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 The Fabric of Reality List: The work of David Deutsch

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 1001 members
Re: Quantum Mechanical Probability
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 Probability itself is also a big Philosophical question of what it is or
really means in Physics anyway.And that before you get to QM.
There need to be explaination behind Probability it self beofore ywe
leave it Oh it just the likely hood of this or that?
Gordon.  Well yes, this is part of the point of FoR. The MWI gives physical
meaning to probability, and to counterfactuals as well (at least
physically possible counterfactuals).
 Gary
june.shippey@... wrote:> Probability itself is also a big Philosophical question of what it is or
> really means in Physics anyway.And that before you get to QM.
>
>
> There need to be explaination behind Probability it self beofore ywe
> leave it Oh it just the likely hood of this or that?  Gary Oberbrunner wrote:
well probability in QM is not primary as Deutsch point out in his paper.
as for Macro stuff and the Philosophy of Math of probability well that
still got alot of loose ends?
Gordon.>
> Well yes, this is part of the point of FoR. The MWI gives physical
> meaning to probability, and to counterfactuals as well (at least
> physically possible counterfactuals).
>
>  Gary
>
> june.shippey@... wrote:
> > Probability itself is also a big Philosophical question of what it is or
> > really means in Physics anyway.And that before you get to QM.
> >
> >
> > There need to be explaination behind Probability it self beofore ywe
> > leave it Oh it just the likely hood of this or that?
>
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/  Is this really right? I'm not convinced that MWI has anything very
useful to say if we try and figure out what we mean when we claim for
example: there is an 80% chance that Michael Schumacher will win the
next Grand Prix. If I have missed something, I would be delighted to be
enlightened.
Wade
> From: Gary Oberbrunner [mailto:garyo@...]
>
> Well yes, this is part of the point of FoR. The MWI gives physical
> meaning to probability, and to counterfactuals as well (at least
> physically possible counterfactuals).
>
>  Gary
>
> june.shippey@... wrote:
> > Probability itself is also a big Philosophical question of
> what it is
> > or really means in Physics anyway.And that before you get to QM.
> >
> >
> > There need to be explaination behind Probability it self
> beofore ywe
> > leave it Oh it just the likely hood of this or that?  I think you can restate that claim like this:
In 80% of the universes starting from our current universe*, M.S.
wins the next Grand Prix.
Does that help?
 Gary
*: by universe I really mean "fungible sheaf of universes" of course.
Wade Allsopp wrote:> Is this really right? I'm not convinced that MWI has anything very
> useful to say if we try and figure out what we mean when we claim for
> example: there is an 80% chance that Michael Schumacher will win the
> next Grand Prix. If I have missed something, I would be delighted to be
> enlightened.  I suppose some MWI'ers might claim that the statment "there is an 80%
chance that Michael Schumacher will win the next Grand Prix" means: if we
follow the evolution of our current slice of the multiverse, the collection
of subslices in which Michael Schumacher wins the next Grand Prix, has a
relative thickness of 80%.
However, such a view is based on an incorrect understanding of what we mean
when we talk about probability. Let me give an example. Suppose I throw a
die in the air and then I ask: what is the probability it will land as a 6.
The above interpretation of probability may well give an answer above 99%,
very close to 100%. The reason is that the die is very large, so it can in
theory be calculated how it will land. Quantum effects are unlikely to be
large enough to change the result of the calculation, hence the probability
according to the above view will be very near either 1 or 0.
The correct answer is, of course, 1/6.
At 03:53 PM 4102002 +0100, you wrote:>Is this really right? I'm not convinced that MWI has anything very
[Nontext portions of this message have been removed]
>useful to say if we try and figure out what we mean when we claim for
>example: there is an 80% chance that Michael Schumacher will win the
>next Grand Prix. If I have missed something, I would be delighted to be
>enlightened.
>
>Wade
>
>
> > From: Gary Oberbrunner [mailto:garyo@...]
>
> >
> > Well yes, this is part of the point of FoR. The MWI gives physical
> > meaning to probability, and to counterfactuals as well (at least
> > physically possible counterfactuals).
> >
> >  Gary
> >
> > june.shippey@... wrote:
> > > Probability itself is also a big Philosophical question of
> > what it is
> > > or really means in Physics anyway.And that before you get to QM.
> > >
> > >
> > > There need to be explaination behind Probability it self
> > beofore ywe
> > > leave it Oh it just the likely hood of this or that?
