Ok as promised here is what I think is the definitive paper on the two slit experiment
http://arxiv.org/abs/quant-ph/0703126
It shows how the quantum formalism works. Most text books as Marcella points out never show a consistent explanation from the principles of quantum mechanics. The analogy is made with classical optics one never sees a quantum explanation. I really wish this paper were known more widely it's a gem.
Wednesday, 19 January 2011
Tuesday, 18 January 2011
Demystifying quantum mechanics prologue
Ok it was bound to happen sooner or later I would be provoked by an article or TV program on quantum mechanics claiming that it's all mysterious, no one can understand it, it is totally counterintuitive and so forth. I'm afraid I find all this talk at misleading and at worse really no more than absolute tosh. The culprit in question was last nights Horizon programme shown on BBC2 last night. I can only sketch my objections into what I imagine will be a big theme of these blogs. For now I just want to point out some of the claims that I object to and I will try and provide appropriate references for each of the claims in a series of posts.
1) The two slit experiment implies that particles split in two and then reform before impinging on a screen.
2) Particles after separating from a common source still stay in communication with each other and send signals faster than the speed of light
3) Every time a measurement is made a parallel universe is made
4) Objects are created simply by an act of measurement
and so forth,
Ok to give some clues to more detailed posts, the interpretation I favour, if it can be called an interpretation is the minimal statistical model. It seems to me that much of the so called mystique surrounding the interpretation of quantum mechanics stems from the fact that people refuse to take the probabilistic aspects of quantum mechanics seriously. I will expound more in a later post but let's just take the two slit experiment for example. The facts are that it is only possible to see the classic interference pattern emerging as a result of a cumulative number of events. Indeed it is only after a statistical significant events have occured that anything like wave like properties can be attributed to a photon or electron. Conversely it makes sense to speak of certain attributes of particles such as their mass or charge as belonging to individual particles. Rather than as some people would have it that particles split in two and then magically reform why not simply admit that the so called interference pattern is no different from say the way in which other probability distributions emerge from a collection of events eg the binomial distribution. OK the interesting question is why the probability distribution in events like the two slit experiment are not the same as would be classically expected. But please do not try and interpret what is primarily a statistical phenomenon on what is alleged to happen to a single particle. It has just as much significance as a single throw of the dice does or a single roll of a roulette wheel. If particles really did split into when they pass through slits why are we bothering with the Large Hadron collider ?
I will provide a link to a paper which shows how the formalism of quantum mechanics taken for what it is can explain the essential features of the two slit experiment without having to invoke wave particle duality or the idea that particles split in two when passing through slits. The essential feature is that the slits can be seen as measuring devices the uncertainty in position measurement allows for the uncertainty in momentum arising in an interference pattern.
1) The two slit experiment implies that particles split in two and then reform before impinging on a screen.
2) Particles after separating from a common source still stay in communication with each other and send signals faster than the speed of light
3) Every time a measurement is made a parallel universe is made
4) Objects are created simply by an act of measurement
and so forth,
Ok to give some clues to more detailed posts, the interpretation I favour, if it can be called an interpretation is the minimal statistical model. It seems to me that much of the so called mystique surrounding the interpretation of quantum mechanics stems from the fact that people refuse to take the probabilistic aspects of quantum mechanics seriously. I will expound more in a later post but let's just take the two slit experiment for example. The facts are that it is only possible to see the classic interference pattern emerging as a result of a cumulative number of events. Indeed it is only after a statistical significant events have occured that anything like wave like properties can be attributed to a photon or electron. Conversely it makes sense to speak of certain attributes of particles such as their mass or charge as belonging to individual particles. Rather than as some people would have it that particles split in two and then magically reform why not simply admit that the so called interference pattern is no different from say the way in which other probability distributions emerge from a collection of events eg the binomial distribution. OK the interesting question is why the probability distribution in events like the two slit experiment are not the same as would be classically expected. But please do not try and interpret what is primarily a statistical phenomenon on what is alleged to happen to a single particle. It has just as much significance as a single throw of the dice does or a single roll of a roulette wheel. If particles really did split into when they pass through slits why are we bothering with the Large Hadron collider ?
I will provide a link to a paper which shows how the formalism of quantum mechanics taken for what it is can explain the essential features of the two slit experiment without having to invoke wave particle duality or the idea that particles split in two when passing through slits. The essential feature is that the slits can be seen as measuring devices the uncertainty in position measurement allows for the uncertainty in momentum arising in an interference pattern.
