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Author Topic:   A definition of infinity?
JavaMan
Member (Idle past 2319 days)
Posts: 475
From: York, England
Joined: 08-05-2005


Message 27 of 41 (372514)
12-28-2006 7:39 AM
Reply to: Message 22 by Phat
12-27-2006 8:30 AM


Re: Forever and ever and ever
One thing I never figured out is how human minds (which are finite by definition) were able to quantify an infinite definition.
I'm not sure what 'quantify[ing] an infinite definition' means, but the origin of our notion of infinity is fairly commonplace, I think.
We observe that we can take any number and add one to it, and add one to that number, and so on without end. That gives us our notion of an infinite set of things.
And we observe that space extends in all directions as far as we can see. If we imagine ourselves at the edge of space, pushed up against the boundary, as it were, we can imagine that we could stretch out just a little further... And that gives us our notion of infinite extension.
And, just as with numbers, we can imagine adding another second to the time, and another second, and another without end, giving us our notion of infinite duration.
Is there anything more to it than that, do you think?

'I can't even fit all my wife's clothes into a suitcase for travelling. So you want me to believe we're going to put all of the planets and stars and everything into a sandwich bag?' - q3psycho on the Big Bang

This message is a reply to:
 Message 22 by Phat, posted 12-27-2006 8:30 AM Phat has not replied

Replies to this message:
 Message 31 by Casey Powell, posted 01-03-2007 6:03 PM JavaMan has replied

  
JavaMan
Member (Idle past 2319 days)
Posts: 475
From: York, England
Joined: 08-05-2005


Message 30 of 41 (373692)
01-02-2007 12:24 PM
Reply to: Message 28 by Son Goku
12-28-2006 9:15 AM


Re: Infinity and QM
An example would be:
I get 33.3% for path 1, 33.3% for path 2 and 66.6% for path three. However the maths says I have to subtract the last probability from the other two.
So I get a 33.3% + 33.3% - 66.6% = 0% chance of the particle arriving at point B. A result you never get at the classical scale. The more paths you have to a location never reduces your chance of getting there.
Could you explain this a little further? Classical probability is just a statistical thing: if path X has a probability of 0.2, all this means is that in 100 cases of the ball travelling from A to B, then the ball is likely to follow path X in 20 of them. What does the probability of 0.2 mean in the quantum case?

'I can't even fit all my wife's clothes into a suitcase for travelling. So you want me to believe we're going to put all of the planets and stars and everything into a sandwich bag?' - q3psycho on the Big Bang

This message is a reply to:
 Message 28 by Son Goku, posted 12-28-2006 9:15 AM Son Goku has not replied

  
JavaMan
Member (Idle past 2319 days)
Posts: 475
From: York, England
Joined: 08-05-2005


Message 32 of 41 (374333)
01-04-2007 8:10 AM
Reply to: Message 31 by Casey Powell
01-03-2007 6:03 PM


Re: Forever and ever and ever
Yup....how do we imagine an infinite being such as God for instance?
What is it you imagine?
Personally, my notion of God is rather vague. It's just what I've picked up from reading, and from Sunday School classes as a child. As I don't believe there is such a thing, I haven't explored my notion any further.

'I can't even fit all my wife's clothes into a suitcase for travelling. So you want me to believe we're going to put all of the planets and stars and everything into a sandwich bag?' - q3psycho on the Big Bang

This message is a reply to:
 Message 31 by Casey Powell, posted 01-03-2007 6:03 PM Casey Powell has not replied

  
JavaMan
Member (Idle past 2319 days)
Posts: 475
From: York, England
Joined: 08-05-2005


Message 38 of 41 (375280)
01-08-2007 8:55 AM
Reply to: Message 33 by Son Goku
01-04-2007 2:25 PM


