Quantum Mechanics Flashcards
1
Q
What is the Copenhagen view of quantum mechanics?
A
A collection of views by Bohr and Heisenberg about QM including:
- Inseparability of system and apparatus
- Necessity of description of the world in terms of classical concepts for communication purposes
- Quantum of action in all uncertainty relations
- No atomic things in themselves
- No more complete theory than QM
- Renunciation of classical causality
2
Q
What were Einstein’s critiques of QM?
A
It is:
- Incomplete
- Statistical
- Non-local
- Violates determinism/causality
3
Q
What is the Copenhagen interpretation II?
A
The thinking of Neumann, Heisenberg and Pauli including:
- The wavefunction can be applied to the state of the quantum system alone
- There is wave particle duality
- There is collapse of the wavefunction on measurement
4
Q
What does epistemic mean in philosophy?
A
Relating to knowledge or the study of knowledge e.g. Ignorance, certainty, determinism
5
Q
What does ontic mean in philosophy?
A
Relating to or having real existence
6
Q
What are some examples of things that are epistemic in QM?
A
Uncertainty, predictability, chaos
7
Q
What are some examples of things that are ontic in QM?
A
Indeterminacy
8
Q
What is an observable in QM?
A
A physical quantity that can be measured e.g. position, energy, momentum and spin
9
Q
What is superposition in QM?
A
If you have 2 quantum states with respect to some observable of some system, then any state of the sum of the two states each multiplied by a constant also exists.
10
Q
What is wave particle duality?
A
The concept that every particle or quantum entity may be described as either a particle or a wave.
11
Q
What is the uncertainty principle for position and momentum?
A
One cannot assign exact simultaneous values to position and momentum of a physical system. The more certain about one you are, the less certain you are about the other.
12
Q
What are Quantum states represented by?
A
Vectors in Hilbert Spaces
13
Q
What is a Hilbert space?
A
Complex separable vector space complete in the norm induced by the inner product
14
Q
What is an eigenstate?
A
States that are definite with respect to the value of a physical quantity.
15
Q
What do operators do?
A
Mapping from the vector space itself
16
Q
What are Hermitian operators and what do they represent?
A
They have real eigenvalues that represent the outcomes of measurements e.g. spin, position, momentum
17
Q
What is the effect of a measurement represented by in a Hilbert space?
A
Unitary operators
18
Q
What do non-commuting variables represent?
A
Incompatible observables
19
Q
What is the Born rule?
A
The probability of getting an outcome for measurement of an observable on a state is given by the modulus squared of the amplitude of the eigenstate.
20
Q
What is the collapse postulate?
A
After a measurement of an observable that yields an outcome, the system will be in the eigenstate/eigenspace associated with it.
21
Q
What collapses systems into eigenstates?
A
Measurements
22
Q
What is completeness?
A
A necessary condition: Every element in physical reality must have a counterpart in the theory
23
Q
What is the goal of the EPR argument?
A
To show that there exists an element of reality that is not referred to by the theory for this they need a criterion for reality.
24
Q
What is the reality criterion?
A
If without any way disturbing a system we can predict with certainty the result of measuring a physical quantity then there is a corresponding element of physical reality
25
What are the the main elements of the reality criterion?
- It is independent of determinism
- Should be time-indexed
- Likely to be justified but inference to the best explanation
- Not the same as realism
25
What are the the main elements of the reality criterion?
- It is independent of determinism
- Should be time-indexed
- Likely to be justified but inference to the best explanation
- Not the same as realism
26
What is the difference between product states and entangled states?
Product states can be written in some basis so that all terms except one are zero and if this is not the case, the states are entangled
27
What is the basis of the EPR argument?
If P and Q are incompatible then either QM is incomplete or P and Q cannot have simultaneous reality. The thought experiment implies that P, Q can have simultaneous reality thus QM is incomplete
28
What is the original EPR argument?
