How to derive the heisenberg uncertainty relation over dinner?
Hari Seldon
Recently, while having dinner with some of my friends, one of them
asked me to explain to them 'why' the heisenberg uncertainty relation
is true. They already globally knew what it 'meant', but they wanted
to hear some derivation, some 'proof'. In other words: some example
that would make it 'acceptable'.
Since I am a physics student, I have seen various derivations of the
uncertainty relation, to name three: from the postulates and the fact
that momentum is the generator of translations, from the properties of
the fourier transform and through the gamma-ray microscope
gedankenexperiment.
Because my friends do not study physics and know very little math, I
tried explaining to them this latter example. However i soon realised
that this example is based on the formula of the resolving power of a
microscope and I was unable to derive/make them believe this formula.
When looking it up in my two quantum mechanics books I surprisingly
found that in both books this formula was taken for granted. So I
decided to check my optics books and even there I could not find the
formula. So in the end I failed in 'explaining' to them the
uncertainty relations at that dinner and I promised them to try again
some weeks later.
Now I have two questions. First, can anyone provide me with a simple
derivation of the formula for the resolving power of the micoscope in
the gamma-ray microscope gedanken experiment? Or can anyone give me
any reference to such a derivation?
Second, I am wondering how any of you would explain the heisenberg
uncertainty relation to non-physicists? And please do not say that
this is impossible, because as Einstein said: You do not really
understand something unless you can explain it to your grandmother. :)
Thank you in advance,
Hari Seldon
anbar
> Hi,
>
> Recently, while having dinner with some of my friends, one of them
> asked me to explain to them 'why' the heisenberg uncertainty relation
> is true. They already globally knew what it 'meant', but they wanted
> to hear some derivation, some 'proof'. In other words: some example
> that would make it 'acceptable'.
>
[CUT]
>
> Now I have two questions. First, can anyone provide me with a simple
> derivation of the formula for the resolving power of the micoscope in
> the gamma-ray microscope gedanken experiment? Or can anyone give me
> any reference to such a derivation?
>
The simplest I have in mind relies on Fourier transforms... but if you
assume that gamma rays are actually formed by photons, you may derive
the uncertainty relations by the procedure outlined below and then
derive the resolving power.
> Second, I am wondering how any of you would explain the heisenberg
> uncertainty relation to non-physicists? And please do not say that
> this is impossible, because as Einstein said: You do not really
> understand something unless you can explain it to your grandmother. :)
>
You could explain it by starting with the empirical fact that
particles interfere (e.g. the two slit experiment, see Feynman-Hibbs,
par.1-2) and then showing that this is absurd unless the uncertainty
relations hold, because otherwise you could observe *both* the
particles' tracks (e.g. by means of the recoil of the screen with the
slits) *and* the interference pattern.
Stress the point that the interference pattern is experimentally found
to be formed by a *single* particle at the time: it is this fact which
makes the above hypotetical finding absurd.
The input data are: the momentum P of the incoming particles, the
distance D between the slits, the distance L between the screen with
the slits and the final screen, and the distance N between the fringes
(all supposedly known from the experiment). From the experiment you
also find that the relation
N=h*L/(P*D)
(assuming L>>D) is satisfied, where h is some constant... :)
In order to see the interference pattern the position of the screen
with the slits must be known to an accuracy dx<N, and in order to
measure its recoil its momentum must be known to an accuracy dp<P*D/L.
Putting all together you find
dx*dp<h
but this would lead to the absurd result mentioned above, so dx*dp>h
and you're done!
I'm going to visit my grandma for these christmas holydays... I don't
think she's interested in this stuff that much, but I'll give a try!
:)
cheers
a
Frank Iannarilli
> Recently, while having dinner with some of my friends, one of them
> asked me to explain to them 'why' the heisenberg uncertainty relation
> is true. They already globally knew what it 'meant', but they wanted
> to hear some derivation, some 'proof'. In other words: some example
> that would make it 'acceptable'.
A possibly satisfying "derivation" is in a paper "Uncertainty
principles and ideal atomic decomposition", by Donoho and Huo, in IEEE
Trans. Info Theory (November 2001). In this, they show that if two
bases (e.g., Dirac basis, Fourier sinusoids basis) are "mutually
incoherent", then no signal can have a *sparse* (read here: localized)
representation in both bases simultaneously. I found this result
interesting because an uncertainty principle holds not just for the
Dirac/Fourier transform pair, but among a variety of bases pairs.
