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Posts posted by pmb

  1. The author of Quantum Mechanics Eugen Merzbacher hs a page online about the Copenhagen Interpretation. He concludes the artilce by saying

    In recent times, the predictions of quantum mechanics, analyzed in terms of the Copenhagen interpretation, have been confirmed experimentally for ever more entangled states. This is the topic of Anton Zeilingerís subsequent talk in this symposium. The play Copenhagen has provided us once more with a memorable opportunity for examining these fundamental issues.

    Case closed! :P

  2. Now you confound "The Copenhagen interpretation" with "the probabilistic rules of the Copenhagen interpretation". You are confound the Copenhagen rules and the Copenhagen interpretation.

    He's not confused. They refer to exactly the same thing. I.e.


    The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta, entities which fit neither the classical idea of particles nor the classical idea of waves. According to the interpretation, the act of measurement causes the set of probabilities to immediately and randomly assume only one of the possible values. This feature of the mathematics is known as wavefunction collapse. The essential concepts of the interpretation were devised by Niels Bohr, Werner Heisenberg and others in the years 1924–27.


    The term 'Copenhagen interpretation' suggests something more than just a spirit, such as some definite set of rules for interpreting the mathematical formalism of quantum mechanics, presumably dating back to the 1920s.


    immortal: Please take note that juanrga has never provided nor recognized the definition for the terms that he's using. In this way he keeps his straw argument alive and kicking. I recommend ignoring him unless and until he states the definitions of wave-particle duality and Copenhagen interpretation. Also, did you notice that juanrga never provided a reason why the 'Copenhagen interpretation' is supposed to be wrong?

  3. hello, what are the best links and or books for someone whom would like to be introduced to dimensional analysis "basic level?"

    I doubt that there are any textbooks on that subject. It's too trivial tomake a text out of it. What you might want to do is to pick up a chemistry text and go over the section of dimensional analysis.


    What I would like to find is the position of the electron, please don't laugh, I think it is possible...

    There are no theoretical barriers to finding the positin of an electron so there's nothing to laugh about. Even quantum mechanics doesn't give a limit of the precision on measuringthe position of an electron.

  4. Read this paper - Can wave-particle duality be based on the uncertainty relation? - Stephan Durr and Gerhard Rempe from the Max Planck Institute, Germany.

    I'm going to bed right now. Tommorow when I wake up I'll go cash my check and buy an ink cartridge for my printer so that I can print that out and read it. At that time I'll get back to you on this.


    Severian - Do you believe that there is a wave-particle duality? If so then can you please post a definition of it? Thanks.

  5. I would disagree with that statement. The Copenhagen interpretation is not needed for quantum mechanics. That is why it is an "interpretation". It is used by us to "philosophically make sense" of quantum mechanical predictions. But the predictions would stand without it.

    Here's the way I see it. From Principles of Quantum Mechanics - 2nd Ed. by R. Shankar, page 116. The autrhor writes

    Postulate III


    If the particle is in a state [math]|\psi>[/math], a measurement of the variable (corresponding to) [math]\Omega[/math] will yield one of the eigenvalues [math]\omega[/math] with probability [math]P(\omega) = |<\omega|\psi>|^2[/math]. The state of the system will change from [math]|\psi>[/math] to [math]|\omega>[/math] as a result of the measurement.

    To my thinking this is the Copenhagen interpretation. Without it we'd be without this postulate and not know what the wavefunction means. I.e. we'd have the prediction but we wouldn't know what it meant or what to do with it. We can't make a prediction without this interpretation to tell us what it is we're looking to measure. Taking away the Copenhagen interpretation takes away our understaning of the meaning of the wavefunction. In that sense I disagree with you.


    I think what pmb was saying was that it was the most accepted theory to date in the context of quantum field theory.

    I was referring to quantum mechanics, not quantum field theory.


    No one is arguing that the Copenhagen Interpretation is a complete conception and not without its problems today, there is a real problem and we all know it.

    I don't understand. What are you saying that its problems are? There is the concept that the observer making the measurements are a quantum system. Is this what you're referring to?

  6. I want to get some ideas and oponions from my the people I've grown to admire here. Please check the paper I wrote called On the Concept of Mass in Relativity at http://arxiv.org/abs/0709.0687


    Please take a glance throught it and let me know what you think. Let's start with the abstract. I changed my mind on what I want the purpose of this article should be about. I want it to address all the errors used in counter arguments used against the concept of relativity and to give counter examples where needed. Here's the abstract as it reads now.

