View Full Version here: : Quantum P and GR
22-06-2011, 03:42 PM
As a casual reader it is hard to understand the. "conflict" between QPhysics and General Relativity so I read what I can find.
One thing I came across gave me the impression Quantum Physics seems to suggest (at least in the case of the hypothised graviton that thijg can happen instantly which for me raises the question "isn't that wrong nothing can exceedC."..
Moreover why can't the two be reconcilled.
Does each camp accept the premises of the other and they simply can't satisfactorily link the two..?
22-06-2011, 04:15 PM
They can't be "linked" just like that because completely different math is used to describe each one of them..
It's a bit like digital and analogue electronics... Digital deals with discrete levels (one's and zero's) while analogue electronics deals with any voltage in between and out...
In this crude example the link of course exists (currents and voltages)... but I can tell you from my experience that not many "digital" guys will understand analogue electronics at all .. it is "black magic" for them :P.
Which is very good for us, "analogue" people ;)
22-06-2011, 04:20 PM
Hmm .. there's a lot more to this than meets the eye.
The fundamental difference between the two is 'background independence' or 'universality' which in turn, stems from a philosophical difference. There has been heaps written on this and the philosophical debate still rages.
Quantum Gravity has been attempting to unite it all for years .. unsuccessfully. String theory comes closest.
Don't ask me to distinguish the philosophical differences though
22-06-2011, 04:47 PM
Thanks for that I was starting to think it was just me.At one level they seem to agree but of course the material I cover is like a documentary where a complex topifvgets 45 minutes to cover the lifetime work of many scientists.
Actually some of the discussion you guys have becomes so informative and helpful as you somehow give more sides to matters unapparent.
The complexity of it all is stagering...I gave up on advanced math support after going to a math site and finding the index was book lenght let alone the material...
I find the prospect of instant comunication difficult to accept one would think time must elapse between particle interaction. .even if they eant faster than C surely it can't be instant...mmm. only one entity can do that...oh no Better revise my atheiest stand. .
Craig why don't you throw some more light on the background irrespective of its speed.
22-06-2011, 05:55 PM
The inability of combining QM and GR is a scale related issue and has nothing to do with instantaneous interactions.
QFT (Quantum Field Theory) is a relativistic QM theory.
In the development of QFT the main issues encountered by theorists was that by combining QM and SR (not GR) produced a couple of very strange calculations.
Firstly since QM is a theory based on probabilities, the probability P of a particle being in a particular state is in the range 0<= P<=1.
In QFT however probabilities could have negative values which is of course an absurdity.
Secondly in QFT particles could exist in negative energy levels which is difficult to interpret in QM.
Unfortunately this where a knowledge of mathematics comes into play on how theorists overcame these hurdles by incorporating concepts such as second quantization where a field could be quantized like the characteristics of particles describing energy, angular momentum etc.
Instantaneous travel in QFT is meaningless. It's like trying to explain the double slit experiment in terms of a photon or particle being at both slits simultaneously due to instantaneous travel rather than the Heisenberg uncertainty principle at work, or the photon or particle wavefunction collapsing when an observer makes a measurement. A graviton should it exist will operate on the same principle.
22-06-2011, 06:17 PM
Hmm .. Steven .. just been doing some reading up … it seems that a basic difference between GR and QM/QFT is that GR theory is not dependent on any preferred type of space-time (ie: no frame of reference is 'special' over another), hence it is regarded as a 'background independent' theory.
In QM/QFT, however, the properties of the elementary particles have to do with their relationships to the state of the 'background' vacuum. Ie: the vacuum has different states which ultimately gives rise to the different properties of the elementary particles: ie: mass, position, momentum, spin, and charge.
Hence QFT is called a 'background dependent theory'.
If so, I think I can get this ..
22-06-2011, 06:27 PM
Thank Steven that was excelent. Again I focused on something that confused me.
