- I think this is a big off-topic, but it could be easy to prove the finitude of atoms (always with based upon the nowadays approved theories)

1) At the beginning it was the Big-Bang, all matter condensed at one point.

2) The age of the universe is believed to be around the 15*10^3 million years. We can state a wide upper bound, say about 10^4 million years.

3) The highest speed for mass-particles is lesser than c=3*10^8 m/s.

4) The smallest atom radius is that of the hydrogen with its electron over the first level: 5*10^(-11) meters.

5) Considering our space as an euclideus one - near true -, the volumen of a sphere is V = 4/3*pi*r^3 with r its radius.

6) With 4) and 5), making a sphere of an atom, it would have a volume around v_atom = 4/3 * pi * [5*10^(-11)]^3 = 5,236 * 10^(-31) m^3

7) Using 2) and 3), supposing and uniform and at-highest-speed expansion, the filled-with-matter-universe radius is R = 10^10 * 365 * 24 * 3600 * c = 9,4608 * 10^25 m.

8) By 5) and 7), the volume of the universe sphere is V_universe = 4/3 * pi * [9,4608 * 10^25]^3 = 3,715 * 10^78 m^3

8) Using 6) and 8), and making the mad supposition that space is fullfilled with the smallest atoms, then if the number of atoms we have is N, roughly it will be V_universe = N * v_atom --> N = V_universe / v_atom = 3,75 * 10^78 / 5,236 * 10^(-31) =7,09 * 10^108 atoms!

Remarking: 10^109 is a big upper bound for the number of atoms in our universe.

So we can do assertions like "factorising a 10^7 bit number will require more than a year of operations if every atom in the universe were a pentium I" and other stuff like this.

Jose Brox

----- Original Message -----

From: Jon Perry

To: Prime Numbers ; Paul Leyland

Sent: Monday, April 28, 2003 9:00 PM

Subject: RE: [PrimeNumbers] Primes vs. Atoms

'> http://web.singnet.com.sg/~huens/paper23.htm

>

> in the Abstract, 2nd sentence:

>

> 'There are more primes than the number of atoms in the universe.'

>

> This a proven fact? I had naturally assumed |atoms| was

> finite, but this sentence makes me question myself.

It's difficult to see how it can be proved. It's easy to prove that there

is a countably infinite number of primes, but by no means easy to prove that

there are a finite number of atoms in the universe or that the statement

even makes sense.

<me>True.</me>

If we restrict ourselves to real atoms in the observable universe, it's

fairly clear that the number is finite (we can only observe a finite volume

and atoms have a non-infinitesimal size) but the number is far from

constant. Atoms are both created and destroyed in large numbers.

<me>True.</me>

If, on the other hand, we include virtual atoms, those which momentarily pop

into and out of existence as a result of vacuum zero point energy

fluctuation it's not obvious to me whether their number is finite, countably

infinite or uncountably infinite.

<me>True.</me>

Where are the theoretical physicists when you need them? David: are you

listening?'

<me>True.</me>

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry/maths/

http://www.users.globalnet.co.uk/~perry/DIVMenu/

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http://www.brainbench.com

-----Original Message-----

From: Paul Leyland [mailto:pleyland@...]

Sent: 29 April 2003 16:40

To: Jon Perry

Subject: RE: [PrimeNumbers] Primes vs. Atoms

> http://web.singnet.com.sg/~huens/paper23.htm

>

> in the Abstract, 2nd sentence:

>

> 'There are more primes than the number of atoms in the universe.'

>

> This a proven fact? I had naturally assumed |atoms| was

> finite, but this sentence makes me question myself.

It's difficult to see how it can be proved. It's easy to prove that there

is a countably infinite number of primes, but by no means easy to prove that

there are a finite number of atoms in the universe or that the statement

even makes sense.

If we restrict ourselves to real atoms in the observable universe, it's

fairly clear that the number is finite (we can only observe a finite volume

and atoms have a non-infinitesimal size) but the number is far from

constant. Atoms are both created and destroyed in large numbers.

