Just a quick post to inform readers that my results are out
I got grade 3 for music with 61% OCAS (TMA's not bad since I only submitted 5 out of 6 ( and there is no substitution ) and 65% for the EMA (Extended Module Assessment) so reasonable there is as yet no feedback for the EMA but it's forthcoming
As for Fluids I failed with 37% for the exam and 71% for the continuous assessment I've been offered a resit but it will be capped most I can get is grade 4 .
Still as I would like the opportunity to hone my exam technique and reconsolidate the material it will be worth doing. Also it's another excuse to keep up with partial differenctial equations and mathematical methods.
My course schedule for this year is
SM358 Quatum mechanics exam in October
M381 logic and number theory starting in October
Physics project on entanglement Feb 2014
Also for music
I will enrol for grade 4 theory exam in November with a theory exam every 6 months or so till I get to grade 8 start piano lessons in September and hopefully do grade 1 piano exams in March 2014
I decided it would be far to much for me to take on board AA308 the third level course in philosophy this year round. It's allegedly in it's last presentation this year with a replacement in Oct2014 but going on previous form I can't see this happening so hopefully it will be available in October I really hope so as from a preliminary survey I don't really like the prospectus for the new course without being to harsh it fits into "waffle philosophy".That is philosophy good for discussion at dinner parties but hardly cutting edge philosophy that one would expect for a third level course in the subject. On the other hand AA308 whilst not perfect does cover philosophy of the mind at a level comparable to that of other 3rd year undergraduate brick level courses.
I am seriously begining to think the only way in which to get a rigorous training in philosophy is to bite the bullet and do the external London BA in philosophy even though I wont be able to start for another two years. Watch this space.
Friday, 26 July 2013
Saturday, 20 July 2013
SM358 quantum mechanics TMA03
Ok so back to quantum mechanics I have just submitted the third TMA and am reasonably confident I've done enough to get a grade two pass not that this matters for the assessment as one only needs above 30% in seven of the assessments of which at least two must be TMA's. Due to the intensity of revising for both my music course and fluid mechanics I was unable to complete the second TMA but will look at it for the exam.
Anyway a breakdown of the TMA questions is as follows
1) A question on the time dependence of spin states the basic theory of which under pins magnetic resonance imaging. One had to calculate how a composite spinor would vary with time the expectation values of the Sx and Sy spin components and check that the results were consistent with the generalised Ehrenfest theorem I got consistent answers so am reasonably confident I got most of this correct.
2) A question involving the symmetries of a system of two particles in a square well. Given a spin state one with a given Spin quantum number S one had to determine the symmetry of the spatial wavefunction. So if the spin state is zero say for a pair of fermions with a wavefunction that is asymmetric if the spin part is antisymmetric, the spatial part of the wavefunction must be symmetric to maintain the overall antisymmetry of the wave function. This was again relatively straightforward although one had to calculate the probability that both particles would be in the left hand side of the box from the joint wavefunction and this was quite tedious also causing word to crash a number of times as the equation editor can't handle to much copying of equaitons without it crashing. Always remember to save the document after writing complicated equations.
3) A question on the polarisation states of a pair of photons and a gentle run through of the steps leading to the violation of the Bell inequalities or in our case to be more precise the Clauser Horne Shimony (CHSH) inequalities. Plus a short description of what a non local hidden variable theory was. All this was straightforward and satisfying. Although I do feel that the way the text has phrased the two conditions of realism and non realism slightly misleading to say the least
It defines the features of a local hidden variable theory as follows
a) Realism implies that observables have values independent of meausrement
With of course the implication that if the so called collapse of the wavefunction is seen as a physical process observables in quantum mechanics are not independent of measurement. That is not strictly true its only non commuting variables that on the standard view do no have values independent of measurement. Quantities such as mass and charge are commutative and so do have values of measurement. Also if as I have argued in many posts before the wavefunction is just a means for calculating the correct probabilities and nothing physical then nothing can be said to collapse.
b) Locality implies that events at any location cannot influence what happens at another location before a light signal could travel between the two locations
This is of course the standard view with the implication that in situations such as the Aspect experiment when a measurement is made on one photon it causes the other photon to jump into the opposite spin state even though they may be miles away thus implying some faster than speed of light influence between the particles.