But thanks to you all of you I am trying to understand it all without trying to rewrite anything...but its not easy for me. I looked into getting a math tutor but gave up on the idea so it is a frustration to have these interests and no tools so to speak. You would have noticed the thread re the trcking in the double slit..that was very interesting.
22-06-2011, 07:07 PM
The vacuum is a field in the lowest or ground state. There are different types of vacuums, such as the quantum electrodynamic (QED) vacuum or the quantum chromodynamic (QED) vacuum.
The issue with gravity as a Quantum Field theory is that it is non- renormalizable. A gravitational interaction between 2 particles changes the particles from a state A to a state B. If you sum all the momenta going from state A to B you end up with infinite values. This is prevalent at the Planck scale. There is no way you can renormalize or "cut out" the infinite terms as you can with QED or QCD.
This is where string theory is an advantage. By making your strings larger than the Planck scale, the infinities are averted.
22-06-2011, 07:12 PM
No problems Alex.
The maths behind QFT is very difficult.
Maths for GR on the other hand is simpler and much more intuitive.
PS Here is Richard Feynman who won the Nobel prize for his work on QED.
It's encouraging that QED is also difficult to a genius.
22-06-2011, 07:35 PM
Thanks Steven …
More reading to do on all this I'm afraid .. ;)
That's "action at a distance (http://plato.stanford.edu/entries/qm-action-distance/)". There is no conflict or contradiction.
23-06-2011, 05:02 PM
Thanks very much for this link. I am only half way thru but the math was totally understandable because it showed what each input symbol represents.
I am at chapter 7 which covers specificaly what concerned me.
I have not read any of the references but I will select some on my second reading.
23-06-2011, 05:53 PM
I did find..."many believe relativity per se prohibits transport of matter-energy and or action at a distance"...there is another view presented after that but that is what
I was interested in mostly.
I find this just like reding a High Court judgement...it seems to labour upon things one would never think twice about...and many references to associated law and "dicta" of other judges. And do we ever get to know exactly what a particle is doing or is it all probability.
And that poor cat in the box. ..is it probably dead...and. if so is it dead on the bottom of the box...it could be stuck on the ceiling I guess....my attempt at humour.
I will read it again and some of the references ..thanks something I can get my teeth into.
23-06-2011, 08:29 PM
Y'know Alex .. that's a very interesting question. I don't know myself.
A few articles have appeared lately that have thrown me when it comes to this question
here's a thread about 'The Shape of an Electron' (http://www.iceinspace.com.au/forum/showthread.php?t=76163) .. one of the articles in the thread says ..
so how is it that they can measure accurately the shape of an electron, at this degree of precision, and yet the Heisenberg Uncertainty Principle is frequently cited as a reason why such precision cannot be achieved ? Clearly, it can be achieved ! What purpose does the Uncertain Principle serve in this case ? Is it as relevant as it once was ?
And I've been pondering another one
Startling thermal energy behavior revealed by neutron scattering. (http://www.physorg.com/news/2011-06-startling-thermal-energy-behavior-revealed.html)
.. in this one, they have found that the vibrations of atoms in a crystal lattice in thermal equilibrium, (the vibrations are indicative of thermal energy), self-organise into discrete packets, called intrinsic localized modes (ILMs) that break the symmetry of the crystal. They found that the ILMs self-organised according to a regular pattern. Whilst this is indicative of a chaotic phenomenon forming fractal patterns of both regularity and irregularity, (which is no great surprise to yours truly), my question is: How do they measure this kind of stuff when QM is telling us that its all a matter of probability ? This particular test made use of neutron scattering to collect the vibration data of atoms trapped within the lattice structures.
Another recent one is: Quantum physics first: Researchers observe single photons in two-slit interferometer experiment. (http://www.physorg.com/news/2011-06-quantum-physics-photons-two-slit-interferometer.html)
In this, they have developed a way to make momentum and distance measurements on photons which may ultimately lead to tracing their paths backwards to the specific slit they went through.
