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Aufbauwerk 2045
This is an interesting QM video. It would be interesting to get opinions about it from the QM students and experts alike.
There was no mention of EM waves in the video as far as I can remember!woody stanford said:I'm uncomfortable with the application here of a probability amplitude being applied to the relationship between the electrical and magnetic field in a beam of light. I'll be honest with you. I'm not saying it isn't so, I'm just saying I'm uncomfortable with the assumption that it applies here. Just because the probabalistic interpretation applies to much of QM I think doesn't necessarily mean its extensible to areas the discipline of physics is quiet on.
Aufbauwerk 2045 said:This is an interesting QM video. It would be interesting to get opinions about it from the QM students and experts alike.
Are you thinking that the wave function is a representation of the experimenter's knowledge, a relative type of thing?mike1000 said:The description of wave collapse surprised me. It was not what I was expecting based on what I have read. However, to me, it makes perfect sense to zero out the part of the probability distribution where you know the particle is not located, so that only the non-zero part of the wave function remains. Something was learned from the measurement...where the particle was not located and the probability distribution is updated accordingly. But the measurement operator did not zero out the wave function, did it? The zeroing out the has to be something the experimenter does, mathematically, after the measurement, to create the final state, not something the actual measurement did?
Jilang said:Are you thinking that the wave function is a representation of the experimenter's knowledge, a relative type of thing?
Jilang said:Yes, I saw that bit. I believe there is a sense in which it is collapsed which is independent of whether anyone observes the interaction or not.
Jilang said:Have you seen a bubble chamber?
Jilang said:It's a nice example of continuous collapses. The trail of bubbles localises the particle and It happens whether or not anyone is recording it. It would not be just a calculation so to speak, as the bubble chamber exists independently of the experimenters.
Jilang said:Convolution, that is an interesting word, The particle becomes convoluted with the equipment and the equipment is already convoluted with the experimenters since it is macroscopic.
mike1000 said:Convolution between two quantum mechanic states is physically impossible according to this paper. I am sure you already knew this, but I did not.
https://arxiv.org/pdf/quant-ph/0309070.pdf
It is becoming clear to me that entanglement is the quantum mechanical process that takes the place of convolution.
That paper has a lot descriptions that I am now able to understand. In particular, on page 3 it says "a state change of an isolated system must be reversible...which lead to Unitary operations on the state"
That implies, according to something else I read, that wave function collapse maybe implemented by applying a non-unitary operator to the wave function (ie not reversible)
I can definitely see an interaction between the particle and the measuring device, but it is pretty hard to swallow that the effect of that operation is to create a new state in which all the location eigenstates of the particle, where the measurement indicated the particle could not be, would be zeroed out by some natural phenomena.
Weird thing to say. The very fact that there are time and position intervals means that the measurement is not exact and ideal!BvU said:Exact time interval and position interval ?
Why ? The bounds of those intervals are razor sharp and cause an unlikely sharp wave function at collapse.ShayanJ said:Weird thing to say. The very fact that there are time and position intervals means that the measurement is not exact and ideal!
mike1000 said:I have found answers to some of my questions regarding "collapse".
The process of collapse is different for a discrete spectrum operator and a continuous spectrum operator. For a discrete spectrum operator, wave collapse means that all of the non-zero probability amplitudes in the state vector before measurement, collapse to zero after measurement, all except one that is, the coefficient of the eigenstate in which the particle is found. So collapse means all the ##C_{k \ne j}## go to zero while ##C_j## does not, i.e. state vector collapses to a single state.
For a continuous spectrum operator( such as the position operator) the wave function never collapses to a single eigenstate. In these cases the wave function partially collapses to a linear combination of "close" eigenstates that embodies the imprecision (whatever that means) of the measuring device. This explains what they show in the video for the particle moving at 4 meters per second.
https://en.wikipedia.org/wiki/Wave_function_collapse
The more I think about what the video shows, zeroing out the parts of the state vector where the particle was not detected has got to be done, after the fact by the experimenter or included somehow in the measuring process. It represents the new state. It is the state in which the particle was found. The detector determines which parts of the probability distribution must be zero. (ie need to be collapsed). If the particle was detected the probability distribution outside the detector is zeroed. If the particle was not detected, the probability distribution inside the detector is zeroed. That is the new state vector.
Quantum mechanics is a branch of physics that studies the behavior of particles at a subatomic level. It explains the strange and counterintuitive behavior of particles such as photons and electrons, and is essential for understanding the behavior of matter and energy on a microscopic level.
Quantum mechanics is important because it provides a deeper understanding of the fundamental laws that govern the universe. It has led to technological advancements such as transistors, lasers, and MRI machines, and has also played a crucial role in fields such as chemistry, materials science, and cryptography.
Classical mechanics describes the behavior of macroscopic objects, while quantum mechanics applies to particles at a microscopic level. Unlike classical mechanics, quantum mechanics allows for particles to exist in multiple states simultaneously, and the behavior of particles cannot be predicted with 100% certainty.
Visualization plays a crucial role in understanding quantum mechanics because the concepts and phenomena at the subatomic level are often abstract and difficult to visualize. By using visual representations such as diagrams and animations, we can better grasp the complex concepts and theories of quantum mechanics.
While the principles of quantum mechanics may seem esoteric, they have practical applications in everyday life. For example, the principles of quantum tunneling are used in scanning tunneling microscopes, which are used in nanotechnology research. Quantum entanglement has also been proposed for use in secure communication methods.