HTH,
Suresh __NoJunkMail kumar
There are several derivations of the uncertainty principle. The
popular version of this principle found in many college textbooks,
usually says, that you cannot measure position and momentum with
certainty because if you try to exactly measure position, u would need
a higher resolution microsope and an higher resolution microscope,
means, more smaller lamda, and hence a larger frequency. However,
From the debroglie wavelength equation
2 pi / lamda = p / hbar
where p is the momentum and lamda is the wavelength.
Suppose we are tryin to measure an electron.
The incoming photon has momentum h / lamda. As a result of the
collision, the photon transfers part of all of its momentum to the
electron. The uncertainty in momentum is Dp = h / lamda. We also know
that the photon is also a wave. So, the uncertainty in position is
about Dx = lamda.
so Dp * Dx = h
Well, it's ok, at the high school or fresh man college level, to say,
that this derivation is sensible and so acceptable.
However, is it? IMHO, no, it is in fact misleading and leads to a lot
of confusion and sometimes even creates a havoc between your high
school physics and you in an truthfullness of uncertainty principle.
I agree that that uncertainty principle is correct, but the question
is if the above explanation is sufficient, necessary or in fact,
admissible to exactly describe the truth of the uncertainty principle.
I am a stronger believer in Einstien. You can even say, that i even
worship him. After all, i am indian. And i am allowed to do ascestry
worship, [although he is not an ancestor of mine]. In fact, there is a
famous picture of Bose [ yes, the Bose-Einstien condensation guy],
with a picture of Einstien's picture hung among the God's and with
Bose, paying homage to Einstien, by putting his hands in a position,as
people do, when they pray. Yes, Einstien's photo even has the dot on
it.
I will tell you, why I am a strong believer of Einstien. First and
foremost, in my opnion, Einstien wasnt wrong about what he felt, in
fact, he was right, more right than anyone, of his time. His gut
feeling is inscapbable. In fact, the famous EPR paradox after all, is
in fact, as real, as me or you.
When srchodinger developed wave mechanics, (anectodally, passed to me,
from many internet sites), Einstien did believe that it was a
successful description of nature. However, when Von Neuman showed that
schrodinger's picture and hisenberg's picture, einstien started
raising his doubts.
Basically, here's the deal with the uncertainty principle. The most
important thing to note about the uncertainty principle is that the so
called uncertainty does not apply to a single particle, but to an
ensemble of particle.
The Dx, is just another 'lousy' way of writing the standard deviation
of x. sigma_x = sqrt(< (x - <x> )^2 >). The second to note is that,
the standard deviation is taken over distribution, not a single
particle. It makes all the difference in the world, to say that
something is a statistically true and something is always true. As
much difference as walking into a feminist colony and proclaming that
since the mean of SAT maths scores of female students is 30 points
lower than males, then all women should be poor at math compared to
any man. This will also get you killed, if you add a racist twist to
this statistics.
First and foremost, it is important to understand the concept of
statiscal 'proof' , what it means to have a correlation and what the
notion of average means. The average, basically, takes a distribution
of numbers and turns it into one number. And from that 1 number, you
cannot say what the other numbers are. The standard deviation, is
another number from the average, that takes a distribution of numbers
and turns it into a single number.
sigma_p = sqrt(< (x - <p> )^2> )
sigma_x = sqrt(< (x - <x> )^2> )
So, basically, it says something like this. Suppose you have your wave
equation W(x)
sigma_p^2 = int_x=[-infty,infty] ( W*(x) ( p - <p> )^2 W(x) )
sigma_x^2 = int_x=[-infty,infty] ( W*(x) ( x - <x> )^2 W(x) )
Then sigma_x * sigma_p >= hbar/2
Basically, the uncertainty principle in its pureform is
< (delta_A)^2> < (delta_B)^2 > >= 1/4 |<[A,B]>| ^2
It's very, very important to not that, the uncertainty principle, does
not say anything about a single particle and it's also important to
pay attention to the expected value in that expression.
In fact, the debroglie formula
lamda = h / p
has a new dimension in wave mechanices. This formula does not
literally translate into wave mechanics.
I am sure, you are familar with taylor serier.
f(x+ a) = f(x) + a f'(x) + a^2/2! f''(x) + a^3/3! f'''(x) + ....
Now, intresting you can also write the above expression as
f(x+ a) = exp(a D/Dx) f(x)
= [ 1 + a D/Dx + a^2 D^2/Dx^2 + a^3 D^3/D^3 x] f(x)
= f(x) + a Df(x)/Dx + a^2 D^2 f(x)/Dx^2 + ...
