Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: The Scientist on 28/12/2010 05:52:51
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Or is there a limit? Please share your views with us. Thanks!
Sorry everyone. There are too many typing errors I made [xx(] The question goes:
Is infinity what you get when you place two plane mirrors parallel to each other?
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Or is there a limit? Please share your views with us. Thanks!
us??
You mean you are not really THE SCIENTIST? There are more of you??
You may have to consider calling yourself "WE SCIENTISTS"
Can you or your committee rephrase your question in order to make it a little clearer?
I am not certain as to what the real nature of your question is
Thanks for your help
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Or is there a limit? Please share your views with us. Thanks!
us??
You mean you are not really THE SCIENTIST? There are more of you??
You may have to consider calling yourself "WE SCIENTISTS"
Can you or your committee rephrase your question in order to make it a little clearer?
I am not certain as to what the real nature of your question is
Thanks for your help
Hi there Foolosophy, there is only one of myself. The reason why I use 'us' is so that we can all share knowledge with one another instead of using the word 'me'. Thanks for letting me know about the question. Typo errors, my mistake.
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Hi there Foolosophy, there is only one of myself. The reason why I use 'us' is so that we can all share knowledge with one another instead of using the word 'me'. Thanks for letting me know about the question. Typo errors, my mistake.
[/quote]
I can't dissagree with that sentiment.
So are you really "THE" Scientist or just "A" Scientist?
Are WE really in the presence of cosmic emminence?
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Hi all
I believe I understand what The Scientist is trying to say. 2 mirrors which are parallel to each other, will give you and image formed that is replicas of the two mirrors, so you'll see many identical mirrors. Hope it helps!
MGM
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Hi all
I believe I understand what The Scientist is trying to say. 2 mirrors which are parallel to each other, will give you and image formed that is replicas of the two mirrors, so you'll see many identical mirrors. Hope it helps!
MGM
I think you may well be right
Well done
Thanks for your assistance on this critical issue
Best wishes
Foolosophy
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If the mirrors are perfect i would say yes, but since mirrors are never perfect you will not get an infinite amount of reflections.
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If the mirrors are perfect i would say yes, but since mirrors are never perfect you will not get an infinite amount of reflections.
are you saying that something happens to the photons that are bouncing between the imperfect mirrors?
is there a mathematical or physical barrier that prevents an infinite number of reflections from being generated? (even if it's a theoretical barrier?)
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I think the reality here is that you (one, anyone, a person etc. for the benefit of nit-pickers)could never actually know. It might be safe to say that the number of images could be infinite, in theory, but in reality, the only way to know would be to count them, which would not be possible if infinity was involved.
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hmmm :)
Ah yes, ignoring the discussion entirely (as usual:), doing my (as usual:) eloquent monologue I must say that I agree..
With what you might wonder?
Well, with myself naturally :)
If we assume perfectly reflecting mirrors, and no energy/momentum loss for that photon as it 'bounces'? Infinity ahoy, here I come :) So, let us assume that we are 'propagating' beside it, being 'still' relative it, will 'it' still represent a infinity to us?
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And if you think it does, what would differ that 'infinity' from the first example.
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will 'it' still represent a infinity to us?
How would you know if it was infinite?
Have you been at the booze? [;D]
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Sad to say, no :)
If you happen to have a dram, send it :)
The first example assuming perfectly reflecting mirrors and no momentum energy loss, as well as no 'outside influences' naturally, I think should be able to 'tick' forever. And that should be a 'infinity' to me at least.
In the second idea you have all kind of possibilities though, depending on where you stand looking at it, well, as I see it:)
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Ah, that would be the idea. "stand looking at the idea" I mean :)
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No it will not project to infinity - the reason why is that light cannot be projected off a mirror into infinity - eventually the mirror absorbs the photon energy.
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light cannot be projected off a mirror into infinity - eventually the mirror absorbs the photon energy.
