It was my understanding that the hidden-variable thing had
been pretty well disposed of a long time ago.
http://en.wikipedia.org/wiki/Hidden_variable_theory
Of course, I suppose it could be like the gods. We don't
see any, but there might be one under the bed when we're
not looking. Same with hidden variables, I imagine.
A hidden variable is the only possibility in QM. If there is nothing
there then there is no outcome. If there is something there then it is
hidden.
................
>> It was my understanding that the hidden-variable thing had
>> been pretty well disposed of a long time ago.
>> http://en.wikipedia.org/wiki/Hidden_variable_theory
The hidden variable theory is not compatible with the properties
of the wave function usually used in quantum mechanics.
>> Of course, I suppose it could be like the gods. We don't
>> see any, but there might be one under the bed when we're
>> not looking. Same with hidden variables, I imagine.
>A hidden variable is the only possibility in QM. If there is nothing
>there then there is no outcome. If there is something there then it is
>hidden.
Observed outcomes behave like probability. If hidden variables
would explain the situation, there would be a joint distribution
of position and momentum. It is easy to give examples where
this joint distribution does not exist, since probabilities have
to be non-negative.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
As has Galilean Relativity and Young Earth Creationism.
But that doesn't stop nutters from posting about
any of them.
-jc
Then you assert that appearance itself has degrees of appearance. I
already said that this was not an adequate response.
> If hidden variables
> would explain the situation, there would be a joint distribution
> of position and momentum. It is easy to give examples where
> this joint distribution does not exist, since probabilities have
> to be non-negative.
If position and momentum are not players on the field, then how does one
assert something?
>
> If position and momentum are not players on the field, then how does one
> assert something?
One normally asserts something in words.
If you have a better way, please let us in on it.
I'm fascinated by JJ's ability to elicit responses with his language
which closely approaches quantum randomness. However, there is a
reasonable underlying language/philosophical question.
We believe that there is no cause that can effect the lifetime of the
decay of a particle. So it seems to me that we could attribute a label
of 'hidden variable' to that information itself. IOW, while we do not
claim a cause, we could argue that the lifetime could as easily be
*determined* at the instant of creation of the particle as at the
instant of decay. So there would be a piece of information about the
particle which is inaccessible rather than non-existent.
-tg
> If you want to claim it's not so you then need to explain the
> result of various experiment. Experiments that you've clearly
> never heard of...
>
> >But ponder this...wasn't the scientific term "random"
> >invented to support a verbal fantasy world created by the quantum
> >physicists? It's understandable. After all, every discipline, including
> >maths, likes to have its own non-religious menagerie of supernatural
> >objects and processes, where infinities abound far beyond the mortal
> >realms of grammar and sense.
>
> David C. Ullrich
>
> "Understanding Godel isn't about following his formal proof.
> That would make a mockery of everything Godel was up to."
> (John Jones, "My talk about Godel to the post-grads."
> in sci.logic.)
But without position and momentum there is nothing substantial to assert.
> I'm fascinated by JJ's ability to elicit responses
> with his language which closely approaches quantum
> randomness. However, there is a reasonable underlying
> language/philosophical question.
I agree that these questions about quantum randomness
and others like them are reasonable. But the program of
consulting our intuition about their answers has expired,
has ceased to be: it is an ex-program.
The assumptions of Bell's Theorem are that the
outcome of a quantum measurement is (i) determined
by properties of the particle and apparatus
(whether or not we can measure the properties
themselves), and (ii) /not/ affected by anything
that happens at some arbitrarily large distance
(which are often abbreviated as "local reality"
and may, for many purposes, be referred to as
"our intuition").
The theorem puts a limit on how strongly correlated
certain pairs of widely separated measurements
can be. Quantum mechanics claims that some of these
measurements will break those limits. It turns out
experimentally that quantum mechanics is right and
"local reality" (AKA "our intuition") is wrong.
> We believe that there is no cause that can effect
> the lifetime of the decay of a particle. So it seems
> to me that we could attribute a label of
> 'hidden variable' to that information itself. IOW,
> while we do not claim a cause, we could argue that
> the lifetime could as easily be *determined* at the
> instant of creation of the particle as at the instant
> of decay. So there would be a piece of information
> about the particle which is inaccessible rather than
> non-existent.
I'm afraid I don't find your description of this
whatever-it-is (that does not cause the particle's
decay but does determine it) to be very coherent.
If the time of the decay of the particle is a function
of this 'hidden variable', then the conditions
of Bell's Theorem are met and there is a limit on
correlations between widely separated measurements
which is at least sometimes broken by our measurements.
I take this to mean that there is, in fact, no such
hidden variable, whether or not we can access it.
Someone might object that we don't know that the
results of the intuition-destroying experiments
apply to decaying atoms as well as pairs of
gamma rays. Personally, I find experimental
results that dodge our constraints but only
when we can't see them doing so to be considerably
less intuitive than the loss of local reality.
Perhaps a better answer would be to point out
that the way physics proceeds, the way science
proceeds is to generalize alleged laws to the
utmost extent ("Energy is conserved everywhere
in the universe.") and then wait for contradictions
to pour in from the experimentalists. ("But, wait!
I've got some radium that behaves very oddly.")
Is there some contradiction, some troubling
experimental result that makes it necessary to
suppose there is this 'hidden variable'?
Jim Burns
http://en.wikipedia.org/wiki/Bell%27s_theorem#Importance_of_the_theorem
I question this: you yourself take a position, and you
post so much as to have a certain momentum, and yet
you still have nothing substantial to assert.
Marshall
The idea of a hidden variable is a grammatical consequence of any
quantum theory, as I argued.
That's obviously bullshit. If attempting to use a word in more than
one way were to be any impediment to meaning, then nothing
would mean anything. Every word is used more than one way;
some words are used dozens if not hundreds of different ways.
Hell, *every* field of human endeavor uses everyday terms
in idiomatic ways.
The closest true thing to what you wrote above is that if one
enters a new field, one has to learn the field-specific meanings
for its terms, and that can confuse the ignorant and the
indolent. (Since you're both, this is a particularly heavy
burden in your case.)
Bleah, I'm replying seriously to a troll; I need to go
wash my hands.
Marshall
I wrote rather quickly but I thought it was understandable; let me try
again:
1) I do not claim that something causes the particle's decay.
2) That nothing causes the particle's decay does not mean that the
lifetime is not determined at the creation of the particle. By
determined I only mean that it is inevitable, that there is nothing
that can change it.
3) If you believe that this would violate QM, then you should be able
to describe a hypothetical experiment whose outcome would be different
if my proposed conjecture is incorrect.