    Within the past fifteen years the use of the concept of "relativistic mass" has been on the decline and has been replaced by the concept of "proper mass" (aka "rest mass") - ?simply referred to as "mass" and labeled "m" by its proponents. This decline in usage appears to be due to arguments presented in several journal articles over the last thirty-five years, as well as to standard practices in the field of particle physics. The aforementioned debate consists of arguments as to how the term "mass" should be defined to maximize logic as well as to be less confusing to the layman and people just starting to learn relativity. Lacking in the debate is a clear definition of all types of mass and all its usages in a wide variety of cases. The purpose in this article is to bring a unifying perspective to the subject. In doing so I will explore those things omitted from previous articles on this subject including the importance of point particles vs. extended objects; open vs. closed systems and gravitational mass. Although I argue for the usage of relativistic mass I do "not" argue that proper mass is not an important tool in relativistic dynamics.

    Mind you that I don;t wamt people to get the idea that I'm pushing the conecept of relativistic mass since people who know about it have already made up their minds for the most part. The goal here is to present arguments used against the concept of rel-mass which are erroneos, such as the claim that its just another term for energy. I give a counter example on that point whereby I present a worked out example where the relativistic mass is not equal to the energy/c2 as is often claimed.


    I eagerly await your result.


    This is not an excuse for those who oppose the idea to try to prove that nobody uses it. That would be hijacking this thread.

  7. Pete, what do you understand the periodic table to mean?

    A test? Don't I get a chance to study for it? :P


    The periodic table is a list of the known elements arranged according to their properties


    What do you mean by a periodic structure when calculating Brillouin Zones?

    Nothing, becase I never talk about the periodic table. :P


    I forgot what those zones are. Its been decade since I've studied it.


    By periodic I mean that if f(a) is a solution then f(2a) is a solutions as is f(na). Or that something repeats regularly along at least one cordinate axis.

    Your definition does not conform to the standard definition which is as follows: the definition of a periodic function means that f(x) = f(x + L) where L is the period of the function. What you have doesn't define a periodic function. E.g. your function could meet that meaning "f(a) is a solution then f(2a) is" but have arbitrary values inbetween a and 2a and etc. and it'd still be periodic by your account.


    Solitary travelling waves can be considered to repeat everywhere along an axis

    Solitary stationary waves are the combination of a wave within the stationary envelope and an envelope function.

    What do you mean by "solitary"?

  8. !

    Moderator Note

    We want you to use the report feature. We want you to point out, in thread, when someone is using a logical fallacy to support their argument. We prefer that you don't try enforcing the rules by mentioning them in thread, it just adds a level of defensiveness to the discussion that isn't necessary, and can derail the topic. The use of logical fallacies automatically affects how people view the argument when it's pointed out. Our rules are for repeated offenses, but it normally sorts itself out when the weakness of the argument is pointed out before having to bring in the staff and the rulebook.

    Thank you. Yes. That's what I've been doing. I have to admit that being human means having to restrain myself when what I really want to do is say that they're breaking forum rules. Is it okay to say that their argument is outside mainstream physics and therefore belongs in the speculation forum? If not then I appologize for having done that. :(

  9. pmb, ...

    I prefer Pete, even in open forum. :)


    in your original classical wave equation a is equivalent to my omega a period. The arbitrary functions F and G do not need of themselves to be periodic.

    You wrote


    [math]\Psi(x, t) = Ae^{i(kx - \omega t)}[/math]


    We need to put this in a similar form so we write


    [math]\Psi(x, t) = Ae^{ik[x - (\omega/k)t]}[/math]


    Let [math]v = \omega/k[/math]. This is the phase velocity of the wave. We now have


    [math]\Psi(x, t) = Ae^{ik(x - vt)}[/math]


    which is now in the form


    [math]\Psi(x, t) = F(x - vt)[/math]


    In your later exposition of Schrodinger, n is periodic.

    Numbers aren't periodic. n is an integer which labels the wave-parameter andenergy eigenvalues. The wave function is periodic in the temporl sense but not in the spatial sense. Note that the wave function goes to zero outside the walls of the potential. This is not a spatially perriodic function though.


    As soon as you introduce some integer that can be 1..2..3..4.... you have introduced periodicity.

    I disagee. Quantizing a variable does not make it periodic whatsoever. Bound particles do not have a spatially periodic wavefunction.

