Bentley's paradox and Isaac Newton

Bentley’s Paradox: How An English Scholar Once Stumped Isaac Newton With a Simple Question?

About 500 years ago, we barely knew anything about the universe. Let alone the vast universe; we didn’t even know there are planets beyond Saturn. We had no description of any of the four fundamental forces in nature, many believed that the Earth was flat (some still do!), and everything revolves around the Earth, comets were seen as bad omens, foretelling the death of the king, the universe was considered static with the stars and the planets hanging as specks in the night sky. But slowly and gradually, things started changing.

Bentley's Paradox: How An English Scholar Once Stumped Isaac Newton With a Simple Question? 2

The first leap came when humans began analyzing nature right there in front of them. “Why did the apple fall on the ground?” “Why doesn’t the Moon fall on the Earth”? These two questions asked by an English physicist changed the course of history. While the first led to the development of the classical theory of gravity, the latter laid the foundations of differential calculus, one of the most important tools to study the dynamics of the Universe.

Newton Comes To Spotlight

Before we jump to Bentley’s paradox, let us see how he came across Isaac Newton. In 1682, Halley’s comet passed over London. People were mesmerized by this heavenly body, and they wondered where it came from. Some people were bothered as they still believed it to be a curse. However, there was one wealthy gentleman, Edmond Halley, who was so intrigued by this celestial visitor that we went straight to Isaac Newton, one of the greatest scientists of the day. Halley asked Newton if he knew anything about the comet.

Halley's comet
Halley’s comet on 8th March, 1986

Newton replied humbly, “I have been tracking this comet for the past few days with my telescope. It is traveling in an elliptical trajectory, which is consistent with my theory of gravity.” When Halley asked how he knew all this, Newton said that he had calculated it.

Halley was pretty impressed by Newton’s work. He offered to pay for the publication of this new theory, and finally, in 1687, Newton published his epic work, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). This work changed the course of history. You can read about it in detail here.

The fact that a few equations could explain the motion of distant planets amazed the scientific community. Along with Kepler’s laws, Newton’s gravitation law was a breakthrough in celestial mechanics. So great was the impact of Principia in the salons and courts of Europe that the poet Alexander Pope wrote:

“Nature and nature’s law lay hid in the night,
God said, Let Newton Be! and all was light

Alexander Pope

Newton was elated to discover that the very laws that governed the motion of the objects on Earth also applied to the universe. With a single stroke, he explained the motion of objects in the universe. While he was basking in the fame brought to him by the publication of Principia, he discovered that his theory gives rise to several paradoxes.

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Bentley’s Paradox

The first blow to Newton’s theory of gravity came from an English scholar, critic, and theologian, Rev. Richard Bentley. In a single letter, Bentley stumped Newton. He asked such a simple question that even Newton had no answer. In 1692, five years after the first publication of Principia, Bentley wrote that if gravity is an attractive force, then any collection of stars would naturally collapse into themselves. If the universe were finite, then all the stars would plow into each other and form a superstar due to gravity. As we watch, the night sky would have been a scene of absolute carnage.

Bentley's paradox
Richard Bentley

But Bentley also pointed out that if the universe was infinite, then the force on any object, tugging left or right, would also be infinite, and therefore the stars should be ripped to shreds in a fiery cataclysm.

Newton’s Escape

Apparently, Newton was stumped. If the universe is finite, then all the stars should collapse into themselves. If it is infinite, then the stars should be ripped apart. Either of the two is a fatal blow to his theory that was still in its cradle. But, Newton found a way out of this paradox.

In his reply to Bentley, Newton wrote that he would prefer an infinite universe but one that was totally uniform. A star that experiences an infinite force from the left also experiences the same amount of force from the right. The forces nullify each other leading to a stable stellar system.

Read all the articles of the Basics of Astrophysics series here

It might seem Newton found an escape route to save his theory, but he was clever enough to admit a flaw in his response to Bentley. If what Newton says is true, then the universe is analogous to a house of cards: a little jitter would collapse the whole system.

Newton’s feeble response was a ‘divine power’ that prevented his house of cards from collapsing. “A continual miracle is needed to prevent the Sun and the fixed stars from rushing together through gravity,” he wrote.

According to Newton, the universe was like a gigantic clock wound at the beginning of time by God, which has been ticking away ever since, according to the laws of motion, without Divine interference. But at times, even God himself had to intervene and tweak the universe a bit to prevent it from collapsing.

Bentley's Paradox: How An English Scholar Once Stumped Isaac Newton With a Simple Question? 3

Hence Newton solved Bentley’s paradox by claiming that God prevented the collapse by making “constant minute corrections.” Newton’s explanation was rather unsatisfactory from a cosmological aspect. But Bentley’s paradox could explain the Big Crunch, the opposite of the Big Bang. The paradox comes into the picture when applying Newton’s laws to cosmology. It becomes superfluous when you stop applying Newton’s gravitational theory to cosmological mass.

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16 thoughts on “Bentley’s Paradox: How An English Scholar Once Stumped Isaac Newton With a Simple Question?”

  1. In these times when people praise content creator like tikotkees, I praise you. I never read something this much as I do on this page. Keep doing the good work ??

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  3. This may be the first ever blog on this subtle point raised by Bentley. A Good Job.
    But Newton’s answer though brilliant may be unduly confusing at the latter half. 300 years after Newton, we would know about Virial Theorem.
    Think of a star cluster comprising thousands of stars. Why doesn’t the cluster instantly collapse into a superstar due to the mutual attraction and potential energy (V) of all the stars?
    What prevents such a dissater is the kinetic enetgy (KE) associated with the random motion of the stars. As per the Virial Theorem,
    V + 2T =0
    On a same note, one may wonder why the planets are not hurtling towards the Sun because of the mutual gravitational potential energy?
    The answer is the angular momentum and rotational kinetic energy of the planets.
    Bentley’s query would not vanish even in general relativity. Thus Einsten had to hypothesize repulsive Cosmological Constant to give stabilty to his finite static universe.
    One may think that this problem gets resolved with the hypothesis of an expanding universe. But only partly.
    Returning to Newton’s answer, for an uniform infinite universe, the net force on any galaxy would be zero. But thete are always local inhomogeneities on various spatial scales, galaxy cluster, supercluster etc. It is such inhomogeneities which cause net gravitational tug on a local scale, and sets galaxies into motions. Again the Virial Theorem may take care , The local excess gravitational attraction is neutralized by random motions of galaxies and their clusters

  4. The heavens are crashing into each other and flying apart at the same time. Momentum, the vastness of low-density space, and the weakness of gravity are all of the obvious answers (accessible to Newton at the time) to these questions and we know, even today, that essentially one of those scenarios will eventually play out in a Big Crunch, or Heat Death, it’s just that gravity is so weak and the universe so large, that it won’t happen for a long, long time.

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