Notice that apply exp( a D/Dx) translates f(x) to f(x+a). In Quantum
mechanics, momentum is a generator of translation. as we saw in the
above expression
Suppose i claim that exp( a D/Dx) we say above can be written as exp(
i a O )
where a is the translation distance and O is some kind of operator,
related to D/Dx and i the famous complex number. Now, you may say,
why we need an i in there. First, we know that momentum causes
translation. that means
exp( i a p) f(x) = f(x+a)
However, the units is all wrong. The expresion a*p is required to be
unitless . The above expression is a classical wave expression.
exp( i a p) = cos(a p) + i sin(a p)
So, p must be some kind of frequency, taken over space, not over time.
Now, we go back to our debroglie relation.
2*pi / lamda = p/ h
1 / lamda = p / (h/2*pi)
1/ lamda = p / (hbar)
Our p / (hbar) expression will statisfy both the frequency aspect of
p and units of m ^-1.
so exp( i a p / hbar) should be our expression
so if i apply exp( i a p /hbar) f(x), i should get f(x+ a). So, now,
we claimed that p is an operator so, it related to D/Dx.
if exp( i a p / hbar) f(x) = f(x+a)
then p must be (hbar/i D/Dx)
so exp( i a (hbar/i D/Dx) p / bar) = exp( a D/Dx)
Now, you may be inclined to ask, why we thru all the trouble, of
putting the complex i and hbar in there, after all, it cancels itself
out. The prensence of hbar in p, gives it the correct units as
momentum. The presence of i is tricky to understand. (even i have
trouble admitting to myself that it is needed). Until, i found a nice
page on the web,
http://www.umassd.edu/1Academic/CArtsandSciences/physics/Research/Quantum/Quantum.html
which explains why i is there. Although, i remain unconvinced, because
by inducing the i into the expression, we have introduced wave like
behaviour into nature of things. However the expression,
exp( i a (hbar/i D/Dx) p / bar) = exp( a D/Dx)
itself does not need the i.
Now, our commutation expression
< (delta_A)^2> < (delta_B)^2 > >= 1/4 |<[A,B]>| ^2
A = x
B = ih D/Dx
[A,B] = AB - BA
that is to
x*-ihbar D/Dx - (-i) hbar D/Dx * x
Now, the expresion may be even confusing. The way to look at it to say
that commuation actions on some function
(x* -ihbar D/Dx + ihbar*D/Dx *x) f(x)
= -x*ihbar D f(x) /Dx + ihbar * D/Dx (x* f(x) )
D/Dx ( x * f(x) ) = x * D(f(x))/Dx + f(x) * Dx/Dx
D/Dx ( x * f(x) ) - x* Df(x)/Dx = f(x)
ih [ D/Dx ( x * f(x) ) - x * Df(x) / Dx ] = ih f(x)
So [x,p] = ihbar
taking |<[x,p]|>|^2 = |ihbar|^2 = hbar^2
So, we have
< (delta_x)^2 > < (delta_p)^2 > >= hbar^2/4
-----
About the relation
< (delta_A)^2> < (delta_B)^2 > >= 1/4 |<[A,B]>| ^2
Now, if you wonder, where i came up with the above formula, i would
say that you consult an advanced physics book. A very good book,
probably found in your college library is 'Introduction to Quantum
Mechanics' by Griffiths. Now, if you are lookin for a much more
advanced text, 'Modern Quantum Mechanics' By J.J. Sakurai, IMHO, i
can tell, is much more than a book. It's an art. This is book used in
a graduate Introduction to QM, at Rutgers. Ofcourse, for an beginer,
following the book, is not easy. If cannot afford a book, or goin to
the library, there are many websites, decidated to this. However,
IMHO, whether you skim thru a book, or goto a website, its more
important to seek a sense of statisfaction with an explanation, then
accept an explanation to be true. If you not satisfied, then, do more
research until you have convincing explanation for yourself of the
genuine meaning of the uncertainty principle. Then, you can explain it
to your friends over dinner. Or even, to your first born, on his first
birthday.