It seems to me that the best argument against what I am suggesting is
that it is not parsimonious, but I'm not even sure that such a
position holds up. As I said in the first place, this is a question
of language and philosophy, not physics. I find the use of decay as
the knee-jerk example to explain randomness to be facile.
-tg
There's a video of John Bell giving a talk archived
at iop.org:
< http://download.iop.org/john-bell-lecture.wmv > .
David Bernier
Here is my understanding of /randomness/: the outcome of
an experiment (like rolling a die) is /random/ if, in all
the possible worlds that are /identical/, there is more
than one outcome (more than one face lands up). By
/identical/ I mean that /everything we know/ about
all the causal paths leading to our experimental
outcome is the same in each possible world.
My understanding of /quantum randomness/ is that we
consider all the possible worlds where /everything/
is identical, instead of /everything we know/, but
there is still more than one outcome of the experiment.
I see two interpretations that you might intend (and
a third option -- that I just don't get it).
(1) If we draw a box around the space-time just before
the decay of the atom, we can look at all the possible
worlds where the contents of the box is identical.
Because the decay of the atom has quantum randomness,
there are still different times of decay for the atom
in different possible worlds. HOWEVER, if we, in our
imaginations, mark the time of the decay on the box
(our hidden variable -- hidden because it plays no
part in the physics, being imaginary), then we can
further subdivide the possible worlds so that boxes
marked with the same time are grouped together.
Presto! The outcome is no longer random, because
these groups of possible worlds all have single outcomes
(the atom decays at the same time in each possible
world -- /within each subgroup/, that is).
Under this view, I suppose there is no quantum
randomness, but there is no randomness either,
nor any probability except 0 and 100%. There are no
uncertain outcomes because every outcome will be what
it will be, tautologically. I don't know, but this
view may be logically consistent, but it seems to
me completely useless. It certainly isn't physics.
(2) We have almost the same situation as before:
a box around the space-time just before the decay
of the atom, a collection of all the possible worlds
where the contents are identical. Except that, under
this view, in stead of marking the time of decay
on the outside of the box, it's placed inside the
box, inside a lockbox, let us say, so that we know
it can't be used in the processes leading to the outcome.
I think this might qualify as a physical theory,
but this is also the sort of situation that
Bell's theorem applies to. It doesn't matter that
the decay time written inside the lockbox does
not participate. The theorem does not ask whether
a particular parameter /participates/, just as the
theorem does not ask whether /we know the value of/ a
particular parameter.
> 3) If you believe that this would violate QM,
> then you should be able to describe a hypothetical
> experiment whose outcome would be different
> if my proposed conjecture is incorrect.
I think the experimental verification of quantum mechanics
over local reality are what you are asking for. If you
are considering scenario 2 above, then you are trying
to fix local reality by partitioning the possible worlds
finely enough that the outcome appears non-random.
I don't think local reality is fixable.
> It seems to me that the best argument against
> what I am suggesting is that it is not parsimonious,
> but I'm not even sure that such a position holds up.
> As I said in the first place, this is a question
> of language and philosophy, not physics. I find
> the use of decay as the knee-jerk example to explain
> randomness to be facile.
If what you describe is only a question of
language and philosophy, then maybe my first
interpretation is the correct one. If that is so,
then the point you are making is that it is
possible to change the meaning of
"quantum randomness" so that what you have
turned it into does not exist.
I don't find that a very interesting point.
Jim Burns
Yeah, option 3, and I also think you have been over-consuming
caffeinated beverages or something. I always wonder about people who
can't read through a couple of short paragraphs before rambling on
with a reply that is nowhere near the point.
-tg
Alas, the universe disagrees.
Haiku Jones
All-righty, then. I'll give you the Reader's Digest version
below.
And here is the executive summary of the Reader's Digest version:
You're wrong.
Jim Burns
I wrote:
> tg wrote:
>
>> I'm fascinated by JJ's ability to elicit responses
>> with his language which closely approaches quantum
>> randomness. However, there is a reasonable underlying
>> language/philosophical question.
>
> I agree that these questions about quantum randomness
> and others like them are reasonable. But the program of
> consulting our intuition about their answers has expired,
> has ceased to be: it is an ex-program.
> http://en.wikipedia.org/wiki/Bell%27s_theorem#Importance_of_the_theorem
Makes my point. You can't make a clear statement of what I'm wrong
*about*, so you either throw up a lot of chaff and do a lot of hand-
waving, or do the indignation dodge.
If someone can describe an experiment to test my proposed conjecture,
I'm listening.
-tg
>>>http://en.wikipedia.org/wiki/Bell%27s_theorem#Importance_of_the_theorem
................
Many have tried to come up with a good answer. I gave a
simple counterexample to the possibility of a joint distribution
more than 50 years ago; all one has to do is to consider the
wave function of one of them as constant on a finite interval.
This lack of a joint distribution is a problem in understanding,
but not a problem in computation.
A similar problem is that of the multi-slit experiment. If one
knows which slit, the distribution is totally unlike the very
useful observed distribution.
sure wish, someone'd bury that stinky cat of Schoredinger
('s joke .-)
> > > Perhaps a better answer would be to point out
> > > that the way physics proceeds, the way science
> > > proceeds is to generalize alleged laws to the
> > > utmost extent ("Energy is conserved everywhere
> > > in the universe.") and then wait for contradictions
> > > to pour in from the experimentalists. ("But, wait!
> > > I've got some radium that behaves very oddly.")
> > > Is there some contradiction, some troubling
> > > experimental result that makes it necessary to
> > > suppose there is this 'hidden variable'?
> > >http://en.wikipedia.org/wiki/Bell%27s_theorem#Importance_of_the_theorem
> > The idea of a hidden variable is a grammatical consequence of any
> > quantum theory, as I argued.
> Alas, the universe disagrees.
thus:
saw the latest rendition of Rubik's Hexahedron at a store;
it is just a vari-colored light in the center of each face,
which apparently uses an acceleraometer to orient itself
(with respect to thee .-)
> Let me try a ring rotating around the equator(XY plane)at
> 360 degs/t and a 2nd ring rotating (pole to pole, XZ plane)
> at 180 degs/t, then the *ratio* of the rings rates of
> rotation is 2:1 and no CS transformation can change that
> ratio.
thus:
nice, constructive analysis;
wouldn't an approach via the Fermat point
of a trigon, be useful?
(L'Ouvre: http://wlym.com .-)
> In terms of convex hulls we are finding the largest line segment contained
> in it and then finding the midpoint of the line segment perpendicular to the
> largest line segment that runs through the largest line segment's midpoint.
