know the answer until we “observe” ... but then, if we observe, dose that action change the cat’s sex? Perhaps Schrödinger was unaware that his cat has 512 “genders.” This is spooky stuff, indeed.
Bookmark for myself for review during normal waking hours.
Sort of like measuring a sine wave on an oscilloscope - the amplitude is different at each point of the wave, which actually represents an instantaneous point in time.
It cannot be the same wind. The wind at different times is composed of different molecules of air. Therefore, it is not the same wind.
Until you open your eyes and sample it, you don’t even know whether or not it’s a cat.
How can you be 2 places at once when you’re not anywhere at all?
“No man ever steps in the same river twice.” -Heraclitus.
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