-suresh
Garfunkel
> Second, I am wondering how any of you would explain the heisenberg
> uncertainty relation to non-physicists? And please do not say that
> this is impossible, because as Einstein said: You do not really
> understand something unless you can explain it to your grandmother. :)
When non-physicists ask me about the Heisenberg uncertainty relation,
I like to give an analogy with sound waves (or radio waves). If a
sound wave is very short, such as from firing a bullet, or from a
quick tap on a muffled snare drum, it is difficult to assign it a
frequency. If the sound wave persists for a long time, though, its
frequency (or component frequencies, as in the case of the harmonic
content of many musical instruments) can be determined with
considerable accuracy. The Heisenberg uncertainty relation is this
same idea applied to particles: if the particle's position (duration
of the sound wave) is not well defined (the sound wave lasts for a
long time), then its momentum (frequency of the sound wave) can be
determined rather accurately; if the position of the particle IS well
defined (the sound wave is very short), then its momentum cannot be
determined as accurately (difficult to determine the frequency of the
sound wave).
This certainly has practical aspects in the design of Surface Acoustic
Wave filters for radio frequency applications. If you want the filter
to have certain "sharpness" qualities in the frequency domain, the
associated time-length of the filter (given the velocity of sound in
the piezoelectric crystal) must be generally consistent with the
"uncertainty principle": (delta-frequency) * (delta time) is
approximately equal to 1 (or 2*pi, or 1/2*pi, or something near unity,
in any case).
Ahmet Gorgun
news:cac73902.02120...@posting.google.com...
>
In fact, there is a
> famous picture of Bose [ yes, the Bose-Einstien condensation guy],
This is Satyandranath Bose, right? There is also J.C. Bose, who invented the
first "solid state diode detector device" which Marconi used in his first
transatlantic wireless signal (the iron-mercury-iron coherer).
http://www.qsl.net/vu2msy/JCBOSE.htm
And is it true that "boson" is named after Bose?
zirkus
> I will tell you, why I am a strong believer of Einstien. First and
> foremost, in my opnion, Einstien wasnt wrong about what he felt, in
> fact, he was right, more right than anyone, of his time. His gut
> feeling is inscapbable. In fact, the famous EPR paradox after all, is
> in fact, as real, as me or you.
There is another Indian named Unnikrishnan who now claims that
Einstein is vindicated regarding the EPR issue:
http://arxiv.org/abs/quant-ph/0206175
http://arxiv.org/abs/quant-ph/0206190
Einstein did about 6 or 7 things each worthy of a Nobel prize, and he
also thought that black holes were nonsense. Perhaps Einstein might
also be vindicated regarding black holes for the following two reasons
(it might be interesting one day when someone can clearly explain why
the papers below should be wrong or correct):
1) The theory of black holes does not make sense. If you think it
does then please explain clearly the solution to the black hole
information problem, and while your at it, could you please also give
the correct microscopic theory of thermodynamics for BHs.
Furthermore, here is a recent paper which argues that there can never
be observational evidence for event horizons:
http://arxiv.org/abs/astro-ph/0207270
2) Let's not forget about the historical efficacy of Occam's razor,
and thus consider these possibly simpler explanations:
P.O. Mazur and E. Mottola have posed gravitational Bose Einstein
condensates (GBECs also called "gravastars") as an alternative
solution for gravitational collapse. This solution avoids the
mathematical problems of black holes and is thus a seemingly more
elegant solution, but it is not clear how gravastars would
physically come into being and remain stable. Here's their paper about
these ultra compact objects (UCOs):
http://arxiv.org/abs/gr-qc/0109035
S.L. Robertson and D.J. Leiter have provided evidence for the
existence of intrinsic magnetic dipole moments in galactic black hole
candidates, and it is claimed that this evidence is compatible with A.
Mitra's theory of Eternally Collapsing Objects (ECOs):
http://arxiv.org/abs/astro-ph/0208333
A. Mitra suggests that the above gravastars or UCOs should also have
strong intrinsic magnetic fields:
Kevin A. Scaldeferri
zirkus <zir...@hotmail.com> wrote:
>
>Einstein did about 6 or 7 things each worthy of a Nobel prize, and he
>also thought that black holes were nonsense. Perhaps Einstein might
>also be vindicated regarding black holes for the following two reasons
>(it might be interesting one day when someone can clearly explain why
>the papers below should be wrong or correct):
>
>1) The theory of black holes does not make sense.
Maybe not to you. Plenty of well-respected physicists disagree.
> If you think it
>does then please explain clearly the solution to the black hole
>information problem, and while your at it, could you please also give
>the correct microscopic theory of thermodynamics for BHs.
This is a straw man. You're worry about problems completely outside
the domain of GR. They may be interesting and difficult problems, but
they certainly don't imply in any way that the classical theory of
black holes doesn't make sense.