>
>
>
>
>
>
>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
 I'm afriad this still leaves me perplexed.
Firstly, how can we ever know or guess how many universes there out
there in which MS will or won't win?
Secondly I was under the impression that under the MWI view of the world
there were an invinite number of possible universes. If there are an
infinite number of universes where MS does win and an infinite number
where he does not, how can we get to the proportion of "MS Win"
universes? And what about the presumeably infinite number of universes
where say you or I win the Grand Prix ? I suspect it would be possible
to get pretty good odds that I won't win at any rate. Yet if one
imagines the world as a mass of electrons, quarks etc dansing around in
swerls of greater of lesser density, it seems kind of implausible that
there is a Schumacher "swerl of atoms" sitting around in Germany or
wherever which is on collision cause for winning the Grand Prix, when
there are so many billions of similarly complex "swerls of atoms"
scattered around the planet, which haven't got a snowball's chance no
hell of picking up the champers.
This is not to say that I have a better alternative vision of what
probability is all about, just that I cannot quite see how claiming that
in a certain percentages of universes MS wins, we are really throwing
much light on the mystery.
Wade
> From: Gary Oberbrunner [mailto:garyo@...]
>
> I think you can restate that claim like this:
> In 80% of the universes starting from our current universe*, M.S.
> wins the next Grand Prix.
>
> Does that help?
>
>  Gary
>
> *: by universe I really mean "fungible sheaf of universes" of course.
>
>
> Wade Allsopp wrote:
> > Is this really right? I'm not convinced that MWI has anything very
> > useful to say if we try and figure out what we mean when we
> claim for
> > example: there is an 80% chance that Michael Schumacher
> will win the
> > next Grand Prix. If I have missed something, I would be
> delighted to
> > be enlightened.
>  Henry Sturman wrote:
>
[Gordon]
> I suppose some MWI'ers might claim that the statment "there is an 80%
> chance that Michael Schumacher will win the next Grand Prix" means: if we
> follow the evolution of our current slice of the multiverse, the collection
> of subslices in which Michael Schumacher wins the next Grand Prix, has a
> relative thickness of 80%.
>
> However, such a view is based on an incorrect understanding of what we mean
> when we talk about probability. Let me give an example. Suppose I throw a
> die in the air and then I ask: what is the probability it will land as a 6.
> The above interpretation of probability may well give an answer above 99%,
> very close to 100%. The reason is that the die is very large, so it can in
> theory be calculated how it will land. Quantum effects are unlikely to be
> large enough to change the result of the calculation, hence the probability
> according to the above view will be very near either 1 or 0.
>
> The correct answer is, of course, 1/6.
>
> At 03:53 PM 4102002 +0100, you wrote:
> >Is this really right? I'm not convinced that MWI has anything very
> >useful to say if we try and figure out what we mean when we claim for
> >example: there is an 80% chance that Michael Schumacher will win the
> >next Grand Prix. If I have missed something, I would be delighted to be
> >enlightened.
> >
> >Wade
>
The probability I was refer too was closer to semi Classical or
Classical realm and not QM realm.  Henry, I think you're just not considering enough universes (IMHO).
There are two things we commonly call probability: those which are
uncertain due to true quantum uncertainty, and those which are uncertain
due to our incomplete or imperfect knowledge ("sensitive dependence on
initial conditions" is an example).
Both can easily be modeled using the same method, in the MWI: to take
your dice example, you just include all the initial universes which vary
from "ours" in the ways in which our knowledge is uncertain. So, for
instance, if you know the throwingforce is between 6 and 10 newtons,
you allow all such universes into the initial sheaf, and similarly for
universes in which the wind in the room is blowing the other way, and so on.
Then proceed as usual: examine all the outcomes in all universes (can
only be done "from outside" of course  we can't predict the future
from our singleuniverse vantage point) and bin the results. You'll of
course find each face of the die occurring with measure 1/6.
 Gary
Henry Sturman wrote:> I suppose some MWI'ers might claim that the statment "there is an 80%
> chance that Michael Schumacher will win the next Grand Prix" means: if we
> follow the evolution of our current slice of the multiverse, the collection
> of subslices in which Michael Schumacher wins the next Grand Prix, has a
> relative thickness of 80%.
>
> However, such a view is based on an incorrect understanding of what we mean
> when we talk about probability.  Wade Allsopp wrote:
> I'm afriad this still leaves me perplexed.