So I'm starting to wonder just how much use are these QM Principles going forward in such research ? Just about every day, I find that some scientists have put these 'guidelines' (ie: QM 'guiding principles') aside, and measured very small particles, such that very useful insights can be obtained.
What physical applicability do these principles have, if they are simply guiding researchers by challenging them to find ways around them ?
Are we not picking up on the message that these QM Principles are not quite the deterrent they once used to be and hence, are they applicable guidelines for researchers, going forwards ?
23-06-2011, 09:01 PM
I am glad you asked Craig as I can answer all your questions very simply...I have no idea...:)
From my view the uncertainty principle pointed out an exception to the rule but in effect the. exception became the rule. The rcent double slit experiment suggests to me others think similar..they look where they expect is my simple view.
I am still trying to understand how some of this counter intuitive stuff gets a run but I guess the way things work is state a premise and prove it with math if that works the idea will be observed in experiment.
I find it difficult to accept because if a premise appears counter intuitive any subsequent proof won't satisfy me.
I amnot sure how the things you ask about are worked out..maybe a computer model and it linked to an experiment that suggests the model can be relied upon and the model is where measurement is made.As I said I don't know....unless we introduce an eather that is...:lol::lol::lol:
23-06-2011, 09:03 PM
Thanks for the links a I will read them with interest
24-06-2011, 12:29 AM
They not measuring a shape. What they are trying to do is measure an electron's dipole moment. The more distorted the shape, the greater the dipole moment. If an electron is perfectly spherical the electron dipole moment is zero.
Hmmm if the size of the crystal is greater than it's Compton wavelength, then the measurements are entirely predictable and not quantum mechanical.
Interestingly enough the reasercher's themselves are not claiming to violate the uncertainty principle.
What the experiment does challenge is the Copenhagen interpretation of QM, where a wavefunction collapses when a measurement is performed.
24-06-2011, 12:45 AM
I might have a look at your replies, Steven, tomorrow. Getting a bit bleary eyed here:)
The last one has quite a few consequence for QM and many of its offshoots...one in particular, the many worlds interpretation. I think you'll know where I'm heading with this one:)
24-06-2011, 07:52 AM
I don't necessarily see that any of these 'violate' the Uncertainty principle. I don't think any of them do, as they all seem to make use of indirect measurements.
The observation I'm querying here is that the Uncertainty Principle was for many years, an absolute in QM. These researches don't seem to accept it as such, and in fact are using it as a challenge to push measurement technologies beyond any perceived limits.
If this is an accurate observation, then I'm left wondering what purpose does the Uncertainty principle serve in doing this research ?
Yep .. fair enough .. the Scientific American article says that an electron actually drags a cloud of virtual particles around. As the electron whizzes around, it drags this particle cloud, which ultimately results in an imbalance of the dipole magnetic moment. (It seems the cloud is considered to be part of the 'electron'). If they find this cloud is deformed, then they say
so, there are a few caveats in there, and until they can uncover the asymmetry, all is good, but my point is that the absoluteness of the Uncertainty principle is clearly not serving as a deterrent factor for these researchers. So what role is it serving in this case ?
They seem to be careful in pointing out that the vibrations they're measuring are at the atomic level and are independent of the crystal lattice (??)
Yep and that point should be made very clear, also.
so there's 'interpretation' of QM coming into this ? Does this mean that the Uncertainty principle is also an interpretation of something ? I'm not challenging the Uncertainty principle here .. I'm really just challenging my understanding of it and other such principles in QM, as well as the role it plays in guiding research.
There's nothing 'wrong' with QM
there's only (as always) something wrong with my understanding.
24-06-2011, 08:50 AM
The uncertainty principle is opperational in my quantum mechanics and QFT as I am uncertain about all of it...not its validity but my comprehension of what I read.
And by the way I have no problemwith an answer being the result of probability if it came across that way.
I can't wait to read views re. "other worlds".