Of course the formalism of quantum mechanics says nothing about what might be causing the correlation but that hasn't stopped all sorts of weird and wonderful ideas about it.
A more prosaic view would say that non locality is essentially the fact that the probability distributiion function for a joint pair of variables is non separable whereas for local theories they are. All that happens in the Aspect experiment is that because the pair of particles have to have a net angular momentum of zero and this dicatates the form of the wavefunction for the joint pair of particles leading to the correlation. But no more can be said certainly there is no need to invoke faster than light signalling as some people are prone to. That is an addition to the formalism not warranted by the facts.
Finally whilst it's true to say that local hidden variable theories have been refuted the current form of hidden variable theories are in fact non local. The issue is still wide open, What one can't have is the usual view that quantum mechanics is both non realist and non local. If you claim that quantum mechaincs is non realist with respect to non commuting variables then there is no need to claim that quantum mechanics is non local. And also the non realism associated with quantum mechanics is only a limited form of non realism.
I didn't have the space to go into this in any detail in the assignment. It does concern me slighthly that misleading interpretations are being passed of as fact when in fact the situation is not as black and white as some people make out. Watch this space for when I embark on the entanglement project.
Anyway a breakdown of the TMA questions is as follows
1) A question on the time dependence of spin states the basic theory of which under pins magnetic resonance imaging. One had to calculate how a composite spinor would vary with time the expectation values of the Sx and Sy spin components and check that the results were consistent with the generalised Ehrenfest theorem I got consistent answers so am reasonably confident I got most of this correct.
2) A question involving the symmetries of a system of two particles in a square well. Given a spin state one with a given Spin quantum number S one had to determine the symmetry of the spatial wavefunction. So if the spin state is zero say for a pair of fermions with a wavefunction that is asymmetric if the spin part is antisymmetric, the spatial part of the wavefunction must be symmetric to maintain the overall antisymmetry of the wave function. This was again relatively straightforward although one had to calculate the probability that both particles would be in the left hand side of the box from the joint wavefunction and this was quite tedious also causing word to crash a number of times as the equation editor can't handle to much copying of equaitons without it crashing. Always remember to save the document after writing complicated equations.
3) A question on the polarisation states of a pair of photons and a gentle run through of the steps leading to the violation of the Bell inequalities or in our case to be more precise the Clauser Horne Shimony (CHSH) inequalities. Plus a short description of what a non local hidden variable theory was. All this was straightforward and satisfying. Although I do feel that the way the text has phrased the two conditions of realism and non realism slightly misleading to say the least
It defines the features of a local hidden variable theory as follows
a) Realism implies that observables have values independent of meausrement
With of course the implication that if the so called collapse of the wavefunction is seen as a physical process observables in quantum mechanics are not independent of measurement. That is not strictly true its only non commuting variables that on the standard view do no have values independent of measurement. Quantities such as mass and charge are commutative and so do have values of measurement. Also if as I have argued in many posts before the wavefunction is just a means for calculating the correct probabilities and nothing physical then nothing can be said to collapse.
b) Locality implies that events at any location cannot influence what happens at another location before a light signal could travel between the two locations
This is of course the standard view with the implication that in situations such as the Aspect experiment when a measurement is made on one photon it causes the other photon to jump into the opposite spin state even though they may be miles away thus implying some faster than speed of light influence between the particles.
Of course the formalism of quantum mechanics says nothing about what might be causing the correlation but that hasn't stopped all sorts of weird and wonderful ideas about it.
A more prosaic view would say that non locality is essentially the fact that the probability distributiion function for a joint pair of variables is non separable whereas for local theories they are. All that happens in the Aspect experiment is that because the pair of particles have to have a net angular momentum of zero and this dicatates the form of the wavefunction for the joint pair of particles leading to the correlation. But no more can be said certainly there is no need to invoke faster than light signalling as some people are prone to. That is an addition to the formalism not warranted by the facts.