This has to be done from "outside" the multiverse; all we can do from
>
> Firstly, how can we ever know or guess how many universes there out
> there in which MS will or won't win?
any one universe is to guess the way we usually do; by experiment and
theory formation.
> Secondly I was under the impression that under the MWI view of the world
Yes there is an infinite number of universes, but using the concept of
> there were an invinite number of possible universes. If there are an
> infinite number of universes where MS does win and an infinite number
> where he does not, how can we get to the proportion of "MS Win"
> universes? And what about the presumeably infinite number of universes
> where say you or I win the Grand Prix ?
"measure" you can say that within that infinite set, there are many more
elements in which MS or some other competitor wins the GP than there are
in which you or I win. It's much like measuring the area of a curve by
integration. Even though there are infinitely many dArea elements, it's
still easy to compute the total, or in this case the fraction of the total.
Does that help at all?
 Gary  Well, yes. But I was describing how many MWI'ers would define probability,
and pointing out a problem with that. Indeed, your method is much better,
but it demonstrates that MWI is no longer of much help with these kinds of
complex event probabilities (e.g. the chance that Michael Schumacher will
win the next Grand Prix), since calculating such a probability now becomes
a mainly problem of what kind of knowledge we are assuming in relation to
the event.
In any case, for the time being, I think the odds out there on the the
sports betting market are the best indication of the values we should
assume for these kinds of probabilities :)
At 09:37 AM 7102002 0400, you wrote:>Henry, I think you're just not considering enough universes (IMHO).
[Nontext portions of this message have been removed]
>
>There are two things we commonly call probability: those which are
>uncertain due to true quantum uncertainty, and those which are uncertain
>due to our incomplete or imperfect knowledge ("sensitive dependence on
>initial conditions" is an example).
>
>Both can easily be modeled using the same method, in the MWI: to take
>your dice example, you just include all the initial universes which vary
>from "ours" in the ways in which our knowledge is uncertain. So, for
>instance, if you know the throwingforce is between 6 and 10 newtons,
>you allow all such universes into the initial sheaf, and similarly for
>universes in which the wind in the room is blowing the other way, and so on.
>
>Then proceed as usual: examine all the outcomes in all universes (can
>only be done "from outside" of course  we can't predict the future
>from our singleuniverse vantage point) and bin the results. You'll of
>course find each face of the die occurring with measure 1/6.
>
> Gary
>
>Henry Sturman wrote:
> > I suppose some MWI'ers might claim that the statment "there is an 80%
> > chance that Michael Schumacher will win the next Grand Prix" means: if we
> > follow the evolution of our current slice of the multiverse, the
> collection
> > of subslices in which Michael Schumacher wins the next Grand Prix, has a
> > relative thickness of 80%.
> >
> > However, such a view is based on an incorrect understanding of what we
> mean
> > when we talk about probability.
>
>
>
>
>
>
>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
 In a message dated 10/8/2002 2:19:51 AM GMT Daylight Time, henry@...
writes:
> Well, yes. But I was describing how many MWI'ers would define probability,
Has anyone *claimed* that the MWI will help decide the outcome of complex
> and pointing out a problem with that. Indeed, your method is much better,
> but it demonstrates that MWI is no longer of much help with these kinds of
> complex event probabilities (e.g. the chance that Michael Schumacher will
> win the next Grand Prix), since calculating such a probability now becomes
> a mainly problem of what kind of knowledge we are assuming in relation to
> the event.
events  at least any better than normal methods of prediction? As far as I
know the MWI (in DD's formulation at least) simply gives an explanation for
what we mean by quantum probability and uncertainty.
The only way in which the MWI appears to allow one to predict chance outcomes
is in the (rather contentious imho) "quantum suicide" / "quantum lottery" 
in which you can allegedly predict that you will win the lottery because all
versions of you which don't cease to exist. But that doesn't help us predict
who will win the Grand Prix in a branch of the multiverse in which we refrain
from such drastic measures.....
Charles
[Nontext portions of this message have been removed]  Gary Oberbrunner wrote:
>
I would have thought that this lefts the "theory" in a somewhat awkward
> This has to be done from "outside" the multiverse; all we can do from
> any one universe is to guess the way we usually do; by experiment and
> theory formation.
predicament. As by definition nothing can be "outside" a universe, the
concept is not even in principle applicable or testable.