Saturday, 8 January 2011
Review of A211 Philosophy and the Human Condition Part 1
As some people seem to be in a reflective mood (Well Nilo anyway) I thought as I'm still between courses I would finally post some initial thoughts on A211. Philosophy and the Human Condition. This year is the last time the OU will be presenting this course and in October a New course will begin. A211 tries to achieve two quite separate aims one is an introduction to critical thinking namely learning how to follow a persons argument and if need be translate it in to premise conclusion form, this is a precursor to formal logic and can be quite useful in teasing out hidden assumptions. The course material covered 6 different areas and whilst some were what I would expect in an introduction to philosophy I have to say others were really quite idiosyncratic choices.
The units were as follows
Unit 1 Arguments for Freedom. This unit looks at the concept of Freedom starting with an account of Isaiah Berlin's distinction between negative freedom and positive freedom. Negative freedom is the freedom to pursue whatever one wants without restriction whereas positive freedom is the claim that we often make bad choices and these restrict us from fulfilling our full potential. Positive freedom is fine, if it's just us becoming aware of how the choices we make (eg watching telly instead of doing a TMA ) interfere with our long term goals. However often in the hands of the state it can become coercive people such as Rousseau or the Catholic church claim to know what is the general good and seek to impose this on other people who don't share their aims. After a brief discussion of Lockes essay on tolerance the core of the unit was devoted to a discussion of Mill's harm principle which is essentially the idea that people should be free to do say or believe whatever they want provided it doesn't cause physical harm to others. To my mind (despite the recent railings of the Pope against liberal secularism) this is a key value of liberal secularism. Liberalism It is not a collapse into moral relativism as religious critics seem to think, For example to take an example which seems to cause liberals much agonising. Many cultural practices such as female circumcison, discrimimation against women, ethnic minorities and people of different sexual orientation are justified in the name of cultural tradition. However these are all clear violations of the Harm principle, it is not cultural imperialism to criticise these as some people would claim but a sense of fighting against unjust and discriminatory practices. When the Pope criticises liberal secularists for not having values he is really saying that he wants his institution to carry out his discriminatory practices free from legitimate criticism. When liberals criticise the Pope's condemnation of the use of condoms this is done as a genuine concern for the harm that turning women into essentially breeding machines in the third world has done to both the women's lives and the dangers of overpopulation. Thus it is not that liberals have no values but there is a real clash of values.
Another key point of Mill is that offence is no harm. If I don't like a play or book because it criticises or mocks my beliefs I have no right to force it to be closed or shut down or cause violence in the streets . I do have a right to criticise it if I don't like it by writing letters to the press, making a peaceful protest etc. On this basis the increasingly successful campaigns to ban certain plays or books such as the Jerry Springer show, the burning of the Satanic verses and the shutting down of a play for fear of mob violence criticising the Seikhs in Birmingham a few years ago has no justification. I'm afraid I have no sympathy with the ease at which some religious fundamentalists be they Christian, Muslim. Hindu or otherwise take offence at certain publications.
I feel that every politician, religious leader and so forth should take on board the insights of Mill here. I found this unit quite thought provoking and relevant to today. Mill's Harm principle seems to me to be an almost universal ethical principle enabling people of different beliefs and life styles to live with each other and the ability to take on board legitimate criticism and toleration of different lifestyles provided no physical harm to other people is caused seems to me to be a necessary part of growing up.
I'll just briefly mention the two units which I didn't find all that inspiring namely the one on animal rights and the one on environmental ethics. I'll talk about the other units in later posts.
The units were as follows
Unit 1 Arguments for Freedom. This unit looks at the concept of Freedom starting with an account of Isaiah Berlin's distinction between negative freedom and positive freedom. Negative freedom is the freedom to pursue whatever one wants without restriction whereas positive freedom is the claim that we often make bad choices and these restrict us from fulfilling our full potential. Positive freedom is fine, if it's just us becoming aware of how the choices we make (eg watching telly instead of doing a TMA ) interfere with our long term goals. However often in the hands of the state it can become coercive people such as Rousseau or the Catholic church claim to know what is the general good and seek to impose this on other people who don't share their aims. After a brief discussion of Lockes essay on tolerance the core of the unit was devoted to a discussion of Mill's harm principle which is essentially the idea that people should be free to do say or believe whatever they want provided it doesn't cause physical harm to others. To my mind (despite the recent railings of the Pope against liberal secularism) this is a key value of liberal secularism. Liberalism It is not a collapse into moral relativism as religious critics seem to think, For example to take an example which seems to cause liberals much agonising. Many cultural practices such as female circumcison, discrimimation against women, ethnic minorities and people of different sexual orientation are justified in the name of cultural tradition. However these are all clear violations of the Harm principle, it is not cultural imperialism to criticise these as some people would claim but a sense of fighting against unjust and discriminatory practices. When the Pope criticises liberal secularists for not having values he is really saying that he wants his institution to carry out his discriminatory practices free from legitimate criticism. When liberals criticise the Pope's condemnation of the use of condoms this is done as a genuine concern for the harm that turning women into essentially breeding machines in the third world has done to both the women's lives and the dangers of overpopulation. Thus it is not that liberals have no values but there is a real clash of values.