--Cap'n Trade & Warren Buffet, together again?
Rep. Waxman's God-am bill, doesn't institute a tarrif, instead!
zzzzzz..........
>>>If someone can describe an experiment to test my proposed conjecture,
>>>I'm listening.
>>
>> >>>http://en.wikipedia.org/wiki/Bell%27s_theorem#Importance_of_the_theorem
> zzzzzz..........
You don't like that answer either?
Here's what you should do:
Keep asking the same question the same way over and over,
and insulting anyone who tries to answer you.
That way, when no one bothers to continue their exchange
with you, you will have proven that you're right.
Or...
If you aren't a troll (and just an asshole, but with
a serious question), consider what I spent the last couple
hours of my weekend writing for you to be a serious
attempt to answer your question. Find it again.
Read it. Respond to it. Maybe I'll answer back.
By the way, that long post was my attempt to clarify
the language we were using. Aren't you posting from
alt.philosophy? Shouldn't that be meat and drink for you?
That post was my attempt to re-ask your question,
but without talking about "causes". Without that,
your question devolves to the original Bell's theorem
situation (or isn't physics, depending upon what
you mean).
Quantum mechanics doesn't actually use language like
"A causes B". It will say "In the case where A is true,
B will happen with probability P." That is all.
If you want to do something un-troll-like, why not
re-ask your question in those terms? Keep in mind
the constraints of local reality -- which does /not/
constrain QM, but if you do go outside those boundaries,
you are implicitly accepting the anti-intuitive,
nonclassical aspects of QM anyway.
As for your request for a specific experiment showing
that what you propose doesn't happen, I dealt with that
in the last two paragraphs of my first response to you.
Jim Burns
Obviously not.
Since you are so familiar with the language of
QM, why don't you propose how we can make the statement, in your form,
about decay:
"in the case where ................ is true, the particle will decay
at time t with probability P."
-tg
> Jim Burns
Obviously not what?
> Since you are so familiar with the language of
> QM, why don't you propose how we can make the statement,
> in your form, about decay:
>
> "in the case where ................ is true, the particle
> will decay at time t with probability P."
I don't know what you're getting at here. How is this related
to your proposed scheme of introducing a hidden variable?
I will answer your question anyway: The sentence you have
is already in the form that I said QM uses. The "........."
would be a description of the quantum state that the atom's
nucleus is in, very often the ground state, and the second
clause would give some probability per unit time. If there
is more than one way for the atom to decay, then each mode
of decay will have its own probability per unit time.
This is not the sort of situation which we can use to
test local reality vs. quantum mechanics using Bell's
theorem. Those situations involve entangled pairs of
particles being measured at macroscopically separated
locations. However, I have already explained once why
the collapse of local reality in those other situations
is still bad news for local reality in this situation.
If you meant "Why don't you, Jim, translate my problem
into quantum mechanics for me", then, no, thank you.
I decline the honor.
That was what I was trying to do Sunday night, but I have
heard since then that my attempts were just a cover
for my ignorance. I'm sure you can do a much better job
than I could.
Jim Burns
****
> This is not the sort of situation which we can use to
> test local reality vs. quantum mechanics using Bell's
> theorem.
Very good.
> Those situations involve entangled pairs of
> particles being measured at macroscopically separated
> locations. However, I have already explained once why
> the collapse of local reality in those other situations
> is still bad news for local reality in this situation.
No, I don't think so. 'Bad news' is not a sufficient characterization
in science or philosophy.
>
> If you meant "Why don't you, Jim, translate my problem
> into quantum mechanics for me",
> then, no, thank you.
> I decline the honor.
>
But I thought that's what you just did---you translated my problem
into the language of QM, which I appreciate. We are not looking for
equations here but clear language and reasoning, so we can consider
the philosophical implications, if any. You have framed this
situation as follows:
*The lifetime of the particle is dependent on its quantum state.*
If that's correct, then we have a variable that determines the
lifetime of the particle, correct?
-tg
> That was what I was trying to do Sunday night, but I have
> heard since then that my attempts were just a cover
> for my ignorance. I'm sure you can do a much better job
> than I could.
>
What I'm good at is listening to people who ask questions, rather than
trying to dazzle them with my book-larnin'. Sometimes that enables me
to give them an answer that is useful to them.
-tg
> Jim Burns
HEY!!!
OVER HERE!!!
Obviously not what?
(Here's a clue: If I have to ask this question,
whatever it is /might/, just /possibly/ not be
as obvious to me as it is to you.)
> Since you are so familiar with the language of
> QM, why don't you propose how we can make the statement, in your form,
> about decay:
>
> "in the case where ................ is true, the particle will decay
> at time t with probability P."
>
> -tg
>
>
>
>
>>Jim Burns
>
>
Which post are you answering?
-tg
What, people don't speak informally in philosophy,
expecting others to fill in the formalities for themselves?
How odd. They certainly do in the sciences.
The bad news is that you cannot assume the constraints
of local reality will hold for a decaying atom, because
they have been shown not to hold for entangled pairs of
particles.
My original justification for extending the implications
of Bell's theorem from entangled pairs of particles to
individual decaying atoms was that this is just how science
works. We generalize to the greatest extent we can when
we theorize, and then use the contradictions from
experiment to drive the next cycle of theorizing.
The maximal generalizing is important because we /want/
contradictions -- or "new" contradictions, at least.
An argument could be made that, if we are not getting
contradictions of theory from our experiments, then we
are not learning anything we didn't already know.
I suppose maximal generalization is "merely" a
methodological concern, but that methodology is more firmly
embedded in the sciences than any theory you could name.
However, it occurs to me that I'm holding this thing the
wrong way around. The tests of various Bell inequalities
do not /validate/ any particular theory. What they do
is /invalidate/ the entire class of hidden-variable theories.
You think that you may have a hidden-variable
theory that side-steps the usual Bell-centric issues.
It's /your/ theory, so /you/ get to explain what the
difference is between decaying atoms and entangled
pairs of particles. Your theory seems to be "Let's
hide the outcome of the quantum measurement (the time
of decay of the atom) somewhere inside the atom
and let that determine the time of decay." How does
this generalize to spin measurements of entangled particles?
The obvious way is to say all quantum measurement
outcomes are somewhere in the quantum system, but
then the predictions for entangled pairs will be
bounded by Bell's theorem and definitely inconsistent
with experiment. Do you refuse to generalize? Then
you must explain why your theory applies in one place
and not another. This is /required/ for what you might
consider methodological reasons: if researchers cannot
answer questions like that from your description of
your new theory, then they will have to seek you out
and ask "Does it apply here?" every time they find
themselves in a novel situation. This is unworkable.
