CAT 2021 Slot 3 · VARC · RC passage 1: The Price of Accurate Timekeeping

The full passage and all 4 questions (Q5–Q8) from CAT 2021 Slot 3, with answers and solutions.

The passage below is accompanied by a set of questions. Choose the best answer to each question.

Keeping time accurately comes with a price. The maximum accuracy of a clock is directly related to how much disorder, or entropy, it creates every time it ticks. Natalia Ares at the University of Oxford and her colleagues made this discovery using a tiny clock with an accuracy that can be controlled. The clock consists of a 50-nanometre-thick membrane of silicon nitride, vibrated by an electric current. Each time the membrane moved up and down once and then returned to its original position, the researchers counted a tick, and the regularity of the spacing between the ticks represented the accuracy of the clock. The researchers found that as they increased the clock’s accuracy, the heat produced in the system grew, increasing the entropy of its surroundings by jostling nearby particles . . . “If a clock is more accurate, you are paying for it somehow,” says Ares. In this case, you pay for it by pouring more ordered energy into the clock, which is then converted into entropy. “By measuring time, we are increasing the entropy of the universe,” says Ares. The more entropy there is in the universe, the closer it may be to its eventual demise. “Maybe we should stop measuring time,” says Ares. The scale of the additional entropy is so small, though, that there is no need to worry about its effects, she says.

The increase in entropy in timekeeping may be related to the “arrow of time”, says Marcus Huber at the Austrian Academy of Sciences in Vienna, who was part of the research team. It has been suggested that the reason that time only flows forward, not in reverse, is that the total amount of entropy in the universe is constantly increasing, creating disorder that cannot be put in order again.

The relationship that the researchers found is a limit on the accuracy of a clock, so it doesn’t mean that a clock that creates the most possible entropy would be maximally accurate - hence a large, inefficient grandfather clock isn’t more precise than an atomic clock. “It’s a bit like fuel use in a car. Just because I’m using more fuel doesn’t mean that I’m going faster or further,” says Huber.

When the researchers compared their results with theoretical models developed for clocks that rely on quantum effects, they were surprised to find that the relationship between accuracy and entropy seemed to be the same for both. . . . We can’t be sure yet that these results are actually universal, though, because there are many types of clocks for which the relationship between accuracy and entropy haven’t been tested. “It’s still unclear how this principle plays out in real devices such as atomic clocks, which push the ultimate quantum limits of accuracy,” says Mark Mitchison at Trinity College Dublin in Ireland. Understanding this relationship could be helpful for designing clocks in the future, particularly those used in quantum computers and other devices where both accuracy and temperature are crucial, says Ares. This finding could also help us understand more generally how the quantum world and the classical world are similar and different in terms of thermodynamics and the passage of time.

Question 5 · RC Inference Questions

None of the following statements can be inferred from the passage EXCEPT that:

  1. A

    the arrow of time has not yet been tested for atomic clocks.

  2. B

    quantum computers are likely to produce more heat and, hence, more entropy, because of the emphasis on their clocks' accuracy.

  3. C

    grandfather clocks are likely to produce less heat and, hence, less entropy, because they are not as accurate.

  4. D

    a clock with a 50-nanometre-thick membrane of silicon nitride has been made to vibrate, producing electric currents.

Pick an option, then check.
Answer & solution

Answer: Option B

We need the one statement that CAN be inferred.

Option 2 can be inferred. Greater accuracy means more heat and more entropy, and quantum computers are named as devices 'where both accuracy and temperature are crucial'. So clocks in quantum computers, being built for accuracy, will tend to produce more heat and entropy.

Option 1 cannot be inferred: what has not been tested for atomic clocks is the accuracy–entropy relationship, not 'the arrow of time'.

Option 3 cannot be inferred: the passage says the opposite tendency – a large, 'inefficient' grandfather clock may create plenty of entropy without being more accurate.

Option 4 reverses cause and effect: the membrane is 'vibrated by an electric current'; it does not produce currents.

Shortcut: in 'None . . . EXCEPT', rule out options that swap terms (arrow of time / accuracy–entropy) or reverse cause and effect.