Another key point of Mill is that offence is no harm. If I don't like a play or book because it criticises or mocks my beliefs I have no right to force it to be closed or shut down or cause violence in the streets . I do have a right to criticise it if I don't like it by writing letters to the press, making a peaceful protest etc. On this basis the increasingly successful campaigns to ban certain plays or books such as the Jerry Springer show, the burning of the Satanic verses and the shutting down of a play for fear of mob violence criticising the Seikhs in Birmingham a few years ago has no justification. I'm afraid I have no sympathy with the ease at which some religious fundamentalists be they Christian, Muslim. Hindu or otherwise take offence at certain publications.
I feel that every politician, religious leader and so forth should take on board the insights of Mill here. I found this unit quite thought provoking and relevant to today. Mill's Harm principle seems to me to be an almost universal ethical principle enabling people of different beliefs and life styles to live with each other and the ability to take on board legitimate criticism and toleration of different lifestyles provided no physical harm to other people is caused seems to me to be a necessary part of growing up.
I'll just briefly mention the two units which I didn't find all that inspiring namely the one on animal rights and the one on environmental ethics. I'll talk about the other units in later posts.
Wednesday, 5 January 2011
Happy new Year
Well another new year starts doesn't feel like it in gloomy Edinburgh going to work in the dark and coming home back in the dark is guaranteed to make me grumpy and also lethargic. I managed to stick to my time table for watching the Ring cycle but my other ambitions took a back burner and I basically vegetated for most of the Christmas break. The materials for M208 have arrived but as I already had a copy no great surprises. The unfortunate thing is that this year the Open University have decided to issue the TMA's on line only. As a consequence despite reading Brannan's book I feel I haven't really started. However as the Introductory units seem to be a basic revision of Unit D of MST221 (without the tedious RSA coding thank goodness) it should be fairly straightforward. The first unit is on curve sketching so I suspect the first question will be a 'Tedious but Straightforward' exercise of systematically finding the asymptotes, stationary points etc of a function which will probably be a rational polynomial of some form or other with at least two zero's. The rest of the Introductory units cover Complex Numbers, proof by Induction (fine if you don't have to do it under exam pressure) and other related proof stuff. Also a first look at the number system in preparation for the analysis units. Block 1 covers the first part of group theory and goes further than MST221. Having used quite a lot of group theory in my physics studies it will be interesting to compare the 'Pure maths approach' with the physicist's approach.
Physicist's are usually given a quick run through of the main definitions then its straight into representation theory (basically reducing all group operations to matrices) with the aim of applying it first to things like molecular vibrations, then when particle physics is studied its continuous group theory with an intuitive approach to Lie groups.
Then a somewhat tenuous link (IMHO) is made to grouping particles by their various quantum numbers. It starts off OK given that the mass of the neutron and proton are roughly the same so it makes sense to see them as identical apart from their charge. This symmetry is called isospin. Then when it comes to grouping various mesons and baryons together there is quite a convincing decuplet and octet which Gell Mann found could be considered simplified using a basis state of three particles known as quarks. Mesons essentially being seen as a combination of a quark and an antiquark and baryons being a combination of 2 quarks with one antiquark. If you postulate as Gell Mann did that quarks have a charge of either 1/3 the charge of an electron or two thirds all the particle states can in principle be constructed from these basic building blocks. This led to the postulation of SU(3) symmetry. However amongst these islands of connection with reality there are a vast combination of possible quark states which do not correspond to any particle.
Furthermore since Gell Mann's day we now know there are 6 quarks instead of the original three. In the standard model of particle physics these are grouped in pairs allegedly of similar mass. Whilst this is OK for the so called first generation, the mass discrepancy for the second generation is quite significant, and by the time you get to the third generation it really seems incredible to group the 5th and 6th quarks together on the basis of their mass. The current masses along with their ratios are as follows
1 u (up) 6 MeV
2 d (down) 10 MeV ratio d/u = 1.67
3 s (Strange) 0.25 GeV
4 c (Charm) 1.2 GeV ratio c/s = 4.8
5 b (bottom) 4.3 GeV
6 t (top) 180 GeV ratio t/b = 180/4.3 = 41.8
It may well be that this current grouping is incorrect, hopefully when data starts coming from the Large Hadron Collider that the top quark is seen as the lower mass of another grouping of quarks, in which case
much of the underlying symmetry of the current Standard model will have to be rewritten. I really hope something new will come along to shake us out of our current complacency.
