What is a “fictitious force”?

—E. Lopez, Los Angeles

California Institute of Technology theoretical physicist and 2004 Nobel laureate David Politzer replies:

The forces you feel in a moving car—those that push you back into your seat when the driver steps on the gas or throw you sideways when the car makes sharp turns—are everyday examples of fictitious forces. In general, these influences arise because the natural frame of reference for a given situation is itself accelerating.

The term “fictitious force” has a precise meaning within Newtonian mechanics—in fact, it is always proportional to the mass of the object on which it acts.

An elegant example of these types of apparent influences is the Coriolis force, which is responsible for the stately precession (or circular rotation) of a carefully suspended pendulum's plane of swing. If such a pendulum were directly above the North Pole, it would appear to an earthly observer to rotate 360 degrees every day. If you viewed this pendulum from a stationary point in outer space, however, it would appear to swing in a single, fixed plane while the Earth turned under it. From the outer-space perspective, there is no sideways force (that is, perpendicular to the plane of swing) deflecting the pendulum's sway. That is why the somewhat pejorative term “fictitious” is attached to this force. Similarly, in the car, no real force pushes you back into your seat, your senses notwithstanding.

Tea leaves offer a charming demonstration of a consequence of the Coriolis force. If a few leaves are present in a stirred cup of tea, they end up in a central pile at the bottom of the cup (and not along the edge, as one might expect, as a result of the also fictitious centrifugal force). If you imagine yourself rotating around in sync with the stirred fluid, most of the fluid would appear to be at rest while the cup counterrotates around you. That rotating cup drags some adjacent fluid along with it. Near the bottom, the Coriolis force on that dragged fluid pushes it—and the tea leaves—toward the center of the cup.

With general relativity, Albert Einstein managed to blur forever the distinction between real and fictitious forces. General relativity is his theory of gravity—certainly the paradigmatic example of a “real” force. The cornerstone of Einstein's theory, however, is the proposition that gravity is itself a fictitious force (or, rather, that it is indistinguishable from a fictitious force). Now, some 90 years later, we have innumerable and daily confirmations that his theory appears to be correct.

Why do apple slices turn brown after being cut?

—A. Suraya, Guntur, India

Lynne McLandsborough, a professor of food science at the University of Massachusetts Amherst, explains:

When an apple is cut or bruised, oxygen introduced into its injured tissue reacts with compounds there, leading to browning. When oxygen is present in the tissue's cells, polyphenol oxidase (PPO) enzymes in the chloroplasts (sites that harbor chlorophyll and conduct photosynthesis) rapidly oxidize phenolic compounds naturally present in apple tissues to o-quinones. These colorless compounds then self-assemble into polymers or react with amino acids or proteins, forming dark-pigmented secondary products in the fruit tissue.

This enzymatic browning can be prevented by either reducing PPO oxidation or lowering the amount of substrate to which the enzyme can bind. Coating freshly cut apples in sugar or syrup can reduce oxygen diffusion and thus slow the browning reaction. Lemon or pineapple juices, both of which contain antioxidants, also can delay discoloration. (In addition, both fruit juices are acidic, and the lower pH that they bring about reduces PPO activity.) And although it changes the fruit's texture, heating can inactivate PPO enzymes—blanching apples in boiling water for four to five minutes will nearly eliminate PPO activity.

Enzymatic browning is not unique to apples. PPO is present in nearly all plant tissues and also exists in bacteria, animals and fungi. In fact, browning from PPO is not always unwanted: the familiar shades of tea, coffee and cocoa come from PPO enzymatic browning during product processing.

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