12-28-11, 02:04 AM #1
My book on physics... (the second chapter)
I appreciate how difficult physics is when explaining it, thus I also appreciate that my book might require some nip and tucks. I am writing this book for an audience who is slightly comfortable with math, and within the age group of 16 and onwards... or to a very very bright 14 year old. I felt compelled to write a book like this because not enough of them are around. I have tended to find you either have a book which explains physics in a very lay way without much mathematical contribution, or you have book which is mostly mathematical and not very good at explaining why something happens. Of course I was aware that too much math might scare some off. So I am still grapping with how much math and how much literature should balance for the perfect novice book.
I am going to post the second chapter of my book. In each chapter I have a small part dedicated to the mathematics of a certain subject. In this part, the math is concerned with angular momentum, aka quantum spin. I would like some honest criticism on my ability to talk about the subjects.
The World of the Infinitessimally small
Atoms, Electrons, Protons and Neutrons... Where does it end?
So now we will take a journey to the world of the quantum. This world is a very small world indeed. In this world, you can fit (in the typical average human) around 7 x 10^27 atoms! An atom, was once believed to be the smallest unit that was physically ''out there.'' Atom's where first proposed by Greek Philosophers who said that the atom would be an indivisible unit.
In fact, this is what the word ''atom'' means in Greek. It means ''indivisible.'' It was a Greek by the name of Democritus in approximately 450 BCE who coined the term átomos, which evolved to the modern day root word of atom. The amount of atoms in the average human body is then:
However, what comes next can be quite startling to the non-scientist. As small as this basic unit of matter is, the atom is in fact made of an even smaller collection of particles. These particles are named ''subatomic particles'' for obvious reasons.
The most basic kind of atom we know about, is the Hydrogen atom. The Hydrogen atom is the chemical element of Hydrogen. Hydrogen is an odorless, colorless and tasteless substance. Water is made of two hydrogen atoms including one atom of Oxygen.
The Hydrogen atom contains two subatomic particles. They are called a proton (which is a positively charged particle) and an electron (which is a negatively charged particle). Together, they make one atomic particle of Hydrogen which will be electrically-neutral because the two charges of the proton and the electron exactly cancel out. Electrons are attracted to the center of the atom under a special force, called the Coulomb Force. The Coulomb Force is an electrostatic force which varies upon the square of the distance. In fact, many laws, such as gravity depend on such an equidistant law where the strength of the force will vary on r^2 from the origin.
Hydrogen is in fact the most abundant observable element in the universe as far as we can tell. There are however many more types of elements which have their own atomic structures. And many of these atomic structures will differ that they may contain inside of them. The proton is what is called a 'nucleon' from the root word nucleus, basically meaning that this particle is always found in the center of particles. However, there are some exotic theories suggesting that certain nucleons might be found in a halo-like structure inside the atoms; but this is a little complicated to understand and really not all too revelevant for the discussion here.
Particles have what are called half lives and their half life is a measure of how long it will take before they will decay into other particles. However, the proton is an exception it seems. It seems to be infinitely stable! It seems this is the case because protons will not decay into other particles on their own because they are the least energetic particles baryon known. Baryon is simply a name we give to a certain class of particles which is a composite particle consisting of three quarks (we shall come to quarks later).
Another type of nucleon which we have not discussed here and which can be found in the center of many atoms is a neutrons. Neutrons are actually electrically-neutral particles which might have been surmised from it's name.
Neutrons actually have a mass which is only a tiny larger than that of a proton. A protons mass is 1,6726 x 10^(-27) kg and the mass of a neutron is 1,6749 x 10^(-27) kg. It differs by quite a little as you can see, using the scientific notation of course. The electron mass is extremely smaller than this. The electrons mass is miniscule in fact 0,00091x10^(-27) kg. In chemistry, it is often taught that because the mass of the electron is so small it is often negligable when calculating the mass of an atom. In fact, you can also speak of the mass of a particle in terms of its MeV (Mega electron Volts). The mass of a neutron is 939.56563 MeV and the mass of a proton is 938.27231 MeV.
The number of protons in an atom make the atoms atomic number. It makes up the charge number of the nucleus, which excludes neutrons since neutrons are electrically neutral. The atomic number, most credibly the outermost electrons (in the electron shell, which we will cover soon) is in fact responsible for electro-chemical bonding between other atoms - in short, particles can share electrons and by doing so, they can keep atoms in close range of other atoms and help create a complex structure giving rise to different elements based on their particular bondings.