Hm I seem to have digressed. For those who want a physicists approach to group theory I refer to the excellent notes given by Peter Osborne for Cambridge Part III students
http://www.damtp.cam.ac.uk/user/examples/indexP3.html
The notes and example sheets are for the course 3P2 Particles and Symmetries. I hope to make a reasonable attempt to read these notes and make a decent stab at some of the example sheets over the next year to complement the Pure maths aspects of group theory that I will be getting from M208.
For those who don't have the background in quantum mechanics then sections 1 and section 5 of the undergraduate course on the principles of quantum mechanics gives a quick overview.
http://www.damtp.cam.ac.uk/user/examples/
Some of you reading this blog will be aware than Duncan and I have tried one or two of the more basic undergraduate problems from the dynamics sheets to do with rotational motion and I hope to continue to work my way through some of the other sheets. Particularly Mathematical Methods, Differential equations and Complex Methods. However I also want to reach for the sky and try my hand at the particle symmetries course.
Physicist's are usually given a quick run through of the main definitions then its straight into representation theory (basically reducing all group operations to matrices) with the aim of applying it first to things like molecular vibrations, then when particle physics is studied its continuous group theory with an intuitive approach to Lie groups.
Then a somewhat tenuous link (IMHO) is made to grouping particles by their various quantum numbers. It starts off OK given that the mass of the neutron and proton are roughly the same so it makes sense to see them as identical apart from their charge. This symmetry is called isospin. Then when it comes to grouping various mesons and baryons together there is quite a convincing decuplet and octet which Gell Mann found could be considered simplified using a basis state of three particles known as quarks. Mesons essentially being seen as a combination of a quark and an antiquark and baryons being a combination of 2 quarks with one antiquark. If you postulate as Gell Mann did that quarks have a charge of either 1/3 the charge of an electron or two thirds all the particle states can in principle be constructed from these basic building blocks. This led to the postulation of SU(3) symmetry. However amongst these islands of connection with reality there are a vast combination of possible quark states which do not correspond to any particle.
Furthermore since Gell Mann's day we now know there are 6 quarks instead of the original three. In the standard model of particle physics these are grouped in pairs allegedly of similar mass. Whilst this is OK for the so called first generation, the mass discrepancy for the second generation is quite significant, and by the time you get to the third generation it really seems incredible to group the 5th and 6th quarks together on the basis of their mass. The current masses along with their ratios are as follows
1 u (up) 6 MeV
2 d (down) 10 MeV ratio d/u = 1.67
3 s (Strange) 0.25 GeV
4 c (Charm) 1.2 GeV ratio c/s = 4.8
5 b (bottom) 4.3 GeV
6 t (top) 180 GeV ratio t/b = 180/4.3 = 41.8
It may well be that this current grouping is incorrect, hopefully when data starts coming from the Large Hadron Collider that the top quark is seen as the lower mass of another grouping of quarks, in which case
much of the underlying symmetry of the current Standard model will have to be rewritten. I really hope something new will come along to shake us out of our current complacency.
Hm I seem to have digressed. For those who want a physicists approach to group theory I refer to the excellent notes given by Peter Osborne for Cambridge Part III students
http://www.damtp.cam.ac.uk/user/examples/indexP3.html
The notes and example sheets are for the course 3P2 Particles and Symmetries. I hope to make a reasonable attempt to read these notes and make a decent stab at some of the example sheets over the next year to complement the Pure maths aspects of group theory that I will be getting from M208.
For those who don't have the background in quantum mechanics then sections 1 and section 5 of the undergraduate course on the principles of quantum mechanics gives a quick overview.
http://www.damtp.cam.ac.uk/user/examples/
Some of you reading this blog will be aware than Duncan and I have tried one or two of the more basic undergraduate problems from the dynamics sheets to do with rotational motion and I hope to continue to work my way through some of the other sheets. Particularly Mathematical Methods, Differential equations and Complex Methods. However I also want to reach for the sky and try my hand at the particle symmetries course.
