As I quoted before:
Electrons do not orbit.
Electrons do not spin.
We know not where they're going.
We know not where they’ve been.
They really do lead physicists a merry dance!
Bridges to Bybeelon.
“People would generally be better off if they believed in too much rather than too little.“ - PT Barnum
“She blinded me with science.“ - Thomas Dolby
“People would generally be better off if they believed in too much rather than too little.“ - PT Barnum
“She blinded me with science.“ - Thomas Dolby
Every circus needs its clowns.
Even if Barnum didn't actually say, "There's a sucker born every minute", there is no denying the truth in the statement!
And, talking of "superposition", Barnum was an expert in the field!
The Feejee Mermaid was a hoax promoted by P.T. Barnum during the 1840s which had the upper body of a monkey sewn to a fish tail:
You'd need to take in about 50 odd pages less the introduction. Specifically on qm
In quantum field theory, everything (except gravity) is described by all pervasivefields which are made up of a series of harmonic oscillators, which give rise toparticles and interactions, or forces between particles. When the field is in its lowestenergy state, all of the harmonic oscillators are in the ground state, however, it isnot necessarily the case that the ground state energy of a harmonic oscillator shouldbe zero. For example, as an oscillating particle is cooled, its oscillations will decreasein amplitude, but it can never be cooled to a point where it is completely stationary;Hesienberg’s Uncertainty Principle forbids it. This residual energy which remainsand allows the particle to move even in its lowest energy state is the zero pointenergy.The energy of the vacuum, or the zero point energy, may be calculated by con-structing the energy operator, or Hamiltonian of a field and applying it to the lowestenergy state, the ground state.
snip
However, it is not the case that quantum field theory is valid at arbitrarily
high energies, indeed, there is an upper energy limit, beyond which ordinary quan-tum field theory is expected to break down. The actual upper limit where quantumfield theory breaks down is unknown
but we shall label this upper limit as Λ...................................
Earlier it goes through the metrics used to decide that the universe is expanding. Variation in ideas and older reason for thinking it does. Super nova are well covered also effects on Einstein's stuff. 😉 The maths are horrific however there are enough comments that indicate the usual problem with cosmology. Models that is some respects are based on questionable foundations that it will be difficult to prove with any real degree of certainty.
🙂 Bayesian statistical methods - I wont be looking at those chapters.
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Could it be that there is a finite size beyond which things can get no smaller (presume Planck length but it may be not as small in practice). So when you see 1/infinity in an equation, just replace it with 1/(Planck length)? Same the other way around - nothing can be infinitely large and 1/0 has no meaning in the natural world.
Infinitesimally small and infinite in size are not natural - they are human mathematical constructs.
Infinitesimally small and infinite in size are not natural - they are human mathematical constructs.
Thanks!
In a classical oscillator like a pendulum, the lowest potential energy level is zero as illustrated by the black line in the diagram below which is in the form of a potential well.
However the lowest energy state of a quantum oscillator, due to uncertainty, is not zero as shown by the red line.
Note the discrete, or quantised, set of energy levels which are in contrast to the continually changing levels of the classical oscillator.
Apparently, the quantum harmonic oscillator is used to describe many real-world phenomena, such as the vibrations of diatomic molecules.
In a classical oscillator like a pendulum, the lowest potential energy level is zero as illustrated by the black line in the diagram below which is in the form of a potential well.
However the lowest energy state of a quantum oscillator, due to uncertainty, is not zero as shown by the red line.
Note the discrete, or quantised, set of energy levels which are in contrast to the continually changing levels of the classical oscillator.
Apparently, the quantum harmonic oscillator is used to describe many real-world phenomena, such as the vibrations of diatomic molecules.
DeBroglie is one of my favs, and why we have lasers and Intelligent Chips. And why quantum dots are very exciting (no pun intended). I used to have the Q lab supply me with quantum dots, which are teeny tiny, of my spec. The particular Q dots came in a toxic solution, IIRC it was toluene, thus I had use a chem lab gas mask out on the balcony when I made the chips, each one a wafer of high reflectivity metals with enough space for photons to enter and to escape. Like an Oreo cookie. Hence my We do Artificial Atoms Right tagline.