The electron shell is basically the configuration of electrons which can be found in an atom. Because of a very interesting dynamical law of atomic physics, no electron can be found to occupy a single electron energy level with another electron (certain ways to avoid violating this law) is by a very special process called quantum spin, which will be discussed very soon.
The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell") and so on. Each shell can only allow a certain amount of electrons. The first shell can hold up to two electrons, the second shell can hold up to eight electrons and again, so on. Electron shells have quite a lot of detail to them which cannot be covered in it's entirety here, for instance, electrons in the outer shell will have a higher energy and will travel farther from the nucleus than those in inner shells. In fact, before the advent of quantum mechanics (the modern theory) we used to believe that electrons would orbit the nucleus much like planets would orbit round their galactic stars. It turned out that this was not the case and the reason for this will be covered in the next part of this chapter, The Quantum Wave Function - but to explain in very simple terms, electron's do not follow defined paths in spacetime. They are actually smeared over all possible paths they might take.
The idea that a particle like an electron could not move around a single path in an atom was in fact a very important factor for quantum field theory. Before quantum field theory, there was a serious problem concerning why electron's simply did not radiate away energy and fall into the nucleus of the atom. Because classical field theory treated an electron with a definate path and position, the electron has a negative charge and should be attracted to the positive charge of the atom which was produced by the proton.
Because of this attraction, classical field theory would have believed that the electron would have spiralled into the nuceus causing a devistating effect. The atom would collapse in a tremendous flash of energy! In fact, every atom would be gobbled up by it's nucleus in about one hundred microseconds.
This is why quantum field theory and it's postulate of the wave function became increasingly popular, along with other reasons. The electron did not in fact have a specific path or a specific position anywhere inside an atom. It did not orbit the nucleus like a planet, but in fact was a product of probability, the measure of the possible states itself of where it might be. This saved the idea that the electron would eventually radiate away energy and fall into the nucleus of atoms; but there was an addition to this postulate as well, known as the Heisenberg Uncertainty Principle.
In much the same respect, this principle created by physicist Werner Heisenberg in 1926 stated that no particle (not bound to electrons alone) have definate locations or trajectories simultaneously. In other words, the Uncertainty principle says that either the location or the momentum of a quantum particle can be known as precisely as one wanted, but as one of these quantities is specified more precisely, the value of the other becomes increasingly indeterminate!
This was a fundamental property of all matter. It has been tested to a high degree and was part and parcel of the reason why electrons simly could not fall into the nucleus of atomic objects.
Particles like the electron and the proton are in a certain class of family. They are called Fermions. Particles which are called Fermions are in fact spin 1/2 particles. Spin is a very interesting subject which we should cover. However, before I begin to cover some of the mathematics of spin, I first want to give an explanation to what it is, or atleast what we believe it is.
The classical electron, is believed to be a sphere with a radius of (e²/Mc²). This is not a measured value. It's a careful analysis of the dimensions of the equation of the radius which says it depends on the electron charge (squared) e² the mass M and the speed of light (squared) c². The quantity in the denominator Mc² actually makes up the rest energy of a particle E_0. The rest energy will be explained in greater detail in the Chapter discussing relativity.
The Classical Electron Radius is in fact 1/137 times larger than the Compton Wavelength. The Compton Wavelength is (h/Mc) where h is Plancks Constant and it has a value of 6.62606957(29)×10^(−34) j.s. The Compton Wavelength itself has a value for the electron as 2.4263102175±33×10^(−12) m (the value varies with different particles) and is a measure itself of the wavelength of a particle being equal to a photon (a particle of light energy) whose energy is the same as the rest-mass energy of the particle. Complicated? Yes it can be.
Basically, all particles have a wavelength. Photon's can never be at rest (again reasons why will be given in the relativity chapter), but the energy of a photon can be low enough to have it's wavelength match any particle who is at rest. It's often seen in the eye's of many scientists as the ''size'' of a particle. Actually, a more accurate representation of the size of an object would be the Reduced Compton Wavelength (reasons given in the chapter references under  ). This is just when you divide the Compton Wavelength by 2π and it gives a smaller representation for the mass of a system.
Now, going back to the electron, the electron as a sphere was accepted by most physicists until the age of the revolutionary quantum field theory. A physicist by the name of Wolfgang Pauli actually predicted a very strange property of all subatomic matter. Using careful experiments, he was able to deduct that particles behaved as though they possessed a spin, just like a spinning top or even better to imagine, the spinning surface of a planet like the Earth.
