Relatively and Quantum Mechanics assignment 5&7
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1. General relativity describes large astronomical scales while quantum mechanics describes microscopic scales. When applying the theories at small scales, general relativity's smooth geometric model of space conflicts with quantum mechanics' principle of uncertainty. 2. Quantum tunneling allows particles to temporarily "borrow" energy to pass through classically forbidden areas, but does not violate energy conservation as any additional energy is given back when measured. 3. Pauli's exclusion principle states that two fermions cannot be in the same quantum state. When compressing fermions, their wavelengths shrink and momenta/energy increase, requiring more energy to further reduce separation below their wavelengths. This creates degeneracy pressure resisting compression.
Relatively and Quantum Mechanics assignment 5&7
- 1. 1Wang Yuqi Brandy Wang (1155031779) MR. CHU Ming Chung UGEB 2341 Relativity & Quantum Mechanics 31 October 2013 Assignment 5&6 1. The usual realm of applicability of general relativity is that of large, astronomical distance scales; while that of quantum mechanics is in microscopic or even ultramicroscopic scales. When pushed to the small, the central feature of general relativity - the smooth geometrical model of space (and of spacetime) is in direct conflict with the central feature of quantum mechanics - the uncertainty principle, according to which everything including the gravitational field is subject to the quantum fluctuations, correspond to a severe warping space. 2. This is incorrect. Quantum tunneling indicates that by quantum fluctuating, particles can "borrow" energy within short enough time that allowed by Uncertainty Principle, making it happen to tunnel through classically forbidden regions. But quantum fluctuations occur only when the energy is not being measured, whenever measured, energy is conserved. So it does not violate the energy conservation. 3. According to Pauli’s Exclusion Principle, two fermions cannot occupy a same quantum state. So when we increase the density of a group of fermions
- 2. 2Wang trying to make their average separation smaller than particle wavelength, the fermions’ wavelengths would be squeezed to decrease and their momenta and energy would then increase, requiring extra energy for further density increasing. In this way fermions have a resisting pressure against squeezing them trying to make their average separation smaller than particle wavelength. Such is the degeneracy pressure. 4. The uncertainty is not only due to measurement errors or measurement disturbance, but also the intrinsic uncertainties. The uncertainty principle indicates that particle's momentum and position (also energy and time) cannot be both precisely determined at the same time. The more precisely we measure the momentum, the less precisely we can measure the position, and vice versa. Particle wave function's wavelength is inversely proportional to its p. Therefore particle with single momentum has a single wavelength and infinity wave function,making it impossible to measure its position. To make a localized particle, many momenta (many wave functions with different wavelengths) superposed together, forming a wave packet. The more precisely the position (the wave crest), the more different wavelengths (various p components) superposed, making a larger Δp and a less precise momentum measurement. Assignment 6 1. E Once the signal is emitted, it would travel at c and take exactly 5 years to reach both Planet X and the earth. But the signal the earth received would be blue-shifted and the Planet X red-shifted. And because the spaceship continues moving when the signal and reply signal travels, the replies won't arrive at the same time.
- 3. 3Wang 2. C There are also bending of light, black holes, free falling objects in Newtonian Mechanics, but in which time is absolute. 3. B Only fission requires energy input and leave radioactive nuclei behind. Not all fusion and fission produce net energy output, depending on the types of particle in use. 4. C When laser is used for cooling and trapping atoms, the frequency is somewhere below the peak where laser can be absorbed due to Doppler's Effect. So being slightly lowered, the probability of baser being absorbs is decreased by a rather small part with the absence of Dopper's Effect since the atoms in trap stand still. 5. E The Uncertainty Principle indicates that particle's momentum and position (also energy and time) cannot be both precisely determined at the same time. 6. B E=hv, the same energy with a decreased h leads to a bigger v, therefore there would be more UV radiation from the sun. The smaller the Planck's constant, the more likely particle tunneling, Alpha decays would occur more often. And Pauli's Exclusion Principle has nothing to do with Planck's constant.