>Furthermore, here is a recent paper which argues that there can never
>be observational evidence for event horizons:
>
> http://arxiv.org/abs/astro-ph/0207270
It does nothing of the sort. It argues that there can never be
observational _proof_, which is a different thing and an argument
which can be leveled against any physics theory. I quote the abstract
though:
Recently, several ways of obtaining observational proof of the
existence of black-hole horizons have been proposed. We argue
here that such proof is fundamentally impossible: observations
can provide arguments, sometimes very strong ones, in favour
of the existence of the event horizon, but they cannot prove
it. This applies also to future observations, which will trace
very accurately the details of the spacetime metric of a body
suspected of being a black hole.
They acknowledge even that strong observational evidence can, and even
does, exist. I don't know if the papers they claim to refute actually
claim that you can observationally "prove" the existence of a
horizon. If so, those authors ought to know better.
>2) Let's not forget about the historical efficacy of Occam's razor,
>and thus consider these possibly simpler explanations:
>
...
>
>S.L. Robertson and D.J. Leiter have provided evidence for the
>existence of intrinsic magnetic dipole moments in galactic black hole
>candidates, and it is claimed that this evidence is compatible with A.
>Mitra's theory of Eternally Collapsing Objects (ECOs):
>
> http://arxiv.org/abs/astro-ph/0208333
>
>
>A. Mitra suggests that the above gravastars or UCOs should also have
>strong intrinsic magnetic fields:
>
> http://arxiv.org/abs/astro-ph/0207056
There is nothing I can say about Mitra's papers on GR which would be
acceptable on this newsgroup.
--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.
zirkus
> This is a straw man. You're worry about problems completely outside
> the domain of GR. They may be interesting and difficult problems, but
> they certainly don't imply in any way that the classical theory of
> black holes doesn't make sense.
This argument doesn't make sense to me because it seems that our
universe is fundamentally *quantum* not classical. I don't care if a
phenomenon seems to make sense classically if it doesn't also make
sense quantum mechanically (e.g. the entropy of black holes).
> They acknowledge even that strong observational evidence can, and even
> does, exist.
This may be dubious because the astronomers have not yet ruled out the
possibility that they might be witnessing evidence of some alternative
such as Mazur and Mottola's proposed gravastars (which is a much more
mathematically elegant solution of gravitational collapse than are
black holes).
> I don't know if the papers they claim to refute actually
> claim that you can observationally "prove" the existence of a
> horizon. If so, those authors ought to know better.
They might not know better because some astronomers don't even seem to
understand their own field, let alone theoretical physics. For
instance, some of them were on the news recently, telling the public
that they had detected two large black holes headed for each other.
What they actually detected were BHCs - black hole candidates, and did
not obtain clear evidence of a BH event horizon nor Hawking radiation.
> There is nothing I can say about Mitra's papers on GR which would be
> acceptable on this newsgroup.
Why the !*%%#!!% not? :-)
Suresh __NoJunkMail kumar
"Ahmet Gorgun" <ago...@att.net> wrote in message news:<a5MJ9.56070$hK4.4...@bgtnsc05-news.ops.worldnet.att.net>...
> And is it true that "boson" is named after Bose?
Alfred Einstead
> Recently, while having dinner with some of my friends, one of them
> asked me to explain to them 'why' the heisenberg uncertainty relation
> is true. They already globally knew what it 'meant', but they wanted
> to hear some derivation, some 'proof'. In other words: some example
> that would make it 'acceptable'.
Earlier I explained why a system given by coordinates (q^1,q^2,...,q^N)
with the q's as functions of time q^A = q^A(t) should have relations
of the form:
[q^A(t), q^B(t + dt)] = i h-bar W^AB(t) dt
for suitably defined W matrix, with W being non-singular.
Assume the coordinates have equations of motion of the form:
q^A''(t) = a^A(q(t), q'(t)).
Just requiring the consistency of the relation above (with
respect to differentiation) already tells you much, all by
itself:
[q^A(t), q^B(t)] = 0
[q^A(t), v^B(t)] = i h-bar W^AB(t),
w^AB = w^BA.
Define also
[v^A{t), v^B(t)] = i h-bar S^AB(t).
Then you have additional compatibility conditions arrived
at by differentiating the last two relations:
i h-bar S^AB(t) + [q^A,a^B] = i h-bar W^AB'(t)
[v^A,a^B] - [v^B,a^A] = i h-bar S^AB'(t).
Thus
W^AB'(t) = ([q^A,a^B] + [q^B,a^A])/(2 i h-bar)
S^AB(t) = ([q^B,a^A] - [q^A,a^B])/(2 i h-bar)
3([v^A,a^B] - [v^B,a^A]) + ([v^A,a^B'] - [v^B,a^A']) = 0.
