Question 1

Bell's theorem shows that quantum theory contradicts any "hidden variable theory" that presumes that a quanton has objectively real properties.

Accepted Answer

The answer of Bell's theorem shows that quantum theory contradicts...

Question 2

Alain Aspect's experiments support the quantum prediction that superluminal connections do exist between measuring devices, connections which in fact violate the special theory of relativity.

Accepted Answer

Alain Aspect's experiments support the quantum prediction of entanglement, where particles can be correlated in such a way that the state of one (whether spin, position, momentum, etc.) instantaneously affects the state of another, no matter the distance between them. This phenomenon does not imply superluminal communication or a violation of the special theory of relativity, as it does not allow for information to be transmitted faster than light.

Question 3

We can consider the state $|+x\rangle$ to be a superposition of $|+z\rangle$ and $|-z\rangle$ states.

Accepted Answer

The state $|+x\rangle$ can be expressed as a superposition of the $|+z\rangle$ and $|-z\rangle$ states in quantum mechanics, typically written as $|+x\rangle = \frac{1}{\sqrt{2}}(|+z\rangle + |-z\rangle)$, where $|+z\rangle$ and $|-z\rangle$ are the eigenstates of the Pauli Z operator, representing spin-up and spin-down along the z-axis, respectively.

Question 4

Why (experimentally) is a set of quantons prepared in a superposition of a given observable's eigenvectors different from a classical mixture of quantons that have "already collapsed" to the different eigenvectors (with the same probabilities as predicted by the superposition)?
A) We can (in appropriate circumstances) show that the superposition is an eigenvector of some other observable, but this is not possible for a mixture.
B) We can construct situations where quantons in the superposition state exhibit interference effects that cannot be observed for a mixture.
C) Both A and B.
D) Neither A nor B (explain).

Accepted Answer

Superpositions allow for interference effects and can be eigenvectors of other observables, distinguishing them from classical mixtures.

Question 5

Creating a quanton in a superposition of an observable's eigenvectors and then determining that observable's value is entirely analogous to putting a coin in a can, shaking the can, and then revealing the coin.

Accepted Answer

Creating a quanton in a superposition of an observable's eigenvectors and then determining that observable's value involves quantum phenomena where the outcome is not determined until measurement, unlike the classical analogy of shaking a coin in a can where the outcome (heads or tails) is predetermined and merely revealed by looking.

Question 6

What, according to the chapter, is the essence of the paradox in Schrödinger's cat paradox?
A) Opening the box (and thus observing the cat) might kill it, contrary to our experience of reality.
B) The cat, though it should be described by quantum mechanics, never displays the features of a superposition state, like microscopic systems do.
C) The cat being alive or being dead are not mutually exclusive possibilities, contrary to what we think.
D) Human consciousness is necessary to collapse the cat's state to being alive or dead.
E) Something else (explain).

Accepted Answer

The essence of Schrödinger's cat paradox is that a macroscopic object like a cat should be described by quantum mechanics and thus be in a superposition of states (alive and dead), but we never observe such superpositions in macroscopic systems.

Question 7

The Quantum Zeno effect shows that determining a quanton's state often enough can prevent its evolution as predicted by the Time Evolution Rule.

Accepted Answer

The Quantum Zeno effect is a phenomenon in quantum mechanics where frequent measurements of a system can prevent its evolution, effectively "freezing" its state, which is in line with the statement about preventing its evolution as predicted by the Time Evolution Rule.

Question 8

(For discussion.) Which do you personally think is the weirdest aspect of quantum mechanics and why?
A) It does not support objectively real quanton properties.
B) It requires possibly superluminal connections.
C) It has two incompatible time evolution rules.
D) There seems to be some kind of unexplained disconnect between microscopic and macroscopic physics.

Accepted Answer

The answer of (For discussion.) Which do you personally think...

Question 9

(For discussion.) On the basis of the information presented, which do you think is the most plausible resolution of the Collapse Rule's problems? Why?
A) The decoherence model.
B) Some modification of the Time Evolution Rule that allows genuine collapse to occur.
C) A human mind, which transcends quantum mechanics, is the agent that collapses quantum states.
D) Everett's many-worlds proposal.
E) The QBist idea that state vectors are not real, but rather only reflect the state of what an observer knows.
F) Something else (describe).

Accepted Answer

The answer of (For discussion.) On the basis of the...

Question 10

Suppose that at a certain instant of time, the wave function shown below describes a certain quanton's state.

If we were to perform an experiment to locate the quanton, what would be the most likely result or results?
A) $x_{A}$
B) $x_{B}$ and $x_{C}$
C) $x=0$
D) $x_{D}$

Accepted Answer

The answer of Suppose that at a certain instant of...