Wolfgang didn't actually name it spin however, that was later coined by Ralph Kronig, George Uhlenbeck, and Samuel Goudsmit in 1925 and then a mathematical theory was developed by Pauli in 1927. The classical idea of spin came from Noether's (a mathematician) ''generator of rotations'' where it describes a real physical rotation of quantum objects.
This idea soon ran into problems however, because modern quantum field theory did not really believe an electron was classical at all, possessing a radius. In fact, as far as physicists can tell, any attempt at measuring a radius for an electron failed and all experimental data seemed to suggest that the electron was really a pointlike system - that is , a particle which does not have any dimensions which we can obtain from the classical radius. It was just a point and thus some problems began to arise from the mathematical theory.
A classical radial system can indeed rotate like a planet. In fact, an electron under this theory could make a 360 degree turn in space and as would be expected would return to it's original orientation. However, for a pointlike system to achieve a rotation and return to it's original orientation it would need to make twice as much as this angle (720 degrees). See, pointlike systems when in accord to rotations don't act like classical radial systems.
So it seemed there was a problem. Either particles do not physically rotate yet still possess an angular momentum with a classical radius, or that quantum particles don't physically rotate but still have a quantum spin and intrinsic property no less. It was decided that spin could not be a real physical spin . Instead, the classical electron would fall into the archives of physical curiosity and the idea that spin was some inherent, instrinsic and fundamental property would live on. I believe this might have been a mistake. The fact that we haven't been able to observe the radius as of yet should not indicate an electron has no size. In fact, scientists have just recently attempted to measure the shape of an electron by measuring it's wobble in a magnetic field. An excellent article which has proposed the experiment can be found in the references of this chapter.
But, as much to my frustration and to many other's, our theory developed to satisfy the contention that electrons did not have a radius (pointlike systems are tremendously simpler to deal with than three-dimensional systems... this maybe one reason quantum field theory took this course). Nevertheless, an interesting factor worth mentioning is that it changes the mathematics in the transition from classical to modern theory by very little. Spin is so important in physics, that is defines not only the behaviour conducted in experimental physics, but also defines the chemical elements itself. Atoms can have more than one electron - in fact, in a more precise statement, no two electrons in a single atom can have the same four quantum numbers; if n, l, and m_l are the same, m_s must be different. This difference is achieved by having different spin states. Spin states can take either an ''up'' or ''down'' spin. One strange fact of quantum mechanics (which will be covered in the quantum wave function part) is that before any state of either ''up'' or ''down'' has been measured, it can result in a superpositioning of states. This inexorably means that a particle can have both a spin ''up'' or a spin ''down'' simultaneously.
A Brief Overview of the Mathematical Application of Spin
Angular momentum is a vector quantity, it points in a particular direction. The spin as a vector points in the angle of direction. There are two kinds of generators of rotations we can speak about. There is which is the total angular momentum which generates complete rotations and then there is which is the orbital angular momentum which moves the system on circles, so it will move round the origin.
We will introduce now commutation relationships
it is also true that
The symbol is called the antisymmetric Levi-Cevita Symbol. Canonical commutation relations simply have the identity . To understand a canonical commutation relation, it is the relation between canonical conjugate quantities. One well-known example in physics of two commutation relations in position and momentum, which is expressed here in what is called a Poissen Bracket
Going back to our relations  and  we have the following:
has eigenvalues where for 
so only integers allowed for 
Now we should introduce the fact that
But what does taking the difference of the total angular momentum and the orbital angular momentum? It just means that will become the generator of rotations for a particle around it's own axis which means we won't be moving the object in this expression.
So we can do some really cool stuff with this expression.
To express how all the identities here commute with each other can be given as
The will commute with is what gives us our . with gives . on gives a minus . Another minus appears, but justification would just take more time to explain. The reason why it would be pointless really to explain why is because after all the mathematics, all the signs collapses to a single anyway.
Then we simply substitute found in our equation  for from  (hopefully noticing that S_i is not expressed with the subscript ''i'' but ''k'' instead to make
Now, there may have been quite a few things in there you have never heard of, like a Cevi-Levita Symbol, Poissen Brackets or Eigenvalues, but I cannot explain everything unfortunately (I will be able to cover Eigenvalues shortly). Hopefully I can give a brief overview of the mathematics and maybe even present it in such a way that it can be easily understood.
Now, remember when I said that a man called Pauli created a mathematical theory of spin? Well he did so using three special matrices called Pauli Matrices, which would help explain the spin of any quantum mechanical particle.
The Pauli Matrices are what are called by Mathematicians and Physicists as Hermitian Matrices. To physicists, Hermitian Matrices are basically the things which we can observe, which are named Observables. The diagonal components of a matrix are real and to understand the following will require a little knowledge on matrices.
