It’s a hooey arguement, suggesting Scientific American is “dumbing it down” a little, which I find disturbing.
If the universe was effectively infinite, then every possible direction you could look in the night sky would have you facing a star, and the entire night sky would appear to be glowing.
Since the universe doesn’t even have an (effectively) infinite number of stars, I see no reason to presume an (effectively) infinite number of planets.
Somebody at Scientific American has been watching too many Star Trek episodes.
Not necessarily. It depends on the nature of the multiverse. If all universes were started by individual Big Bangs as a “simultaneous” event, we would only be able to see the other Bangs after enough time had elapsed. And if they were all more than 18 billion light years away…
Alternatively, if we imagine there is dark matter in our universe, and it’s at the “leading edge” so to speak, perhaps it’s dense enough to prevent light from either penetrating or escaping. Not sure if that hypothesis has any merit, as again, IANA astronomer either.
I must correct myself, as I learnt in a GQ debate it is not proven that the quantum of distance is in fact the Plank’s Distance. It may be quite a different value, Plank’s Distance as the quantum is derived only in some forms of string theory.
Cheers, Bippy
If I have a blue line, it is made up of an infinite number of blue points. Could I correspond each of those blue points with a point in an infinitely lartge universe, so that I had an infinitely large universe filled with blue points?
Bryan Ekers The star in every direction problem you mention only is a problem if the universe is both infinitely large and infinitely old. As mrblue92 points out there are only a finite number of stars that are near enough to any point of observation that have transmitted light to the observer. sciguy . . .
if there are only finitely many position states in a given volume (or surface, or line), there are only finitely many states a particle could move into from its present state.
On the second page, they say that 10 to the 118th protons could be packed into a hubble volume, which they say allows for 2 to the 10 to the 118th possible patterns.
Excuse the ignorance, but does does that mean exactly. Not just twice as many?
Imagine a particle P1 moving from point a at 0,0 to point b at 1,10 in units of distance quanta. And another particle P2 moving from point a to point c at 0,10.
Each particle would move through the same position quanta from 0,0 to 0,4 before diverging at 0,5 (if things can be thought of this simply) but do they both posess the same direction of travel when they are in the same positions? does P1 move from 0,0 to 0,1 in the same diresction as P2 moves from 0,0 to 0,1 ?
I have no idea how to answer this, since if the directions are the same then how does P1 end up in a different location to P2. But if the directions are different then the direction value (quantifiable state) for a particle can be expressed in much finer granuality than any other quantifiable state.
Any QM researchers / Prof’s out there can give a link to understanding the quantisation of direction?
Exion No existant line (no matter what colour ;)) is made up of an infinite number of points. It is either made up of particles (atoms and molecules) which are quite big in the scheme of things we are talking about in this thread. Or it is made up from the path of a particle/wave (blue laser beam for example) in which case it is still expected to be made up of a large number of very small positional jumps by the photons in the beam, each jump of length equal to the distance quantum (which may or may not be the Plank’s distance).
“Exion No existant line (no matter what colour ) is made up of an infinite number of points. It is either made up of particles (atoms and molecules) which are quite big in the scheme of things we are talking about in this thread. Or it is made up from the path of a particle/wave (blue laser beam for example) in which case it is still expected to be made up of a large number of very small positional jumps by the photons in the beam, each jump of length equal to the distance quantum (which may or may not be the Plank’s distance).”
THe same question still remains though. If I have a blue line, can’t I correspond it’s infinite paticles, jumps, etc. into an infinitely large universe?
Exion The blue line, or indeed anything we can construct, is not made up of an infinite number of things. Since any thing can be no shorter than the distance quantum. It can be made up of no more than
(length of line)/(distance quantum)
things, which is finite if (length of line) is finite and (distance quantum) is not zero.
Even though the size of the universe increases, its mass does not. I don’t believe there is another earth out there, partly because it ain’t a matter of distance. You’d need the same mass formed into the same set up formed into the earth creating life and then intelligence and then man.
I’m sure somewhere there is an inhabitable planet, at least if we planted things there, but I’m not ready to accept another earth until they can show me other life.
It’s basic binary math. If all your protons could have two distinct states (call them “on” and “off”), then the number of total patterns is 2[sup]number of protons[/sup].
i.e. if you have three protons, with 0=“off” and 1=“on”, they can have any of the following possible patterns:
000
001
010
011
100
101
110
111
8 patterns = 2[sup]3[/sup]
Note that 8 is not just “twice as many” as 3. If your universe had 5 protons, you’d have 32 possible patterns. If your universe has 10 protons, you’d have 1024 possible patterns.