For instance, for a system with a velocity-independent
acceleration, a(q,v) = a(q), you have:
[q^A,q^B] = 0
[q^A,v^B] = i h-bar W^AB = constant
[v^A,v^B] = i h-bar S^AB = 0.
So, it all comes down to the relation between W and the
mass matrix M.
In the standard Lagrangian formalism, the W matrix is the inverse
of the mass matrix, given by:
M_AB = d^2L(q,v)/dv^A dv^B, for v(t) = q'(t).
Various conditions can be set out which yield this conclusion,
for instance: a set of compatibility conditions for the M matrix.
But it leaves open the question of why it should be so, to begin
with.
In the simplest case, you have a single coordinate q associated
with a mass m, and a relation given by:
[q(t), q(t + dt)] = i h-bar dt/m.
So the question is: why is it a 1/m relation?
To answer this question we work backwards. If q describes the
coordinate of a particle of mass m, the equivalence principle
tells us that the mass m is also proportional to the
gravitational charge, which we'll label g = (G m)/c^2. Then
the relation above comes out to:
[q(t), q(t+dt)] = i L^2 (c dt)/g,
where L is the Planck length.
The relation tells us that the dispersion dq(t) dq(t+dt) is
bounded below by something proportional to 1/g. So, why
should that be? That's the question.
Well, what does g represent? Essentially, it gives you the
intensity of gravitational interaction between the particle
and everything else. This can be understood in the sense
that g gives you the number of gravitational interactions
in a given time that occur with everything else.
But an interaction provides an observation of the particle.
Each observation "collapses" the particle's position. So,
the net effect is that the dispersion will be inversely
proportional to the rate of observation. That's just an
instance of a Zeno effect.
So we should already expect on more basic principles that
if g does, indeed, give you a rate of gravitational
interaction, and since gravity is a long range force
which cannot be shielded, then by way of a gravitational
Zeno effect, one should find a dispersion of its
coordinate which is inversely proportional to g.
Suresh __NoJunkMail kumar
> surku...@yahoo.com (Suresh __NoJunkMail kumar) wrote in message news:
>
> > I will tell you, why I am a strong believer of Einstien. First and
> > foremost, in my opnion, Einstien wasnt wrong about what he felt, in
> > fact, he was right, more right than anyone, of his time. His gut
> > feeling is inscapbable. In fact, the famous EPR paradox after all, is
> > in fact, as real, as me or you.
>
> There is another Indian named Unnikrishnan who now claims that
> Einstein is vindicated regarding the EPR issue:
>
> http://arxiv.org/abs/quant-ph/0206175
>
> http://arxiv.org/abs/quant-ph/0206190
>
disguise. Moreover, i do not understand how he uses the language of
wave mechanics to show that non-local interpretation is not needed.
May be,some one can explain to me, what exactly he is saying.
> Einstein did about 6 or 7 things each worthy of a Nobel prize, and he
> also thought that black holes were nonsense. Perhaps Einstein might
> also be vindicated regarding black holes for the following two reasons
> (it might be interesting one day when someone can clearly explain why
> the papers below should be wrong or correct):
>
> 1) The theory of black holes does not make sense. If you think it
> does then please explain clearly the solution to the black hole
> information problem, and while your at it, could you please also give
> the correct microscopic theory of thermodynamics for BHs.
>
I wish, i had enough money to buy a good textbook on GR, so that i can
teach it myself, correctly.
-suresh
[Moderator's note: Unnecessary quoted text deleted. -MM]
John Baez
zirkus <zir...@hotmail.com> wrote:
> [...] the astronomers have not yet ruled out the
>possibility that they might be witnessing evidence of some alternative
>such as Mazur and Mottola's proposed gravastars (which is a much more
>mathematically elegant solution of gravitational collapse than are
>black holes).
More mathematically elegant, eh?
What is this solution - how does it work, exactly?
>Kevin Scaldeferri wrote:
>> I don't know if the papers they claim to refute actually
>> claim that you can observationally "prove" the existence of a
>> horizon. If so, those authors ought to know better.
>They might not know better because some astronomers don't even seem to
>understand their own field, let alone theoretical physics. For
>instance, some of them were on the news recently, telling the public
>that they had detected two large black holes headed for each other.
>What they actually detected were BHCs - black hole candidates, and did
>not obtain clear evidence of a BH event horizon nor Hawking radiation.
I don't know what these astronomers said, but I suspect you're
being unfair.