Question 11

Suppose that at a certain instant of time, the wave function shown below describes a certain quanton's state. If we were to perform an experiment to locate the quanton, what would be the least likely result or results within the graph's range?

A) $x_{A}$
B) $x_{B}$ and $x_{C}$
C) $x=0$
D) $x_{D}$

Accepted Answer

The answer of Suppose that at a certain instant of...

Question 12

Suppose that at a certain instant of time, the wavefunction shown below describes a certain quanton's state.

The function is zero for $|x|>a$ and sinusoidal with a constant amplitude for $|x|<a$. If we were to perform an experiment to locate the quanton, within which of the ranges above would we be most likely to find it?
A) Range I
B) Range II
C) Range III
D) Ranges I and III have equal probability; I/ smaller
E) All three ranges have equal probability.

Accepted Answer

The answer of Suppose that at a certain instant of...

Question 13

Suppose that at a certain time a quanton has the (unrealistic) wave function shown below.

If we were to perform an experiment to locate the quanton, what is the probability that the result will be $\geq 1 \mathrm{~nm}$ ? (Assume that $\psi(x)=0$ at all points outside the picture.)
A) $1 / 8$
B) $3 / 8$
C) $1 / 12$
D) $1 / 4$
E) $5 / 12$

Accepted Answer

The answer of Suppose that at a certain time a...

Question 14

Suppose that at a certain time a quanton has the (unrealistic) wave function shown below. If we were to perform an experiment to locate the quanton, what is the probability that the result is in the range $-2 \mathrm{~nm} \leq x \leq$ 0 ?

A) $-1 / 4$
B) $-1 / 6$
C) $1 / 4$
D) $1 / 6$
E) $1 / 3$

Accepted Answer

The answer of Suppose that at a certain time a...

Question 15

Consider the function $\psi(x)=A x^{2}+B$, where $A$ and $B$ are constants. Is this function a possible quantum wave function under the right circumstances?
A) Yes.
B) Yes, but only for certain values of $A$ and $B$.
C) Yes, but only if $A$ and $B$ are complex.
D) Yes, if $B$ is zero.
E) No.

Accepted Answer

The answer of Consider the function $\psi(x)=A x^{2}+B$, where $A$...

Question 16

Suppose that at a certain time a quanton has a well-defined wavelength of $0.15 \mathrm{~nm}$. At that time, we perform an experiment to locate the quanton and get the result $x=0.45 \mathrm{~nm}$ to a high degree of precision. What can we say about the wavelength of the quanton's wave function after the experiment?
A) It is still $0.15 \mathrm{~nm}$.
B) It is now $0.30 \mathrm{~nm}$.
C) It is now $0.45 \mathrm{~nm}$.
D) It is now not well-defined.
E) Other (specify).

Accepted Answer

After the experiment, the wavelength of the quanton's wave function is not well-defined due to the Heisenberg uncertainty principle, which states that the more precisely the position of a particle is known, the less precisely its momentum (and thus its wavelength) can be known.

Question 17

Suppose that at a certain time a quanton has a well-defined position $x=0.15 \mathrm{~nm}$. At that time, we perform an experiment to determine the quanton's momentum, and find it has a value that corresponds to a de Broglie wavelength of $0.45 \mathrm{~nm}$ to a high degree of precision. What can we say about the quanton's position after the experiment?
A) It is still $0.15 \mathrm{~nm}$.
B) It is now $0.45 \mathrm{~nm}$.
C) It is now within $\pm 0.45 \mathrm{~nm}$ of $0.15 \mathrm{~nm}$.
D) It is now undefined but probably close to $0.15 \mathrm{~nm}$.
E) It is now completely undefined.
F) Other (specify).

Accepted Answer

The answer of Suppose that at a certain time a...

Question 18

A quanton really has a position at all times, but quantum mechanics does not allow us to predict that position with certainty at future times as we could in Newtonian mechanics.

Accepted Answer

Quantum mechanics fundamentally differs from classical mechanics by stating that particles do not have definite positions or momenta until they are observed. Instead, they are described by a probability wave function, which gives the probability distribution of finding the particle in various locations.

Question 19

A free quanton with a well-defined position can also have a well-defined energy.

Accepted Answer

According to the Heisenberg Uncertainty Principle, a particle (quanton) cannot simultaneously have precisely defined position and momentum (and thus energy, since momentum is related to energy). A well-defined position implies high uncertainty in momentum, leading to high uncertainty in energy.

Question 20

A quanton moving in a system whose $V(x)$ is given by the box potential energy function can never be unbound, no matter what its total energy might be.