Makes use of the fact that the formalism allows for a state that is an eigenstate of the total momentum and the difference in position but not an eigenstate of either the position or momentum of either particle.
29
What was Bohr's response to EPR?
Bohr questioned the meaning of 'without any way disturbing the system' insisting that the system and apparatus are inseparable.
30
What does it mean if QM is incomplete?
There are hidden variables describing the states of quantum systems more fully. This would eliminate the need for collapse of the wavefunction
31
What did Von Neumann, Jauch and Piron show in reference to hidden variables?
According to their theorems, hidden variables are impossible. they did this by showing that they could not reproduce successful predictions of QM
32
What is the most famous example of a hidden variable theory of QM?
Bohm Theory
33
What did Bell's theorem prove?
The local deterministic hidden variable theories cannot reproduce the predictions of QM for the EPR-Bohm experiment
34
What are correlations between distinct events taken as evidence of?
Either:
- A direct casual link between the events
- The action of a common cause
35
What is the EPR-Bohm experiment?
It goes something like this:
The is a source and two detectors with no mechanical or electromagnetic or other connections between the two wings of the apparatus. The switches on each side are independently and randomly set to 1, 2 or 3. On each run of the experiment the source us activated and each detector flashed red or green unless it's path is blocked. When the experiment is run many times:
- Half of the total flashes are green and half are red
- In half of the runs, the same light flashes on both sides and in half of the runs, different lights flash on each side
- In those runs where the detectors are both set to the same number, the same lights never flash (perfect anticorrelation)
36
How can the correlations in the EPR-Bohm experiment be explained?
If each particle carries a state that determines the outcome for each setting and if pairs of particles are created with correlated states that ensure perfect anticorrelation when the settings are the same on each side.
37
How many possible states are there in the EPR-Bohm experiment?
8 (RGR, RRG, RGG, RGR, GGG, GGR, GRR, GRG)
38
Which states give perfect anticorrelation?
RRR and GGG
39
What is realism?
The idea that physical quantities have determinate values independent of our perception or knowledge
40
What is determinism?
The idea that something can be thought of as a feature of theories or of the world e.g. the Schrodinger equation
41
What is seperability?
Idea of independent objects or states in space and time
42
What is parameter independence?
It says the outcome on each side conditional on the hidden variable is independent of the setting the apparatus on the other side
43
What is outcome independence?
It says that the outcome on each side conditional on the hidden variable is independent of the result on the other side.
44
What is a measurement in quantum mechanics?
The establishment of a correlation between the observable state of a system (measuring device) and the unobservable state of another system.
45
What are some examples of wavefunctions collapsing?
- Two slit experiment
- Wigner's thought experiment with spin and beam recombination
- Delayed choice experiments
46
What is wavefunction collapse?
The process of a wavefunction that is initially in a superposition of several eigenstates reducing to a single eigenstate due to an interaction with the external world called an observation.
47
What is psycho-physical parallelism?
The idea that collapse must have taken place by the time the perception of the experiment comes into conscious experience. Prior to this it makes no difference to statistical predictions where measurement occurs.
48
What is the projection postulate?
The idea that measurement projects the system to the eigenstate corresponding to the measured value
49
What are the three statements of the trilemma?
- Quantum mechanics is complete (No eigenstate implies unique definite value)
- All time evolution is unitary in accordance with the Schrodinger equation
- Measurements have unique outcomes
50
Why is the trilemma considered as such?
They cannot all be true for a quantum system that is initially in a superposition of what is being measured.
51
What does denying the 1st of the trilemma mean?
Positing of hidden variables and from Bohm theory this must be non-local. But QM could be incomplete in the sense of not applying to macroscopic objects and requiring a classical quantum cut.
52
What does denying the 2nd of the trilemma mean?
Collapse of the wavefunction is a real process caused by an interaction between quantum and classical systems (observation).
53
What does denying the 3rd of the trilemma mean?
