25 tonne concrete floor on pneumatic dampers, multistage mass spring isolation system, comprehensive electromagnetic shielding.
Refinements that no respectable home workshop should lack!
At that level of extremely tiny forces, many artefacts can happen of the kind noboby thought about it.
I wonder how they balanced the wheel with those pretty heavy brass weights, for an ultimate no wobbling no vibration.
I presume aerodynamic effects ask for the entire set up in vacuum.
I think all this asks for a far out of space experiment, away from most ambiant influences but solar wind and cosmic rays.
Here are my garage workshop brain stormings.
I wonder how they balanced the wheel with those pretty heavy brass weights, for an ultimate no wobbling no vibration.
I presume aerodynamic effects ask for the entire set up in vacuum.
I think all this asks for a far out of space experiment, away from most ambiant influences but solar wind and cosmic rays.
Here are my garage workshop brain stormings.
That sounds like APPLIED physics.25 tonne concrete floor on pneumatic dampers, multistage mass spring isolation system, comprehensive electromagnetic shielding.
Refinements that no respectable home workshop should lack!
A.K.A. engineering.
I returned all my Physics books to the Library last week. I got fed up with not understanding ANYTHING about Quantum Mechanics and Gravity. My ego was suffering, I wasn't sleeping properly with the worry of it all.
Took an arty break with watching "To Kill a Mockingbird" with Gregory Peck which was amazing, and picked up an Inspector Wallander Crime novel and a book about Betty Bacall, who is one of my favourite actors/actresses.
But some recent light Physics listening on Radio 4 over the last few days, and DO TELL ME if you can get these outside the UK:
https://www.bbc.co.uk/sounds/play/p0hbmml3
The Infinite Monkey Cage. See, if I follow, the Higgs Boson breaks the electroweak symmetry between electrons and the W and Z bosons.
Much talk of Mexican Hats, and how in the early Universe, the Higgs was on the top if the hat, so effectively not doing anything to create mass.
Brian Cox was loving it, since it was about Physics.
Dear old arty Melvin Bragg is always game for a bit of Physics too:
https://www.bbc.co.uk/sounds/play/m001wq9h
Heisenberg's Uncertainty Principle. I must admit I dozed off at what might have been a crucial bit, but it seems that Heisenberg worked out a better bit of Maths than Neils Bohr had for the Hydrogen atom.
And then his supervisor pointed out that he was doing Matrix Mechanics where AxB is not the same as BxA.
The Physics community had never encountered Matrices before, so his ideas went up like a lead balloon initially'
Schrodinger then came up with Wave Mechanics, which everybody liked. But it then became clear they got the same answers.
The learned Professor on the Bragg show said he much prefers Heisenberg's interpretation, since it avoids all that Schrodinger's Cat nonsense!
What does this mean? I think I must battle away with Matrices next. See Heisenberg says electrons and other things Quantum only exist as a Mathematical construction.
I wonder if this applies to us too?
Took an arty break with watching "To Kill a Mockingbird" with Gregory Peck which was amazing, and picked up an Inspector Wallander Crime novel and a book about Betty Bacall, who is one of my favourite actors/actresses.
But some recent light Physics listening on Radio 4 over the last few days, and DO TELL ME if you can get these outside the UK:
https://www.bbc.co.uk/sounds/play/p0hbmml3
The Infinite Monkey Cage. See, if I follow, the Higgs Boson breaks the electroweak symmetry between electrons and the W and Z bosons.
Much talk of Mexican Hats, and how in the early Universe, the Higgs was on the top if the hat, so effectively not doing anything to create mass.
Brian Cox was loving it, since it was about Physics.
Dear old arty Melvin Bragg is always game for a bit of Physics too:
https://www.bbc.co.uk/sounds/play/m001wq9h
Heisenberg's Uncertainty Principle. I must admit I dozed off at what might have been a crucial bit, but it seems that Heisenberg worked out a better bit of Maths than Neils Bohr had for the Hydrogen atom.
And then his supervisor pointed out that he was doing Matrix Mechanics where AxB is not the same as BxA.
The Physics community had never encountered Matrices before, so his ideas went up like a lead balloon initially'
Schrodinger then came up with Wave Mechanics, which everybody liked. But it then became clear they got the same answers.
The learned Professor on the Bragg show said he much prefers Heisenberg's interpretation, since it avoids all that Schrodinger's Cat nonsense!
