Are we big or small?

Question

How does the size of humans compare to the size of other objects in the universe? Are we among the relatively large or the relatively small things?

My very preliminary research suggests that the smallest thing in the physical universe is the quantum foam which should be about Planck length or 10^-35 m. While the universe is about 10²⁶ m. This would seem to bias us toward the big side by about 9 orders of magnitude.

I am skeptical of this estimate because it is pretty close to the middle of the scale and I am always skeptical of measures that put humans in the center. So is there another way of thinking about/ quantifying this question?

Edit: it seems that the smallest thing we have actual evidence of is a neutrino which is 10^-24 m, which would put us even closer to the center!

Answer 1

One could make an argument that we are just about the size we need to be. There is a fascinating paper from 1980 by William H. Press: Man's size in terms of fundamental constants, where he argues that intelligent beings have to have a scale of $$ L_H \sim \left( \frac{\hbar^2}{m_e e^2} \right) \left( \frac{ e^2 }{ G m_p^2 } \right)^{1/4} \sim a_0 10^9 \sim 5 \text{ cm} $$ And does so on very general grounds. The whole paper is worth a read, and is short (2 pages), but I'll summarize the key points here. The assumptions are that a intelligent creatures require:

1. complicated chemistry
2. nontrivial atmosphere
3. cannot break when they trip.

From this he builds up in steps the expected density of the creature, temperature of its environment, mass of it's planet, radius of it's planet, size of the creature, and timescale for the creature.

The one fudge factor in the analysis is the fraction of a Rydberg the relevant chemistry takes place on, which he takes as $\epsilon \sim 0.003 \text{ Ry}$ which corresponds to typical hydrogen bond strengths, but his size estimation is weakly dependent on this $\epsilon$, going like $\epsilon^{1/4}$, while his time scale is strongly dependent on it $\epsilon^{-2.75}$, suggesting that intelligent life out there ought to be within a couple orders of magnitude of us in size, and live on an planet with similar mass and size as earth, but may have drastically different characteristic time scales, given their local star.

Answer 2

The best you will get is ‘middle/small’, assuming you treat humans as a whole. Here’s why:

• Usually, ‘large scale’ physics as given by GR (or even SR) does not apply to us: The gravitational force between two humans is small and the curvature in spacetime caused by a human being is absolutely negligible.
• At the same time, ‘small scale’ physics, described by quantum mechanics, does not apply to us either: You can run against a wall as often as you like, but you won’t get through it. However, this point relies on the description of humans as a whole, rather than made up of ‘small’ atoms. This is only partly true for us, as many biological systems rely - at least to some extent - on quantum mechanical (non-classical) effects. Were minor parametres (magnitude of the Van der Waals force, for example) to change suddenly, we certainly would notice (and die).

Planetary objects, stars and black holes nearly do not rely on such small-scale effects. Nuclear fusion will probably even take place if some forces double or triple and a black hole won’t stop existing just because quantum fluctuations change slightly.

Hence, as we rely ‘more’ on small-scale physics than on large-scale physics, we are certainly more on the ‘small’ side of stuff, but since we are much larger than actually ‘small’ things (atoms), ‘middle/small’ is probably the best you can get.

But really, ‘large’ and ‘small’ only make sense in relation to some other object: We are about as large as trees, smaller than the moon, much smaller than the sun and much larger than atoms. I guess you knew that already ☺.

Answer 3

I am taking a different approach to answer this question.

I'm terms of numbers there are approximately 8,000,000,000 humans on the planet there are more than 8,000,000,000 star systems in our galaxy alone. There are also just as many if not more smaller systems ie. Molecular systemm. In terms of quantity that easily places humans in the middle/large group.

This of course all depends on perspective and your definition of "object" If by object you mean individual systems that together can comprise an object than scale becomes arbitrary (besides a few special cases ie black holes and the like) as most objects are made from individual atoms(systems of neutron,proton,electron) which in themselves are composed of systems of quanta.

This to me seems a very ambitious question and without a firm definition of "object" can be interpreted in countless ways.

Answer 4

In an infinitely large universe I believe we are neither big, nor small, but a relative size in we which we use to measure other objects from.

Observable universe is probably just a grain of sand in an infinitely big universe where there are things so large and so small it is impossible for us to fathom and current math will simply not be able to handle.