That said, how this proves that there’s another Earth out there on which I decided not to write this post escapes me.
It’s actually surprisingly simple. As Bippy the Beardless, if you look at the universe as a collection of pingpong balls (protons) at the quantum level and make the following assumptions
1 the universe is infinite
2 matter/energy is distributed more or less evenly
3 that matter has a finite number of states it can be in (a proton is there or it isn’t)
eventually, that random pattern will repeat itself.
intuitively it doesn’t make sense because it’s dificult to imagine that YOU could form on a similar planet somewhere else in the universe, let alone a duplicate universe. But when you consider how mind numbingly large 10^10^28 m is, it seems like it might be possible. I’m guessing its on an order of magnitude of if our entire known universe was the size of a proton, your doppleganger would be somewhere at the edge of the universe at its present scale, to the power of something big, really really big.
The stuff about 7 and 8 dimensions or universes existing on separate planes is a little tough to grasp.
Actually a better way to look at it is if you know there are 1024 peossible pattersn (which we can calculate) and you know the dimensions of a single pattern. You can figure that the the pattern (ie you) will duplicate in the edge of that pattern x number of possible patterns distance from here.
Now my head hurts. I’m going to Cafe Society where I can discuss Simpson quotes and debate Godzilla vs the Enterprise.
“Exion The blue line, or indeed anything we can construct, is not made up of an infinite number of things. Since any thing can be no shorter than the distance quantum. It can be made up of no more than
(length of line)/(distance quantum)
things, which is finite if (length of line) is finite and (distance quantum) is not zero.”
Excuse my geometry, but I thought that lines were, by definition, infinite. I’m not talking about a line I drew on a piece of paper, that would be a segment if I recall.
Exion: I think Bippy’s confusion might’ve been that in geometry, a line segment has as many points as an infinitely long line, and his argument was that the geometric argument breaks down when segments are made up of quantum lengths.
Now you bring in an infinitely long line, which would contain an infinite number of quantum lengths, but of course in our finite observable universe, you can’t have an infinitely long line.
You could probably bring in the difference between countably infinite (which would be the cardinality of quantum points in an infinite line) and un-countably infinite (the cardinality of geometric points in an infinite line or segment), but since this whole discussion rests on our observable universe being finitely sized, I don’t think it would apply. So because we’re dealing with quantized values and a finite observable universe, we’re going to have to ignore geometric arguments as not applicable, since the axioms of geometry posits zero-sized points and an infinite space.
Think about it this way - let’s say the universe is huge. Trillions of light years in size. Or even infinite.
Furthermore, let’s say that it came into existance 25 billion years ago.
If that’s the case, then only the light from stars within 25 billion light years would have reached Earth by now. In other words, we live in a ‘bubble’ 25 billion light-years around, and we can see no further than that, because 26 billion years ago, there was nothing.
As time goes on, our ‘bubble’ will get bigger and bigger - not because space is increasing in size, but because more and more stars are becoming visible to us as their light finally reaches us. Light from stars 50 billion light years away is on its way here, and will arrive in 25 billion years.
A good analogy would be a man walking through a huge field with a lantern. He can only ever see as far as the lantern will shine, but that doesn’t mean there isn’t a huge field out there.
10^10^28 is far bigger than you think it is. It’s big enough that you hardly need units; 10^10^28 picometers is essentially the same as 10^10^28 gigaparsecs. If you reduce the visible universe to the size of a proton, you’re introducing a multiplicative factor. A proton has a diameter of about 10^-24 m. The visible universe is about 10^10 light-years across, or 10^25 m. That’s 49 orders of magnitude. Anyway, (10^10^28)/(10^49)=10^(10^28 - 49) which is essentially just 10^10^28. You’d need to repeat your procedure of reducing your universe to the size of a proton and then zipping over to the opposite side of the new universe about 10^26 times before a new planet identical to the earth appeared on the opposite side.
I think perhaps some people who believe a duplicate of the earth is unlikely even in an infinite universe haven’t thought carefully enough about the distance scales involved. Infinity includes some very, very big numbers–even numbers so big that there would be no way to express them even if we used every particle in the visible universe to record our notation.
It’s true that things like position aren’t always quantized, but that doesn’t kill the argument. Because of fundamental quantum uncertainty, distances below a certain size don’t matter because their effects are dwarfed by chance–true randomness, not just thermal noise. Pick a degree of precision. Do you want every particle in the duplicate Earth to be in the same position it is in our Earth to within 10^-36 meters, one trillionth of a proton diameter? Fine. It’s possible to redo the calculation with a slightly bigger number in the appropriate place and it will give you a distance.
. . .