24-06-2011, 10:33 AM
I find myself in the same boat as you ! :eyepop:
There are so many concepts, theorems, principles etc, involved in all this QM material, I also find it very difficult to comprehend. I'm not so worried when I watch YouTubes of Feynman lectures though, (like the one Steven posted the other day), where he is also pointing out what he stuggled with, as well.
Most of what they write invariably seems to be expressed in terms of analogies and concepts, which I guess are fine, provided one can even understand the analogies & concepts !
I guess this is because the theory is all coming from the physical expression of what's going on .. in the language of maths. (I don't think maths coaching will help much here, either by the way … ;) )
This article (http://physicsworld.com/cws/article/news/46284) goes into a better explanation of 'weak' measurements (such as the two slit experiment article I posted). It also helped me in visualising wavefunctions also. Here's a good quote from it:
So from this, apparently to date, they haven't really ever had a good consensus definition of what a wavefunction is.
This would seem to be a crucial first step in bringing it all closer to a grounded physical, real-world level, eh ?
24-06-2011, 11:43 AM
I can not believe wave function is a real world feature in so far as intuition tells me a medium is required and a wave must be a result of energy effects on the medium. We'll I have lost the plot right there as that is at odds with everything. I think the eather was thrown out unreasonably and a conclusion that light did not behave as expected should not have been seized upon to remove eather from the mix.
Anyways I have been years trying to understand these matters and find I know less and. less about more and more. My main problem is I think that everything must come down to a physical presence..a descrete particle..even energy I think must be matter sosmall we will never see it. Same as a field I suspect it is a flow of particles rather than limitless potentials. So I see frame dragging as a measure of the drag of an. eather rather than a distortion of field...But these days at least I understand how offensive my ideas must present to. ..well all you guys really...But it is becoming more like law for me...few things are clear cut and were not arrived at in an instant...much law came from an evolution of centuries...insurance law came from a desire to manage.the gambling on cargo ships arrival or non arrival in port...with that little snippet on the history insurance becomes more understandable.
And scientists must be similar to lawyers not being happy to change things that have taken years to develope and they know why the choosen way works better to a new uninformed suggestion.
Fortunately changing science is easier thanchanging law mmm or is it.?
For me science can only ever be an interest in fact at my age maintaining an interest in anything is a task.
I am fortunate to be able to access material which years ago would not have been possible.
24-06-2011, 11:55 AM
Where this experiment is challenging the Copenhagen Interpretation is in the way they have measured the two values...momentum and position...of the particles passing through the double slit (or whatever they were using...can't remember). The traditional interpretation would be that the moment the measuring of the photons done, you would get either a wave or a particle detection, not both. This is collapse of the wavefunction of the photons and hence the basis of the Uncertainty Principle, being you cannot measure more than one property of particle at any one time without affecting the other.
However, what we have here in this experiment is the measurement of both position and momentum of a quantum system simultaneously which would appear to violate the principle. But, in fact, it's not breaking the principle as what they're measuring isn't the position and momentum of an individual particle, but the bulk properties of all the photons participating in the experiment and using those to define a position and momentum vector for the individual particles. In effect, what they're measuring is the total or universal wavefunction of the system. What is interesting is that they have done this without the wavefunction collapsing upon measurement. Hence, it's possible, it appears, to be able to measure the properties of the universal wavefunction to define simultaneous properties of individual particles within that wavefunction without causing that wavefunction to collapse but still uphold the Uncertainty Principle in the measurement of individual particles. It would appear from this that the universal wavefunction, whilst made up of many other wavefunctions of the particles and waves within it, is a fundamental property of the whole system and unaffected by wavefunction collapse (Copenhagen). It's similar to a harmonic system, with a fundamental tone being the base tone for the whole system and the halftones and harmonics being embedded imprints upon the fundamental tone.