[...]
> But I thought that's what you just did---you
> translated my problem into the language of QM,
> which I appreciate. We are not looking for
> equations here but clear language and reasoning,
> so we can consider the philosophical implications,
> if any. You have framed this situation as follows:
>
> *The lifetime of the particle is dependent on its
> quantum state.*
>
> If that's correct, then we have a variable that
> determines the lifetime of the particle, correct?
I would agree with the starred statement, but I want to
be sure you mean the same thing by "lifetime" as I do.
The lifetime I am talking about is NOT how long any
particular atom lives, from creation to decay.
It is a parameter for a probability distribution
that permits us to calculate the probability of a
certain number of these atoms decaying with a
certain period of time, or the probability of
one particular atom decaying within a certain period
of time, or many other things. But it will not give
a guarantee of the time the atom will decay.
I confess, I do not see the connection to your
original idea.
Jim Burns
I was returning to the second-to-last post you made
(now the third-to-last post), in order to ask you again
what "Obviously not." refers to. I pointed my post
at your last post, because I thought it would be easier
for you to see there.
Am I beating a dead horse? That's hard to say.
If we were moving along, smoothly understanding each
other, then it might make more sense to just shrug
it off. But we aren't. (I hope we can agree on that,
at least.)
Third time: Obviously not WHAT?
Jim Burns
Does that merit a woof? I don't think so.
"Joint distribution" needs to say more than what the technical or
immediately semantically available implies.
What I am saying is that this term needs sounding out. You must provide
it with a foundation, just as I provided a foundation for my own
observations.
It's obviously NOT. It's self-evident. Look at it! am I talking to Mr.
stupido? If you describe something in non-meaningful terms then it is
meaningfully vacuous. Comprende?
> If attempting to use a word in more than
> one way were to be any impediment to meaning, then nothing
> would mean anything. Every word is used more than one way;
No. So far wrong it's a long time getting back.
A word is a sign. The sign does not have a meaning. The meaning we
'give' the sign is nothing that the sign displays to us.
> some words are used dozens if not hundreds of different ways.
> Hell, *every* field of human endeavor uses everyday terms
> in idiomatic ways.
>
> The closest true thing to what you wrote above is that if one
> enters a new field, one has to learn the field-specific meanings
> for its terms, and that can confuse the ignorant and the
> indolent. (Since you're both, this is a particularly heavy
> burden in your case.)
>
> Bleah, I'm replying seriously to a troll; I need to go
> wash my hands.
>
>
> Marshall
And how many on the other side feel sick?
Fine. Oh great. I'll tell my mum.
YOu never read the original post did you.
>Marshall wrote:
>> On Nov 15, 11:45 am, John Jones <jonescard...@btinternet.com> wrote:
>>> Quantum mechanics employs everyday terms to support its mathematical
>>> structure. My complaint, a valid one, is that these terms are no longer
>>> employed with their standard meanings, thus making Quantum theory
>>> meaningfully vacuous.
>>
>> That's obviously bullshit.
>
>It's obviously NOT. It's self-evident. Look at it! am I talking to Mr.
>stupido? If you describe something in non-meaningful terms then it is
>meaningfully vacuous. Comprende?
Sometimes you seem stupid. "no longer employed with their
standard meanings" is not the same as "non-meaningful".
>
>> If attempting to use a word in more than
>> one way were to be any impediment to meaning, then nothing
>> would mean anything. Every word is used more than one way;
>
>No. So far wrong it's a long time getting back.
>A word is a sign. The sign does not have a meaning. The meaning we
>'give' the sign is nothing that the sign displays to us.
>
>
>> some words are used dozens if not hundreds of different ways.
>> Hell, *every* field of human endeavor uses everyday terms
>> in idiomatic ways.
>>
>> The closest true thing to what you wrote above is that if one
>> enters a new field, one has to learn the field-specific meanings
>> for its terms, and that can confuse the ignorant and the
>> indolent. (Since you're both, this is a particularly heavy
>> burden in your case.)
>>
>> Bleah, I'm replying seriously to a troll; I need to go
>> wash my hands.
>>
>>
>> Marshall
>
>And how many on the other side feel sick?
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
It obviously is. If I use the noun "set", it can mean
one thing to a mathematician, another thing to
a tennis pro, a third to a theatrical designer,
and a fourth to a dog breeder. None of
these is "meaningfully vacuous", you just have
to derive the current meaning from the current
context -- something speakers of English do
all day long, generally effortlessly, unless they
happen to wander into an area in which they
are technically ignorant.
Haiku Jones
> > Alas, the universe disagrees.
>
>
> Fine. Oh great. I'll tell my mum.
Better yet, write it up for _Annalen der Physik_.
Convince the readers of that rag, and there's
a Nobel Prize in it for you. Guaranteed.
Haiku Jones
Of course...and that in no way contradicts his assertion that
words can be given more than one meaning (and in English
at least, most are). A chemist and I can give "mole" one
meaning and a vertebrate biologist and I can give it another
meaning. And practitioners of each field would know what
I was talking about, know it to a degree of specificity
not usually found in casual conversation.
Haiku Jones
>On Nov 17, 9:10�pm, John Jones <jonescard...@btinternet.com> wrote:
>> Marshall wrote:
>> > On Nov 15, 11:45 am, John Jones <jonescard...@btinternet.com> wrote:
>> >> Quantum mechanics employs everyday terms to support its mathematical
>> >> structure. My complaint, a valid one, is that these terms are no longer
>> >> employed with their standard meanings, thus making Quantum theory
>> >> meaningfully vacuous.
>>
>> > That's obviously bullshit.
>>
>> It's obviously NOT.
>
>It obviously is. If I use the noun "set", it can mean
>one thing to a mathematician, another thing to
>a tennis pro, a third to a theatrical designer,
>and a fourth to a dog breeder. None of
>these is "meaningfully vacuous", you just have
>to derive the current meaning from the current
>context -- something speakers of English do
>all day long, generally effortlessly, unless they
>happen to wander into an area in which they
>are technically ignorant.
Like Christians telling atheists what our POV "really" is.
Which isn't just ignorant, it's arrogant and sociopathic.
>Haiku Jones
> YOu never read the original post did you.
Would that be a problem for you?
I just assumed from your peculiar style that
you wanted to drive potential readers away.
However, it just so happens that I did read your
original post, and my post just upthread serves as
my answer to you, possibly better than it did as an
answer to tg.
Do you have any problems with my proposed definitions
of randomness and quantum randomness? No?
Then, your "argument" is just the assertion
that if we knew everything about a quantum system,
then we would be able to predict with certainty
the outcome of quantum measurements.