  10. and that the Copenhagen interpretation "is surely wrong".

    That comment flies in the face of mainstream quantum mechanics. The Copenhagen interpretation is one of the postulates of quantum mechanics.

    To claim otherwise is personal conjecture and as such it doesn't belong in the ordinary physics forums but belongs in the speculation forum.

  11. Forgive me, pmb but I thought the wave equation under discussion here was the schrodinger wave equation

    Yeah. That's true. It was just easier describing waves in general.


    [math]i\hbar \left( {\frac{{\partial \psi }}{{\partial t}}} \right) = - \frac{{{\hbar ^2}}}{{2m}}\left( {\frac{{{\partial ^2}\psi }}{{\partial {z^2}}}} \right) + V\psi [/math]



    Which has solution the De Broglie waves given by



    [math]\psi = D{e^{i\left( {kz - \omega t} \right)}}[/math]


    Which is periodic in omega.

    Note on jargon: The typical way to refer to that is to say that is that its periodic in time. By the way, I only meant to imply that waves aren't periodic by definition. And not all waves in quantum mechanics are periodic.


    The expression you just gave is the solution for a free particle with a well defined momentum. It isn't a general solution. There really isn't a geneal solution to Schrodinger's equation since the equation has the potential as a variable in it.


    Let's take a look at the situation of an infinite step potential well where V(0) = + infinitity and V(L) = infinity and V(x) = 0 for 0 < x < L . The solution is of the form


    [math]\psi(x) = C_1e^{ikx} + C_1e^{-ikx}[/math]


    where C1 and C2 are constants. Putting [math]\psi(0) = 0[/math] we get


    [math]\psi(x) = C_1(e^{ikx} - e^{-ikx})[/math]




    [math]\psi(x) = A sin kx[/math]


    Applying [math]\psi(L) = 0[/math] requires sin kL = 0 or [math]kL = n\pi[/math]


    This means that k is restricted to the following values


    [math]k_n = \frac{n\pi}{L}[/math]


    The energy eigenvalues are


    [math]E_n = \frac{n^2h^2}{8mL^2}[/math]


    The complete solution has then the following eigenfunctions


    [math]\Psi_n(x, t) = A_n sin \frac{n\pi x}{L} e^{-i(E_n/\hbar)t}[/math] 0 < x < L


    [math]\Psi_n(x, t) = 0[/math] (x < 0 and x > L)


    These are standing waves of course. The most general solution is a sumation of these eigenfunctions. When that is done the result no longer specifies a particle with well defined momentum.


    You construct wave packets mathematically from two waves connected by fourier methods (series or transform)

    A wave packet is locaized in space. To create one you have to have a superposition of a continuum of wave numbers to form a Fourier integral.


    Wave packets aren't always periodic either.

  12. why not we consider time just as a massurement tool

    That's the way most people percieve it to be, including myself.


    and not relate it to any thing as directly propportional. my day is a lenght which i describe as 24 hours but but a turtle might feel it as 12 hours and thats why he lives like that.

    That's called personal time which is seperate and distinct than objective time, which is the time that we all agree on.

  13. The one fundamental property of a wave is not probability it is periodicity.

    A classical wave is defined as any function that satisfies the classical wave equation


    [math]\nabla^2\Psi = \frac{1}{a^2}\frac{\partial^2\Psi}{\partial t^2}[/math]


    The general solution is of the form


    [math]f(x, t) = F(x - at) + G(x + at)[/math]


    There is no requirement for the wave to be periodic. A wave-packet is a good example of wave which isn't periodic. See details at http://en.wikipedia.org/wiki/Wave_packet


    The wavefunction in a potential well isn't periodic either.

  14. No, I'm not happy with that definition. I think it is incomplete.

    How so? Can you elaborate? I.e. what would you like to add on to it?


    Further it implies that the only fundamental entities are particles and that the probability function is somehow 'tacked on' and further that probabilities can only be applied to particles.

    It's not intended to address anything except for particles. Sure, there are other things besides particles such as fields. But that doesn't pertain to the wave-particle duality. Each particle has a wave function to it and that wavefunction is interpreted according to its probability density. The definition was never intended to speak about all fundamental entities in quantum theory, only particles and their associate wave property.


    I am old fashioned and think that it is far better in discussions for the promoter to start off by defining one's terms and the abbreviation symbols used in equations along with any restrictions of application.