What does this mean? I think I must battle away with Matrices next. See Heisenberg says electrons and other things Quantum only exist as a Mathematical construction.
I wonder if this applies to us too?
I'm reminded of John Horgan's writings, he's a science writer I've been following for some time, his "Quantum Experiment" was his attempt to learn it the way physicist learn it. He links to it here:
https://johnhorgan.org/cross-check/ten-tough-terrific-quantum-books
I'm streaming the monkey thing now from the USA.
https://johnhorgan.org/cross-check/ten-tough-terrific-quantum-books
I'm streaming the monkey thing now from the USA.
Matrices! I can't begin to tell you how excited I was when I studied them at basement level back in the day!
Apparently, the matrix mechanics representation of quantum mechanics interprets the physical properties of particles as "matrices that evolve in time"!
As you say, Stephen, Heisenberg's matrix mechanics and Schrödinger's wave mechanics were shown to be equivalent.
Attached is a brief description of Heisenberg's matrix mechanics for those who are motivated to learn a little bit more.
Attachments
Thanks for the link. My QM book was stolen with all the other college texts 9/20. No great loss, I bombed out of phys 410 at the problem where one was supposed to solve schrodinger's equation by expansion using euler equations. I met with the professor, he lost me at "it is obvious that". I inspected in the library a book on euler equations, it was a list of equations and their numerical values for various values of x. ????
I found out twelve years later from another D- student (at a seminar for electronics techs), the 11 guys making A's were meeting in a residence hall after dinner where one of the students was teaching the other ten how to solve the problems. Upset me. I was paying Rice University hard earned cash to teach me between 7 AM and 5 PM when I was on campus. Residence halls were IMHO for rich kids spending their parent's money. Full of tobacco & pot. I would not have been able to breathe if I did have rich parents.
Maybe matrices, which I was once pretty good at, will be easier to manipulate.
That story reminds me of many that I have (speaking of the gravity of higher education), I'll just share two.
Having lived almost all my life in and around Atlanta, I've known of Georgia Tech all my life. My father attended for a couple years, then apparently got a letter from his Senator that got him into USNA where he graduated. I wanted to go, but for various reasons didn't get to. But more recently, about ten years ago I was at the local makerspace where I saw a Tech student wearing a tshirt with the back saying "I go to Georgia Tech where I skip class to study for my other classes." I think I have a digital photo of that somewhere.
Another college, the biggest in the state is University of Georgia in Athens, and if anything, it has an opposite reputation. I've actually heard of it in national rankings as the nation's biggest party school. One statement I heard comparing them is "at UGA the teachers teach but the students don't learn, but at Tech the teachers don't teach, but the students learn."
Having lived almost all my life in and around Atlanta, I've known of Georgia Tech all my life. My father attended for a couple years, then apparently got a letter from his Senator that got him into USNA where he graduated. I wanted to go, but for various reasons didn't get to. But more recently, about ten years ago I was at the local makerspace where I saw a Tech student wearing a tshirt with the back saying "I go to Georgia Tech where I skip class to study for my other classes." I think I have a digital photo of that somewhere.
Another college, the biggest in the state is University of Georgia in Athens, and if anything, it has an opposite reputation. I've actually heard of it in national rankings as the nation's biggest party school. One statement I heard comparing them is "at UGA the teachers teach but the students don't learn, but at Tech the teachers don't teach, but the students learn."
I'm finding Heisenberg's matrix mechanics tough going! https://everything.explained.today/Heisenberg's_entryway_to_matrix_mechanics/
When we say that AB ≠ BA we are not referring to a single value of A and a single value of B, but to a matrix of values of A and a matrix of values of B.
So, when multiplying A times B or B times A we are talking about the matrix multiplication of the two matrices, the result of which is a third matrix.
In particle terms, matrix A could represent position and matrix B momentum.
It would appear that, having passed the relevant maths exam, I must once have understood the rules of matrix multiplication: https://www.khanacademy.org/math/pr...g-matrices-by-matrices/a/multiplying-matrices
I completely understand.
In 'A Brief History of Time' Stephen Hawking relates how he was told that for every equation he put in the book he would lose half his (remaining) audience.
He stopped at E=mc^2.
(Apologies for the caret rather than a superscript 'power of 2': I am a programmer, not an editor / publisher.)