Yours is a coherent, sensible claim, that could
have turned out to be true. In fact, Einstein,
Podolsky,and Rosen expected it to turn out
to be true. However, it did not: your assertion
is false. That is why we have all this talk about
Bell's theorem and tests of quantum mechanics
against local reality. This is how we know your
assertion is false.
By the way, I think I heard that John Bell himself
expected his theorem to prove EPR /right/. If the
unexpressed part of your argument is "You all
have to be wrong; that just doesn't make sense",
then you will have a lot of agreement on the second
part. Quantum mechanics does not make sense.
Nonetheless, quantum mechanics is right, and
the assumptions of local reality and you are wrong.
Jim Burns
:What I am going to tell you about is what
:we teach our physics students in the third
:or fourth year of graduate school... It is
:my task to convince you not to turn away
:because you don't understand it. You see
:my physics students don't understand it.
:... That is because I don't understand it.
:Nobody does.
-- Richard P. Feynman, Nobel Lecture, 1966
Top Post interjection---please ignore the obviously not; you are now
apparently paying attention.
Not bad, but I thought it invalidated the entire class of hidden
variable theories *that purport to be consistent with and as complete
as QM*. But anyway, I accept that you now see more fully why I don't
like the facile use of decay as an example in this discussion.
> You think that you may have a hidden-variable
> theory that side-steps the usual Bell-centric issues.
OMG. I am being so cautious that I use the somewhat awkward phrase
"proposed conjecture", and suddenly I have a Theory. Now, you are
either a creationist improperly using the term, or, JJ-like, setting
up quite the strawman.
This last is an interesting aspect of the topic. Are you sure? If you
can calculate the probability of one particular particle decaying
within a certain period of time, then you appear to be agreeing with
JJ. Why don't you elaborate on this point.
> or many other things. But it will not give
> a guarantee of the time the atom will decay.
See above.
-tg
>>>>This is not the sort of situation which we can use to
>>>>test local reality vs. quantum mechanics using Bell's
>>>>theorem.
>>
>>>Very good.
>>
>>>>Those situations involve entangled pairs of
>>>>particles being measured at macroscopically separated
>>>>locations. However, I have already explained once why
>>>>the collapse of local reality in those other situations
>>>>is still bad news for local reality in this situation.
>>
>>>No, I don't think so. 'Bad news' is not a sufficient
>>>characterization in science or philosophy.
>
> Top Post interjection---please ignore the obviously not;
> you are now apparently paying attention.
As near as I can tell, your "Obviously not." was intended
to be a meaningless interjection. No, thank you; I can
do meaningless on my own.
I'm going to go do something else now. I may read any
responses from you, I may not. We'll see.
I probably won't be responding, though.
Good luck with your questioning.
I don't think I've asked for much from you, and I've
given you quite a lot of my time, actually. I would
like to ask a favor in return:
Please don't do the You-can't-make-a-clear-statement-
of-what-I'm wrong-*about*,-so-you-either-throw-up-a-
lot-of-chaff-and-do-a-lot-of-hand-waving,-or-do-the-
indignation-dodge thing again. TIA.
Why would a physicist want a theory that was inconsistent
with QM (that is, with experiment) or is not as complete
as QM?
> But anyway, I accept that
> you now see more fully why I don't like the facile use
> of decay as an example in this discussion.
Uhmmm. I guess you don't see why the facile use of decay
is perfectly appropriate in this discussion.
Sorry; time's up. You get to work it out on your own now,
unless you can entice someone else into having this
conversation.
>>You think that you may have a hidden-variable
>>theory that side-steps the usual Bell-centric issues.
>
> OMG. I am being so cautious that I use the somewhat awkward phrase
> "proposed conjecture", and suddenly I have a Theory. Now, you are
> either a creationist improperly using the term, or, JJ-like, setting
> up quite the strawman.
If you don't have a theory, then you have nothing
worth spending time on. It doesn't have to be a very
detailed theory; maybe just "What you guys say,
except for this".
But it's your <fill in the blank/>. You decide.
Am I sure what I mean? Yes.
I'm not entirely sure that this use of "lifetime"
is standard. However, you can bet your life (as I
would mine) that the ideas and equations are as
standard as anything in science.
If you wish to insist upon a JJ-style meaning for
"lifetime", that is, a specific time of decay for each
atom, then I disagree with the starred sentence above,
and I think you would have a hard time finding someone
who understands the situation and agrees with that
meaning.
> If you can calculate the probability
> of one particular particle decaying within a certain
> period of time, then you appear to be agreeing with JJ.
> Why don't you elaborate on this point.
However it appears to you, I am not agreeing with JJ.
(Not that this would be a bad thing in itself.
I'm sure that JJ sometimes gets things right,
by chance if no other way.) Anyway, JJ seems to
say that an atomic decay would not appear random
if we knew more. Giving a probability (except for
0 and 100%) is utterly unlike this lack of randomness
that JJ claims. (Not that this matters to JJ's claim.
That is about what /would/ be the case /if/ we knew
everything.)
You ask for elaboration, but I don't know what to
give you. Equations, I suppose.
Suppose that some radioactive isotope has a
/lifetime/ T (my sense of the word).
Then, if we know that the atom has NOT YET decayed
at time t0, then the probability that it WILL NOT
decay before time t1 is
p(t1-t0) = exp( -(t1-t0)/T )
If we know that the atom has NOT YET decayed
at time t1, then the probability that it WILL
decay before time t2 is
1 - p(t2-t1) = 1 - exp( -(t2-t1)/T )
If we know that the atom has NOT YET decayed
at time t0, then the probability that it WILL
decay between time t1 and time t2 is
p(t1-t0)*[1 - p(t2-t1)] =
exp( -(t1-t0)/T )*[1 - exp( -(t2-t1)/T )]
exp( -(t1-t0)/T ) - exp( -(t2-t0)/T )
If the time interval dt = t2-t1 is small, then
the probability that the atom will decay within
an interval dt near time t1, after time t0 --
which is the latest we know that the atom has not
yet decayed -- (where was I? ... Oh, yeah) that
probability is
p(t1-t0)*dt/T = exp( -(t1-t0)/T )*dt/T
This last seems to be closest to what you want,
a specific time of decay, t1. However, all you get
is a probability that it decays near any particular
time t1.
>>or many other things. But it will not give
>>a guarantee of the time the atom will decay.
>
> See above.
Answered above.
>>I confess, I do not see the connection to your
>>original idea.
Ditto.
Jim Burns
.....
For any lurkers, since JB isn't going to read this, and we don't have
to spare his feelings:
Nonsense! "Hidden variable" is a concept, not a predictive outcome.
