> =20
> The responses I got (thanks by the way) were based entirely on the MWI =
> which said that the probability remained unchanged. However, in the =
> context of the WFCI I believe this question remains valid. In response =
I would agree that with the Wave Function Collapse Interpretation,
reverse time travel is paradoxical, just as it is in any single
history interpretation of reality.
> to Russell Standish's comments I wrote:
>
> Would the split
> > created by an event of uneven probabilities of outcome give rise to
> > identical universes? That is, a 2 to 1 event results in a three-way =
> split,
> > two of which are identical and will forever remain identical. If so, =
> what is
> > to determine that the split proceeds along the lowest common multiple, =
> i.e.
> > why not 4 & 2, or 6 & 3, or even 1 & 0.5 (whatever that means)?
>
>
> And his answer:
>
> That is not the way I look at it - a 2 to 1 event gives rise to two
> universes, one of which has twice the measure of the other. In fact
> most splits I believe are on a continuum, but we use the finite split
> case in discussion as it is easier to visualise.
>
> Your view of the 2 to 1 event splitting 3 ways, with 2 identical
> universes is really an equivalent way of looking at it when there are
> only a finite number of outcomes. I don't believe it is a useful
> picture when there is a continuum of outcomes.
>
> These answers do not seem so clear-cut to me, particularly as there =
> seems to have been so much confusion about what 'measure' is. =
The confusion about measure in this discussion group is confusion
about what 'measure of conciousness' might mean. Measure is a well
defined mathematical concept on structures called Banach
spaces. Quantum Mechanics is built on top of a Hilbert space, which is
a special case of a Banach space - therefore measure is quite well
defined. Quite what measure might mean for Max's Ensemble Theory is
another matter, as presumably the ensemble includes non-Banach spaces
as well.
> Furthermore, I do not understand the notion of 'splits on a continuum'. =
This is probably a matter of me being fast and loose with the
language. QM ordains an evolutionary operator (e^{iHt} - where H is
the Hamiltonian operator) which takes the state of the system at time
0 into the state at time t. (\psi(t)=e^{iHt}\psi(0)) The elementwise product
\psi(t)*\psi(t) denotes a probability distribution for what an
observer might see. If the operator corresponding to a particular
variable of interest has discrete eigenvalues, then the observer will
see a value \lambda with probability <e_\lambda,\psi(t)*\psi(t)>. This
corresponds to the case your are normally thinking of, of a Universe
splitting into a countable number of outcomes as a result of a
measurement at time t. However, if the operator has a continuous
spectrum (the classic, or archetypical case is asking the question of
where a particular electron is located) then the result of the
measurement can take on any value from a continuum. In this case,
there is a continuous infinity of different universes diverging from
that act of measurement.
> Either time is discrete (with the unit of Planck-length) or it is =
> infinitely divisible. If it is discrete, then the MWI seems to limit the =
> splitting process to once every Planck-length.
The splitting Universe is an effect of making a measurement. What
happens in between measurements is immaterial. One could argue that
conciousness measures the universe continuously, but I would doubt
that. It seems more likely that it is sampling reality at a rate of
around 10Hz (for humans). Even if there are other conciousnesses
around sampling at higher rates, it doesn't matter, as each
conciousness follows its own track through the multiverse. Whenever
two conciousnesses disagree about the value of a particular
observable, they find themselves irretrievably in different branches
of history.
This is the main gripe I have about the WFCI - in this case, two
conciousnesses could never disagree about a particular value.
However, it is reasonable =
> to suggest that there may be two totally different events occurring far =
> away from each other at the same time. Does this mean therefore that =
> there are multitude of universes springing up at every instant?
> How are simultaneous events integrated into the MWI? On the other hand, =
> if time is continuous we are faced with the possibility of an infinite =
> number of universes springing up at every instant - a daunting
> prospect. =
Since each observer follows an independent thread through the
multiverse, simultaneity of events is only defined by that
observer. Certainly, general relativity offers an explanation of what
is simultaneous to a particular local reference frame - esentially the
3D "light-cone".