As was stated there are three Pauli Matrices given as
This matrix is Sigma 1.
This is sigma 2.
And the final matrix as you probably could have surmised is sigma 3, the final Pauli Matrix. Just a quick summery, has both an eigenvalue of and . An Eigenvalue is attached to the definition of a linear system of equations; vectors are expressed in what is called a Hilbert Space which allows you to compute the configuration of system, usually this is called a configuration of states and physical observables are given by operators. Moreover, the values that the observables take are given by their Eigenvalues. This is purely a postulate of quantum physics.
The Pauli matrices are Hermitian matrices as has been noted, but what makes a matrix Hermitian? Well, the matrix requires two things. It needs to be symmetric and real. A symmetric matrix is a square matrix (as most matrices are) that is equal to it's Transpose. If M is some matrix, then if M is symmetric then
Where for notational purposes, the on indicates it is the Transpose. To make it Hermitian, you need to Transpose the matrix but then you must complex conjugate everything. Doing so, one can state the matrix as
Where the conjugate transpose is given is as . The most simplest case of complex conjugates, is given by a complex number where and are real numbers, the conjugate is .
Consider the unit vectors which incidently has a magnitude of 1 (in other words, is equal to 1). Then we can have
which is the ''dot product''. It will allow us to express this as
But what does physically mean? Well, is very basically and very simply, the component of spin along the direction of . In fact
Is also Hermitian. A neat way to write this is as
We obtain and from these equations
There are many things we could have potentially covered concerning this topic but which I have no room to mention. The application of quantum angular momentum is vast with many topics which could be discussed. Hopefully I have given some kind of taster in what quantum mechanics has to say about this area.
Later, we will see some fascinating predictions by quantum mechanics and spin, one which is called quantum entanglement. Entanglement is such a deep subject in physics, so we won't discuss it here. I will however briefly mention that it involves a classical proof by John Bell, called Bells Inequality. You can actually talk about Bells Inequality in terms of set theory, which is not an algebra but can form the analog of an algebra.
Three circles which are symmetrically touching and perhaps even overlapping and with each compartment specially numbered, you can use the set theory to describe an inequality which reads:
Which has three properties, defined as , and . These can be any properties. stands for the ''number of entities,'' and then it reads off that ''the number of properties in and not plus the number of properties in and not is greater or equal to the number of properties in and not .''
The fact of mentioning this, is because Spin can be defined two different ways. In Bells original paper, he treated the system with one spin axis. Indeed, a new realm of quantum investigation challenges that proposal using two axes which will define spin 1/2 particles.
Violation of Bells Inequality which can be found in quantum mechanics gives an experimental varification of spin 1/2 particles. It may also be indicating that particles are not pointlike at all. A one-dimensional spin state does not have any structure, but a two spin axial particle can with what is called a spin microstructure. The violation is achieved when understanding that the two simultaneous axes form a resonance state which is also known as the spin fringe. 
The spin microframe is simply related to the ordinary coordinate frame by a simple rotation in space.  It is an interesting fact also to mention that it is impossible to distinguish the 1 dimensional spin and the 2 dimensional spin when a magnetic field is present. Particles will spin a particular direction when placed into a magnetic field.  I will leave you with one final interesting fact of quantum mechanical spin and the fundamental nature of particles. There has been some composite particles which have no spin at all, called zero-spin particles. However, as interesting fact is that all fundamental quantum particles possess non-zero spins.
And it gets even smaller!
And particles, as small as we have been able to cover, now get's even smaller. We don't just have protons and neutrons, but we have even smaller particles. A proton and neutron are composite particles, made from what are called quarks. An interesting fact of nature, is that you don't seem to find quarks on their own either. Quarks when created, are always created in like company which give rise to the B-Meson Family which is interesting, as it would make them composite in a sense.  The quark comes in six types, called Flavors. Those Flavors are up, down, strange, charm, bottom, and top.
The up and down quarks are known to have the smallest masses and the heavier quarks (simply meaning they have a greater mass) tend to be shortlived and will decay into other quark particles.
Quarks are the only particles known which interact with all the forces in nature, those being the Gravitational, Electromagnetic, Strong and Weak forces. The Gravitational force should be recognizable. It is the force which keeps us attracted to the Earth's center. The reason we don't pass right through the earth however, we can thank the electromagnetic force for that. The reason why is because the electrons in your body and the electrons making your chair act like tiny little magnets, give rise to an electrostatic repulsion. Now the Strong and Weak forces are basically nuclear in nature. The weak force is responsible for the decay of a particle into another particle. However the strong force is one of the more interesting forces to consider for this part, since it is mediated by a particle called the Gluon.