Many worlds / Everettian view:
- Asserts the wavefunction is objectively real and there is no collapse of the wavefunction
- Implies that all possible outcomes of quantum measurements exist in some universe
54
What does denying the 3rd of the trilemma mean?
Many worlds / Everettian view:
- Asserts the wavefunction is objectively real and there s no collapse of the wavefunction
- Implies that all possible outcomes of quantum measurements exist in some universe
55
Explain the Schrodinger's cat paradox
- A cat is penned up in a steel chamber with a device containing a Geiger counter with a tiny amount of radioactive substance
- If an atom decays, the counter tube discharges and through a rely, releases a hammer that shatters a flask of acid
- If on average one of the atoms decays per hour and we left this setup for an hour, the cat lives if there is no decay and dies if there is decay
- The wavefunction of the system would express it having the living and dead cat mixed (superposed) together
- It is typical that an indeterminacy at the atomic level transforms into macroscopic indeterminacy which is resolved by direct observation i.e. until there is an observation, the cat is both dead and alive
56
Explain the Schrodinger's cat paradox
- A cat is penned up in a steel chamber with a device containing a Geiger counter with a tiny amount of radioactive substance
- If an atom decays, the counter tube discharges and through a rely, releases a hammer that shatters a flask of acid
- If on average one of the atoms decays per hour and we left this setup for an our, he cat lives if there is no decay and dies if there is decay
- The wavefunction of the system would express it having the living and dead cat mixed (superposed) together
- It is typical that an indeterminacy at the atomic level transforms into macroscopic indeterminacy which is resolved by direct observation i.e. until there is an observation, the cat is both dead and alive
57
Explain the Wigner's friend paradox
Consider another human in the Schrodinger's cat paradox who is observing the first observer making the quantum measurement. Did the wavefunction collapse when the original observer conveyed the information to the other person or did it collapse when the original observer made the observation. the implication is that there is more than one wavefunction collapse which is not possible
58
What is antirealism?
The idea that there is no quantum reality or at least one that we know about. The wavefunction represents how the world might be.
59
What does the Qbist view say about the measurement problem?
The wavefunction represents only our beliefs or knowledge of the system
60
What do hidden variable theories assert?
Quantum mechanics is incomplete and the measurement problem is solved by denying the e-state/e-value link. Reality is determinate and not hidden. The probabilities of QM are epistemic arising from our ignorance about hidden variables of particles.
61
What does the wavefunction represent in Bohmian mechanics?
The wavefunction of more than one particle is not defined over 3D space but over configuration space. Configuration space is 3N dimensional for N particles. The theory has dual ontology consisting of particles with classical trajectories in spacetime and the wavefunction that guides them in a very high dimensional configuration space.
62
What are the 2 forms of Bohm theory?
- First order equation of motion with a scalar wavefunction guiding the velocity of particles
- Second order equation of motion with a new quantum potential alongside the classical potential
63
When is an observable said to be contextual?
It's value depends on how it is measured
64
What is the only non-contextual observable in Bohmian mechanics?
Position. It asserts all measurements are really measurements of position.
65
How does Bohmian mechanics violate the e-value/e-state link?
When QM says that a particle has a definite spin, Bohmian mechanics denies that there is such a property
66
What are some of the problems with Bohmian mechanics?
- Spoils the symmetry of Hilbert Space
- Non-local to the extent of violating parameter independence
- Leaves the particle distribution unexplained
- Violates action-reaction principle since particles are acted n by the wavefunction but not vice versa
- Particles don't really posses their properties
- The particles play no role in the solution of the measurement problem
67
How does dynamical collapse solve the measurement problem in Bohmian mechanics?
By denying that all time evolution is in accordance with the Schrodinger equation. Collapse of the wavefunction is a real physical process that on the microscopic scale will prevent the appearance of macroscopic indefiniteness as entanglement of particles means that when one particle in a measurement system collapses it will drag the rest of the particles with it.
