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Measurement
- Define measurement.
- What is the simplest example of measurement in nature?
- In what sense do fermions need to be measured so that they occupy different locations in phase-space? And in what sense do bosons get measured?
Measurement
- Measurement is a relationship with reality as when we don't share a relationship with God.
- The fact that direction of spin not fixed until measurement is related to the fact that the axes are all distinct until the measurement and the assembling of the coordinate system.
- Consider how moduli spaces (parameter spaces) relate to my notion of emergent coordinate systems that separate observer and observed, ground the collapse of the wave function and also the creation of space time.
- Gravitational force arises when there is a coordinate system that can mediate what is inside the system and outside the system. There is no gravitational force when there is no coordinate system. There is no gravitational force within a system. There is only gravitational force across a coordinate system. Same with electric charge? Consequently there is no infinite potential, there is no possibility of particles coming to each other to occupy the same place with infinite force between them. These forces are related to the exclusion principles whereby two particles don't occupy the same state.
- Coordinate system relates inertial mass F=ma and gravitational mass. Mass comes from a coordinate system.
- Think of Schroedinger equation as describing the state of nonmeasurement whereby a particle drifts into ever greater uncertainty. Measurement is a sharp reversal of this process.
- Gamtoje yra galimybės. Iš jų atsirenka viena galimybė tiktai esant matavimui. Žmoniškasis mąstymas tai yra toksai atsirinkimas. O dieviškasis mąstymas vyksta atvirkščiai. Kaip atsiranda matavimas gamtoje? Matavimas reikalauja nepriklausomo taško.
- Measurement is the notion of definition but rooted in the perspective of the participant of the system who is trying to reconstruct the definition, redicscover it. Rediscovery is the ways of figuring things out. Definition is established in the equation of life, God's dance. Measurement is the basis of geometry, which is central in math. Measurement is the determination of the relation of one to one's circumstances, one's self.
- When we measure spin - we impose the spin axis we are expecting - but that is an imposition of expectations related to the "waiting" that I am modeling. Also, how is that waiting related to emotional life and expectations? Comparing measurements yields "information" and it may be information which is limited by the speed of time.
- Measurement (crucial in physics) can be defined in terms of covectors, as being dual to vectors. Covectors can be thought to point in the same direction as vectors - they are complements of each other with regard to the inner product. This duality is thus fundamental to the concept of measurement.
- The vector and the covector divide a scalar field into its local variation (given by the vector) and its global scaling (given by the covector) which together give the value of the scalar. Thus vector and covector define the duality of local and global extremes which come together as the scalar field.
- Idea: You can measure something super exactly but then you don't know what you've measured. And that may be why all electrons are the same electron, indistinguishable.
Coordinates
- Entanglement - particle and anti-particle are in the same place and time - and they have the same clock and coordinates
- John Baez about observables (see Nr.15) and the paper A topos for algebraic quantum theory about C* algebras within a topos and outside of it.
- Electrons are particles when we look at them and waves when we don't.
- How many parameters do I need to describe the system? (Like an object.) Minimize constraints. It becomes complicated. Multipole is abstracting the levels of relevance. Ordering them inside the dimensions I am working with. What is the important quantity? Measures quality. How transformation leaves the object invariant. Distinguish between continuous parameters that we measure against and these quantity that we want to study. We use dimensions as a language to relate the inner structure and the outer framework. To measure momentum we need to measure two different quantities.
- Measurement has to do with navigating the continuum.
- When a particle is measured, it is simply entangled with the measuring apparatus. Thus it has a definite value with regard to the apparatus which it maintains. Instead of collapse, consider entanglement with measurement device. The entangled system doesn't involve independently by the Schroedinger equation.
- A particle is forced to use a simplistic language to communicate its state, such as its spin. At that point it answers randomly as per its wave function, which considers all possible paths and how they interfere with each other. Thus the random choice reappears in the other side as a regularity which is apparent through repeating similar experiments.
- Collapse of the wave function occurs when the operator {$-2h\frac{\textrm{d}}{\textrm{dx}}$} becomes the variable {$p$}. This suggests that before the collapse there is a notion of {$\textrm{dx}$}.
- Contrary to Griffith, a particle has a time. It is the time since the most recent collapse of its wave function.
- Time is the subject dimension and arises from the measurer.
- Consider what observables (that arise from computing the integral of the wave function) say about measurement.
- How are adjoint operators related to adjunction? What are their two worlds?
Apparatus in quantum mechanics.
- Apparatus has a blank space.
- Apparatus can tell the difference between the chosen particle and any other particles. Because remeasuring the chosen particle should give the same value.
- Apparatus is able to repeatedly look at the same particle and that is the presumption for a coordinate space. It means that we can return to the same space (as given by the rest frame of the particle) at different points in time. Being able to have rest frames for multiple particles and their groups.
- Turning the apparatus gives results in terms of cos theta. But if the spins are organized in three dimensions will the probabilities be the same as for two dimensions?
- What if Bob sends a message to Alice that is garbled (90% chance of going through correctly). How does that affect Alice's measurement of spin?
- Quantum Zeno effect and anti-Zeno's effect
- The collapse of the wave function resets the internal clock, the time, to zero, and thus makes everything exact, but then it evolves to smear.
- povms Positive-operator valued measurements. A kind of generalization of observables - where the condition of orthogonality for measurement observables is dropped