The Gluon is what is often called ''the quantum glue'' which holds particle's very tight together. Quarks actually exchange this stuff all the time. There are eight types of gluons which are defined by calling these colours. We don't mean that there is actually any colour to these sticky particles, just like we don't infer that quarks have any flavor to them.
Gluons could also come in a kind of exotic matter, called Glueballs. These particles are composite particles made from entirely gluon energy. Whilst theoretically they should be allowed to exist in nature, they would be very hard to detect because they will mix easily with ordinary matter states.
As far as we know, matter is not made up of any smaller units than these and so that is us; we have taken a journey from the small (atoms) to the fantastically small (quarks) and now we shall venture into the world of Quantum Mechanics, the Bigger Picture.
Why Doesn't the Electron Fall Into the Nucleus? Franklin Mason and Robert Richardson, J Chem. Ed. 1983 (40-42)
On the Einstein Podolsky Rosen Paradox by John S. Bell http://www.drchinese.com/David/Bell_Compact.pdf (online paper)
Electrons are spherical: What's round and measures a billionth of a millimetre? http://www.thenakedscientists.com/HT...ive/news/2277/
 The Compton Wavelength depends on the Planck Constant given as h. However, there is something called a reduced Planck's Constant. The reduced Plancks Constant is ħ and is obtained from dividing Plancks Constant h by 2π (here π is just pi) and it gives a ''smaller'' value of the original Constant.
 I've just attempted to explain that whether or not physical particles have a radius, spin might still be an intrinsic effect. We have had to deal with many aspects of quantum theory which seem unusual. The idea that a system might still have a radius but spin remaining as an intrinsic property should not be outside the realm of possibilities. Though this has never been suggested before as far as I am aware. However the idea of completely pointlike systems may still trouble some quiet physicists and as far as I am aware, many non-scientists are indeed troubled by such a thought that something can contain a mass and not a volume. The classical condition of mass is dependant on volume and density.
 This realm of physics using the spin microframe deals with taking the sum of the vectors. In example, you might have
where is the unit vector, we can see that you calculate twice the magnitude along a particular direction. We haven't spoke about the magnetic moment and unlikely to in this book.
Last edited by Reiku; 12-28-11 at 04:47 AM.
12-28-11, 02:06 AM #2
Some of the latex has came up messed up. I will fix it soon.
12-28-11, 02:19 AM #3
12-28-11, 04:08 AM #4
You are not going to get far posting stuff like this. It displays all of the behaviour which elicits the sort of replies you don't like.
Firstly you are in no position to be writing a book on material you don't fully grasp. Secondly do you really think bringing commutation relation, something taught to 2nd year undergrad students is appropriate for 16 year olds? Not in the slightest. So you are writing in appropriate material when you haven't even covered yourself! Just because you aren't to post this stuff in the main physics forum doesn't mean you are to post it elsewhere. All of the complaints made about previous examples of your posts like this apply here, they were not forum specific. Don't you get why people get tired of posts like this from you?
12-28-11, 04:14 AM #5
I have to ask - is any of this based on experiments/procedures/tests you have run yourself, or are you simply recompiling data others have gathered and extrapolating new "facts" from that? If the former, please explain, if the latter... why?
12-28-11, 04:17 AM #6
Difference is, you are not humble. I will always admit I don't know everything. Physics is an area which people don't understand.
If this post however, is a measure of yourself saying ''well, I know more than you and because of this, you know nothing and you don't understand the subjects,'' then so be it, you do know more than me and I'll admit this, but I won't admit I don't understand these things, because I do!
12-28-11, 04:17 AM #7
Do something good for once, and tell me how to write a Poisson Brackets in latex?
12-28-11, 04:18 AM #8
''Don't you get why people get tired of posts like this from you? ''
Well, just a few days ago a couple of members here actually said they'd prefer reading my posts than to maybe your's or proms, so forgive me If I am not hurt by this comment.
12-28-11, 05:15 AM #9
Pretty much everything I did as an undergrad I look back on now and think "Why didn't I see it like that, it was so much easier to understand that way!". Many times I've had flashes of realisation years after the original material has been taught to me about WTF the lecturer was on about.
You may have read plenty of lay person material on this stuff but you haven't worked through the required mathematics to get to a position where you can gain a working understanding of commutation relations. Vectors, linear algebra, matrices, they are all required learning before even touching such stuff and you could read lay person books from morning till night for the rest of your life and you wouldn't gain the necessary information because this is precisely the stuff they remove.