    As a general rule, I disagree. This is a forum which has several purposes, one of which is to help people learn physics and/or particular aspects of physics. In this case qft123 started a thread to learn about the wave-particle duality, i.e. to learn what the definition is. He couldn't very well have come here to state what something is when his purpose was to learn all about it.


    I always try to address a promoter's terms (not my own) unless I think a genuine mistake has been made.

    For the sake of argument, how would you define the wave-particle duality? How would you have me change the definition that I gave? If I disagree with other people's definitions then that's perfectly fine. I'll just refer to this as my definition. I think it'd be hard to get a definition which we'd all agree on.


    studiot - Thank you very much for your input.

  15. Easy does it!


    Don't get photons and electrons mixed. I know it applies to both but it is confusing if you swop horses mid race.



    When I talk about particles scattering off step potentials I can't use photons as an example because they don't interact with step potentials. When I talk about the double slit experiment I use photons since that's what I'm most familiar with in that experiment. That's all.


    When no one is observing a quantum object the Copenhagen interpretation says that whether you call it wave properties or particle properties and Kinematic properties or dynamic properties they are not assigned to the quantum object. The properties whether it is of a wave or of a particle is assigned to an object depending on the context of the measuring device and the experimental set up.


    This is the accepted consensus. Got it?

    The problem is that he's not acknowledging the associated wavelength of a particle with the particlelike aspects of quantum particles. You'll never get him to acknowledge that fact since he's employing a straw argument which doesn't allow for it.


    A particle does not act as a wave. So bizarre as you must find this idea, a particle acts as a particle.

    We have already pointed out to you that this is not what the wave-particle duality is about. We know all too well that an individual particle is not wave. If it had been then there'd be no wave-particle duality. Please stop arguing a mistake that nobody here has made. I also explained to you that when you use the argument you have, rather then an argument actually pertaining to the wave-particl duality, you commit the logical fallacy known as the straw argument which is defind as follows

    straw argument: attacking a straw argument occurs when a weakened imitation of an opponents argument is attacked instead of the opponents original argument because he imitation is easier to refute. The weakened imitation is know as the straw argument.

    This is precisely what you do when you claim that an individual particle does not act like a wave. Nobody in this thread has disagreed with that all too simple point. We know that quite well and the fact that you refuse to aknowledge this is quote irritating to all of us as their posts have demonstrated.


    For the purpose of this thread I propose that we define the wave-particle duality as follows.


    1) An particle with a well defined momentum has the following associated wavefunction


    [math]\Psi(x, t) = Ae^{i(kx - \omega t)}[/math]


    where the wave number k is related to the momentum p through the de Broglie relation


    [math]p = \hbar k[/math]


    An arbitrar wave function for a particle is made by summing individual wave functions either by a Forier sers or a Fourier integral.


    2) From Principles of Quantum mechanics - 2nd Ed. by R. Shankar (graduate level quantum mechanics text), page 113

    We found that entities such as the electron are particles in the classical sense in that when detected they seem to carry all their energy, momentum, charge, etc. in localized form: and at the same time that are not particlelike in that assuming they move along definite trajectories leads to conflict with experiment. It appears that each particle has associated with it a wave function [math]\Psi(x, t)[/math], such that [math]|\Psi(x, t)|^2[/math], gives the probability of finding it at a point c at time t. This is called wave-particle duality.


    All this has been explained to you already and you ignored it and keep repeating yopur straw argumen.


    Note: To the members of the forum who are participating in this thread, please review the definition I gave for the wave-particle duality and let me know if you object to using it as the definition for the wave-particle duality. Thank you.

  16. A logical fallacy is also a flaw in an argument, and pointing out flaws in arguments is part of the normal discussion process. Peer-response*, a category to which reputation belongs, tends to reduce the use of logical fallacies.


    *edit: such as pointing out that such a device is invalid. Pointing out that it's a against the rules is frowned upon.

    I don't understand. Are you trying to say that it we report someone whom we believe is breaking the rules that its frowned upon?


    I've gotten feeback from people who have said that they were not happy about being mislead in certain cases/topics. That happens when I send then a part of a text that explains the relevant details. We need to take that kind of thing seriously. And I'm not saying that they need to be silenced. I'm saying that their argument should be moved to the speculation forum where people can read about it when they care to and not being confused about it in a normal discussion of bread and butter physics.


    I find it incredibly irritating when someone uses the logical fallacy of the straw argument and the moderators do nothing about it when they are informed of it. Also when the opponent refuses to acknowledge and respond to your counter arguments its also very irritating. That happens quote a lot. Isn't there a rule against that?