> A third possibility which gets around these problems is that time is =
> indeed continuous but we define an instant as the time between the two =
> most closely separated events ever to occur. This will mean that no two =
> events can be simultaneous since we can proceed to the nth decimal place =
> along the measure of time to find a difference.=20
>
> Anyway, I've probably said enough for now.=20
> =20
>
>
>
>
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>
> <!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
> <HTML>
> <HEAD>
>
> <META content=3Dtext/html;charset=3Diso-8859-1 =
> http-equiv=3DContent-Type>
> <META content=3D'"MSHTML 4.72.2106.6"' name=3DGENERATOR>
> </HEAD>
> <BODY bgColor=3D#ffffff>
> <DIV> </DIV>
> <DIV>Let's try to establish a few cogent premisses. I realise you =
> probably won't=20
> agree with them all, but I'd be interested to know why:<BR>1]. =
> Consciousness is=20
> neither dependent upon nor implied by intelligence (a man with Downs' =
> syndrome=20
> is no less conscious than a genius).<BR>2]. Consciousness is neither =
> dependent=20
> upon nor implied by memory (a <FONT color=3D#000000 face=3DArial =
> size=3D2>man=20
> suffering from amnesia is no </FONT>less conscious than a man <FONT=20
> color=3D#000000 face=3DArial size=3D2>who remembers every detail of his=20
> life)</FONT>.<BR>3]. Consciousness is neither dependent upon nor implied =
> by=20
> knowledge (you cannot increase your consciousness through memorising the =
>
> Encyclopaedia Britannica).<BR></DIV>
> <DIV>4]. Consciousness is fundamentally a physical phenomenon since it =
> is=20
> clearly affected by physical processes (alcohol, injury, =
> sleeping).</DIV>
> <DIV> </DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2>I have been following =
> this discussion=20
> for a few days now and there seem to me to be some things which either I =
> simply=20
> haven't understood (quite possible - I confess I'm not a physicist =
> (yet)) or=20
> have not been addressed in the discussions.</FONT></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2></FONT> </DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2>Firstly, on the subject =
> of quantum=20
> suicide and what happens to your consciousness at the instant of the =
> terminal=20
> event. It seems to me this question is closely linked with the idea that =
> someone=20
> else raised about somehow proving the validity of the MWI. Topologically =
>
> speaking, if one can travel from one structure to another it would =
> suggest that=20
> the two structures are not only connected, but actually part of, or =
> existing=20
> within, the same thing. Hence, if it were possible to prove the =
> existence of=20
> another 'world' it would mean that it is not really another world at =
> all.=20
> Furthermore, I have considerable difficulty with the idea of an =
> uninterrupted=20
> 'flow' of consciousness. This invokes the idea of a massless entity =
> travelling=20
> between physical structures. While I am not averse to the notion of=20
> consciousness being without mass (it may for example be some form of =
> field=20
> generated by the brain) I fail to see how it can exist unchanged, even =
> for only=20
> a Planck-length of time, without the physical body that is generating =
> it.=20
> </FONT></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2></FONT> </DIV>
> <DIV><FONT face=3DArial size=3D2>And apart from the moment of death, =
> what happens at=20
> the moment of birth? More particularly, what happens at around the age =
> of two=20
> when human children become self-aware, an ability which I believe is =
> crucial to=20
> the notion of consciousness. Are we all dependent upon some version of =
> us dying=20
> in another world so that we can receive their consciousness? Is there =
> therefore=20
> a 'Conservation of consciousness' law? But there is not a single instant =
> at=20
> which a child suddenly realises to himself "Hey, here I am!" =
> It is a=20
> more gradual process than that. I must qualify my first three opening=20
> assumptions here by saying that though the properties listed may play a =
> part in=20
> creating a consciousness, they are not necessary to maintain it and =
> therefore=20
> consciousness is not defined by them. It's like climbing a flight of =
> stairs -=20
> once you reach the landing the stairs are no longer =
> relevant.</FONT></DIV>
> <DIV><FONT face=3DArial size=3D2></FONT> </DIV>
> <DIV><FONT face=3DArial size=3D2>On the subject of computers generating =
> random=20
> programs in the hope that among them there will be the seeds of =
> consciousness, I=20
> am reminded of an analogous proposition put forward by the physicist =
> George=20
> Ganong in his book "One, two three... infinity." He described =
> the=20
> construction of a printing press that, with its 50 mechanical wheels =
> each=20
> bearing all letters and symbols of the English language, would be set =
> the task=20
> of printing at random. Such a machine he said would ultimately print =
> everything=20
> that can be written - all history, all scientific discoveries, all human =
>
> thoughts, all literature. Among the unimaginable reams of nonsense would =
> lie the=20
> discoveries of the future and even, if it exists and be expressed in =
> words and=20
> symbols, the Theory of Everything. The problem of course is that of =
> shear=20
> numbers. He showed that even if every atom in the universe was a =
> printing press=20
> working at the speed of atomic vibrations, it would take vastly longer =
> than the=20
> age of our universe to gain anything useful from the experiment. This is =
> surely=20
> a prohibitive statistic for own experiment, particularly in view of the=20