>
Let me introduce another example, which I believe it would be difficult
> Yes there is an infinite number of universes, but using the
> concept of
> "measure" you can say that within that infinite set, there
> are many more
> elements in which MS or some other competitor wins the GP
> than there are
> in which you or I win.
to explain under your interpretation.
Suppose I am given a die but am told it is a loaded die, only I am left
to guess which number it is loaded in favour of. It seems to me that
from my perspective the probability of me rolling a "3" is still 1/6.
However as far as I can understand from your account, the probability
would either be signicantly greater than this or significantly less than
this depending on whether the die was loaded in favour of a "3" or some
other number.
I think what this type of example illustrates is that it is not possible
to give a satisfactory "realist" account of probability in the way you
have attempted, any more than it is possible to give say a realist
account of ethical values.
Wade Allsopp  Wade Allsopp wrote:
> Gary Oberbrunner wrote:
I agree with you here, mostly; no observer in a single universe can have
>
>>This has to be done from "outside" the multiverse; all we can do from
>>any one universe is to guess the way we usually do; by experiment and
>>theory formation.
>
> I would have thought that this lefts the "theory" in a somewhat awkward
> predicament. As by definition nothing can be "outside" a universe, the
> concept is not even in principle applicable or testable.
access to the entire multiverse, so this theory does not help such an
observer predict the outcomes of any experiment more accurately than any
other theory. What it does do is give a physical underpinning, an
*explanation*, of why probability should take the form it does, and why
it is possible for the multiverse to be deterministic while not allowing
any singleuniverse observer to predict the future. In this I think it
has no predicament.
> Let me introduce another example, which I believe it would be difficult
Again, this is a choice of pointofview. See my previous post. From
> to explain under your interpretation.
>
> Suppose I am given a die but am told it is a loaded die, only I am left
> to guess which number it is loaded in favour of. It seems to me that
> from my perspective the probability of me rolling a "3" is still 1/6.
> However as far as I can understand from your account, the probability
> would either be signicantly greater than this or significantly less than
> this depending on whether the die was loaded in favour of a "3" or some
> other number.
your perspective, when computing the probability, you must consider all
those universes in which the die was loaded toward any number of pips
(and there *are* such universes). From the dieloader's point of view,
he should only consider those universes in which the die is loaded as he
knows it was loaded.
This is really nothing other than a physicalization of the common
concept of conditional probability, P(ab) = P(a&b)/P(b). As I said
above, it does not improve our ability to predict the future, it simply
gives it a physical, noncounterfactual, basis.
 Gary > Yes there is an infinite number of universes, but using the concept
of
> "measure" you can say that within that infinite set, there are many
more
> elements in which MS or some other competitor wins the GP than
there are
> in which you or I win. It's much like measuring the area of a
curve by
> integration. Even though there are infinitely many dArea elements,
it's
> still easy to compute the total, or in this case the fraction of
the total.
>
Gary,
> Does that help at all?
>
>  Gary
this gives me the pretext to get into this discussion and throw in
a few doubts and questions ... thanks in advance for your time.
The reason why integration 'works' is that the actual area of each
dArea you mention 'tends to 0', and although there are an infinite
number of such areas, the "Sum over the dAreas for their number going
to infinity" converges to a finite number. This solves paradoxes
like Zeno's "The Turtle and Achilles" and many similar. Does this mean
that the actual Universes (in the MWI) have any feature that tends to
zero? In the MWI, what is the cardinality of the set of all
multiverses? I would dear suggesting 'numerable' (the cardinality
of N, the set of integral numbers 0, 1, 2, ....), as there can only
be a (incredibly large, but) finite number of particles in each
Universe, which can only 'trigger' an (even larger, but) finite
number of interactions...
Thanks.
Marco risus_abundat wrote:
> The reason why integration 'works' is that the actual area of each
Yes, the feature that tends to zero is the relative "thickness" of a
> dArea you mention 'tends to 0', and although there are an infinite
> number of such areas, the "Sum over the dAreas for their number going
> to infinity" converges to a finite number. ... Does this
> mean that the actual Universes (in the MWI) have any feature that
> tends to zero?
given slice of the multiverse, compared to another given slice.
A universe should as far as I understand it, be considered as a sheaf of
a large number, perhaps infinite, of identical (fungible) universes.