True, but also because the initial reflection is a finite action, as are subsequent reflections, and nothing finite can become infinite.
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Exactly.
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Quantum Clue; after witnessing a recent exchange in another thread, I have to ask if you mind that I abbreviate your name to"QC" in the quotes?
Yor_on; I would happily send you a dram, but my ancient lap-top is not up to such extravagant feats. [:-'(]
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No, of course not, I don't mind at all. :)
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The durations of the reflections are all possible to define as finite, I agree. but their interaction with those perfect mirrors have no limit. And where you can't find a limit I would say you have a good contender for 'infinity' :)
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Ah, i knew there was a limit to E-mails..
Da*n
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And where you can't find a limit I would say you have a good contender for 'infinity' :)
You know from elsewhere that I will not be able to let that pass without comment. [:P]
You might have a good contender for a mathematical infinity; in reality, unbounded might be OK, but infinity is a different thing altogether.
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consider renormalizations.
why do we need them?
Heh ::))
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But I agree, I've never felt that I've got 'infinity' spiked down, once and for all. I still get hiccups thinking of smaller and larger infinities. Like, can I put a larger infinity inside a smaller? After all, they're both infinities, are they not? And if I did, would it still be the smaller infinity?
And now somebody gonna prove it to me too, right :)
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Renormalization was created because scientists did not like running into infinities. Some scientists - notably Dirac believed renormalization was an ugly feature of quantum mechanics, and was never quite satisfied by it.
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And where you can't find a limit I would say you have a good contender for 'infinity' :)
You know from elsewhere that I will not be able to let that pass without comment. [:P]
You might have a good contender for a mathematical infinity; in reality, unbounded might be OK, but infinity is a different thing altogether.
I agree with Bill S. It takes a finite time for the light to bounce from one mirror to the other. It only takes a few nanoseconds for light to travel between mirrors that are ~ 1 meter apart. That's fast, so that you would get something near a billion bounces between those two mirrors in 1 second, but it's not infinite. Even if you set these mirrors up in the early universe and timed the bouncing, it would still not be infinite. Multiplying 1 billion bounces times the age of the universe in seconds, I get roughly 1026 bounces in the age of the entire universe. That's certainly a huge number, but it's not infinite. In practice, all you're really doing here is using the bounces to time the age of the universe, so if the universe's age isn't infinite, this won't form infinite images.
The concept is quite nice, though. Light travels so fast that hundreds of images seem to appear instantly to our eyes, and they appear to be continuing to infinity, so this experiment gets across the idea of infinity, but it's important to realize that nothing is becoming infinite in this experiment in reality.
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If the mirrors are perfect i would say yes, but since mirrors are never perfect you will not get an infinite amount of reflections.
so how many reflections will the mirrors get in general?
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If the mirrors are perfect i would say yes, but since mirrors are never perfect you will not get an infinite amount of reflections.
so how many reflections will the mirrors get in general?
That depends on the properties of the mirror. Mirrors have a property called reflectivity, denoted by R, which tells you the amount of incident light that gets reflected. If the amount of light hitting a mirror is denoted by I, then the amount reflected is RI. After n bounces, amount of light left is Rn times the incident light.
I don't know if that's all confusing or not, but what it means is that you can calculate how much light is left after a bunch of bounces if you know how good the mirror is at reflecting light. Two mirrors with 90% reflectivity (which is really good for a household mirror) would lose over 99% of the original light after 44 bounces. If you had an incredibly well engineered mirror for a technical application which reflects 99.9% of the light, it would take 4603 bounces to lose 99% of the light.
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So the amount of light remaining in the reflecting beam approaches ZERO as the "n" goes off to infinity.
And as we know it will take an infinite anoutn of time to acheive this
So the remaining light will never completely vanish to zero
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In theory, yes. In practice, you'll eventually have so little light that you can't hope to measure it any more.