  17. Sometimes a collection of particles behaves collectively as a wave. E.g. a collection of photons under certain restrictions behave as a EM wave, but each individual photon behaves as a particle. A collection of electrons in a double-slit experiment generate a interference pattern that resembles a classical wave, but each individual electron behaves as a particle, following the laws of the quantum mechanics of particles.

    That is a not uncommon misconception. An free electron with a well defined momentum has the following associated wavefunction


    [math]\Psi(x, t) = Ae^{i(kx - \omega t)}[/math]


    where the wave number k is related to the momentum p through the de Broglie relation


    [math]p = \hbar k[/math]


    This is what it means to say that an elecron has wavelike aspects. The wavefunction can scatter off a step potential like a wave can. When a single photon impinges on a double slit its location is localized like that of a particle. But when this reslt is compared to the results of a large ensemble of identical experimental setups the interference pattern appearns but it can't be said that the electrons interact with each other. It is for these reasons, not for the single particle nature of electrons/photons, that there is said to be a wave-particle duality.


    You have set up a straw arguement whereby you keep repeating what we all klnow very well and purport it to mean that it proves that thre is no wave-particle duality. The error in your straw argument is that nobody is saying that an individual partilce is physically behaving like a wave all by itself. That's not what the wave-particle duality is all about. Its exactly what I just said it was about, i.e. that to every particle there is an associated wavelenth and wavefunction.


    Straw arguments are logical fallacies and as such are not allowed in the forum.

  18. Perhaps those that are expert on the particular topic the view could indicate a post that is wrong ( or they think is wrong) or contrary to scientific concensus, but do it without 'enforcement'.


    Perhaps we should have a new thread to discuss this issue?

    That's a good idea studiot. swansont said that they enforce the rules. Let's take a look at the rules. From http://www.scienceforums.net/index.php?app=forums&module=extras&section=boardrules

    4.The use of logical fallacies to prove a point is prohibited. The use of fallacies undermines an argument, and the constant use of them is simply irritating.


    10.Keep alternative science and your own personal conjecture to the appropriate forum (Speculations). Threads in the ordinary science forums should be answered with ordinary science, not your own personal hypothesis. Posting pet "theories" in mainstream science forums is considered thread hijacking.

    I found this very interesting. It's nice to know that using logical fallacies is mpt allowed. And that's what's being used. In this case its a straw arguement that we've been concerned about, i.e. an

    Straw argument: Attacking a straw argument occurs when a weakened imitation of an opponents argument is attacked intsead of the opponents original argument because the imitation is easier to refute. The weakened imitation is know as the straw argument.

    I'm sure we have all recognize examples of this kind of thing in the past. Well now you know how to report it and since its a logical fallacy it can't be used. And when someone presents an argument which contradicts stanard textbook physics that's an example of personal conjecture and should be moved to the appropriate forum as stated in the rules.

  19. I didn't know that; considered it as more of a historical terminology, in fact (-> "photoelectric effect").

    Yes. I have seven quantum mechanics/modern physics texts. Most, but certaintly not all, of them has a section on the wave-particle duality but all of then employ the wave-particle duality equation which is de Broglies equation


    [math]\lambda = \frac{h}{p}[/math]


    which connects the wave aspect of a particle to its particle properties. I.e. every particle with momentum p has a wavelength [math]\lambda[/math].


    The wave-particle duality concept isn't always defined explicitly. Sometimes its just buried in there. But whenever you have a particle with an associated wave equiation tied to it then, in essense anyway, you have the wave-partuicle duality. If you looked up where it defines the de Broglie expression connecting the wave and particle aspects of a particle then you'll see the wave-particle duality being touched on.


    This relationship is embedded in all aspects of quantum mechanics. Its used to define the wave function of the particle snd is used to write Forier Integrals and transforms.


    ...which happens to be all of the book I have at hand at the moment. That's admittedly only from looking into the index, not from reading through all of the books just to disprove your point...

    My point is that every QM text uses the wave-particle duality properties of matter through the De Broglie equation. It's true that many texts have a section on the wave-particle duality but not all of them I tried to be very careful so that I didb't claim that they all had a section on that. I appologize if I wasn't clear on that point.