Friday, 24 December 2010
Happy Christmas to you all (Bah Humbug)
Not having a family or partner I shall be spending Christmas on my own however whilst those of you forced to entertain the in laws, spend a vast fortune on presents for your kids which will be discarded within a couple of days, and eating tasteless turkey/ I shall be watching Wagner's Ring cycle a rough time table is as follows
Tonight from 7 : pm - 9:30
Das Rheingold
10:30 to midnight approx
Act 1: Das Valkyrie
Christmas Day
10:00 am to 12:30 pm Act II Das Valkyrie (the Crucial act in my opinion)
2:00 - 3:30 Act III Das Valkyrie (Means I wont be watching the queen';s speech oh dear what a pity ;))
Cook my special dinner
6:00 - 7:30 Act I Siegfried
9:00 - 10:30 Act II Siegfried
Boxing Day
10: 11:30 Act III Siegfried
1:00 - 3:30 Act I Gotterdammerung
5:00 - 6:30 Act II Gotterdammerung
8:00 - 9:30 Act III Gotterdammerung
So I've stocked up on food and booze and if I get through that timetable I shall be as high as a kite and pissed as a newt and sufficiently energised to get back to some maths after that. I'll give a post on what I think the ring cycle means
Anyway whatever you are doing over the festive season have a good one
Best wishes to you all Chris
Tonight from 7 : pm - 9:30
Das Rheingold
10:30 to midnight approx
Act 1: Das Valkyrie
Christmas Day
10:00 am to 12:30 pm Act II Das Valkyrie (the Crucial act in my opinion)
2:00 - 3:30 Act III Das Valkyrie (Means I wont be watching the queen';s speech oh dear what a pity ;))
Cook my special dinner
6:00 - 7:30 Act I Siegfried
9:00 - 10:30 Act II Siegfried
Boxing Day
10: 11:30 Act III Siegfried
1:00 - 3:30 Act I Gotterdammerung
5:00 - 6:30 Act II Gotterdammerung
8:00 - 9:30 Act III Gotterdammerung
So I've stocked up on food and booze and if I get through that timetable I shall be as high as a kite and pissed as a newt and sufficiently energised to get back to some maths after that. I'll give a post on what I think the ring cycle means
Anyway whatever you are doing over the festive season have a good one
Best wishes to you all Chris
Saturday, 18 December 2010
Test of Dropbox
Thanks to Nilo he pointed me to a way in which files can be shared called dropbox. As a test of whether or not it works I enclose a link to my simplified big bang calculation
http://dl.dropbox.com/u/16049029/Bigbang_simp.pdf
As stated in an earlier post, it is quite surprising just how a simple calculation like this can get close to the results for the real calculation. I know that there is speculation that the extrapolation from the 1st 100th second backwards breaks down, however this bit is I would claim robust physics, in that it is the only convincing explanation of the relative abundances of Hydrogen and Helium in the early universe. A large piece of the jigsaw. Given the relative simplicity of the calculation it should be accessible to any one with a mathematical knowledge equivalent to MS121 and physics at the level of S207 or anyone with A level/higher physics and A level/higher mathematics. As such I believe it should be more widely known. If the dropbox link works I'll post a whole lot of other files here. At the minute this is a pdf of a word document I hope over the next year or so to migrate to LaTEX.
Best wishes Chris.
http://dl.dropbox.com/u/16049029/Bigbang_simp.pdf
As stated in an earlier post, it is quite surprising just how a simple calculation like this can get close to the results for the real calculation. I know that there is speculation that the extrapolation from the 1st 100th second backwards breaks down, however this bit is I would claim robust physics, in that it is the only convincing explanation of the relative abundances of Hydrogen and Helium in the early universe. A large piece of the jigsaw. Given the relative simplicity of the calculation it should be accessible to any one with a mathematical knowledge equivalent to MS121 and physics at the level of S207 or anyone with A level/higher physics and A level/higher mathematics. As such I believe it should be more widely known. If the dropbox link works I'll post a whole lot of other files here. At the minute this is a pdf of a word document I hope over the next year or so to migrate to LaTEX.
Best wishes Chris.
Thursday, 16 December 2010
Results In
Hi I'll post more later but my results for Both A211 Philosophy and the Human Condition and MST221 are both in. I managed to get 85% for both exams so just scraped a distinction for both courses. I was really surprised for A211 as my essays only averaged 78% well within grade 2 territory. They must have applied some discretion. Anyway needless to say I'm chuffed to bits. I apologise for not posting much before a combination of a severe cold and the bad weather. I'm currently looking at solving differential equations by series solution of which more later
I'll also post my thoughts on A211 in the next few days
I'll also post my thoughts on A211 in the next few days
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