Hence, the answer is option 2.

Question 6 · RC Detail and Fact Based Questions

The author makes all of the following arguments in the passage, EXCEPT that:
  1. A
    The relationship between accuracy and entropy may not apply to all clocks.
  2. B
    Researchers found that the heat produced in a system is the price paid for increased accuracy of measurement.
  3. C
    There is no difference in accuracy between an inefficient grandfather clock and an atomic clock.
  4. D
    In designing clocks for quantum computers, both precision and heat have to be taken into account.
Pick an option, then check.
Answer & solution

Answer: Option B

This is the official answer (option 2), though some experts dispute it.

Why option 2 is the official answer: the passage says the price of accuracy is paid 'by pouring more ordered energy into the clock, which is then converted into entropy'. Heat is only how the entropy of the surroundings rises. So the author does not argue that heat itself is 'the price paid' – the price is ordered energy turned into entropy.

Option 1 is argued: 'We can't be sure yet that these results are actually universal'.

Option 4 is argued: future clocks for quantum computers are devices 'where both accuracy and temperature are crucial'.

Option 3 relates to the line that 'a large, inefficient grandfather clock isn't more precise than an atomic clock' – the author's point that more entropy does not make a clock more accurate.

Note for students: many experts (2IIM among them) argue that option 3 fits better, since 'isn't more precise' is not the same as 'no difference in accuracy'. The official key, however, is option 2.

Shortcut: read the exact wording of the passage. 'Paying for it' is tied to 'ordered energy . . . converted into entropy', not to heat.

Hence, the answer is option 2.

Question 7 · Purpose & structure

“It’s a bit like fuel use in a car. Just because I’m using more fuel doesn’t mean that I’m going faster or further . . .” What is the purpose of this example?
  1. A
    If you go faster in a car, you will tend to consume more fuel, but the converse is not necessarily true. In the same way, increased entropy does not necessarily mean greater accuracy of a clock.
  2. B
    The further you go in a car, the more fuel you use. In the same way, the faster you go in a car, the less time you use.
  3. C
    If you measure the speed of a car with a grandfather clock, the result will be different than if you measured it with an atomic clock.
  4. D
    The further and faster you go in a car, the greater the amount of fuel you will use, the greater the amount of heat produced and, hence, the greater the entropy.
Pick an option, then check.
Answer & solution

Answer: Option A

Huber uses the car example right after saying that the relationship is only a limit on accuracy: a clock that creates the most entropy is not therefore the most accurate.

In a car, going faster tends to need more fuel, but burning more fuel does not mean you are going faster or further. In the same way, accuracy costs entropy, but more entropy does not mean more accuracy. That is option 1.

Option 2 compares distance and time, which has nothing to do with entropy or accuracy.

Option 3 is about measuring a car's speed with different clocks – not the point.

Option 4 says more speed means more fuel, heat and entropy – it misses the key idea that the converse does not hold.

Shortcut: 'Just because . . . doesn't mean' signals a one-way relationship. Pick the option that says 'the converse is not true'.

Hence, the answer is option 1.

Question 8 · RC Main Idea and Central Theme

Which one of the following sets of words and phrases serves best as keywords of the passage?
  1. A
    Electric current; Heat; Quantum effects.
  2. B
    Silicon Nitride; Energy; Grandfather Clock.
  3. C
    Measuring Time; Accuracy; Entropy.
  4. D
    Membrane; Arrow of time; Entropy.
Pick an option, then check.
Answer & solution

Answer: Option C

The passage is about measuring time and its cost: the more accurate a clock, the more entropy it creates.

Option 3 – Measuring Time; Accuracy; Entropy – covers the three central ideas.

Option 1 lists details: electric current drives the membrane; heat and quantum effects are secondary.

Option 2 lists details: silicon nitride and the grandfather clock are only illustrations.

Option 4 has 'Entropy' but 'Membrane' is a detail and 'Arrow of time' is a side point; it misses accuracy.

Shortcut: keywords should name the topic and its main relationship, not the experimental details.

Hence, the answer is option 3.

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