I have to admit that when speaker design discussions progress to algebra I move to the next Google entry.
Back in the 'good old days' in the UK...
In school the teachers taught you things.
In university the lecturers taught you how to learn things.
These days there are only teachers in both institutions, according to one of my old lecturers, anyway...
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Try using a VPN server based in the UK - that might work.
The Infinite Monkey Cage is always a good listen!
BTW, I have just noticed a something about the BBC Sounds webpage media player - the volume control goes up to 11! Who says the BBC has no sense of humour?
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https://www.amazon.co.uk/Schaums-Outline-Matrix-Operations-Outlines/dp/0071756043
Excellemt series on all sorts of things.
Same here!
I thought at least I could try to understand the basic nomenclature of quantum mechanics, so I put my google hat on!
Quantum theory deals with 'system' (wavefunction), 'measurement' (operator) and 'measurable quantity' (eigenvalue).
Since all measurements in physics yield real numbers, the eigenvalues must be real, requiring that any measurable quantity is associated with a Hermitian operator.
I'm now stumped by maths again, but all kudos to Charles Hermite for his 'Hermitian matrix': https://www.cuemath.com/algebra/hermitian-matrix/
Boy, doesn't Charles look fed up?
And, having got this far, so am I!
I just asked my resident AI bot to tell me how big the universe would be if I packed it into a single cube with the density of water. The answer I got back was 145 billion light years. I complained and said that’s bigger than the diameter of the observable universe, please regenerate the answer. On the second try, it got 45.7 billion light years. So I did it by hand and the answer I got was a cube of sides 317 light years. I asked the AI chatbot what it thought. ‘That seems correct. What an interesting way to try to understand how much matter there is in the universe’.
Caveat Emptor
Caveat Emptor
First and foremost, an inquiring Physicist must remind themselves of the 24 letter Greek alphabet:
Otherwise this highly commended, albeit lecturer coughing and spluttering with some random virus, video makes no sense:
Seems Heisenberg (Matrix Mechanics) and Schrodinger (Wave Mechanics) hated each other.
I think that is because Schrodinger was bitter that he never attended the top Gottingen University.
Heisenberg simply recognised the mediocrity of Schrodinger's redbrick approach. A feeling I too get when I encounter people who don't adopt the Standard Model of Physics.
I am fairly convinced by Heisenberg. 4D Diagonal Matrices are familiar to Special Relativicisists. Hermitian Matrices give Real solutions.
I am fascinated that uncertainty is a conserved quantity.
To this day, people prefer visualisable Waves to abstract Matrices. But, IMO, Matrices it is. Get over it.
The Three Workers doubtless got it right:
I know this because I know a bit about harmonics:
Of course, we ask ourselves if it relativistically invariant.
Actually, I am frequently struck by mine own younger resemblance to Pascual Jordan. I wonder if we are related?
Further Study on the history of the Hydrogen atom here:
https://arxiv.org/pdf/1501.05894.pdf
An excellent read IMO.
Best Regards from Steve in Portsmouth, UK.
Otherwise this highly commended, albeit lecturer coughing and spluttering with some random virus, video makes no sense:
Seems Heisenberg (Matrix Mechanics) and Schrodinger (Wave Mechanics) hated each other.
I think that is because Schrodinger was bitter that he never attended the top Gottingen University.
Heisenberg simply recognised the mediocrity of Schrodinger's redbrick approach. A feeling I too get when I encounter people who don't adopt the Standard Model of Physics.
I am fairly convinced by Heisenberg. 4D Diagonal Matrices are familiar to Special Relativicisists. Hermitian Matrices give Real solutions.
I am fascinated that uncertainty is a conserved quantity.
To this day, people prefer visualisable Waves to abstract Matrices. But, IMO, Matrices it is. Get over it.
The Three Workers doubtless got it right:
I know this because I know a bit about harmonics:
Of course, we ask ourselves if it relativistically invariant.
Actually, I am frequently struck by mine own younger resemblance to Pascual Jordan. I wonder if we are related?
Further Study on the history of the Hydrogen atom here:
https://arxiv.org/pdf/1501.05894.pdf
An excellent read IMO.
Best Regards from Steve in Portsmouth, UK.
Must be the glasses!
P.S. As included in Stephen's post, Jordan, Born and Heisenberg produced the 1925 paper Zur Quantenmechanik II that completed the formal development of matrix mechanics.
