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Dave W.
Info Junkie

USA
26020 Posts
Posted - 10/01/2008 :  11:31:14   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Right, BPS. And the speed of light as a universal "speed limit" only applies to things moving through space, not to the expansion of space itself. So starting with Hubble's constant (and not including acceleration of the expansion), we find that anything more than 4,276.6 megaparsecs away will be receding from us at faster than light speed. That's 13.95 billion lightyears.

So, something that right now is 28 Bly away emits light towards us. After 14 billion years, the light has covered half that distance, but in the meantime, the space between us and the halfway point has expanded by 14 Bly, so the light still has 28 Bly to cover before it reaches us (and the original object would then be 56 Bly away). It can never get more than halfway to us (and in fact can't even get halfway, but I'm not going to do the calculus to make this simple example more realistic).
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
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BigPapaSmurf
SFN Die Hard

3192 Posts
Posted - 10/01/2008 :  12:13:43   [Permalink]  Show Profile Send BigPapaSmurf a Private Message  Reply with Quote
Thanks for the numbers Dave, you rock as usual.
"...things I have neither seen nor experienced nor heard tell of from anybody else; things, what is more, that do not in fact exist and could not ever exist at all. So my readers must not believe a word I say." -Lucian on his book True History

"...They accept such things on faith alone, without any evidence. So if a fraudulent and cunning person who knows how to take advantage of a situation comes among them, he can make himself rich in a short time." -Lucian critical of early Christians c.166 AD From his book, De Morte Peregrini
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Simon
SFN Regular

USA
1992 Posts
Posted - 10/01/2008 :  12:29:34   [Permalink]  Show Profile Send Simon a Private Message  Reply with Quote
Originally posted by Dave W.

Right, BPS. And the speed of light as a universal "speed limit" only applies to things moving through space, not to the expansion of space itself. So starting with Hubble's constant (and not including acceleration of the expansion), we find that anything more than 4,276.6 megaparsecs away will be receding from us at faster than light speed. That's 13.95 billion lightyears.

So, something that right now is 28 Bly away emits light towards us. After 14 billion years, the light has covered half that distance, but in the meantime, the space between us and the halfway point has expanded by 14 Bly, so the light still has 28 Bly to cover before it reaches us (and the original object would then be 56 Bly away). It can never get more than halfway to us (and in fact can't even get halfway, but I'm not going to do the calculus to make this simple example more realistic).


Make sense. The balloon is inflating faster than the ant can travel on the balloon's surface.

And then, the evil clown shows up.
Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam.
Carl Sagan - 1996
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Cuneiformist
The Imperfectionist

USA
4955 Posts
Posted - 10/01/2008 :  12:33:20   [Permalink]  Show Profile Send Cuneiformist a Private Message  Reply with Quote
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Kil
Evil Skeptic

USA
13476 Posts
Posted - 10/01/2008 :  12:39:04   [Permalink]  Show Profile  Visit Kil's Homepage  Send Kil an AOL message  Send Kil a Yahoo! Message Send Kil a Private Message  Reply with Quote
Simon:
Make sense. The balloon is inflating faster than the ant can travel on the balloon's surface.

And then, the evil clown shows up.

Now that really brings it down to a level that even I can understand. Even if it is a joke...
Uncertainty may make you uncomfortable. Certainty makes you ridiculous.

Why not question something for a change?

Genetic Literacy Project
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Ricky
SFN Die Hard

USA
4907 Posts
Posted - 10/01/2008 :  15:06:07   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
(and in fact can't even get halfway, but I'm not going to do the calculus to make this simple example more realistic).


Are you sure Dave? The derivative of the percentage of distance traveled seems to always be positive. I think you may be forgetting that space "behind" the light is expanding as well.

Then again, I have been known to make mechanical errors...

Edit: Whoops, I seem to have forgot to include that space "behind" the light is increasing as well in my calculations. This makes things a bit harder...

Edit #2: I completely screwed up the setup. My equations were simply an approximation to the solution to the differential equation at t=0. Find the exact solutions now...
Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
Edited by - Ricky on 10/01/2008 15:33:31
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Ricky
SFN Die Hard

USA
4907 Posts
Posted - 10/01/2008 :  16:11:31   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
Ok, first some constants and functions:

b(t): distance of the "beam" of light to Earth, with time t in seconds, expressed in mega parsecs.
o(t): distance of the original "object" that the beam was shot out of and Earth, with time t in seconds, expressed in mega parsecs.
p(t): Percentage of distance traveled by the beam of light. 0 is at earth, 1 is at the object "o".
SoL: Speed of Light in mega parsec per second.
H: Hubble's constant in (mega parsec per second) per mega parsec.
D: original distance between the object the light was shot out of and Earth, expressed in mega parsecs.
e: Euler's constant.