How does this affect the many world interpretation (MWI)??. It bolsters it considerably. The MWI basically states that for every event a particle or a system partakes in, the path or spacetime line that the particle/system can take will branch off into an infinite number of possible paths, all of them real. That being, each split creates a new and separate universe for each and every event. Each universe is defined by its own wavefunction and all the particles within it are defined by their own wavefunctions which are a subset of the universal, fundamental, wavefunction. However, the Copenhagen Interpretation would say that there is only one existing universe, the one in which the observer was situated and that the other "universes" were only probable superpositions of state that when observed, would collapse back into the most probable state....that of the observer. The other states are phantoms, in this case. MWI would consider them to have real, physical existence. This experiment would back MWI as it has shown that the universal wavefunction of a system may not act in the typical accepted way, i.e. Copenhagen. Observing any one particle and where it might go would cause the wavefunction to collapse for that individual particle. You could either measure its position or its momentum, but not both. The same would be true for all the particles. But in measuring the universal wavefunction for the whole system of particles you are, in effect, measuring all the properties that those individual particles possess at any one given time...both their position and momentum simultaneously. So, if some of the particles were going to go off in direction X and others in direction y, you could tell which way each particle was going to go by observing the inherent bulk properties of the system they resided in. The different directions would be present as "polarisations" of the universal wavefunction of the system. The particles wanting to go of in either direction would also exhibit those particular polarisations. After the particles went their merry ways and hit the detectors, they would each inhabit their own particular realities with their own universal wavefunction ...those in x direction and those in y. However, the properties of the original wavefunction would be conserved in that the summation of the realities of each individual particle would be equal to the total reality of the bulk system or original universal wavefunction. Each reality would be 100% probable, depending on what reality the observer chose. Although for each reality the observer chose, the other realities would appear less probable depending on their distance of split from the reality the observer was in. However, because the observer can arbitrarily make any decision on whatever reality they wanted to observe, each reality in effect is equally as probably (100%) of existence as any other. The number of decisions an observer could make is infinite. Therefore the number of different realities an observer can observe is infinite, even though an observer can only observe one reality at a time. The only way an observer can see all possible realities together is to observe the original wavefunction. By making an observation of any one particle within that universal wavefunction, the observer becomes part of that particular particle's wavefunction, hence its reality. Hence the apparent collapse of the other realities, which in effect is an aberration of observation.
24-06-2011, 12:48 PM
Hmmm …. I'm not so sure that these kinds of measurements are saying anything one way or the other, about MWI or Copenhagen .. specifically (??)
The trick seems to be that they are not doing direct, hard measurements which result in the wavefunction collapsing completely. (This is the beauty of the 'weak' measurement technique). For example, they are only inducing a very small amount of polarisation (10 degrees), and because this is so small, the system, supposedly, isn't 'greatly' disturbed.
With the Uncertainty principle, measuring a quantum system without effectively destroying it before the wavefunction is fully known, has been previously deemed virtually impossible. But now, they have directly measured the wavefunction of identical single photons for the first time without destroying the wavefunction.
If this is the case, (ie: no wavefunctions have been destroyed), then the measurement has been done to the system in a sort of quasi-real state (sort of 'inferred' reality). They talk of real and imaginary components comprising the end result.
If no reality has been definitively established (by a destructive measurement), then can we really say that has this 'branching' has occurred (as per the MWI) thereby adding support to this interpretation ?? Similarly, the Copenhagen interpretation seems to be avoided also (for the same reason) ??
It seems to me that their technique dances around both MWI and Copenhagen ??
I'm open to correction here …
24-06-2011, 01:10 PM
They are, actually. Copenhagen specifically states that act of measuring a quantum system collapses the wavefunction so that the most probable outcome of that collapse is the reality which the observer makes the observation within. MWI states that there is no collapse of the actual wavefunction and that the reality the observer finds themselves within is just one of many actual realities. This experiment is pointing to the latter conclusion...the universal wavefunction of the system doesn't collapse upon measurement. What you're in fact measuring is the application of the Uncertainty Principle on a localised level, that of individual particles, but that the overall system remains as it is. That's the only way they can measure the simultaneous position and momentum of the particles. Weak measurements come in the observation of the system's bulk properties and the strong measurements come in the measurements of the individual particles. To measure both the momentum and the position of an individual particle you can either treat it as the universal wavefunction within its own reality or measure its polarisation w.r.t. the bulk or original universal waveform of the system of particles.