The most comprehensive theory is required to make predictions for all
cases, so even if we wish to calculate the trajectory of a billiard
ball, we should be able to use QM to do it. It would be awkward and
difficult, but we could demonstrate that by applying the rules we
could indeed make a three-cushion bank shot.
Now, it should be obvious to the most naive that there are
circumstances where hidden variables exist and we recognize that
fact---otherwise, this whole confusion about 'randomness' would never
exist. People like JB love to say "randomness in particles is not
like randomness in a gas; if we knew everything about the gas
molecules we could predict the location and momentum of an individual,
but that's not true for particles." Well, if that (gas molecule) isn't
a hidden variable situation, what is? And, are gas molecules subject
to the rules of QM? Of course, since QM is a comprehensive theory.
So we come back to my original question: Let's say I propose that the
actual lifetime of a nucleus is determined at the moment of it's
creation. How would the world of QM be different if this were the
case? Come on, there must be a Bell out there; what would the
experiment be like?
BTW, this is a serious question even though I am trying to make a
point about philosophy and language. There may be such an experiment,
but I can't see it.
......
Here, dear readers-other-than-JB, we have what seems to be an outright
error in reasoning, or maybe awkward phrasing. Perhaps a statistician
can help out.
Let's say nucleus A has a .5 probability of decaying to B in 1 sec.
And let's say this takes place in a box which becomes transparent
every second, so we can see whether we have an A or B in it.
Certainly, at time t0, we can calculate a probability of what we will
find in the box at t1, say 5 sec. But JB says "if we know that the
atom has NOT YET (his caps) decayed at t1......".
As I understand it, if we see A in the box at some t1, however many
seconds that is, then the probability that we will see A in the box at
the next second is still .5 .
-tg
Snip
> Here, dear readers-other-than-JB, we have what seems to be an outright
> error in reasoning, or maybe awkward phrasing. Perhaps a statistician
> can help out.
>
> Let's say nucleus A has a .5 probability of decaying to B in 1 sec.
> And let's say this takes place in a box which becomes transparent
> every second, so we can see whether we have an A or B in it.
> Certainly, at time t0, we can calculate a probability of what we will
> find in the box at t1, say 5 sec. But JB says "if we know that the
> atom has NOT YET (his caps) decayed at t1......".
>
> As I understand it, if we see A in the box at some t1, however many
> seconds that is, then the probability that we will see A in the box at
> the next second is still .5 .
Probability is present in neither past nor future.
The flip of a coin demonstrates that you are correct. :-)
The whole point of the concept of 'non-standard meanings' is that their
signs can be used in two ways - 1) non-meaningfully, and 2) in the case
of mathematics, as an ellipsis for syntactical, meaning-void, procedures.
Those are different signs. We are talking about using the smae sign to
mean something else. which is an impossibility. you can't use the "same"
sign in a non-standard way!
But it's another thing to say that a meaning has been given a
non-standard interpretation.
I've lost the whole plot here. I can't find who said what or anything.
Newton's "theory" was probably about as important
as Descartes ridicuulous explanation
for the law of refraction (see l'Ouvre, below .-)
> > By the way, I think I heard that John Bell himself
> > expected his theorem to prove EPR /right/. If the
> > :Nobody does.
thus:
dood said, Numbertheory;
if you don't want to know that, you don't want to know any thing
in science, vis-a-vu *mathematica* --
not the God-am programme of the Wolframites / KNU Kinda Science;
see l'Ouvre, below!
> You have a point of view Marxist, mine is Platonist. What is the
thus:
Lord Berty was quite an evil pacifist (see larouchepub.com), but
he also made me realize that "silly" must be derived from syllogism;
apparently, he was completely fried by Godel's thing, although
Whitehead would not have been.
> Gorgias lived 2400 years ago. Maybe Russel borrowed from him :)
thus:
I have always meant to study difference equations, alas. anyway,
I never googol anything that I am dyscussing online,
particualry when using the googol front-end for Usenet
at some public terminal. I recently saw who owned altavista.com, but
I forgot, though I've used it, when needed.
> A new verb, "google," a synonym for search, has
thus:
the original poster had mentioned 754 and 854,
which latter I'd seen mentioned, somewhere on the IEEE website, but
I wasn't a member. anyway, 754 is an article in Computer (magazine),
from 1980; its implimentation is quite variable, I think.
anyone got a reference to link?
> The current IEEE 754 standard is IEEE 754-2008. Last year, not a
--l'Ouvre: www.wlym.com
Stop the second cap & trade rip-off;
install a tariff on imported oil -- dumb-*** "republicans R Them!"
what
thus:
well, one of HSJ's gedanken experiments bore fruit
with your own programming; makes me want almost
to get into it, myself. I always thought it amuzing,
though others aver that it makes no difference, that
the curvature of Earth (i.e. space) isn't considered as a part
of the problem -- truly, it is generally devized as a pure
application of planar graphtheory, which includes spherical
as a special case, I hear (more elementary stuff to grok),
just as the four-color theorem was turned into that,
in order to save on ink-coloration-by-hand.
now, on the other hand, going beyond the modality
of zero-sum-games with the nodal overview
of both of the could-be salesforce
-- thanks to John "Memorial Nobelist-economist" Nash --
such a communicative approach would be required, if
it was Two Travelling Salesfolk Orienteering (which is
just another version of my new game, EGO,
for one or more players .-)
> As an experiment, I also tried setting the distances equal to the
> costs instead, but to my surprise that worked much less often than the
> distance normalized version. Though in retrospect it's fairly obvious
> why; much of the time, having the two travellers seek to stay close to
> one another is actually a bad idea. Consider nodes arranged in a
> circle with pairs of points close to one another, but in which the
> pairs themselves are far apart, for example.
--go l'OEuvre!
http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon.pdf
http://wlym.com/~animations/fermat/index.html
thus quoth:
(1) Ampère's demonstration of the physical presence of an angular
force, essentially overthrowing the fundamental assumption of
potential theory as still taught, and its conclusive experimental
proof by the 10-year collaboration of Carl Friedrich Gauss and Wilhelm
Weber;
(2) The 1855 Weber-Kohlrausch experiment, establishing the relative
velocity at which the force between electrical particles is reduced to
zero, and provoking Bernhard Riemann to propose (1858) a similarity in
the propagation of light and the electrodynamic potential;
(3) Weber's subsequent deduction (1871) of the bound state of pairs of
like-charged particle/waves within the confines of a 10-16 to 10-13 cm
spherical radius, establishing the natural basis for the formation of
the atomic nucleus.