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This also ties in very closely with what Soul Surfer put very well here:
http://www.thenakedscientists.com/forum/index.php?topic=36266.msg336978#msg336978
There's a lot of processes in nature in which things decrease exponentially so that they "never" stop decreasing. In practice, there's a point at which you can't really see them anymore, since the thing you're trying to measure has become too small for your measuring equipment.
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In theory, yes. In practice, you'll eventually have so little light that you can't hope to measure it any more.
true - but it can never be equal to ZERO (exactly)
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ahh yes, forgot about that one. But may I point out that they can't exist either, those perfect mirrors :)
So I would like to point out that the universe in which those mirrors are situated will be a 'perfect' one, me as its master, working through eternity..
Yes, I'm building it as we write..
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true - but it can never be equal to ZERO (exactly)
It's Zeno's paradox, again, but when the bouncing light gets down to one photon, any further reduction must result in zero.
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In practice, all you're really doing here is using the bounces to time the age of the universe, so if the universe's age isn't infinite, this won't form infinite images.
Interesting point,JP. The corollary of this is that if the Universe's age is not infinite, which seems to be the case, it can never become infinite, even though it may be boundless.
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:)
A new one to me, not bad either as we talk about 'SpaceTime'.
But it build on the premise that 'times arrow' disappear as entropy takes its toll.
And also on that there is no such concept as a 'time' without an arrow.
As if that was, then it doesn't really matter if we have an arrow or not. It will still be 'there', whatever that may be :)
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Xeno's paradox indeed, Bill.
However the paradox is not a paradox anymore.
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In practice, all you're really doing here is using the bounces to time the age of the universe, so if the universe's age isn't infinite, this won't form infinite images.
Interesting point,JP. The corollary of this is that if the Universe's age is not infinite, which seems to be the case, it can never become infinite, even though it may be boundless.
Unless the universe was infinite to begin with, which is apparently consistent with the big bang. (Don't ask me for proof, since I'm not a cosmologist.) The general idea I've read is that the universe could be hot and dense, but still infinite in size just after the big bang.
But in general, I think you're right that it isn't possible to build something infinite in size from a bunch of finite steps.
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JP, its a paradox in more than one way, what you are doing is to define 'discrete events' namely the 'light clock ticks'. Then you state that as soon there are 'discrete events' there can be no infinity.
That should mean that as soon we allow the concept of a 'discrete event' we disallow the concept of infinity. So either we have 'discrete events' or we have infinities, But we can't have both :)
Like it:)
It seems like a debate sailing up here ::))
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You're right, Yor_on. I think my original post was imprecise.
What I was trying to say is that you can't get an infinite set of things by a process that adds one object to the set at a time, when each step takes finite time and the universe is only 14 billion years old... This is a physical limitation, not a mathematical one. In this case, each bounce generates one more image, but each bounce takes finite time, so you can't generate infinite images in finite time.
You can certainly form an infinite set of things from discrete elements. For example, there are infinitely many natural numbers (i.e. 1,2,3,4,5,...), but these are clearly discrete elements. The trick is that I just constructed this set theoretically--in other words, I didn't physically list each number. If I tried to write out, or have a computer compute, each natural number, it would never finish since that would take infinite time.
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I know JP :)
It was just such an opportunity for a tease.
Not everyday one get a chance with you :)
Not that you don't have humor, far from it..
Eh..
That sounds?
A double negation?
Let me state this way. I know you have a humor..
Thank God.
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The Phantom Scientist vanishes into the abyss of silence once again
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You can certainly form an infinite set of things from discrete elements. For example, there are infinitely many natural numbers (i.e. 1,2,3,4,5,...), but these are clearly discrete elements.
Here comes the infinite series, again! [::)] You are right, of course, if you tried to write down, compute or do anything practical with these numbers you would never reach infinity. We can say that the natural numbers (etc.) are boundless; I just think its unfortunate that we use the word infinite, rather than boundless, in this context.