The real and imaginary components would be the reality of the observer (the real) and the other probabilities within the system (the imaginary). But that is nothing more than the perspective of the observer. In MWI, all the realities are equally probable, only that the observer can observe one reality at a time...the other realities seeming less real depending on the distance they split from the reality that was being observed.
The branching within this experiment occurs in two places...firstly, where the particles "polarisations" within the universal wavefunction have been determined and/or set, and, secondly where the particles go their separate ways after passing through the prisms/slits.
Their technique isn't the thing dancing around either interpretation, it's the wording of their research.
24-06-2011, 01:10 PM
That was excellent Carl...I am starting to understand. ... in law we once had "fictions."...something that did not exist but its existence was recognised so we could proceed to a point where its existence was no longer necessary to proceed and that being the case we could dispose of the fiction...to an outsider such contrivance seemed strange..and it was strange but put in context it was the only way to get around an impass....
I gather no actual new universes open..but they could but if they did our observation of one specific universe shows the others do not exist.
24-06-2011, 02:33 PM
The reference to real and imaginary components in this context is mathematical.
A wavefunction is complex valued.
A complex number is in the form a+bi. "a" is the real part of the complex number, "b" is the imaginary part of the complex number. i=sqrt(-1)
Similarly a wavefunction is composed of real and imaginary components.
Mathematically the complex number is the measurement.
24-06-2011, 03:12 PM
Thanks Steven (& Carl) ..
They say the real part is provided by the shift in the 'pointer' related to the position of the photon, and the imaginary part is the shift in the pointer related to the momentum of the photon.
But somehow, they then jump to making the statement that the position is weakly measured but the momentum is strongly measured (implying that there is no overlap in the initial and final values in the momentum part, but there must be some overlap in the same for the position part).
Presumably, (recollecting from my days gone by), all sorts of things can be derived if the real and imaginary parts of the complex number are known. Why the real and imaginary parts are associated with position and momentum in the first place … I'll have a guess and say its something to do with the complex function describing the generalised wavefunction ? (Its a wild guess, though .. probably wrong ..)
PS: I notice the square of of a wave function's absolute value is interpreted as a three dimensional probability density function. The wave function itself, returns the probability amplitude of a position or momentum for a particle. All possible states of a systems are considered to be the whole number set, (hence the inclusion of the imaginary component). I think that answers my own question. Cool. Cheers.
24-06-2011, 03:55 PM
Just off topic here, for a moment, but if you look in the journal Nature there's a topic just above this one which will turn the EU fools hair grey:):P
That "four letter word"....reconnection:):P
Now, back to topic.....
24-06-2011, 04:01 PM
Guys, do you have the actual research paper for this?? If not, let me know as I've just downloaded it from Nature and can send it to you.
24-06-2011, 04:44 PM
This is the uncertainty principle at work.
delta(x).delta(p)>h/2 x and p are position and momentum respectively.
In a weak measurement for x, the uncertainty in the measurement of x (delta x) is small hence the uncertainty in the measurement of p (delta p) is large for the inequality to hold.
I don't fully understand what is going on here. Perhaps I should take Richard Feynman's advice and go to another Universe where the physics is easier.:lol:
A wavefunction can be expressed in either position space (x-space) or momentum space (k-space).
The relationship between position and momentum operators is given by
p=-ih(d/dx). That is where your imaginary i term comes into it.
Unfortunately it's not that simple to state your real terms correspond to position and imaginary terms to momentum.
In both x-space and k-space the wavefunctions are complex valued.:)
It seems the key to this is the coupling of the wavefunction of the photons to the pointer (which is also a wavefunction).