You didn't respond to my comment about how stuff taught to 19 or 20 year olds in full time education is not going to be appropriate to 16 or clever 14 year olds. Do you think it is? Now you're asking me about Poisson brackets. Do you think they are appropriate for 16 year olds? I personally covered them during my 3rd year, because they are used in Lagrangian formalisms to prove things about complicated dynamical systems. These are things beyond any 16 year old.
Come on, think about it. At 16 you don't even know what a derivative it yet you're asking about Poisson brackets, something which involves partial derivatives of functions by functions to construct a symplectic space. Do you really think that's appropriate? Even if you understood them you shouldn't be talking about them if the intended audience is 14~16.
As for whether some members prefer reading your posts, I don't care. Some members here think the scientific method is dubious or evolution isn't true. Do you think I give a nanosecond's thought to their opinions of me? Are these people as uneducated and intellectually dishonest as you? If they are even in the same post code then I couldn't care less what they think of my posts. I'd rather be honest and disliked than a popular fraud.
You aren't allowed in the physics forum for specific reasons. Threads like this in the physics forum lead to that decision. Posting them elsewhere will only lead to further restrictions on your ability to post.
If you believe yourself competent at things like commutation relations and Poisson brackets, to a working level, enough to teach others about them, it wouldn't be hard to engage you in discussion to probe such understanding. You fell on your face with differential forms quickly enough.
12-28-11, 06:06 AM #10
And yes, I am quite knowldgeable of phsyics. You of course are much more knowledgeable, but then I admit this. But I am not incompetent as you'd like everyone to believe. I believe for instance, I have a better grasp at explaining physics than you do. Some times you don't understand how to explain a topic very well to people. Just accept it. I've seen your replies to me, and even james has admitted that your posts have made little sense to him as well!
You seem to be mistaking also that if I attempt to explain a subject, then I am saying I am knowledgeable in all physics. Get it right for once please...
...I explain these subjects because I have a certain level of knowledge to be able to talk about them. Not because I have a PhD, but because I have studied the subjects enough to talk about them the way I have.
It is your repeated attempts to present yourself as such a person when you demonstrably are not such a person which keeps getting you banned.
This is why I am banned, then don't label it as something else, because I have never seen this given as a reason for my bannings. Unless of course you are saying that generally this is why people (some) don't like me and this is why mods will find any good old reason to ban me, in which case, I'd agree. The moderator reasons are laughable half the time.
But yes, I will be explaining langrangians in my quantum mechanics part of my book because of fermion fields. Just because something is labelled ''langrangian'' should not scare young people away. In fact, I find it highly troublesome why anyone should think a young lay should not be shown a few basics of quantum field theory with the appropriate language and explained well, for it will seed a good understanding of when they approach it quantitatively later in life. There is nothing wrong being shown basics, and maybe some higher stuff, so long as you do just that, keep it basic.
Quantum Mechanics can be like chinese to people. But just because you are learning a language, should not mean you tackle small words first, but this is the way of education. But if you can construct a simple sentance with a few big words in it, then you are still learning, and it is still an education.
As I said, I want to break this habit of thinking a lay should not be learning about langrangians, time derivatives, dot products, Poisson Brackets. Thinking they should not be allowed to learn this stuff is a little less than forcing them to understand things in a certain way. Some lay's might not even make it to college, but they may want to know a few neat tricks along the way. I certainly wanted to. I know that many people do.
But as I also said, I think it is very appropriate to show them the neat stuff. It might even make the audience want to go and learn more. It's unfortunate phsyics and math's has to be boring enough to always use the basics. Whilst this is a good approach, it is still boring and sometimes makes people not want to take it further. I want to show this does not always need to be the case, for instance, still teach the simple stuff, but throw some interesting stuff in there too. Keep the audience interested, so-to-speak, so they will return next semester!
I am not a fraud. Not sure in what way you really mean this, but I am popular for exactly all the above. Not because I will rabbit in their hear about the simple boring stuff which is often taught to them, but because I am keeping their interests alive by showing them your imagination is an important tool in physics, and that I will not come across as condescending (as you often do with people) when trying to explain this stuff, even if you actually manage to do that.
Such as where with quarks posts. I remember him making some statements like ''dimension'' in which I was like... hold on dude... I need some more information. You might find that strange, but that is just me and my condition. I don't understand the english you use. I knew for instance, dimension was used in many topics, I even named a few, but I wanted a more precise working example, not a trivia quiz.
Last edited by Reiku; 12-28-11 at 06:22 AM.