Any quantum event causes that sheaf to split into many now nonfungible
sheaves, each of which is "thinner" than the original; if the quantum
event is a proton decay at time t, e.g., then at time t+dt some fraction
of the original sheaf contains the decay products and some fraction
contains the original nondecayed proton. The relative thicknesses
still sum to 1. Then those can split into subslices and so on.
Now, can this splitting continue indefinitely? That bears on your next
question:
> In the MWI, what is the cardinality of the set of all
I assume you mean universes. This is, AFAIK, an open question. Some on
> multiverses?
this list have suggested that it is finite but very large, while others
say it has the same cardinality as the integers, while yet others I
think say even that is too small, and it must be at least aleph1.
I think what some folks argue is that if you keep on making thinner
universesheaf slices by quantum events happening, that eventually all
possible combinations of matter and momentum in the entire universe are
"populated" (if you think of each combination as a single cell in a huge
matrix) and any further splitting would just repeat cells. But I'm not
at all sure I agree with that. My current guess is that universes can
be put into 1:1 correspondence with the reals, but I can't prove it.
 Gary  In a message dated 10/15/2002 3:34:52 PM GMT Daylight Time,
risus_abundat@... writes:
> In the MWI, what is the cardinality of the set of all
I believe it's the same as the power of a continuum? (I.e. not numerable)
> multiverses? I would dear suggesting 'numerable' (the cardinality
> of N, the set of integral numbers 0, 1, 2, ....), as there can only
> be a (incredibly large, but) finite number of particles in each
> Universe, which can only 'trigger' an (even larger, but) finite
> number of interactions...
Charles
[Nontext portions of this message have been removed]   In FabricofReality@y..., PaintedDevil@a... wrote:
> I believe it's the same as the power of a continuum? (I.e. not
numerable)
>
Ok. But why? Normally, the trick used to 'handle' cardinality with
> Charles
infinity in mathematics is to prove that there is a 11
correspondance between set A and set B, where you know the
cardinality of set A. Otherwise, we could prove that such a 11
correspondence can not exist (leads to contradiction), which, despite
not acceptable for constructivist, could still be considered an
acceptable enough proof (reductio ad absurdum) just for the sake of
this discussion.... My argument for 'believing' the set of all
universes is at the very maximum numerable (N) is: 'this' universe
(the one of which we have or think to have direct knowledge of)
contains a finite number of particles (the unbelievably large 10^80
or similar sometimes we hear of). The number of particle interactions
between these particles is finite and if a universe 'splits' as a
result of an interaction (at any level), then we can only have a
finite number of 'splits', hence of universes. One observation here is
that we do not know how many 'other universes' exit 'already' (is the
Big Bang the origin of all these splits? Or is the Big Bang just a
'collision' between 'sheets'?). But then isn't it the case that,
because there is no way we can even theoretically have information
exchange between different universes, this is an issue which we will
never be able to solve?
Marco  In a message dated 10/15/2002 8:07:35 PM GMT Daylight Time, garyo@...
writes:
> I think what some folks argue is that if you keep on making thinner
If the SWE is accurate, the outcome of any quantum event is a continuum of
> universesheaf slices by quantum events happening, that eventually all
> possible combinations of matter and momentum in the entire universe are
> "populated" (if you think of each combination as a single cell in a huge
> matrix) and any further splitting would just repeat cells. But I'm not
> at all sure I agree with that. My current guess is that universes can
> be put into 1:1 correspondence with the reals, but I can't prove it.
>
>
possible states. Hence to cope with one quantum event the multiverse must
have the cardinality of a continuum. I believe this can scale up indefinitely
(to any number of quantum events, including a nondenumerable number of
them). If so the MV has the cardinality of a continuum, surely? Is that a 1:1
with the reals? (no if real numbers are expressible as one integer divided by
another, yes if Pi is a real number....I can't remember the definition)
Charles
[Nontext portions of this message have been removed]   In FabricofReality@y..., Gary Oberbrunner <garyo@g...> wrote:
> Yes, the feature that tends to zero is the relative "thickness" of
a
> given slice of the multiverse, compared to another given slice.
This reminds me of one of the most discussed issues in philosophy
>
about infinity: the distinction between "infinity in action" (ex. the
continuum of the points on a segment between 0 and 1) and "potential
infinity" (The numerable, N). In the first case the infinity is a
'fact': there *is* a (in this case nonnumerable) infinite number of
points between 0 and 1. But with N the matter differs a lot: you will
*never* see that infinity as a 'fact', for otherwise you should have
'seen' all numerals. You can draw a segment with an infinity of
points, but you will never be able to draw a segment with all
numerables.
