- 2810 - UNCERTAINTY - principle in physics? - Quantum Mechanics describes the behavior of matter on the ‘microscopic scale“. Albert Einstein’s physics worked on the extreme velocity cases and it also was the same as Newton’s math on ordinary cases. Quantum Mechanics math had to be invented to work on the atomic scales.
--------------- 2810 - UNCERTAINTY - principle in physics
- Quantum Mechanics describes the behavior of matter on the ‘microscopic scale“. Isaac Newton’s physics worked great in our everyday lives. But, the math did not work at very high velocities or at very high fields of gravity. It does not work on very small scales either.
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- Albert Einstein’s physics did work on the extreme velocity cases and it also was the same as Newton’s math on ordinary cases. Quantum Mechanics math had to be invented to work on the atomic scales.
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- Much of this Quantum Mechanic’s math relied on two principles, the “Uncertainty Principle” and the “Exclusion Principle“. This review covers Uncertainty, the review 2703 covers the Exclusion Principle. Both of these introduced math that we had not seen before.
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- In 1924 Louis de Broglie defined all mass as having wavelengths as well. Read that again: mass has wavelengths! Everything has a “particle-wave duality” but it only becomes noticeable at the microscopic level, at the Quantum Mechanic’s level.
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- Broglie said that the product wavelength * momentum is always a constant = to Planck’s Constant of Action = 6.626*10^-34 joule*seconds. Momentum, ”p” = mass * velocity, “m” * “v”:
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----------------------------- wavelength * momentum = Planck’s Constant
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----------------------------- w*p = 6.6*10^-34
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----------------------------- w * m * v = 6.6*10^-34
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- If the product, (w*m*v) is a constant that means that if mass increases, wavelength decreases. If mass decreases, wavelength must increase. All matter has waves, but, only very small stuff has waves big enough to notice.
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- Let’s take a particle of dust that is very small and has a mass of 10^-9 kilograms. It is not moving very fast, say 10 meters / second. The calculation for its wavelength is
6.6^-26 meters. This wavelength is so small as not to be noticeable.
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------------------- wavelength = 6.6*10^-34 / mass * velocity
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------------------- w = 6.6*10^-34 / 10^-9 * 10
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-------------------- w = 6.6 * 10^-26 meters
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- However, let’s take something much smaller than a dust particle, say an electron. It has a mass of 9.1*10^-31 kilograms. If we get down to the atomic scale these small waves become noticeable.
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- The electron’s velocity is usually 10^6 meters / second. Its wavelength is therefore 0.7 nanometers. The diameter of an atom is 0.1 nanometers. Now the wavelength is extremely noticeable. It is 7 times bigger than the atom
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-------------------- w = 6.6*10^-34 / mass * velocity
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------------------- w = 6.6*10^-34 / 9.1*10^-31 * 10^6
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-------------------- w = 0.7 *10^-9 meters
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- Neutrons in a gas cloud having a temperature of 35 Kelvin will have an average velocity of 1500 meters / second. The mass of a neutron is 1.6*10^-27 kilograms. Its wavelength is 0.28 nanometers. As a result of these neutrons having a wavelength it can be shown that they have an interference pattern just like other waves , or like photons of light.
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- Passing a stream of neutrons with 2 nanometers wavelength through a double-slit that is 20,000 nanometers wide separated by 104,000 nanometers creates an interference pattern of circular bands on the screen similar to a light beam. Similar to a water wave.
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- The electron has a mass of 10^-30 kilograms. Its orbital speed inside an atom is 10^6 meters per second. Its momentum is therefore 10^-25 kilogram*meters/second. The diameter of the atom is 10^-10 meters.
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- Can we pin down the location of an electron to within 10% of the atom’s size, therefore to within 10^-11 meters? The Uncertainty Principle says there is a trade-off between knowing the electrons “position” and its “velocity“.
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- “ Any attempt to localize a particle to within a distance of some Uncertainty of Location necessarily limit’s a simultaneous determination of that component of the particle’s momentum to an Uncertainty of Momentum. The product of these two uncertainties must always be greater than Planck’s Constant of Action.
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---- Uncertainly of Location * Uncertainty of Momentum > Planck’s constant / 2*Pi
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---- Uncertainly of Location * Uncertainty of Mass * Velocity > Planck’s constant / 2*Pi
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---- Uncertainly of Location * Uncertainty of Mass * Velocity > 1.05*10^-34 joule*seconds.
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---------------------- dx * m*dv > 1.05*10^-34
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- This same Uncertainty Principle goes on to relate Time and Energy. If an energy measurement is to be carried out in time, Uncertainty in Time, and the accuracy, in Uncertainty in Energy, in which the energy can be measured in this time interval is limited to :
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---- Uncertainly in Energy * Uncertainty in Time = > 1.05*10^-34 joule*seconds.
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------------------------ dE * dt > 1.05*10^-34
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- This uncertainty quantity of 10^-34 is very, very small. We need not concern ourselves with it when dealing with macroscopic things like rockets, baseballs or even dust particles. However, when we get to the size of electrons this Constant of Action is huge.
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- If we try to pin down the location of an electron to within 10% of the size of atom. The momentum is so huge relative to the atom that we can not be certain that the electron can remain inside the atom. To deal with this situation we must begin using calculations with “probabilities” from Quantum Mechanics.
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- Quantum Mechanics is different from any of Newton’s theories. It does not make any predictions about the outcome of a single event. It makes predictions only about the probabilities of different outcomes. Quantum Mechanic’s math can not be used to predict the future behavior of a system, only the probability of a set of possible behaviors.
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----------------------------- See other Reviews:
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- 2703 - The Exclusion Principle
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- 1028 - How Quantum Mechanics applies to Astronomy. Stars and Blackholes.
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- 1032 - The atom’s stability with the Uncertainty Principle. Atom’s ground energy state calculations using the Conservation of Energy.
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- August 31, 2020 1026 2810
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