> massively more complex nature of the brain. This is not to say that =
> artificial=20
> consciousness is non-realisable, only that we cannot hope to achieve it =
> through=20
> a purely random process. We must have some parameters to limit the flow =
> of=20
> nonsense and in order to do so we must have a better understanding of=20
> consciousness. </FONT></DIV>
> <DIV><FONT face=3DArial size=3D2></FONT> </DIV>
> <DIV><FONT face=3DArial size=3D2>I appreciate you guys might not have =
> the time or=20
> inclination to bring me fully up to speed on what I understand to be the =
> two=20
> main quantum theories concerning the outcome of an event, namely the =
> Many Worlds=20
> Interpretation and the Wave Function Collapse (or Copenhagen) =
> Interpretation.=20
> However, some time ago I asked :</FONT></DIV>
> <DIV><FONT face=3DArial size=3D2></FONT><FONT color=3D#000000 =
> face=3DArial=20
> size=3D2></FONT> </DIV>
> <DIV>
> <DIV><FONT face=3DArial size=3D2><EM>Two people make a bet based on the =
> toss of a=20
> coin while a third unobserved person looks on discretely from the =
> corner. The=20
> probability of heads or tails is fifty-fifty, 0.5. The coin lands heads, =
> one of=20
> them loses, fair enough.</FONT></EM></DIV>
> <DIV><FONT face=3DArial size=3D2><EM></FONT> </EM></DIV>
> <DIV><FONT face=3DArial size=3D2><EM>Having seen this, our voyeur steps =
> out of the=20
> room, gets in his time machine, and returns to witness the same event. =
> But what=20
> are the probabilities of heads and tails now? Are they still =
> fifty-fifty, or are=20
> they now 1 and 0 respectively?</FONT></EM></DIV>
> <DIV><EM></EM> </DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2><EM>This little =
> argument seems to=20
> pose 3 possible conclusions.</FONT></EM></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2><EM>1. Time travel is=20
> impossible</FONT></EM></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2><EM>2. Probability (and =
> therefore our=20
> human concept of free will) is an illusion (assuming of course, that =
> someone=20
> with a capital S is watching over the proceedings).</FONT></EM></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2><EM>3. There is a =
> fundamental flaw in=20
> this line of reasoning.</FONT></EM></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2></FONT> </DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2>The responses I got =
> (thanks by the=20
> way) were based entirely on the MWI which said that the probability =
> remained=20
> unchanged. However, in the context of the WFCI I believe this question =
> remains=20
> valid. In response to Russell Standish's comments I wrote:</FONT></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2></FONT> </DIV>
> <DIV><EM>Would the split<BR>> created by an event of uneven =
> probabilities of=20
> outcome give rise to<BR>> identical universes? That is, a 2 to 1 =
> event=20
> results in a three-way split,<BR>> two of which are identical and =
> will=20
> forever remain identical. If so, what is<BR>> to determine that the =
> split=20
> proceeds along the lowest common multiple, i.e.<BR>> why not 4 & =
> 2, or 6=20
> & 3, or even 1 & 0.5 (whatever that means)?<BR></EM></DIV>
> <DIV> </DIV>
> <DIV>And his answer:</DIV>
> <DIV><BR><EM>That is not the way I look at it - a 2 to 1 event gives =
> rise to=20
> two<BR>universes, one of which has twice the measure of the other. In=20
> fact<BR>most splits I believe are on a continuum, but we use the finite=20
> split<BR>case in discussion as it is easier to visualise.<BR><BR>Your =
> view of=20
> the 2 to 1 event splitting 3 ways, with 2 identical<BR>universes is =
> really an=20
> equivalent way of looking at it when there are<BR>only a finite number =
> of=20
> outcomes. I don't believe it is a useful<BR>picture when there is a =
> continuum of=20
> outcomes.</EM></DIV>
> <DIV><EM></EM> </DIV>
> <DIV>These answers do not seem so clear-cut to me, particularly as there =
> seems=20
> to have been so much confusion about what 'measure' is. Furthermore, I =
> do not=20
> understand the notion of 'splits on a continuum'. Either time is =
> discrete (with=20
> the unit of Planck-length) or it is infinitely divisible. If it is =
> discrete,=20
> then the MWI seems to limit the splitting process to once every =
> Planck-length.=20
> However, it is reasonable to suggest that there may be two totally =
> different=20
> events occurring far away from each other <U>at the same time.</U> Does =
> this=20
> mean therefore that there are multitude of universes springing up at =
> every=20
> instant?<BR> How are simultaneous events integrated into the MWI? =
> On the=20
> other hand, if time is continuous we are faced with the possibility of =
> an=20
> infinite number of universes springing up at every instant - a daunting=20
> prospect. A third possibility which gets around these problems is that =
> time is=20
> indeed continuous but we define an instant as the time between the two =
> most=20
> closely separated events ever to occur. This will mean that no two =
> events can be=20
> simultaneous since we can proceed to the nth decimal place along the =
> measure of=20
> time to find a difference. </DIV>
> <DIV> </DIV>
> <DIV>Anyway, I've probably said enough for now. </DIV></DIV>
> <DIV><FONT color=3D#000000 face=3DArial size=3D2> =20
> </FONT><BR><BR><BR></DIV></BODY></HTML>
>
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>
>
----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 7123
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
----------------------------------------------------------------------------
Received on Sun Jan 31 1999 - 20:57:14 PST