It seems to me that our two examples (the integration of a curve and
the 'number' of universes) belong to two different cathegories: the
integration 'works' because it delas with 'infinity in action': you
actually can have an infinity of infinitesimal (approaching zero size)
dAreas whose 'sum' converges to a finite number (mind you: that is not
always the case: the area between x=0 and x=1 delimited by the curve
f(x)=1/x is not finite). But, as I understood from your argument,
the "relative thickness" of a slide 'becomes' thinner as universes
split: so those thickesses would tend to zero in a potentially
infinite amount of time: now those thickess are not zero size,
otherwise they could not get 'thinner'.
I can't help thinking that this 'MWI' and the 'slices' and 'sheets'
are beautiful but forced extrapolations of our mathematical models
about reality: we observe phenomena, we build models, we test them,
we find them successful in explaining a certain amount of other data
and then we jump to assuming that reality *is* that model. Sometimes
that has actually worked (and this is a reason for ecouraging these
speculations and welcoming the sceptics) like the extrapolation from
(if I remember correctly) De Broglie equation to the hypothesis of the
existence of antimatter. But most of the times it has not (ex. the
ether for electromagnetic propagation).
Marco  In a message dated 10/16/2002 2:01:54 PM GMT Daylight Time,
risus_abundat@... writes:
> Ok. But why? Normally, the trick used to 'handle' cardinality with
The short answer is: because the Schrodinger equation describes a continuous
> infinity in mathematics is to prove that there is a 11
> correspondance between set A and set B, where you know the
> cardinality of set A. Otherwise, we could prove that such a 11
> correspondence can not exist (leads to contradiction), which, despite
> not acceptable for constructivist, could still be considered an
> acceptable enough proof (reductio ad absurdum) just for the sake of
> this discussion.... My argument for 'believing' the set of all
> universes is at the very maximum numerable (N) is: 'this' universe
> (the one of which we have or think to have direct knowledge of)
> contains a finite number of particles (the unbelievably large 10^80
> or similar sometimes we hear of). The number of particle interactions
> between these particles is finite and if a universe 'splits' as a
> result of an interaction (at any level), then we can only have a
> finite number of 'splits', hence of universes. One observation here is
> that we do not know how many 'other universes' exit 'already' (is the
> Big Bang the origin of all these splits? Or is the Big Bang just a
> 'collision' between 'sheets'?). But then isn't it the case that,
> because there is no way we can even theoretically have information
> exchange between different universes, this is an issue which we will
> never be able to solve?
range of outcomes for any given situation. So *any* split will be into a
continuum of outcomes.
Charles
[Nontext portions of this message have been removed]  PaintedDevil@... wrote:
> The short answer is: because the Schrodinger equation describes a continuous
I guess that depends on quantization, right? If momentum is quantized,
> range of outcomes for any given situation. So *any* split will be into a
> continuum of outcomes.
>
> Charles
then an emitted photon can only take on 1 of N values, and if time is
quantized, then it can only be emitted at certain times. Another
question is whether position and/or angle are quantized, however. Those
may not be, in which case Charles' answer is correct.
 Gary  In a message dated 10/17/2002 7:13:15 PM GMT Daylight Time, garyo@...
writes:
> I guess that depends on quantization, right? If momentum is quantized,
I've got the impression that quantisation is a "local" feature which occurs
> then an emitted photon can only take on 1 of N values, and if time is
> quantized, then it can only be emitted at certain times. Another
> question is whether position and/or angle are quantized, however. Those
> may not be, in which case Charles' answer is correct.
>
>
within any branch of the multiverse but not the multiverse itself. But I may
be wrong...
Charles
[Nontext portions of this message have been removed]   In FabricofReality@y..., Gary Oberbrunner <garyo@g...> wrote:
> PaintedDevil@a... wrote:
Thanks to both of you. Of course. My mistake was to think of possible
outcomes of quantum interactions as in the famous examples "cat
dead/alive", or "radioactive atom decayed/not decayed", or "the
photon went through slit A or B", when I should have thought of
the "sum over all possible histories" that Feynman proposed. In this
case, I guess the question is "Is space quantized?", or "Can a photon
occupy any possible position?". So my next question for you: do you
think that any thing a part from energy is quantized? What about
position, time, ...? I would think mass is, as mass is energy.
Regards
Marco
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