Re: Omega Point theory and time quanta
Stathis Papaioannou writes: There has been some discussion in recent posts about Tipler's Omega Point theory, which postulates that an infinite amount of subjective time can be squeezed into the last few moments of a collapsing universe. This is straightforward mathematically using infinite series, but if time is quantised, it would not work in reality; and it seems to be widely accepted that time is indeed quantised. Is there a way around this difficulty? At http://www.sciam.com/askexpert_question.cfm?articleID=000A03B0-6000-1C71-9EB7809EC588F2D7 John Baez, a widely respected physicist, responds to the question, is time quantized: The brief answer to this question is, 'Nobody knows.' Certainly there is no experimental evidence in favor of such a minimal unit. On the other hand, there is no evidence against it, except that we have not yet found it. There are no well-worked-out physics theories incorporating a fundamental unit of time, and there are substantial obstacles to doing so in a way that is compatible with the principles of General Relativity. Recent work on a theory of quantum gravity in which gravity is represented using loops in space suggests that there might be a way to do something roughly along these lines--not involving a minimum unit of time but rather a minimum amount of area for any two-dimensional surface, a minimum volume for any three-dimensional region in space and perhaps also a minimum 'hypervolume' for any four-dimensional region of space-time. So I think it is an oversimplification to say that it is widely accepted that time is quantized. It is pretty clear that something strange must happen as we go to smaller and smaller time and distance scales, but nobody knows what. Tipler's Omega Point theory is basically a theory of general relativity and I don't think it incorporates quantum mechanics. So it has to be viewed as extremely speculative on that basis, although the same thing might be said of the Big Bang, or of discussion of black hole singularities, both of which involve infinities much like the Omega Point theory does. I'll tell you something else about the OP that most people don't know. Many people may think of the universal collapse as providing an energy source and/or effective time speedup which leads to this prediction that an infinity of calculating can be done. But this is not the case. With overwhelming probability, a natural Big Crunch will not allow for infinite calculations, rather only a finite amount of computation is possible. The only way to get an infinite amount of calculation is for the collapse to take a very special and peculiar form, in which the universe oscillates unstably from one extreme shape to another. Instead of collapsing as a nice little ball getting smaller and smaller, the universe has to stretch in first one direction, then another, ever more extensively. Such wild gyrations will not occur naturally, yet they are the only way for infinite calculations to occur. Only this will create the ever more extreme temperature variations that can drive ever-faster calculations. Tipler's idea is that life itself will take over control of the universe's collapse. Just as we may some day control the weather by predicting its course with extreme accuracy and modifying inputs to make it do what we want, so, Tipler theorizes, life could control the very shape of the universal collapse by measuring it, making short and long term predictions, and then making small modifications to the energy and matter under life's control in order to shape the path. Since the universal collapse is a chaotic system, as is the weather, it might theoretically be possible. Life's task will become ever more difficult as each oscillation of the collapse occurs. With each gyration, life must move more quickly and accurately to keep the universe on its path. A single slip-up anywhere along the line and the potential for infinite calculation is lost. And meanwhile the temperature is rising exponentially, threatening the physical stability of whatever substrate of mass and energy life has adopted to provide for continuity of existence. Oh, and I forgot to mention that life at one side of the universe can't communicate with life at the other side. Infinite computation may be possible but not infinite communication. The photons won't get there before the collapse occurs. So all of this delicate balancing act must be accomplished without any global communication, each part of the universe must act on faith that every other part is going to perform exactly those steps required to make the whole thing come together and work perfectly. All this is without any pre-arrangment beyond what we can accomplish in this era. We better get our acts together before we head out colonizing. Given these immense challenges, which increase in difficulty and complexity literally without limit, improbability piled upon impossibility, we can throw in the still-unknown
Re: Omega Point theory and time quanta
From: Stathis Papaioannou ...an infinite amount of subjective time can be squeezed into the last few moments of a collapsing universe This reminds me of a strange story I've learned long time ago. A dynamical system which passes through a succession of states, at constant time intervals, is a clock. Clocks measure times, and, coupled with other systems, can also measure the duration of a physical process. Clocks can also be used to control the duration of a process, or the evolution of a physical system. In this case if a clock has a good time resolution, there is some energy exchange between the clock and the controlled process, that is the evolution of the physical system under control. Both the evolution of the physical system and the clock are then perturbed, because when you include the clock mechanism in the Hamiltonian describing the quantum system to be observed, or to be controlled, you get this perturbation. If then a clock is too precise, a sort of quantum Zeno effect occurs - the evolution of the physical system under control may be even halted.