Accepted Answer

The box potential energy function is an infinite potential energy barrier outside the box and zero potential energy inside the box. This means that a quantum particle can never escape from the box, no matter how much energy it has.

Quiz 5: Matter Behaves Like Waves Quantum Physics

Bell's theorem shows that quantum theory contradicts any "hidden variable theory" that presumes that a quanton has objectively real properties.

Alain Aspect's experiments support the quantum prediction that superluminal connections do exist between measuring devices, connections which in fact violate the special theory of relativity.

We can consider the state $|+x\rangle$ to be a superposition of $|+z\rangle$ and $|-z\rangle$ states.

Why (experimentally) is a set of quantons prepared in a superposition of a given observable's eigenvectors different from a classical mixture of quantons that have "already collapsed" to the different eigenvectors (with the same probabilities as predicted by the superposition) ?

Creating a quanton in a superposition of an observable's eigenvectors and then determining that observable's value is entirely analogous to putting a coin in a can, shaking the can, and then revealing the coin.

What, according to the chapter, is the essence of the paradox in Schrödinger's cat paradox?

The Quantum Zeno effect shows that determining a quanton's state often enough can prevent its evolution as predicted by the Time Evolution Rule.

(For discussion.) Which do you personally think is the weirdest aspect of quantum mechanics and why?

(For discussion.) On the basis of the information presented, which do you think is the most plausible resolution of the Collapse Rule's problems? Why?

Consider the function $\psi(x) =A x^{2}+B$ , where $A$ and $B$ are constants. Is this function a possible quantum wave function under the right circumstances?

A quanton really has a position at all times, but quantum mechanics does not allow us to predict that position with certainty at future times as we could in Newtonian mechanics.

A free quanton with a well-defined position can also have a well-defined energy.

A quanton moving in a system whose $V(x)$ is given by the box potential energy function can never be unbound, no matter what its total energy might be.

Quiz 5: Matter Behaves Like Waves Quantum Physics

Bell's theorem shows that quantum theory contradicts any "hidden variable theory" that presumes that a quanton has objectively real properties.

Alain Aspect's experiments support the quantum prediction that superluminal connections do exist between measuring devices, connections which in fact violate the special theory of relativity.

We can consider the state ∣+x⟩|+x\rangle∣+x⟩ to be a superposition of ∣+z⟩|+z\rangle∣+z⟩ and ∣−z⟩|-z\rangle∣−z⟩ states.

Why (experimentally) is a set of quantons prepared in a superposition of a given observable's eigenvectors different from a classical mixture of quantons that have "already collapsed" to the different eigenvectors (with the same probabilities as predicted by the superposition) ?

Creating a quanton in a superposition of an observable's eigenvectors and then determining that observable's value is entirely analogous to putting a coin in a can, shaking the can, and then revealing the coin.

What, according to the chapter, is the essence of the paradox in Schrödinger's cat paradox?

The Quantum Zeno effect shows that determining a quanton's state often enough can prevent its evolution as predicted by the Time Evolution Rule.

(For discussion.) Which do you personally think is the weirdest aspect of quantum mechanics and why?

(For discussion.) On the basis of the information presented, which do you think is the most plausible resolution of the Collapse Rule's problems? Why?

Suppose that at a certain instant of time, the wave function shown below describes a certain quanton's state. If we were to perform an experiment to locate the quanton, what would be the most likely result or results?

Suppose that at a certain instant of time, the wave function shown below describes a certain quanton's state. If we were to perform an experiment to locate the quanton, what would be the least likely result or results within the graph's range?

Suppose that at a certain time a quanton has the (unrealistic) wave function shown below. If we were to perform an experiment to locate the quanton, what is the probability that the result is in the range −2 nm≤x≤-2 \mathrm{~nm} \leq x \leq−2 nm≤x≤ 0 ?

Consider the function ψ(x) =Ax2+B\psi(x) =A x^{2}+Bψ(x) =Ax2+B , where AAA and BBB are constants. Is this function a possible quantum wave function under the right circumstances?

A quanton really has a position at all times, but quantum mechanics does not allow us to predict that position with certainty at future times as we could in Newtonian mechanics.

A free quanton with a well-defined position can also have a well-defined energy.

A quanton moving in a system whose V(x)V(x)V(x) is given by the box potential energy function can never be unbound, no matter what its total energy might be.

We can consider the state $|+x\rangle$ to be a superposition of $|+z\rangle$ and $|-z\rangle$ states.

Consider the function $\psi(x) =A x^{2}+B$ , where $A$ and $B$ are constants. Is this function a possible quantum wave function under the right circumstances?

A quanton moving in a system whose $V(x)$ is given by the box potential energy function can never be unbound, no matter what its total energy might be.