Although we classically think of a particle as a fixed object, quantum mechanics describes particles as waves using properties such as position and energy. The quantum mechanical wave describes the probability that the particle's properties take on certain values. Take, for example, rolling a six-sided die. For each roll there is a one-in-six chance that any single number will result. After rolling, however, only one single number will be observed. If the die is rolled enough times, one can deduce that the die has six sides and that landing on each side is equally likely. However, one can never be completely sure, because rolling dice is probabilistic in nature. Quantum mechanics states that the same is true of the position (and other properties) of a particle. A particle trapped in a closed box has some finite probability of being at any location within the box. Open the box once and you'll find the particle at only one location. Open the box enough times and you'll see all the particle locations and the frequency at which they are achieved. From this, one can deduce the original properties of the quantum mechanical wave, just as one could deduce the properties of the die.

The counterintuitive properties of quantum mechanics initially provoked many strong philosophical debates—Einstein himself once quipped that, "God does not play dice with the universe." Over the last 70 years, however, irrefutable evidence has abounded that verifies the truth of the theory of quantum mechanics.

Which of the following best expresses the main idea of the passage?

(A) Particles are not fixed objects but rather exist in the form of waves.
(B) Controversial theories are often found to be correct.
(C) Quantum mechanics correctly postulates the probabilistic nature of particles.
(D) Many questions still exist about the nature of particles and quantum mechanics.
(E) Experiments can be designed to test the quantum mechanical nature of particles.



Based on the information in the passage, which of the following would best explain Einstein's motivation for stating that "God does not play dice with the universe"?

(A) Einstein did not believe that particles should be governed by probability as in a game of dice.
(B) Einstein believed that God should control the fate of the universe.
(C) Einstein was opposed to the theory of quantum mechanics on the grounds that it violated causality.
(D) Einstein's religious beliefs did not allow him to fully understand the theory of quantum mechanics.
(E) Einstein believed that God created the universe such that particles would be modeled probabilistically as in quantum mechanics.



Consider each of the answer choices separately and indicate all that apply.

Which of the following can be properly inferred based on the information in the passage?

A. The location of a particle within a closed box cannot be known for certain without observing the particle.
B. Properties such as position and energy of a particle can never be measured.
C. Particles can be properly described as quantum mechanical waves.