That would be great Carl.
24-06-2011, 05:08 PM
Aha !! … ok … that makes sense, now !
Ya caught me out before I could eliminate the 'eigenvalue' "furphie" which sneaked into my reply post .. (later stealthily removed .. :evil: ) …
Undeterred by this however, I'll assume that you mean the bit about how they're associating the real and imaginary parts with position and momentum, though ..(??).. :)
I notice the use of the term 'pointer' .. it seems to be defined a bit like an index 'pointer' in database terminology … the coupling would seem to be the source of establishing the weak part. This 'weak theory' stuff is pretty controversial too, I notice. Not much agreement on its application by QM theorists, apparently ...
Ditto .. thanks Carl .. (although I fear what's in it )!!
PS: I'm having recall here at present … this mathematics is so close to applied maths in electrical engineering it ain't funny .. if only my memory was better ..
25-06-2011, 01:54 AM
Here it is...
25-06-2011, 01:58 AM
Give me a day or so to read it and I'll see if I can make head or tail of it. I had a quick read this arvo. Didn't look too stressful:)
There are quite a few '(Quantum) Wave Functions for Dummies'-type articles to be found online.
25-06-2011, 09:49 AM
Well, despite that being the case, why not avail us with your knowledge and give us a rundown on what the theory says. Especially, if you're a physicist. Who better to learn off.
26-06-2011, 07:00 PM
Read the Nature article. It doesn't go into great detail in how the real and imaginary components of the wavefunction are equated to position and momentum respectively. These are mentioned in the footnotes.
The mathematics in the article is quite skimpy resulting in logical inconsistencies with the mathematics that is presented.
26-06-2011, 07:13 PM
Yep .. Steven;
I was waiting for your advice on this .. just below equation (1) there is some dialogue about how it is supposed to come about. Unfortunately, it kind of just states that the 'expectation value' can be complex number and because of this, the weak value 'could be used to indicate both real and imaginary parts of the wavefunction'. (No further explanation seems to be given).
I wasn't too sure about my interpretations of it all, but it seems that you may see it as being a bit deficient, also.
Not to worry
I'll bet there's a whole textbook on all this somewhere and I'll bet the unintuitive part is explained in the derivations of equations (1) and (2).
Thanks for reading up on it though.
Just the measurement apparatus is hard to understand
let alone how it relates to the wavefunction !
Thanks for access to the paper too, Carl.
26-06-2011, 07:26 PM
The problem with the Nature article, is as Steven said. It's assuming too much of the maths that's presented in it to cover the explanations given in the article. It's assuming that the reader already knows the maths behind it, so they don't go into the details of the maths. Just leave it to the footnotes for people to follow up.
Has nice piccies, though:P
26-06-2011, 07:26 PM
Might go check arXiv to see if there's anything there.
26-06-2011, 07:27 PM
Equations (1) and (2) is textbook quantum mechanics.
The problem lies in this statement.
Followed a few lines later by
This implies that the expectation value of <A> is real.
For this condition to be true A needs to be a Hermitian operator not an arbitrary variable A as stated in the first quote.
While this may seem trivial if you made this error in a maths exam on quantum mechanics, would result in certain failure.
26-06-2011, 07:35 PM
This 'Lundeen' guy has written several papers (6 since 2005) on weak measurement and double slits. He's also specialised on sorting out this 'Hardy's Paradox'.
I think the explanation for all this must be somewhere in the other papers ..
(if one has the energy to wade thru 'em all).
26-06-2011, 07:42 PM
Just checked....plenty of articles but none of them are too specifically related to this article (direct quantum wavefunction measurement). At least, those I saw listed there and not using the methods from this article.
Lundeen has 27 papers listed at arXiv.org.
26-06-2011, 07:48 PM
It probably is, seeing that these earlier papers probably lead upto this one. At least some of the theory would've been covered in the earlier articles.
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