12-28-11, 06:07 AM #11
Now are you going to give some qualitative view on the chapter of my book, or are you just going to do as you always do, divert this back on me?
12-28-11, 06:09 AM #12
This is why people have problems with books that are written in the style of wiki articles. But yes, I will also extrapolate new facts of my own in my book. The chapter in which I will do this most in the chapter titled ''Consciousness'' which I will dedicate an entire part to my own theories (both mathematical and in literature).
12-28-11, 06:11 AM #13
I will even have a terminology guide and mathematical symbols guide as well for extra support.
12-28-11, 10:19 AM #14
Yes, there's plenty of things in QM which are counter intuitive but that doesn't mean if you know a lay person description then you're able to understand it to the same level as someone doing QM research. Else why would universities bother spending years, decades, even teaching more and more elaborate mathematical models to students and then researchers in quantum mechanics? If you're in a position to explain this stuff why must university lecturers have PhDs in the subject before they can lecture on it?
No matter how you spin it you are simply not in a position to be a viable teacher of anyone on the subject, especially when you bring mathematics into it. If your entire post were devoid of any mathematics you might be on slightly stronger ground but you had to throw in some algebra and reference to things simply beyond you. It's flat out dishonest.
Do you claim otherwise?
Here is a set of lecture notes which cover, in the relevant places, Poisson brackets. They build on numerous notions utterly alien to most physics students at university, never mind 16 year olds! That pdf is the last quarter of a 3rd year Cambridge course! And you have to ask why it wouldn't be appropriate for a 16 year old?!
Besides, do you think what I post here is the full extent of my abilities? A typed out post I spend maybe 30 minutes on and cannot easily support pictures, interact with the person and engage in discussion? Unlike you I don't have the regular inclination to spend VAST quantities of time writing lengthy essays out of the blue about stuff I read in some pop science book. But unlike you I can evaluate my presentation, communication and mathematical abilities against other people with similar levels of knowledge, education and research abilities.
It's a sign of a hack that they want to jump to the 'cool' stuff which seems flashy, especially when they don't want to do the details, only the concepts. Look at Farsight, he crashed and burned doing that method.
12-28-11, 10:58 AM #15
And I don't think Farsight is a failure. That is your forte of judgement. I think he's actually a very nice man and have had many personal conversations with him in the past [even though I have found our opinions of physics usually differ quite a lot].
If I started in university, where you had, went up the ladder, even through the boring stuff, how could I not?
Arguably I'd fly through the first year with the grasps I have already. Afterall, if I can talk about a ''fourth year topic'' like the dirac equation, then arguably the work I'd encounter in my first year would be piss easy.
Maybe you should just start accepting I come across like that simply because I don't hash down on attitude. I may come across as knowledgeable because of that.
Trust me, I have taste believe it or not.
Was nice to see you put your foot in it....
So what... you think I've spent superfluous hours learning about quantum field theory, the dirac equation, pauli spin matrices, spin itself (could go on for a while with other examples)... but for what? Just to come here and troll? It's clear I've spent more than ''just a few days'' writing up my first chapter, in presentation and effort to explain it to the lay.
It's not the sign of a hack. It's a sign of a very eager person who may actually have more passion for physics than even you, whoever that person may be.
Don't talk to me about honesty, or you can hold yourself a ''walking example'' as you put it to me, that your heavily hypocritical yourself. Afterall, you accused me of plagiarism and you haven't even removed your comments after being proven wrong. Secondly, you accused me of not being able to pass exams, I mean, where do you get this stuff from?
Would you be surprised to know my first year at college doing physics, I was 1 of 3 people who actually passed their exams, while the rest of the class failed?
12-28-11, 01:42 PM #16
Mister, Post #1: . . . a GREAT read! . . . . look forward to your completed manuscript.
12-28-11, 01:49 PM #17
AN Post #9: "You recently showed in the Susskind discussion you don't have a working grasp of this material, you are just parroting."
Most commercially published (for public purchase) books DO parrot the current theories and hypotheses. Also, see a lot of similar "parroting" of the Standard Model by the 'talking-heads' on Sciforums!
12-29-11, 06:16 AM #18
Learning math is not like learning Chinese. Chinese has some basic system, and then you can quickly branch out to whatever categories of dialogue you want. You don't need to know about construction industry vocabulary to order fried shrimp. Math doesn't work that way, concepts build on earlier ideas which build on earlier ideas still, and the chain goes a long, long ways back.