First of all, you'll never hear astronomers talk about black
hole "candidates" on the *news* - in case you haven't noticed,
news programs never allow scientists to put in all the
careful phrasing and caveats that are necessary in actual science.
Everything must be made VERY SIMPLE.
Secondly, the theory that black hole candidates are actual black
holes is so widely accepted by now, that only in research focused
on this question is it regarded as crucial to call them mere "candidates".
Whatever they are, we see a lot of them; it's not so terrible to
call them "black holes" as long as we bear in mind a sliver of doubt,
and are willing to change our tune if we're proved wrong.
Finally, you are asking the impossible if you expect astronomers
to find "clear evidence of Hawking radiation" in typical black hole
candidate. Only for very tiny black holes would we ever have a chance
of seeing this. Nobody has ever seen such tiny black holes. Ahem -
black hole candidates.
>> There is nothing I can say about Mitra's papers on GR which would be
>> acceptable on this newsgroup.
>Why the !*%%#!!% not? :-)
His papers are full of mistakes.
In your articles, you refer to lots of papers on the preprint arXiv.
I often wish you could spend more time checking the details of these
papers before citing them. Some of them make sense. Others don't.
Many are in the grey zone somewhere between these extremes. It makes
me very nervous how you sometimes lump them all together without
distinction! For example, when you cite Mitra's papers along with a
bunch of others, it makes me feel I can't trust *any* of them.
Personally I usually avoid referring to papers unless I feel confident
in their results. Of course I still screw up, but I like to think
that being cautious this way is a good thing.
zirkus
> More mathematically elegant, eh?
>
> What is this solution - how does it work, exactly?
See the paper [1] which is only 4 pages long, but a news article [2]
about these gravastars mentions some reasons why experts are skeptical
about the idea of gravastars, although the article also states:
"But other astronomers are intrigued, both because black holes
themselves remain mere theory, not fact, and because gravastars might
explain strange physical observations that black holes don't."
> Finally, you are asking the impossible if you expect astronomers
> to find "clear evidence of Hawking radiation" in typical black hole
> candidate.
I wasn't expecting the astronomers to have detected any "clear
evidence of Hawking radiation", and this was partially my point.
> In your articles, you refer to lots of papers on the preprint arXiv.
> I often wish you could spend more time checking the details of these
> papers before citing them. Some of them make sense. Others don't.
> Many are in the grey zone somewhere between these extremes. It makes
> me very nervous how you sometimes lump them all together without
> distinction! For example, when you cite Mitra's papers along with a
> bunch of others, it makes me feel I can't trust *any* of them.
But you don't have to be nervous because you are not clueless ! And
if it should turn out that loop QG is correct and that string theory
is false then perhaps up to 60-85% of the papers on hep-th could be
flawed !
I am not citing papers in some kind of official way, but just
mentioning ideas for potential discussion. You need to be both
skeptical and open-minded to be able to adapt to new ideas, and e.g.
Lubos Motl used to be quite critical of loop QG but because he is very
bright he has been able to adapt and to consider what may be an
important new finding in loop QG, i.e. Dreyer's result.
Also, Abdus Salam would consider any idea that someone brought to him
because he was smart and confident enough to feel that he could see if
something should or must be wrong. If something were easily and
obviously wrong then he could ignore it, but otherwise he knew that he
might still learn something from a theory that turned out to be wrong.
For instance, there is a paper [3] which looks at a binary pulsar and
concludes that gravitational radiation cannot exist. I recently saw a
paper on Reissner-Nordstrom black holes which discussed the effects of
gravitational radiation back-reaction which makes me wonder if the
author of [3] has even considered the possibility of gravitational
radiation back-reaction.
I don't know much of anything about binary pulsar systems, so even if
paper [3] is wrong I still might learn something such as where the
effect of gravitational radiation back-reaction should arise and to
what extent (assuming that people with more expertise can discuss this
for me).
[1] http://arxiv.org/abs/gr-qc/0109035
[2] http://www.space.com/scienceastronomy/astronomy/gravastars_020423.html
John Devers
(John Baez) wrote in message
> > [...] the astronomers have not yet ruled out the
> >possibility that they might be witnessing evidence of some alternative
> >such as Mazur and Mottola's proposed gravastars (which is a much more
> >mathematically elegant solution of gravitational collapse than are
> >black holes).
>
> More mathematically elegant, eh?
