# Are we big or small?

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!

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@CrazyBuddy I am not saying that there are only 9 orders of magnitude in the universe but rather there are 26 oom above us and 35 oom below us so the smallest thing is 9 oom further from us than the biggest thing. – KennyPeanuts Nov 15 '12 at 17:16
Have you looked at Scale of the Universe? – Emilio Pisanty Nov 15 '12 at 17:34
As Goldilocks would say, "We're juuust right." – Kitchi Nov 15 '12 at 18:49
@EmilioPisanty that's an awesome link. – McGarnagle Nov 15 '12 at 18:56
With respect to your edit, neutrinos like electrons have no known size. None. Where ever you got that figure it is at best a limit. – dmckee Nov 19 '12 at 3:03

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 ☺.

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Cool, that is an interesting way to approach it - not thinking about the actual size but the scale of the forces that affect us... – KennyPeanuts Nov 15 '12 at 20:11

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.

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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.

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That is an interesting point if you consider humans alone, I was mainly interested in human-sized things when I was thinking about this though. – KennyPeanuts Nov 15 '12 at 20:12
But, see, there are $8 \times 10^{9}$ humans, but only 8 planets - with a few moons and the sun and a few million comets maybe $10^{4}$ objects in the solar system. Since it is quite likely that there are other civilisations out there, some probably spread over multiple planets or even solar systems, we can probably easily claim that ‘human-sized livings’ are one of the largest groups in the universe. Really, numbers are just…numbers. – Claudius Nov 15 '12 at 20:28

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.

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Granted the question is poor, but this seems like a philosophy answer rather than a physics one. – Brandon Enright Jul 12 '14 at 19:51
@BrandonEnright What do you mean a philosophy answer? – user53011 Jul 12 '14 at 19:53
"I believe", "probably just a gain of sand in an infinitely big universe", "impossible for us to fathom", "current math will simply not be able to handle". None of this is physics or mathematical reasoning. – Brandon Enright Jul 12 '14 at 19:56
While, I certainly don't agree with @BrandonEnright that the question is poor :) - I do agree that you seem to have missed the point of what I am asking. as far as I understand it, the universe is not infinite. There is a finite amount of mass. So if you were to arrange those things with mass in the present universe from biggest to smallest, would human-sized things be closer to the big end or the small end? – KennyPeanuts Jul 13 '14 at 1:29

## protected by Qmechanic♦Jul 12 '14 at 19:26

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