Finally whilst it's true to say that local hidden variable theories have been refuted the current form of hidden variable theories are in fact non local. The issue is still wide open, What one can't have is the usual view that quantum mechanics is both non realist and non local. If you claim that quantum mechaincs is non realist with respect to non commuting variables then there is no need to claim that quantum mechanics is non local. And also the non realism associated with quantum mechanics is only a limited form of non realism.
I didn't have the space to go into this in any detail in the assignment. It does concern me slighthly that misleading interpretations are being passed of as fact when in fact the situation is not as black and white as some people make out. Watch this space for when I embark on the entanglement project.
Sunday, 7 July 2013
What is an explanation ?
This post is motivated by some debates I've been having on the OU quantum physics fora about the nature of explanation especially in physics. In quantum mechanics we have what I consider to be, a rather bizzare claim that despite the fact that trained physicists are able to use the formalism to predict measurable quantities about atomic systems such as the energy levels or particle decay rates. The claim is made in many circles that no one is able to understand quantum physics. Yet clearly those who can use the formalism of quantum mechanics to successfully model say the properties of solids, lasers, the properties of stars etc obviously do understand a great deal about how qunatum physics works.
I suppose the problem is that quantum physics (at least in it;s Non-relativistic formalism) uses a quantity called the wavefunction, but, as I've argued before in previous posts better seen as a probability state vector who's modulus squared gives rise to a probability density function and whos eigenvalues can be related to the energy levels or decay rates of atoms, molecules or solids. The problem is that for an N body system the so called wavefunction becomes a function of the 3 N coordinates of the system. So if it is seen as a field analagous to an electromagnetic field or the gravitational field. It is a field in the 3N+1 configuration space of the system rather than our normal 3 dimensional space. Matters are even more complicated when extra variables such as spin are also included. Spin has no spatial or time component so what is spin really ?
The other key issue is the notorious collapse of the wave function if there is a possibility that a particle can be in one of two or more states then it is said to be in limbo until a measurement is made and then it collapses into one of it;s states and in situations like the Aspect experiment this influence is said to occur at speed's faster than the speed of light because given a pair of photons emitted from a common source then so the story goes if I measure the spin of one photon it immediately causes the other photon which could be miles away to have the opposite spin.
So alleged mystery on mystery even if the formalism gives a precise mathematical description of the wave function and there are precise rules which can be learnt by anyone prepared to put the effort in learning the maths how to use it to predict the essential features of quantum systems.
As I've explained before much of the mystery can be dissolved if the wave function is seen for what it is mathematically namely the complex square root of a probability distribution function or a complex probability amplitude. The configuration space of an N body system is simply the probability sample space associated with the system and one can include spin variables in this with out any worry about the existence of such an entity as a field in configuration space. The only difference between qunatum probability and every day probability is that one needs to use complex probability amplitudes and the Born rule in order to obtain the correct probability density function for a given situation.
I explain how all this works here
http://chrisfmathsphysicsmusic.blogspot.co.uk/search?q=Two+state+
I can not stress to highly how it really is quite instructive to cast the language of classical probability in terms of quantum probablilty. No one claims that the probability state vector of a coin or dice is a real superposition of head or tail states why should we do the same for quantum systems.
Accepting the intrinsic statisitical nature of quantum physics seems to me to dissolve a lot of the conceptual problems associated with quantum physics. The superposition of quantum states is a superposition of quantum probablities and the quantum state is a mathematical description of the possibilities open to a given system. Nothing collapses physically when a measurement is made and nothing exists in (3N+1)*S configuration space where S is the sum of all the allowable spin states.
OK we still don't know why we have to use complex probability amplitudes, but once we accept that then the rest follows. I would say the successful use of the formalism by physicists to model more and more complicated situations does mean that we do understand how quantum physics works and those who are able to use it can genuinely be said to understand the phenomenon they are trying to model.
As a final point even Classical physics which was claimed to be understood used quantities which were quite mysterious, No one knew what gravity was apart from the fact that it obeyed an inverse square law. No one knew how electromagnetic waves could propagate through free space or what entropy was. Of course that didn't stop people (as today with the wave function) trying to visualise what an electric field was but these speculations got no where. Helmholtz in a move, seen as desperate by a lot of the people at the time. getting so tired of the endless speculation, claimed that Maxwell's theory was Maxwell's equations.
