The strength of the force of Gravity as an example of cosmic fine tuning

The important point is how the strength of gravity compares with the strength of the electrostatic force. This is the force that operates between things that have electric charges. It holds electrons in their orbits in atoms, and it is responsible for the chemical bonds between atoms.

The electrostatic force is a billion billion billion billion times stronger than the force of gravity (10³⁶ times stronger). It you are a chemist and you are interested in how atoms react with each other, you do not need to worry about gravity. It is too weak to make any difference.

So why does gravity seem so strong to us, here on the surface of the Earth?

Electric charges can be positive or negative. Charges that have the same sign repel each other, while charges of opposite sign attract. The stuff around us contains almost exactly equal numbers of positive and negative charges, so when you look at things on the large scale, the electrostatic forces cancel each other out.

But gravity is always attractive. And there are a lot of atoms making up the Earth. The gravitational pull of a single atom is too small to notice, but together, they mount up. That is why gravity seems strong to us, even though it is so much weaker than the electrostatic force.

The strength of the force of gravity appears to be fine tuned to make life like ours possible. What would happen if it were different?

Weaker gravity

We can imagine a universe in which the force of gravity was repulsive rather than attractive. Things would fly apart, rather than falling towards each other. In such a universe you would not get galaxies or stars or planets. In fact, it’s very difficult to imagine any kind of complicated structure (such as a plant or an animal) in a universe without some kind of force pulling things together on a large scale.

We could also imagine a universe in which gravity was zero – there was no force of gravity either attractive or repulsive. This would also seem to rule out complicated structures.

So it looks as if zero is a lower limit on the strength of gravity.

Stronger gravity?

What about an upper limit? What would happen if gravity were stronger?  A stronger force of gravity would affect the size of things, in several important ways. Martin Rees discusses this in his book ‘Just Six numbers’:

The size of animals

The force of gravity doesn’t affect the way individual atoms and molecules behave – this is controlled by the electrostatic forces between them.  This means that the strength of materials would be the same, whether steel girders, concrete, bones, or tree trunks.  But in a strong gravity world, the weight they would have to support would be much more. As animals or plants get larger, there would come a tipping point, where they would no longer be able to support their own weight. And as the force of gravity gets stronger, this tipping point comes sooner – with smaller animals:

‘In an imaginary strong-gravity world, even insects would need thick legs to support them, and no animals could grow much larger. Gravity would crush anything as large as ourselves.’ (Rees 1999:34)

So:

‘If, for instance, we increased the strength of gravity on earth a billionfold the force of gravity would be so great that any land-based organism anywhere near the size of human beings would be crushed.’ (Collins, Evidence, p. 15)

The size of stars and galaxies

On an astronomical scale, galaxies, stars and planets would all be much smaller:

‘What would happen if it [gravity] weren’t quite so weak? Imagine for instance, a universe where gravity was ‘only’ 10³⁰, rather than 10³⁶ feebler than electric forces. Atoms and molecules would behave just as in our actual universe, but objects would not need to be so large before gravity became competitive with the other forces. The number of atoms needed to make a star (a gravitationally bound fusion reactor) would be a billion times less in this imagined universe. Planet masses would also be scaled down by a billion. Irrespective of whether these planets could retain steady orbits, the strength of gravity would stunt the evolutionary potential on them.’ (Rees 1999:33-34)

So stars would be smaller; and galaxies would be smaller, and more crowded. Stable planetary orbits would be much less likely – there would be a much higher chance of a planet being knocked out of its orbit by another passing star:

‘Galaxies would form much more quickly in such a universe, and would be miniaturized. Instead of the stars being widely dispersed, they would be so densely packed that close encounters would be frequent. This would in itself preclude stable planetary systems, because the orbits would be disturbed by passing stars – something that (fortunately for our Earth) is unlikely to happen in our own Solar System.’ (Rees 1999:34)

The lifetime of stars

Because stars would be smaller in a strong-gravity world, they would burn up more quickly:

‘But what would preclude a complex ecosystem even more would be the limited time available for development.  Heat would leak more quickly from these ‘min-stars’: in this hypothetical strong-gravity would, stellar lifetimes would be a million times shorter. Instead of living for ten billion years, a typical star would live for about 10,000 years. A mini-Sun would burn faster, and would have exhausted its energy before even the first steps in organic evolution had got under way. Conditions for complex evolution would undoubtedly be less favourable if (leaving everything else unchanged) gravity were stronger.’ (Rees 1999:34)

Collins disagrees with Rees’s figure of stars’ lifetimes being a million times shorter. However, he agrees that they would be much shorter than they are at present, so the heart of Rees’s argument is not changed:

‘[S]tars with life-times of more than a billion years (as compared to our sun’s lifetime of ten billion years) could not exist if gravity were increased by more than a factor of 3000.’  (Collins, Evidence, p.21)

He comments that ‘This would have significant intelligent life-inhibiting consequences.’  So it appears that the force of gravity cannot be more than 3,000 times its actual value, if complicated creatures like us are to exist.

Conclusions

In a strong-gravity universe, there would not be plants and animals anything like the size of human beings; galaxies, stars and planets would all be much smaller; planets would be more frequently pulled out of their orbits by passing stars, and stars would burn for much less time than they do in our universe. All in all, the prospects for complicated life like ours would not look promising:

Though we perceive gravity to be a ‘strong’ force (because we are close to a very massive body) it is actually incredibly weak in comparison with the electrostatic forces that control atomic structures and, for example, cause protons to repel each other. The factor is of order ~ 10^-36. Let us suppose gravity was stronger by a factor of a million. On the small scale, that of atoms and molecules, there would be no difference, but it would be vastly easier to make a gravitationally bound object such as the Sun and planets but whose sizes would be about a billion times smaller. Any galaxies formed in the universe would be very small with tightly packed stars whose interactions would prevent the formation of stable planetary orbits. The tiny stars would burn up their fuel rapidly allowing no time for life to evolve even if there were suitable places for it to arise. Our intelligent life could not have arisen here on Earth if this ration had been even slightly smaller than its observed value. (Morison 2008:327)

How finely tuned?

How finely is the force of gravity tuned? As we have seen, Collins argues that any kind of intelligent life would not be possible in a universe where gravity was more than 3000 times as powerful as it is in our universe.

Increasing the strength of gravity by 3000 sounds like a huge change. It certainly doesn’t sound like fine-tuning. However, with the electrostatic force being 10³⁶ times stronger than gravity, (and the strong nuclear force 10⁴⁰ times more powerful), even a 3000-fold increase in the strength of gravity is still only 1 in 10³⁶ of the total range of forces. So this is actually very precise fine-tuning.