In the period from 1999 to 2006, I was able to apply that
understanding of the Ampere-Gauss-Weber electrodynamics to the
Keplerian model of the atomic nucleus proposed in 1985 by Dr. Moon.2 I
arrived at a structure which at once overcame what had been two of the
leading objections to the Rutherford-Bohr-Sommerfeld model of the
atom, without the need to invoke any new conditions ad hoc. The
objections of leading chemists, Lewis, Parsons, Langmuir and others,
to the Bohr atom were summarized by
> what
If there is half life then how does a collection of a radioactive
element know how many is around together?
They seem to need each other.
Mitch Raemsch
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> If there is half life then how does a collection of a radioactive
> element know how many is around together?
> They seem to need each other.
I have thought that Russels' so-called paradoxes were mostly
linguistic (king's English) hash, akin to Korbyzinski's exercise
in pidgin english, "E-prime;" that is to say,
these are just mind-****s, or inside jokes, or silly-syllogistic
errors. that is to say,
the liar fails to include the element of time, or
a proper use of tenses, which are available to those who try to read
Shakespeare
(if'n y'don't try, y'*lose* the pass/no-fail test).
the barber doesn't cut his own hair;
he makes a get-away to some other village, for the same reason,
I suppose, that even a lawyer will hire another lawyer for his own
indemnification.
Lord Berty, the Peacenik:
http://www.larouchepub.com/other/2002/2949moonification.html
http://www.larouchepub.com/other/1995/2246_british_and_maoism.html
http://www.larouchepub.com/other/2003/3042shock_awe_wwii.html
Well, it was, but only by the philosophic slight-of-hand
of complex probabilty functions. So that's why the people
who understand macroscopic probabilities work on holographics,
light sticks,
and atomic clock wristwatches rather than in 1930 Photo-Electric
labs.
And on HDTV, Blue Ray, Laser-Guided Phasors, Flash Memory, Cyber
Batteries,
Flat Screen Software Debuggers, Distributed Processing Software,
Home Broadband, mp3, mpeg, USB, All-In-One Printers, and Desktop
Publishing,
rather than in 1950 AI Labs.
And on Rapid Protoyping, GPS, Digital Terrain Mapping,
Weather Satellites, Data Fusion, Compact Flourescent Lighting,
UAVS,
Multiplexed Fiber Optics, Self-Assembling Robots, and
Self-Replicating Machines, rather than in 1960 NASA Paint Shops.
>
> Of course, I suppose it could be like the gods. We don't
> see any, but there might be one under the bed when we're
> not looking. Same with hidden variables, I imagine.- Hide quoted text -
Say we have a large number of coins----2^20, for example.
1) We flip all the coins simultaneously, and get half heads and half
tails.
2) We discard all the coins that come up tails.
The process repeats until we are left with one coin.
Question: Is that coin biased?
-tg
> Herman Rubin wrote:
> > In article
> <hdns88$77r$1...@news.eternal-september.org>,
> > John Jones <jonesc...@btinternet.com> wrote:
> >> Herman Rubin wrote:
> >>> In article
> <hdkfq3$kp3$2...@news.eternal-september.org>,
> >>> John Jones <jonesc...@btinternet.com> wrote:
> >>>> *Anarcissie* wrote:
> >>>>> On Nov 13, 11:16 am, John Stafford
> <n...@droffats.net> wrote:
> >>>>>> In article
> <hdjs2g$tb...@news.eternal-september.org>,
> >>>>>> John Jones <jonescard...@btinternet.com>
> wrote:
> >
> > ................
> >
> >>>>> It was my understanding that the
> hidden-variable thing had
> >>>>> been pretty well disposed of a long time ago.
> >>>>>
> http://en.wikipedia.org/wiki/Hidden_variable_theory
> >
> >>> The hidden variable theory is not compatible with
> the properties
> >>> of the wave function usually used in quantum
> mechanics.
> >
> >>>>> Of course, I suppose it could be like the gods.
> We don't
> >>>>> see any, but there might be one under the bed
> when we're
> >>>>> not looking. Same with hidden variables, I
> imagine.
> >
> >>>> A hidden variable is the only possibility in QM.
> If there is nothing
> >>>> there then there is no outcome. If there is
> something there then it is
> >>>> hidden.
> >
> >>> Observed outcomes behave like probability.
> >
> >> Then you assert that appearance itself has degrees
> of appearance. I
> >> already said that this was not an adequate
> response.
> >
> >>> If hidden variables
> >>> would explain the situation, there would be a
> joint distribution
> >>> of position and momentum. It is easy to give
> examples where
> >>> this joint distribution does not exist, since
> probabilities have
> >>> to be non-negative.
> >
> >> If position and momentum are not players on the
> field, then how does one
> >> assert something?
> >
> > Many have tried to come up with a good answer. I
> gave a
> > simple counterexample to the possibility of a joint
> distribution
> > more than 50 years ago; all one has to do is to
> consider the
> > wave function of one of them as constant on a
> finite interval.
> >
> > This lack of a joint distribution is a problem in
> understanding,
> > but not a problem in computation.
> >
> > A similar problem is that of the multi-slit
> experiment. If one
> > knows which slit, the distribution is totally
> unlike the very
> > useful observed distribution.
>
> "Joint distribution" needs to say more than what the
> technical or
> immediately semantically available implies.
>
> What I am saying is that this term needs sounding
> out. You must provide
> it with a foundation, just as I provided a foundation
> for my own
> observations.
what foundation for what own observations ?
is there some contradiction , some troubling experimental result that makes it necessary to suppose there is/isnt/are/arent any/some 'god(s)' ?
does that constitute a proof ?
i answered retoric questions with retoric questions , or didnt I ?
>
>
> http://en.wikipedia.org/wiki/Bell%27s_theorem#Importan
> ce_of_the_theorem
>
regards
tommy1729
First: This, this procedure does not necessarily result in the
survival of a single coin
Second: What degree of bias do you have in mind? Infinitesimal thru
100%?
A double-head coin (100% bias) will always be selected. Coins with
less than 100% bias may be eliminated.
However, if a single coin does survive, its chance of being 100%
biased has the same odds as the possibility that the first flip
results in all coins (2^20) coming up heads..
Why oh why do people always try to change my thought experiments---if
you don't like it, make up your own and start your own thread. ;-).
This is an empirical result as stated, and we work from that.
> Second: What degree of bias do you have in mind? Infinitesimal thru
> 100%?
What I have in mind is the degree of confidence in any prediction
(bet) one might make in such a case. (That's in a subjective, not
formal sense.)
> A double-head coin (100% bias) will always be selected. Coins with
> less than 100% bias may be eliminated.