To find the wavelength equivalent to a moving body, de Broglie[5]: 214 set the total energy from special relativity for that body equal to hν:
De Broglie hypothesis
Propagation of de Broglie waves in one dimension – real part of the complexamplitude is blue, imaginary part is green. The probability (shown as the color opacity) of finding the particle at a given point x is spread out like a waveform; there is no definite position of the particle. As the amplitude increases above zero the slopedecreases, so the amplitude diminishes again, and vice versa. The result is an alternating amplitude: a wave. Top: plane wave. Bottom: wave packet.De Broglie, in his 1924 PhD thesis,[11]proposed that just as light has both wave-like and particle-like properties, electronsalso have wave-like properties. His thesis started from the hypothesis, "that to each portion of energy with a proper mass m0 one may associate a periodic phenomenon of the frequency ν0, such that one finds: hν0 = m0c2. The frequency ν0 is to be measured, of course, in the rest frame of the energy packet. This hypothesis is the basis of our theory."[12][11]: 8 [13][14][15][16] (This frequency is also known as Compton frequency.)
To find the wavelength equivalent to a moving body, de Broglie[5]: 214 set the total energy from special relativity for that body equal to hν:
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I'm afraid vishal, like your previous post, I don't fully understand your meaning.
Perhaps a few more words of explanation? I'd really like to correspond effectively.
Perhaps a few more words of explanation? I'd really like to correspond effectively.
I always imagine a harmonic oscillator as a system in which energy is stored by two different mechanisms and then transferred back and forth between the two. A classic LC circuit for example stores energy in the inductors field and and charge in the capacitor. Similarly, a pendulum stores energy in kinetic and potential forms.
So perhaps there is a proper "atom"... an entity that is not possible to split. Is this the smallest item/length/size possible - even if one could imagine two halves of it...
//
Cold weather comes with benefits, clear skies.
Nice little triangle of the Moon, Aldebaran and Betelgeuse tonight. Both noticeably red stars. Bright Jupiter off to the right:
Feynman book proving heavy going, but I have read the notes, the very deep introduction by Kip Thorne, and the wordy Chapter 1 in which Richard discusses what a quantum theory of Gravity might look like.
Covariance, Unitary Matrices, Trace of the Matrix. Spin 2 gravitons.. interestingly he represents the classical radius of the Electron as e^2 / mc^2 with 4Pi Epsilon nought thrown into the denominator.
About 3fm as opposed to the proton radius which is about 1fm. A fm = 10^ -15m. Also an individual graviton would have a radial frequency given by E = h(bar) w like a photon, but would likely be undetectable, being so small.
I am barely hanging in there! Covariance means Lorentz invariant as all such theories ought to be. I watched a clearly ill Feynman at the Challenger inquiry too.
It was actually well-known the Shuttle o-rings were problematic at low temperatures. But the engineers were overruled by management the night before launch in icy conditions.
I have switched to a lighter Lisa Randall book about Dark Matter which is less deep on the maths.
Nice little triangle of the Moon, Aldebaran and Betelgeuse tonight. Both noticeably red stars. Bright Jupiter off to the right:
Feynman book proving heavy going, but I have read the notes, the very deep introduction by Kip Thorne, and the wordy Chapter 1 in which Richard discusses what a quantum theory of Gravity might look like.
Covariance, Unitary Matrices, Trace of the Matrix. Spin 2 gravitons.. interestingly he represents the classical radius of the Electron as e^2 / mc^2 with 4Pi Epsilon nought thrown into the denominator.
About 3fm as opposed to the proton radius which is about 1fm. A fm = 10^ -15m. Also an individual graviton would have a radial frequency given by E = h(bar) w like a photon, but would likely be undetectable, being so small.
I am barely hanging in there! Covariance means Lorentz invariant as all such theories ought to be. I watched a clearly ill Feynman at the Challenger inquiry too.
It was actually well-known the Shuttle o-rings were problematic at low temperatures. But the engineers were overruled by management the night before launch in icy conditions.
I have switched to a lighter Lisa Randall book about Dark Matter which is less deep on the maths.
I remember we once investigated the 'size' of a proton.
The stated radius of a proton is based on its 'charge radius', and is in the region of 0.84 fm (0.84 fermi).
The charge radius is a measurement of the the radius of the proton's oscillating electrostatic field, and this was first achieved through electron scattering.
Not to be confused with the 'mass radius' which is significantly smaller than the charge radius of the proton and which has not so far been determined by experiment.
EDIT: In 2021, as you pointed out, the mass ratio of the proton was extracted from data and determined to be in the region of 0.55 fm.
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Actually the O rings were problematic at higher temperatures. The Shuttle experience low temperature was 53 degrees. The problem was that Morton Thiokol was put in the position by NASA management at the last minute of having to prove the launch would not (rpt not) be successful. The data Morton Thiokol had was not conclusive regarding very low temperatures, in fact some of the worst cases of erosion and blow-by in the seals occurred at higher temperatures. But lots of things would have to go wrong for there to be a catastrophic failure, and they did go wrong. The temperature was predicted to be 29 degrees the morning of launch. They could have waited a day or two when Temps were predicted to be considerably higher. Woulda shoulda coulda.
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