If, on the other hand, we include virtual atoms, those which momentarily pop

into and out of existence as a result of vacuum zero point energy

fluctuation it's not obvious to me whether their number is finite, countably

infinite or uncountably infinite.

Where are the theoretical physicists when you need them? David: are you

listening?

Paul

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[Non-text portions of this message have been removed] - [OT but...] I can't let Jose have the last word on this.

He is ignoring what is known in the trade as the "Cosmological Principle",

viz. that our (spatial) position is /not/ special, but rather that the

Universe looks (basically) the same to all observers (at a given epoch).

We can see out into space (and simultaneously back in time) to a distance of

about 10^10 light-years, giving a finite number (about 10^79) of atoms in

principle visible to us now (and, because of the Big Bang, not many more than

that).

An observer who is now at a distance of 10^10 light-years from us would say

just the same. And an observer the same distance from him /in that same

direction/, will also say the same. And...

So, unless the Universe has positive spatial curvature (like a ball), and

there is absolutely no observational evidence for this, one is left with the

literally unimaginable conclusion that the number of (real) atoms in the

Universe /now/ is unbounded, i.e. >= aleph_0. Scary...

Mike Oakes

In a message dated 30/04/03 02:05:05 GMT Daylight Time, ambroxius@...

writes:

> I think this is a big off-topic, but it could be easy to prove the finitude

[Non-text portions of this message have been removed]

> of atoms (always with based upon the nowadays approved theories)

>

> 1) At the beginning it was the Big-Bang, all matter condensed at one point.

>

> 2) The age of the universe is believed to be around the 15*10^3 million

> years. We can state a wide upper bound, say about 10^4 million years.

>

> 3) The highest speed for mass-particles is lesser than c=3*10^8 m/s.

>

> 4) The smallest atom radius is that of the hydrogen with its electron over

> the first level: 5*10^(-11) meters.

>

> 5) Considering our space as an euclideus one - near true -, the volumen of

> a sphere is V = 4/3*pi*r^3 with r its radius.

>

> 6) With 4) and 5), making a sphere of an atom, it would have a volume

> around v_atom = 4/3 * pi * [5*10^(-11)]^3 = 5,236 * 10^(-31) m^3

>

> 7) Using 2) and 3), supposing and uniform and at-highest-speed expansion,

> the filled-with-matter-universe radius is R = 10^10 * 365 * 24 * 3600 * c =

> 9,4608 * 10^25 m.

>

> 8) By 5) and 7), the volume of the universe sphere is V_universe = 4/3 * pi

> * [9,4608 * 10^25]^3 = 3,715 * 10^78 m^3

>

> 8) Using 6) and 8), and making the mad supposition that space is fullfilled

> with the smallest atoms, then if the number of atoms we have is N, roughly

> it will be V_universe = N * v_atom --> N = V_universe / v_atom = 3,75 *

> 10^78 / 5,236 * 10^(-31) =7,09 * 10^108 atoms!

>

> Remarking: 10^109 is a big upper bound for the number of atoms in our

> universe.

>

> So we can do assertions like "factorising a 10^7 bit number will require

> more than a year of operations if every atom in the universe were a pentium

> I" and other stuff like this.

>

>

> Jose Brox

>

>

- Hi,

Yes, an big upper bound because the average of atoms/particle in the

interestelar medium is aprox. 1/(cm^3). This would be corrected by the

unknown amount of "dark matter". The hypothesis of the Big Bang is

admitted by the majority of physicists, and now the dicovery of the

polarization of the "fosil" radiation reaffirme the BB.

The mass, number and volume of neutrino particles in the Universe

would be introduced if pertinent.

Ignacio

Jose_Ramón_Brox <ambroxius@...> wrote:I think this is a big off-topic, but it could be easy to prove the finitude of atoms (always with based upon the nowadays approved theories)

1) At the beginning it was the Big-Bang, all matter condensed at one point.

2) The age of the universe is believed to be around the 15*10^3 million years. We can state a wide upper bound, say about 10^4 million years.