No help.
>
> However, if a single coin does survive, its chance of being 100%
> biased has the same odds as the possibility that the first flip
> results in all coins (2^20) coming up heads..
How do we conclude that from the experiment as described? (Perhaps I
don't understand what you mean by 100% biased?)
-tg
I will answer the question you asked, even though
I think you could have answered it. Perhaps you
meant to ask a different question, but I'm not
going to try to read your mind right now.
Yes. There are lots of experimental results that
contradict the theory, for example, that there are
humanoid gods on top of Mount Olympus drinking
nectar and eating ambrosia.I think even theists
are willing to agree that /other people's/
gods do not exist, so I don't expect this to be
controversial.
There are also other god-theories that seem to me
to be intended to dodge a straightforward
falsification, such as that the classical Greek
or Roman gods received. There are at least two
methods used: (1) either the god uses its god-powers
to prevent discovery, or (2) something that
exists but would not otherwise be considered
god-like, such as the laws of physics, is
declared to be a god.
I think either of those methods puts the god-theory it
was intended to save (or so I think) outside
science. Is it logically possible that there is
a god who is Perfectly Undetectable (just as
some suppose a god who is Perfectly Wise)?
Yes, it is logically possible. Is there anything
we poor humans can do to reduce the uncertainties
involved in such a god? No, by definition. Then
we're done here. Such a god is (almost by definition)
Perfectly Uninteresting.
> does that constitute a proof ?
I expect that you know that physics and science
in general do not deal in proof, as math and logic do.
The closest they come is when some theory is
contradicted by evidence. Usually that is enough
for a theory to stop being considered viable.
When a theory resists many efforts to falsify it,
scientists gain some confidence that it will
continue to resist falsification. But as confident
as individual scientists feel, they will still tell
you that their theory has not been proven, just
not disproven. The often-mentioned example that
justifies this caution is Newtonian mechanics,
which passed centuries of strict tests, but which
nevertheless was superceded by special relativity
and quantum mechanics in the twentieth century
-- because of tests it did not pass (experiments
that did not match its predictions).
> i answered retoric questions with retoric questions ,
> or didnt I ?
Perhaps I am not very good at recognizing rhetorical
questions. Did you want your questions answered?
Jim Burns
As I have pointed out before how does a collection of a radioactive
element know how much to decay? Half life depends on quantity. Somehow
then the atoms know how many they are. This may be an incorrect
theory.
Mitch Raemsch
Fair enough. I stand corrected.
> > Second: What degree of bias do you have in mind? Infinitesimal thru
> > 100%?
>
> What I have in mind is the degree of confidence in any prediction
> (bet) one might make in such a case. (That's in a subjective, not
> formal sense.)
>
> > A double-head coin (100% bias) will always be selected. Coins with
> > less than 100% bias may be eliminated.
>
> No help.
>
>
>
> > However, if a single coin does survive, its chance of being 100%
> > biased has the same odds as the possibility that the first flip
> > results in all coins (2^20) coming up heads..
>
> How do we conclude that from the experiment as described? (Perhaps I
> don't understand what you mean by 100% biased?)
I was in error! The odds of all coins coming up heads on the first
flip would be 2^(2^20) not 2^20 as I claimed.
Mea culpa! I withdraw my post in shame :-).
Zinnic
Right, and so the same experiment with radioactive nuclei would
likewise be inconclusive.
-tg
> Arthttp://home.ptd.net/~artnpeg
> As I have pointed out before how does a collection
> of a radioactive element know how much to decay?
> Half life depends on quantity. Somehow then the
> atoms know how many they are. This may be an
> incorrect theory.
The best advice I can give you is for you to get
some actual hands-on experience with things
happening at random. It doesn't have to be atoms
decaying; coins landing Heads or Tails would do
nicely, plus they would be much easier to deal with.
Set up three columns to enter data into:
OBS (the number of Heads observed),
EXP (the number of Heads expected), and
DIFF (the difference between observed and expected).
The "expected" number of Heads is one half for
each time you flip your coin. If you know what
that means, great. Otherwise, that will become clear
later.
Flip the coin. Put either 1 or 0 in the OBS column.
Put 0.5 in the EXP column either way,
and put +0.5 or -0.5 in the DIFF column.
Flip the coin again. ADD 1 or 0 to the OBS column,
add 0.5 to the EXP column,and add or subtract 0.5
to/from the DIFF column.
Flip the coin again. Update your columns again.
Flip the coin a lot, keeping track in the columns.
What you should see is that OBS, EXP, and DIFF
will all get large, but OBS and EXP will get larger
than DIFF.
If you had 4 grams of plutonium-239, you would have
about 1.0x10^22 atoms. The half-life of Pu239 is
24,110 years, so if you waited those 24,110 years,
then the number of atoms /expected/ to have decayed
would be half of that, or 0.5x10^22 atoms.
However, it would be very unlikely that exactly half
of the atoms would decay -- that is just our best
estimate of how many atoms would decay. There is a
99.99% chance that the number of atoms that actually
would decay would be off the expected number by
more than 6.3x10^6 atoms.
Even though the estimate of half the atoms decaying
is not exact, it is really very close if you put it
in perspective. There is only a 1 in 1,000,000,000,000
chance of the observed number of decayed atoms being
off the expected number by more than 3.6x10^11 atoms.
That is a lot of atoms. However, they would weigh
only 9 trillionths of a gram, in a sample of 4 grams.
This great accuracy is only because there are so many
atoms, not because there is some sort of connection
between the atoms.
Jim Burns
Of course it is. All coins are imperfect to some degree and thus
biased. However, the magnitude or even the sign of this bias pdepends
on the way you flip it, the air density, the wind, the surface onto
which the coin will fall, etc.
However, i suspect that if you flip a coin, which is not too visibly
warped, with enough speed and torque - your results will be close to
50-50, i.e., close to unbiasedness.
I suspect that the only way to answer the question as to how more
biased the last remaining coin is compared to those that were rejected
at the first step, is through a Bayesian approach, i.e., by knowing
the original distribution of coin biases. What is the best way to
estimate that?
Since this is cross-posted to sci.math, I'll bite:
What is a "grammatical consequence"? I hope it is not related to the
English grammar, because much of quantum theory was originally
developed in German. Was, like in poetry, something lost in
translation? :-)
>
> > > Alas, the universe disagrees.
>
> > Fine. Oh great. I'll tell my mum.
>
> Better yet, write it up for _Annalen der Physik_.
> Convince the readers of that rag, and there's
> a Nobel Prize in it for you. Guaranteed.
>
> Haiku Jones