A statement very similar to the 'Shut up and calculate' approach of Feynman.and other successful physicists who want to develop the applications of quantum mechanics rather than indulge in pretty fruitless speculation about the real nature of the wave-function. If you want to understand quantum physics learn how it is used engage with the maths and learn how to apply it to the phenomenon you are interested in. That way you will begin to get a feel for how quantum mechanics works, and just as no one claimed we didn't understand classical physics even if we couldn't visualise what an electric field was so we should stop claiming that we don't understand how quantum physics works.
I suppose the problem is that quantum physics (at least in it;s Non-relativistic formalism) uses a quantity called the wavefunction, but, as I've argued before in previous posts better seen as a probability state vector who's modulus squared gives rise to a probability density function and whos eigenvalues can be related to the energy levels or decay rates of atoms, molecules or solids. The problem is that for an N body system the so called wavefunction becomes a function of the 3 N coordinates of the system. So if it is seen as a field analagous to an electromagnetic field or the gravitational field. It is a field in the 3N+1 configuration space of the system rather than our normal 3 dimensional space. Matters are even more complicated when extra variables such as spin are also included. Spin has no spatial or time component so what is spin really ?
The other key issue is the notorious collapse of the wave function if there is a possibility that a particle can be in one of two or more states then it is said to be in limbo until a measurement is made and then it collapses into one of it;s states and in situations like the Aspect experiment this influence is said to occur at speed's faster than the speed of light because given a pair of photons emitted from a common source then so the story goes if I measure the spin of one photon it immediately causes the other photon which could be miles away to have the opposite spin.
So alleged mystery on mystery even if the formalism gives a precise mathematical description of the wave function and there are precise rules which can be learnt by anyone prepared to put the effort in learning the maths how to use it to predict the essential features of quantum systems.
As I've explained before much of the mystery can be dissolved if the wave function is seen for what it is mathematically namely the complex square root of a probability distribution function or a complex probability amplitude. The configuration space of an N body system is simply the probability sample space associated with the system and one can include spin variables in this with out any worry about the existence of such an entity as a field in configuration space. The only difference between qunatum probability and every day probability is that one needs to use complex probability amplitudes and the Born rule in order to obtain the correct probability density function for a given situation.
I explain how all this works here
http://chrisfmathsphysicsmusic.blogspot.co.uk/search?q=Two+state+
I can not stress to highly how it really is quite instructive to cast the language of classical probability in terms of quantum probablilty. No one claims that the probability state vector of a coin or dice is a real superposition of head or tail states why should we do the same for quantum systems.
Accepting the intrinsic statisitical nature of quantum physics seems to me to dissolve a lot of the conceptual problems associated with quantum physics. The superposition of quantum states is a superposition of quantum probablities and the quantum state is a mathematical description of the possibilities open to a given system. Nothing collapses physically when a measurement is made and nothing exists in (3N+1)*S configuration space where S is the sum of all the allowable spin states.
OK we still don't know why we have to use complex probability amplitudes, but once we accept that then the rest follows. I would say the successful use of the formalism by physicists to model more and more complicated situations does mean that we do understand how quantum physics works and those who are able to use it can genuinely be said to understand the phenomenon they are trying to model.
As a final point even Classical physics which was claimed to be understood used quantities which were quite mysterious, No one knew what gravity was apart from the fact that it obeyed an inverse square law. No one knew how electromagnetic waves could propagate through free space or what entropy was. Of course that didn't stop people (as today with the wave function) trying to visualise what an electric field was but these speculations got no where. Helmholtz in a move, seen as desperate by a lot of the people at the time. getting so tired of the endless speculation, claimed that Maxwell's theory was Maxwell's equations.
A statement very similar to the 'Shut up and calculate' approach of Feynman.and other successful physicists who want to develop the applications of quantum mechanics rather than indulge in pretty fruitless speculation about the real nature of the wave-function. If you want to understand quantum physics learn how it is used engage with the maths and learn how to apply it to the phenomenon you are interested in. That way you will begin to get a feel for how quantum mechanics works, and just as no one claimed we didn't understand classical physics even if we couldn't visualise what an electric field was so we should stop claiming that we don't understand how quantum physics works.
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