3) The highest speed for mass-particles is lesser than c=3*10^8 m/s.

4) The smallest atom radius is that of the hydrogen with its electron over the first level: 5*10^(-11) meters.

5) Considering our space as an euclideus one - near true -, the volumen of a sphere is V = 4/3*pi*r^3 with r its radius.

6) With 4) and 5), making a sphere of an atom, it would have a volume around v_atom = 4/3 * pi * [5*10^(-11)]^3 = 5,236 * 10^(-31) m^3

7) Using 2) and 3), supposing and uniform and at-highest-speed expansion, the filled-with-matter-universe radius is R = 10^10 * 365 * 24 * 3600 * c = 9,4608 * 10^25 m.

8) By 5) and 7), the volume of the universe sphere is V_universe = 4/3 * pi * [9,4608 * 10^25]^3 = 3,715 * 10^78 m^3

8) Using 6) and 8), and making the mad supposition that space is fullfilled with the smallest atoms, then if the number of atoms we have is N, roughly it will be V_universe = N * v_atom --> N = V_universe / v_atom = 3,75 * 10^78 / 5,236 * 10^(-31) =7,09 * 10^108 atoms!

Remarking: 10^109 is a big upper bound for the number of atoms in our universe.

So we can do assertions like "factorising a 10^7 bit number will require more than a year of operations if every atom in the universe were a pentium I" and other stuff like this.

Jose Brox

----- Original Message -----

From: Jon Perry

To: Prime Numbers ; Paul Leyland

Sent: Monday, April 28, 2003 9:00 PM

Subject: RE: [PrimeNumbers] Primes vs. Atoms

'> http://web.singnet.com.sg/~huens/paper23.htm

>

> in the Abstract, 2nd sentence:

>

> 'There are more primes than the number of atoms in the universe.'

>

> This a proven fact? I had naturally assumed |atoms| was

> finite, but this sentence makes me question myself.

It's difficult to see how it can be proved. It's easy to prove that there

is a countably infinite number of primes, but by no means easy to prove that

there are a finite number of atoms in the universe or that the statement

even makes sense.

<me>True.</me>

If we restrict ourselves to real atoms in the observable universe, it's

fairly clear that the number is finite (we can only observe a finite volume

and atoms have a non-infinitesimal size) but the number is far from

constant. Atoms are both created and destroyed in large numbers.

<me>True.</me>

If, on the other hand, we include virtual atoms, those which momentarily pop

into and out of existence as a result of vacuum zero point energy

fluctuation it's not obvious to me whether their number is finite, countably

infinite or uncountably infinite.

<me>True.</me>

Where are the theoretical physicists when you need them? David: are you

listening?'

<me>True.</me>

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry/maths/

http://www.users.globalnet.co.uk/~perry/DIVMenu/

BrainBench MVP for HTML and JavaScript

http://www.brainbench.com

-----Original Message-----

From: Paul Leyland [mailto:pleyland@...]

Sent: 29 April 2003 16:40

To: Jon Perry

Subject: RE: [PrimeNumbers] Primes vs. Atoms

> http://web.singnet.com.sg/~huens/paper23.htm

>

> in the Abstract, 2nd sentence:

>

> 'There are more primes than the number of atoms in the universe.'

>

> This a proven fact? I had naturally assumed |atoms| was

> finite, but this sentence makes me question myself.

It's difficult to see how it can be proved. It's easy to prove that there

is a countably infinite number of primes, but by no means easy to prove that

there are a finite number of atoms in the universe or that the statement

even makes sense.

If we restrict ourselves to real atoms in the observable universe, it's

fairly clear that the number is finite (we can only observe a finite volume

and atoms have a non-infinitesimal size) but the number is far from

constant. Atoms are both created and destroyed in large numbers.

If, on the other hand, we include virtual atoms, those which momentarily pop

into and out of existence as a result of vacuum zero point energy

fluctuation it's not obvious to me whether their number is finite, countably

infinite or uncountably infinite.

Where are the theoretical physicists when you need them? David: are you

listening?

Paul

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