Re: Omega Point theory and time quanta
I thought that quantum theory (in all its flavours and interpretations) *does* imply that reality isdigital. For example, if light is quantised, then the light reflected from a real object will produce a pixelated image, albeit far more finely grained than the image on any computer screen. The Bekenstein Bound sets an upper limit to the amount of information that can be contained in a given volume, or a lower limit to how finely grained an object or its representation can be. Everything is digital; analogue is an illusion. Stathis Papaioannou From: Norman Samish [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: Omega Point theory and time quanta Date: Sat, 31 Jul 2004 22:22:01 -0700 Perhaps mathematics, which is digital, is incapable of precise simulation of reality, which is not digital. Norman Samish - Original Message - From: Stathis Papaioannou [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, July 31, 2004 9:36 PM Subject: Omega Point theory and time quanta There has been some discussion in recent posts about Tipler's Omega Point theory, which postulates that an infinite amount of subjective time can be squeezed into the last few moments of a collapsing universe. This is straightforward mathematically using infinite series, but if time is quantised, it would not work in reality; and it seems to be widely accepted that time is indeed quantised. Is there a way around this difficulty? Stathis Papaioannou _ Play Love Hunt to win a $9000 holiday and find love! http://mobilecentral.ninemsn.com.au/mclovehunt/lovehunt.aspx
Re: Omega Point theory and time quanta
Danny Mayes writes:
***
This is my understanding as well. Also, in regards to Hal's comments about
how unlikely the OP theory is, or how our universe does not appear likely to
collapse, even accepting these points if the OP computer is physically
possible it must occur under the MWI (somewhere in the multiverse), correct?
***
Yes, this is true, and I believe Tipler threw it in as an afterthought in
his book. The question arises, however, why would you bother with such an
elaborate mechanism for immortality as the OP theory if the MWI of QM is
correct? The MWI ensures immortality through an infinite number of possible
scenarios which collectively must be far more likely than Omega Point.
***
I'm sure everyone is familiar with the ancient philosophical argument that
time and space must be quantized, because if they were not you could never
get to a determined point in space or time given that the distance left to
travel could be infinitely divided in two...
***
Actually, I thing that this argument (Zeno) came about because the ancient
Greeks did not have any concept of an infinite series which converges to a
finite value. There is a related argument, however: if reality is analogue,
then any physical parameter would require an infinite number of
non-repeating decimal places to describe it exactly. This would mean that
what appears to be a finite system, such as an analogue voltmeter measuring
a voltage, actually contains an infinite amount of information, which is
absurd. Therefore, physical reality must be digital rather than analogue at
the finest level.
I am not sure where I first heard the above argument, and I am not sure
about the absurdity of an infinite amount of information being contained in
finite system.
Stathis Papaioannou
_
Discover the best of the best at MSN Luxury Living. http://lexus.msn.com/
---BeginMessage---
This is my understanding as well. Also, in regards to Hal's comments
about how unlikely the OP theory is, or how our universe does not
appear likely to collapse, even accepting these points if the OP
computer is physically possible it must occur under the MWI (somewhere
in the multiverse), correct?
I'm sure everyone is familiar with the ancient philosophical argument
that time and space must be quantized, because if they were not you
could never get to a determined point in space or time given that the
distance left to travel could be infinitely divided in two...
Stathis Papaioannou wrote:
I thought that
quantum theory (in all its flavours and interpretations) *does* imply
that reality is"digital". For example, if light is quantised, then the
light reflected from a real object will produce a pixelated image,
albeit far more finely grained than the image on any computer screen.
The Bekenstein Bound sets an upper limit to the amount of information
that can be contained in a given volume, or a lower limit to how finely
grained an object or its representation can be. Everything is digital;
analogue is an illusion.
Stathis Papaioannou
From: "Norman Samish"
[EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Omega Point theory and time quanta
Date: Sat, 31 Jul 2004 22:22:01 -0700
Perhaps mathematics, which is digital, is incapable of precise
simulation of
reality, which is not digital.
Norman Samish
- Original Message -
From: "Stathis Papaioannou" [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Saturday, July 31, 2004 9:36 PM
Subject: Omega Point theory and time quanta
There has been some discussion in recent posts about Tipler's Omega
Point
theory, which postulates that an infinite amount of subjective time can
be
squeezed into the last few moments of a collapsing universe. This is
straightforward mathematically using infinite series, but if time is
quantised, it would not work in reality; and it seems to be widely
accepted
that time is indeed quantised. Is there a way around this difficulty?
Stathis Papaioannou
_
Play Love Hunt to win a $9000 holiday and find love!
http://mobilecentral.ninemsn.com.au/mclovehunt/lovehunt.aspx
---End Message---
Omega Point theory and time quanta
There has been some discussion in recent posts about Tipler's Omega Point theory, which postulates that an infinite amount of subjective time can be squeezed into the last few moments of a collapsing universe. This is straightforward mathematically using infinite series, but if time is quantised, it would not work in reality; and it seems to be widely accepted that time is indeed quantised. Is there a way around this difficulty? Stathis Papaioannou _ Play Love Hunt to win a $9000 holiday and find love! http://mobilecentral.ninemsn.com.au/mclovehunt/lovehunt.aspx
Re: Omega Point theory and time quanta
Perhaps mathematics, which is digital, is incapable of precise simulation of reality, which is not digital. Norman Samish - Original Message - From: Stathis Papaioannou [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, July 31, 2004 9:36 PM Subject: Omega Point theory and time quanta There has been some discussion in recent posts about Tipler's Omega Point theory, which postulates that an infinite amount of subjective time can be squeezed into the last few moments of a collapsing universe. This is straightforward mathematically using infinite series, but if time is quantised, it would not work in reality; and it seems to be widely accepted that time is indeed quantised. Is there a way around this difficulty? Stathis Papaioannou