b(t) = SoL*H + (D - SoL*H)e^(Ht)

o(t) = D*e^(Ht)

p(t) = b(t)/o(t) = (SoL*H)/(D*e^(Ht)) + (D - SoL*H)/D

The derivative of the percentage is:

-(SoL*H^2 / D)*e^(-Ht)

This shows that it's percentage is always decreasing (it's always getting a closer percentage to earth). However:

lim as t->infinity of p(t) = (D - SoL*H)/D

Which shows that it never gets below a certain percentage. Plug in D and SoL into the above limit and you will get the minimum percentage of distance the light travels.
Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
Edited by - Ricky on 10/01/2008 18:37:46
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Dave W.
Info Junkie

USA
26020 Posts
Posted - 10/01/2008 :  18:13:15   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
SoL×H = Mpc/s/Mpc × Mpc/s = Mpc2/s2/Mpc, does it not?

How can a number with such a unit be subtracted from one in Mpc alone?
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too.
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chaloobi
SFN Regular

1620 Posts
Posted - 10/01/2008 :  18:19:33   [Permalink]  Show Profile  Send chaloobi a Yahoo! Message Send chaloobi a Private Message  Reply with Quote
Please. It's still nothing a simple FTL drive won't solve. Yawn.

Also, all clowns are evil.
-Chaloobi
Edited by - chaloobi on 10/01/2008 18:20:08
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Dave W.
Info Junkie

USA
26020 Posts
Posted - 10/01/2008 :  18:24:37   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Depends on how much FTL the drive can go.

If I remember the old Star Trek Technical Manual, Warp 9 was equal to 729 c. Anything more than 10.2 trillion lightyears away would remain unreachable at that speed.
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too.
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Ricky
SFN Die Hard

USA
4907 Posts
Posted - 10/01/2008 :  18:32:39   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
Originally posted by Dave W.

SoL×H = Mpc/s/Mpc × Mpc/s = Mpc2/s2/Mpc, does it not?

How can a number with such a unit be subtracted from one in Mpc alone?


Problems fixed... I think.

Edit: Nevermind, the original was right. The original equation is:

db/dt = H*b(t) - SoL
Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
Edited by - Ricky on 10/01/2008 18:39:28
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Ricky
SFN Die Hard

USA
4907 Posts
Posted - 10/01/2008 :  18:44:22   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
In the original equation, the terms all make sense. The speed (derivative of position) of the beam is the net of the expansion minus the speed of light. From here, I am a bit ignorant with what the meaning of the terms are. They are mathematical solutions, and perhaps it's just the value that is important.

*Shrug*
Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
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Dave W.
Info Junkie

USA
26020 Posts
Posted - 10/01/2008 :  18:54:01   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Originally posted by Ricky

Problems fixed... I think.
Well, one of the things that was stumping me was converting H over to something based on time alone, to get your o(t) function. How did you come up with DeHt?
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too.
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Ricky
SFN Die Hard

USA
4907 Posts
Posted - 10/01/2008 :  18:58:08   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
do/dt = H * o(t)

In other words, the speed at which o(bject) is moving away from earth is given by Hubble's constant multiplied by the distance it currently is at. Then:

do/o = Hdt

Integrating both sides:

ln|o(t)| = Ht + C

Raising each side to the e:

o(t) = e^(Ht + C) = Ce^(Ht)

To find C, we know that o(0) = D, so:

D = o(0) = Ce^(0*t) = C

So C = D, and hence:

o(t) = De^(Ht)
Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
Edited by - Ricky on 10/01/2008 18:59:08
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bngbuck
SFN Addict

USA
2437 Posts
Posted - 10/01/2008 :  20:39:39   [Permalink]  Show Profile Send bngbuck a Private Message  Reply with Quote
Dave.....

Beradilli states:
Shortly after the big bang occurred some 13.7 billion years ago, cosmologists think, the universe underwent a brief period that defied current physical laws. The theory goes that during this time, called inflation, space itself expanded at a rate much, much faster than the speed of light. As a result,some of the matter formed with the big bang was pulled more than 13.7 billion light-years away--so far that its light hasn't reached us yet. As a result, that matter can't be observed--or at least, so cosmologists thought.
You comment:
the speed of light as a universal "speed limit" only applies to things moving through space, not to the expansion of space itself.
Understood.

Why does Beradilli say, "the universe underwent a brief period that defied current physical laws."

1. What current physical laws were defied?

2. Is it possible to explain how space expands and what it expands into? Can you put it into words?
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