    Let me give you an example: I have the text Modern Quantum Mechanics by J.J. Sakurai in front of me. The index does't mention "wave-particle duality" at all but its wrong to assume it doesn't engulf the concept in it. On page 47 the author writes

    de Broglie's relation, written in 1924,


    [math]\frac{2\pi}{\lambda} = \frac{p}{\hbar}[/math]


    where [math]\lambda[/math] is the wavelength of a "particle wave"

    That is the wave-particle duality in its essense. The graduate QM text I was going to use a few years ago at UMass Lowell is Principles of Quantum Mechanics - 3nd Ed. by R. Shankar. On page 113 the autor writes

    We found that entites such as the electron are particles in the classical sense in that seem to carry all their energy, momentum and charge, etc. inn localized form; and at the same time they are not particle like in that assuming they move along definite trajectories leads to conflict with experiment. It appers that each particle has associated with it a wave function [math]\Psi(x)[/math], such that [math]|\Psi(x)|^2[/math] gives the probability of finding it at a point x at timne t. This is called wave-particle duality.


    The list goes on and on. But I'm certain that no matter what QM text that you'd pick up it would talk about or use de Broglies equation and employ the concept of the wave-particle duality whereby a particle has an associated wave and has a wave-function which describes it. All these things are the heart of quantum mechanics, can be found in all QM texts and has at their root the wave-particle duality as Shankar's text defines the concept.


    Again, I appologize for writing something which you found misleading. My bad. :P



    Did you read the Wikipedia article on this topic? It's at


    Wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.

    I underlined the statement of the wave-particle duality. Do you see where the author says that its a central concept of qauntum mechanics? I agree with the author on that point.

  20. Do quantum particles exhibit behavior like classical waves?

    Not in all cases. E.g. the wave behaviour of quantumn particles is statistical in nature. That means that if we have an experiment which we keep repeating on a single particle and record measurements then the wave nature of the particle will appear when the ensemble is looked at. E.g. No individual particle will exhibit wave bahavioru in this case but the collection of expeiments shows the interference effects by the statistical properties, i.e. particles will have a high probability of gathering near the amplitude of the wave is high. That in no way is classical wave behaviour.


    I believe that juan has done is to construct a strawman whereby the he created is own interpretation of what the term wave-particle duality means and has argued that his version is a myth. Straw arguments are logical fallacys.


    In reality it has a particular meaning, found in most QM texts, which is quite correct and is what quantum mechanics is based on. I've sent the real meaning to my fellow posters here so they're well educated on the subject and its true meaning.


    CERN has a web site about the wave-particle duality


    Neutrino oscillation

    "Neutrino oscillation" is based on what is known as "the wave-particle duality", that is, according to quantum mechanics laws, a particle, when it is propagated, behaves like a wave.

  21. Agreed.

    Yeah, but how can it be enforced? Its nice in theort but impossible in practice. For example: the wave-partiucled duality is the main staple in quantum mechanics as I'm sure that we all know. Yet it only takes one poster to disturb the discussion with a non-truth, i.e. in this case trying to convince people that its a all just a myth. It's next to impossible to find a QM text which doesn't explain it and its relationship and importance to QM. That really cofuses people as StringJunky told us. Yet the moderators leave it alone.

  22. ..then on top of that we have the electromagnetic field' date=' which is a vector field, ...


    The electromagnetic field is a second rank 4-tensor field. The electric field and the magnetic field are both 4-vector fields. They are defined in General Relativity by Wald on page 64

    For an observer with 4-velocity va, the quantity


    [math]E_a = F_{ab}v^b[/math]


    is interpreted as the electric field measured by that observr, while


    [math]B_a = -\frac{1}{2}\epsilon_{ab}^{cd}F_{cd}v^b[/math]


    is interpreted as the magnetic field,



    and I guess we have the Higgs field on top of it too?

    You got me my friend. I have no idea about all that Higgs stuff. I hope to learn about it someday.

  23. It is ironic that a poster uses an old quote from Dirac about wavefunctions for posting attacks to posters who do not buy the duality myth. This poster calls "crackpot science" to what others call modern quantum physics.

    The wave-paricle duality is no myth. So long as there is a waveklength associated with a particle by


    [math]\lambda = \frac{h}{p}[/math]


    the wave-particle duality will have meaning and exist since that's precisly what it means. The term crackpot refers to someone who is crazy or strange. I'd hazard to guess that immortal believes that you're strange for rejecting the heart of quantum mechanics, i.e. the wave nature of particles. Also, when you post quotations without stating the source it doesn't look good.

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