68
What are the two kinds of dynamical collapse?
- Coupling with an external system of some specified kind
- Spontaneous
69
What is GRW?
A spontaneous collapse theory in which each elementary constituent of any physical system is subjected at random times to random and spontaneous localisation processes around appropriate positions. Position is the preferred basis in this theory. It is represented mathematically by wavefunctions being stochastically hit by gaussian functions localised with a finite width around some spatial position. The localisation cannot be completely sharp or particles would acquire an uncertain and potentially infinite amount of energy. It follows the Born Rule.
70
What are the similarities differences between Bohm theory and GRW?
- Both explanations are realist, solve the measurement problem, are in preferred frame, non-local, psi-ontic and have position as the preferred basis. The main difference is that Bohm theory is deterministic and GRW is not.
71
What is the many worlds/Everettian interpretation of quantum mechanics?
A theory that asserts that the wavefunction is objectively real and that there is no wavefunction collapse. It asserts that all possible outcomes of quantum measurements are physically realised in some 'world'. In this theory quantum objects lack definite unique positions
72
What were Everett's two main considerations for formulating many worlds?
- The way measurement is dealt with in the Copenhagen interpretation is unclear, ad hoc and unphysical
- The Copenhagen theory of measurement is not suitable for a quantum theory of the whole universe since the latter lacks an outside observer
73
What did Everett say about the relativity of actuality?
The quantum jumps exist as relative phenomena while the absolute states change quite continually. From the viewpoint of the theory, all elements of a superposition are actual, non any more real than the rest. Rae said that when a quantum measurement is made, the universe branches into as many components as there are possible results of the measurements
74
What is measurement in many worlds?
The establishment of a correlation between the states of the electrons, the apparatus and the observer.
75
What are branches in many-worlds?
A tensor product of an observer state and the corresponding state of the remainder of the system. The observer state is the state of any subsystem so the quantum particle can be regarded as observing the measurement device and the observer.
76
What are the main benefits of the many worlds interpretation?
- It solves the measurement problem with no hidden variables, no weird objective collapse events and is a realist and local theory
- It is unified with thinking in cosmology about the state of the whole universe
- ontological economy since no qualitative distinction between the physically actual.
76
What are the main benefits of the many worlds interpretation?
- It solves the measurement problem with no hidden variables, no weird objective collapse events an is a realist and local theory
- It is unified with thinking in cosmology about the state of the whole universe
- ontological economy since no qualitative distinction between the physically actual.
77
How does Copernicanism relate to many worlds?
Science has shown our position in the world to be unintuitively unspecial. Relativity shows now time is special so the apparent difference between the actual and possibly is indexical too. Why couldn't QM be similar?
78
how is many worlds intuitively implasusible?
It requires a strong form of realism about QM. The main argument against it is that it seems intuitively implausible but many things seems implasuable such as movement of the earth, evolution from apes, etc
79
What is the basis problem in many worlds?
The quantum state of a system can be written in many bases. if branching takes place then with respect to what basis does it do so?
80
What is the probability problem in many worlds?
If everything that happens is deterministic, how can we recover the probabilistic predictions of ordinary QM? i.e. the Born rule
81
How can the basis problem for many worlds be solved?
decoherence models generally select a position basis and therefore solve the problem or the position basis is smuggled into formalism via form of the potential
82
How can the probability problem in many worlds be solved?
Probabilities can be obtained from branch counting however this does not generally produce the probabilities of QM.
83
What were Deusch's key insights into decoherence in many worlds?
- He introduced a continuous infinity of worlds
- He provided a derivation of the Born Rule based upon position theory
84
What is Oxonian Everettian Structuralism?
the idea that structuralism is about higher level ontology with the basis defined approximately by the theory of decoherence. There are no definite distinct worlds over time scales and macro worlds are irreducibly vague because they are defined with respect to properties that are not properties of the wavefunction.