My files on Gravastars
http://www.space.com/scienceastronomy/astronomy/gravastars_020423.html
Another Gravastar article
http://www.nasa.gov/ntv/breaking.html
Nasa TV schedual
http://www.sciforums.com/t5376/scd6aa1f3497a9a894943c2c19febdb24/thread.html
Copy of New Scientist Gravastar story
My outdated files on Black holes.
http://www2b.abc.net.au/science/k2/stn/posts/topic20042.shtm
See black hole pictures in this thread
http://chandra.harvard.edu/photo/category/blackholes.html
Chandra Black Holes
http://hubble.stsci.edu/news_.and._views/cat.cgi.black_holes"
target=newMillisecond Pulsars as Probes of Mass Segregation in the
Galactic Center
Hubble Black holes
http://hubble.stsci.edu/news_.and._views/pr.cgi.2001+29
Ancient Black Hole Speeds Through Sun's Galactic Neighborhood,
Devouring Companion Star
http://hubble.stsci.edu/news_.and._views/data/2001/29/image.jpg
http://hubble.stsci.edu/news_.and._views/pr.cgi.2001+03"
'Death Spiral' Around a Black Hole Yields Tantalizing Evidence of an
Event Horizon
http://hubble.stsci.edu/news_.and._views/data/2001/03/image.jpg
http://hubble.stsci.edu/news_.and._views/pr.cgi.2000+21
Feasting Black Hole Blows Bubbles
http://hubble.stsci.edu/news_.and._views/data/2000/21/image.jpg
http://chandra.harvard.edu/photo/cycle1/0134/index.html
Chandra M87
http://chandra.harvard.edu/photo/cycle1/0134/m87comp.jpg
http://hubble.stsci.edu/news_.and._views/pr.cgi.2000+20
A Cosmic Searchlight
http://hubble.stsci.edu/news_.and._views/data/2000/20/image.jpg
http://www.gemini.edu/media/IFUImages.html
The core of NGC 1068
http://www.gemini.edu/media/pr_images/NGC1068_medres.jpg
http://www.gemini.edu/project/announcements/press/2002-6.html
Gemini Observatory Captures Multi-Dimensional Movie of Active Galaxy's
Core
http://www.gemini.edu/media/pr_images/NGC1068sv_medres.jpg
http://science.nasa.gov/headlines/y2001/ast23oct_1.htm
Spinning black hole
Spinning black hole from NASA APOD.
http://antwrp.gsfc.nasa.gov/apod/image/0110/bhspin_xmm.jpg
http://chandra.harvard.edu/press/01_releases/press_090501flare.html
Chandra sees comet fall into black hole
http://chandra.harvard.edu/graphics/top/0204_top.jpg
Check out the hundreds of white dwarf stars, neutron stars, and black
holes
around our galaxy's center, the white bit.
http://chandra.harvard.edu/photo/2002/gcenter/index.html
X-Ray Mosaic Of Galactic Center
http://www.mpifr-bonn.mpg.de/gcnews/gcnews/Recent/gcs_fig1.jpg
http://www.news.cornell.edu/releases/Jan00/Eikenberry.blackholes.deb.html
black hole -microquasar GRS 1915+105
How about this one 40,000 light years away?
http://www.news.cornell.edu/releases/Jan00/GRS1915.72.GIF
Or this one 10,000 light years away?
http://www.gsu.edu/~wwwour/doublestarrel.htm
Astronomers find survivor of supernova explosion in double-star pair
Here's one on the other side of our galaxy that doesn't add up.
http://www.nature.com/nsu/011129/011129-13.html
Massive hole makes theories leaky
Also did you know galaxy M33 does not have a Supermassive Black Hole
in it but it's core contains a tiny one?
http://antwrp.gsfc.nasa.gov/apod/ap000104.html
The great attractor
http://antwrp.gsfc.nasa.gov/apod/image/0001/gacluster_wfi_big.jpg
http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/Images/att-graphic_lg.jpg
http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/Images/VirClust_lg.jpg
http://antwrp.gsfc.nasa.gov/apod/ap021008.html
http://antwrp.gsfc.nasa.gov/apod/image/0210/xtej1550_chandra_big.jpg
zirkus
zir...@hotmail.com (zirkus) wrote in message news:
> "But other astronomers are intrigued, both because black holes
> themselves remain mere theory, not fact, and because gravastars might
> explain strange physical observations that black holes don't."
Speaking of alternatives to black holes, the two new papers below
espouse naked singularities. Feynman would sometimes go to the local
nudie bar to practice drawing or to think about physics. I wonder if
would be possible to open a new kind of club which features live naked
singularities.