The Copenhagen Interpretation
Essential randomness of quantum measurement and philosophical problems raised by that.
Central Principles of Quantum Mechanics
Every object or system of objects in the universe is described by a wavefunction, a mathematical function that has some value at every point in space. It doesn’t matter what you’re describing—an electron, a dog treat, a cat in a box—it has a wavefunction, and that wave-function has some value no matter where you look.
Schrodinger Equation governs the behaviour of wave functions.
A quantum object can only be observed in one of a limited number of allowed states.
The wavefunction of an object determines the probability of being found in each of the allowed states. By creating different scenarios for a case, you’ll have a wavefunction and it’ll lead you to that probability.
Measuring the state of an object absolutely determines the state of that object.
Superposition and Polarization
Superposition is having the probability of existing in two different positions (double slit experiment)
Polarization of Light allows us to filter light and absorbe at some point in an experiment setup. It’s like marking the photons so we will know what happen at that step of the experiment, thus the measurement principle is changed. When we measure the polarization using a filter, we will find the photon in one of those two states (either passing through the vertical filter, or being absorbed by it), and not anywhere in between.
Polarized photons thus provide an excellent system for looking at the core principles of quantum mechanics. Each individual photon can be described in terms of a wavefunction, with two parts corresponding to the two allowed states, horizontal and vertical polarization. That wavefunction gives you the probability of the photon passing through a polarizing filter, and after you make a measurement of the polarization with a filter, the photons are in only one of the allowed states. A single photon passing through a polarizing filter demonstrates all the essential features of quantum physics. As a result, polarized photons have been used in many experiments demonstrating quantum phenomena.
Double slit experiment creates an interference pattern which indicates the superposition state. When we block one slit, we know where that photon is going to end up but we don’t know when we have two slits.
Each individual photon is random but when we repeat the experiment, we end up with the interference pattern.
Tries to avoid the problems of superposition and measurement by drawing a strict line between microscopic and macroscopic physics.
Werner Heisenberg insisted quite strongly that it was a mistake to talk about electrons having an independent reality. In his view, the only things we can really talk about are the outcomes of specific measurements. He rejected the whole notion of talking about what the electrons were doing between measurements.
Also seems to be saying that physical reality does not exist until a measurement is made, which poses its own philosophical problems: Scrodinger’s Cat and Wigner’s Friend
Many Worlds Interpretation
- Interference -> coherence -> decoherence
- we have little perception so we couldnt keep up with all of the states of an object and derive wave functions for those superpositions.
- Mach-Zenhder Interferometer
- The reason there is no mathematical method to describe the collapse of the wavefunction, Everett said, is because there is no such thing as the collapse of the wavefunction. Wavefunction is raising exponentially because you cannot separate observer from the measurement.
- Decoherence is the result of random, fluctuating interactions with a larger environment, which destroy the possibility of interference between different branches of the wave-function, and make the world we experience look classical.
- “Coherence” is a slippery word, but when we say that two wavefunctions are “coherent,” we mean that they behave as if they came from a single source.*
Quantum Zeno Effect
- If you have a system that’s moving from one state to another, with the probability of being in the second state increasing over time, you can prevent the state change by repeated measurements. Every time you measure it to be in the first state, you restart the process.”
- Quantom Interrogation: Optically detecting objects without any photons hitting it.
- Sometimes a quantum particle can pass through the barrier and continue it’s way with the same energy in a completely random way.
- The probability of a particle tunneling through a barrier depends on the thickness of the barrier and the quantum wavelength of the particle.
- The probability of tunneling decreases exponentially as the barrier thickness increases—if you double the thickness, the probability is much less than half of the original probability.
- This behaviour is a consequence of wave nature of matter.
- Kinetic and Potential energy also discussed in this chapter.
- Tunnelling is the basis of a device called Scanning Tunnelling Microscope (STM) and it’s used for manufacturing particles.
- The fusion reaction in the core of the Sun (sticking protons together to make Helium from Hydrogen) is also explained by tunneling. Those protons are repelling each other which creates a barrier and they don’t have enough energy to pass through that but TUNNELLING occurs.
- Quantum Tunneling Explained
- We can measure a particle by just measuring it’s quantum entangled particle.
- I have two treats in my hand, one chickend and one beef. If I give you the beef you’d knew that the other dog got the chicken. wtf?
- Einstein says it’s impossible to do that measurement without sharing messages between measured particles but he thinks a little bit classical here because measuring a particle also changes the state of it’s entangled one. Entangled particles act like single object.
- Einstein, Podolsky and Rosen prepared EPR paradox
- Bells Theorem explained all?
- not exactly moving something from somewhere, more like transfering the state from a particle to another one
- no-cloning theorem: it is impossible to make a perfect copy of an unknown quantum state.
- quantum entanglement is used to hack no-cloning theorem.
- we share a pair of entangled photons. I have another photon and make a measurement with my pair of entangled photon and tell you to adjust your entangled photon with respect to the measurement. but I still dont understand the table
- zero point energy: no quantum particle can ever be completely in rest but will always have some energy.
- there are some virtual particles appear and disappear (anti particles) beacuse of that.
- energy time uncertainity: if we make lots of experiments to have better samples about energy but we cant’t say WHEN EXACTLY we measured it and we loose the energy accuracy on the counter case.
- E=mc2 -> mass uncertainity
- Feynman Diagrams and QED
Misuses of Quantum Physics
Some scammers claim they can
- suck the zero point energy from some materials and generate large amount of energy
- do some distant healing with quantum entanglement
- make you feel healty by quantum zeno effect :D
- share your ideas with other people by quantum teleportation lol