It's ridiculous to try and discuss the properties of Poisson brackets before learning what a function is and practicing examples of them and doing lots of graphing and calculating with them. Learning the notation is hardly the concern, what matters are the myriads of logical math concepts which are described using that notation. To understand why this "all you can eat 80 dish buffet" approach to learning math is just plain stupid, you need to properly learn the math (in a way that would let you functionally apply it), and the only way to do that is in the order by which the concepts are actually layered.
12-29-11, 04:40 PM #19
I don't have the inclination to reply point by point and clearly it doesn't sink in much with you anyway....
I could talk all about black holes and quantum phenomena when I was 17. None of it helped at all at university.
The gap between knowing pop science and even passing a 1st year uni exam is HUGE. You just don't realise it because you've never tried to step up to such a test.
If pop science is enough to get you through the 1st year of university physics courses why do such courses include non-pop science stuff? They are going to include things pop science layperson books will not cover, else the books wouldn't be pop science, they'd be textbooks for universities!
Differential forms is covered in 3rd or 4th year courses. You claim your ability to talk about the Dirac equation puts you in good steed for such material, as it too is taught in 4th years or beyond. The fact you couldn't follow what I said illustrates the gulf between what you think a 4th year course on say the Dirac equation involves compared to what it really involves.
You seem to think being able to sprinkle your posts with equations you can find all over the internet means you are competent at the topic. Any kid with access to Wiki can talk about black holes or neutrinos, including throwing in equations. That's a long way from understanding it.
Please list all physics/maths related educational qualifications you have and the grade you have. You have never been to university to do physics so it can't be any of those. Do you have sufficient grades to get into say..... Nottingham for physics or maths? You mentioned how you could be in a position to blast through a 1st year at university and how you're doing well with 4th year stuff like the Dirac equation. Getting say a D at AS Level physics is a long long long way from passing a postgraduate exam on Dirac's quantum field theory work.
I ask because a pass could be as low as 25% in some situations. I know people who 'passed' A Level physics but got less than 50% and who could not possibly get onto a physics degree.
As such the 'talking heads' you mention do the latter, while Mister gives the distinct impression he's doing the former. People capable of the latter generally can spot people doing the former, just as any good teacher can spot when a student's essay is largely lifted from somewhere and then copy/edited to shuffle things here and there. This explains why all physics educated people here don't think Mister is one of their number, sorry our number.
At the end of the day Mister, what is all this going to accomplish for you? Nothing. You haven't really moved on in your understanding, just your ability to patchwork together advanced concepts you've read about but don't have a working understanding of has developed. Yes, it's a skill to take comments from multiple authors and then reword them into a single narrative but it doesn't imply a proper grasp of the subject matter. Instead it's just a technique which serves students well when they can't write their own work in their own words using their own understanding.
You mentioned somewhere that you want to clear your name of plagiarism because in the future you might be wanting a job in physics research and that such accusations might count against you. If you ever get to the stage where you're in the true running for a physics research position you'll stand or fall on your credentials, your interviews and your research, not what someone said years and years ago on a forum. But unless you radically change how you go about learning you'll never get there. Like I said, I speak from experience of having gone through the entire process myself and your approach is going to get you nowhere. You need to realise the 'boring' details are necessary, that's why every single university in the world covers them. They are the glue which holds the more 'cool' concepts together, the foundation on which those concepts are built, developed and interwoven. Until you realise you need to put proper effort in, not just spend an afternoon on Wikipedia looking at the 'cool' stuff in physics, then these sorts of threads will be all you have.
Presently you are completely unrealistic, completely naive and grossly ignorant of the gulf between you and even basic working understanding of physics. Unfortunately it's precisely the position you were in when we first crossed paths 4 or 5 years ago so obviously that 'amazing memory' and all that reading hasn't gotten you anywhere. Do you plan to start doing physics at university at some point? A degree? A masters? A PhD? If you think a research physicist job is a possible future for you then I would guess you do. When is that going to start? You live in Scotland, your university place is, for the time being, free. When are you going to stop talking and start doing? Even if you enrolled next October you'd not be finishing a PhD until something like 2019 or 2020. You'll be 36 or so by then, the clock is ticking. Of course personally I don't think you'll ever get there and you've yet to present a compelling reason for my view to change.
12-29-11, 11:29 PM #20
For instance, the math's I have shown only briefly covers spin; I might want to add more to that in order to cover everything to a better standard, maybe by giving a working example of Pauli matrices in play.
But explaining this as an all you can eat buffet, in a book, targeted at people who have a real burning interest, is not stupid. It's sell-worthy more like. I know what people want from their sci-pop books.
This is it.
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