Re: Measurement, paths and Zeno freezing.
Thanks for your explanation. I did have some further questions, but having read cavediver's response I realise they're rather pointless .
However, I would like to help in your attempt to explain the reality of Zeno freezing. So here's my five cents worth.
I guess most of us think we understand the first part of your description:
I will ... consider the case of an atom on its own which starts in a state of having a 50/50 chance of decaying or not decaying.
I'll write the quantum state of the atom in the following form:
(a,b)
Where:
a=current chance of being mesured as decayed.
b=current chance of being measured as not decayed.
So when we start off the atom is in the state (50,50).
I make a measurement to see if the atom decayed. Let's say I find the atom is not decayed, so the state right after measurement is:
(0,100)
Obviously, because I've measured it to be not decayed it has 100% of being not decayed when I measure it.
This doesn't look any different from the case of a tossed coin, having a 50/50 chance of being heads or tails before you've thrown it, and 100% probability of being one or the other once you've tossed it and taken a look. But your next sentence seems to have no analogy in a classical setting:
Then I leave my equipment and stop measuring the atom. Over time the probability returns to 50/50.
So over a time of about a tenth of a second, the following happens to the state of the particle:
(0,100) -> (10,90) -> (20,80) -> (30,70) -> (40,60) -> (50,50).
It sounds to the uninitiated as though the probabilities describe some property or properties of the atom, rather than being statistical effects as they would be in the case of a tossed coin. So my first question is:
Is the state (10,90) a real state of the atom? This question probably appears naive to you and cavediver, but I think understanding what you mean by the state (10,90) is kind of essential for us non-physicists.
P.S. What do you mean in your later post by 'Zeno freezing is an aspect of ... measurement acting as a projector down onto eigenkets'. That sounds like a beginning of an explanation. (Although I'm sure making me understand what an eigenket is will probably try your patience ).

'I can't even fit all my wife's clothes into a suitcase for travelling. So you want me to believe we're going to put all of the planets and stars and everything into a sandwich bag?' - q3psycho on the Big Bang

This message is a reply to:
 Message 33 by Son Goku, posted 01-04-2007 2:25 PM Son Goku has replied

Replies to this message:
 Message 39 by Son Goku, posted 01-08-2007 3:04 PM JavaMan has replied

  
JavaMan
Member (Idle past 2319 days)
Posts: 475
From: York, England
Joined: 08-05-2005


Message 40 of 41 (375598)
01-09-2007 8:15 AM
Reply to: Message 39 by Son Goku
01-08-2007 3:04 PM


Re: Measurement, paths and Zeno freezing.
Thanks, that was an excellent explanation - I think I understand so far . Now for some more questions:
1. The Zeno freezing pheneomenon seems to be dependent on there being a relatively slow transition from the measured (0,100) state back to a stable - but not measurable - (50,50) state. Why should there be a slow transition, why doesn't the state just jump back to (50,50) as soon as you stop measuring?
2. What's so special about the classical states? Are they special in the quantum system (does the quantum system somehow know to jump to those states under certain conditions?), or are they only special because the measuring is part of a non-quantum macro world (if that makes any sense :confused?
3. Would it be possible under any conditions to directly observe what you call 'generic quantum states'? Will they always be inaccessible to us?
4. My background is in chemistry, so my only knowledge of quantum mechanics is just the very basic stuff you need to understand emission and absorption spectra. Is what you are describing as eigenkets the same phenomenon we observe when we see electrons only ever emitting or absorbing specific quanta of energy? Are the energy levels effectively 'eigenkets' in the terminology you're using? Or is this some different quantum phenomenon?
Edited by JavaMan, : typo

'I can't even fit all my wife's clothes into a suitcase for travelling. So you want me to believe we're going to put all of the planets and stars and everything into a sandwich bag?' - q3psycho on the Big Bang

This message is a reply to:
 Message 39 by Son Goku, posted 01-08-2007 3:04 PM Son Goku has replied

Replies to this message:
 Message 41 by Son Goku, posted 01-10-2007 4:14 AM JavaMan has not replied

  
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