Scale
Following up a post by Kieran at CT quoting Douglas Adams’ line that “You may think it’s a long way down the street to the Chemist’s, but that’s just peanuts to space” I thought I’d try to work out the scale of comparison that is, in some sense directly available to us and compare it to the scale of the universe. (I’m bound to make a mistake here, but what are comments threads for if not to fix these things).
The distances directly available to us range from around 0.1 mm (roughly, a hair’s breadth) to perhaps 10 million km, the distance a regular world traveller might cover in a lifetime. That’s from 10^-4m to 10^10m, or fourteen orders of magnitude. If I have it right, the potentially observable universe includes distances up to about 10 billion light years, or 10^27m, which is seventeen orders of magnitude greater than the maximum human-range distance.
Going the other way, the diameter of the electron is around 10^-18 m (fourteen orders of magnitude smaller than the minimal human scale) and the Planck length is 10^-35 m, another 17 orders of magnitude smaller again.
So, in log terms, the range we can experience directly covers about a quarter of the range from the Planck length to the size of the universe. I suspect you could do something similar for time, taking the human range from tenths of a second to the centuries reachable with two or three handshakes.
Note: (Of course, there are no original ideas. After I wrote this, I found this handy scale at Wikipedia). Still, it’s done now.
A question. (I don’t know the answer, but I’m sure it’s out there somewhere).
What’s the furthest that can be seen with the naked eye? (On dark night from the surface of the earth). Though our eye might be receiving some photons from the edge of the universe, we can’t perceive them, so they don’t count.
When you really, really, really need to go it is a long, long,long way to the bathroom.
http://www.gsfc.nasa.gov/scienceques2001/20011019.htm
(may be northern-hemisphere only)
Andromeda can be seen from almost all populated areas of the Southern hemisphere, but only for a brief time low to the horizon. Also you need to be away from city lights. The rest of the time in the south its the Magellenic clouds, which are about ten times closer.
Bruce, the Triangulum Galaxy is the most distant object visible to the naked eye, about 800 parsecs away.
That polarisation of scale strikes me as wrong-headed in one direction. It surely makes better sense to talk about spans rather than cycles or serials.
World travellers commonly fly around the globe in a series of segmented journeys. The long distance record is probably held by long term inhabitants of space stations, who orbit the globe continuously. These trips are limited in span by the circumpherence of their orbital path.
The greatest distance spanned by a man, relative to this planet, must have been the trips to the moon. These trips traversed about 400,000 km in space. They resulted in the famous shots of the earth from space, which certainly gave us a different perspective on the great scheme of things.
Interesting that the anthropic scale lie almost exactly in the mid-point between the atomic and the cosmic scales.
The size of the smallest possible atomic unit – the Planck length – is 10^-35 m.
The size of a fairly common anthropic unit – a just fertilized egg – is 10^-4 m.
The size of the the largest possible cosmic unit – the diameter of the known universe – is 10^27 m.
This is the sort of fact that excites Space Odyssey fans.
*”10 billion light years, or 10^27m”
This seems to be the wrong distance by a (-) order of magnitude and the wrong scaling by a (+) order of magnitude. But the errors cancel out, giving approximately the right answer.
The know universe is 158 billion light years (ly) in diameter.
Ten billion light years = 10^26 m.
10 billion = 10^10 (ie 10,000,000,000)
1 light year = ~10^16 m (ie 9,460,730,472,580,800 m)
So, in log terms, the universe is 1.58 x 10^27 m in diameter.
“So, in log terms, the range we can experience directly covers about a quarter of the range from the Planck length to the size of the universe.”
I wouldn’t describe either fractions of the Planck length, or the size of the universe, as being able to be directly experienced by humans.
“Distance” may not be the most suitable measure here. For instance, it’s far easier to get almost into space (orbital height) than actually to get there (orbit proper), but on the distance measure they are almost the same.
“The greatest distance spanned by a man, relative to this planet, must have been the trips to the moon. These trips traversed about 400,000 km in space. They resulted in the famous shots of the earth from space, which certainly gave us a different perspective on the great scheme of things.”
And a common, familiar measurement for most humans is the average stride, which is approximately one yard (ca. 90 CM).
90 centimetres to 400,000 kilometres gives us nine orders of magnitude.
The distance from the Earth to the sun is roughly 150,000,000 kilometres.
Comparing a single step to the distance from the Earth to the sun gives us 12 orders of magnitude.