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You might expand on this one.show how it is thought to be doneAs you jumped directly from ω/k=Vp"∂ΨR/∂ x + ∂ΨR/∂ t = 0If we pull the derivative down in respect to x in our function gives ik, and if we pull down our derivative in respect to t gives us iω, and if we take the two from each other we have:"

Yeah! Brilliant post! (Way beyond me of course)

The wave function is a probability distribution over all space and all time, providing the possibilities of any physical system to appear anywhere at any time.

ω/k=V_{p}where V_{p} is the phase velocity, ....Interestingly, the value ω/k can take values which are either +1 or -1.

The meaning of the two becomes more valid under more research. The equation of interest now comes in the form:∂Ψ_{R}/∂ x + ∂Ψ_{R}/∂ t = 0

In which case? If one choose c as unit of speed, what you wrote seems to be valid for photons only. I don't understand.When learning about the Dirac Equation in a class, you must be introduced to the phase velocity in this form. There is no point jumping equations because then nothing is learned.

If we ask how fast a particle goes, with this equation here ω^{2}=m^{2}+k^{2} then we need to compute the group velocity ∂ω/∂k=k/√m^{2}+k^{2}. And this tells us the velocity of a wave.

How did you get this from the Dirac equation? Can you explain?Do you know anything about partial derivates?

Ψ = e^{i(kx-ωt)} is what we need. ∂Ψ_{R}/∂ x + ∂Ψ_{R}/∂ t = 0 whenever you take a wave form like this

Quote from: Geezer on 31/12/2010 07:22:07Yeah! Brilliant post! (Way beyond me of course) Mathematics is NOT a science - its a philosophical game of proofs based on delusional axioms

Quote from: QuantumClue on 31/12/2010 16:10:55In which case? If one choose c as unit of speed, what you wrote seems to be valid for photons only. I don't understand.When learning about the Dirac Equation in a class, you must be introduced to the phase velocity in this form. There is no point jumping equations because then nothing is learned.Sorry, but I haven't understood. I don't know anything about Dirac eq., so what ω stands for? And k? Because, if they had the same meaning they have in non-relativistic QM, the phase velocity cannot be just 1 or -1 (case of photons), but it is (1/k)*sqrt(m^{2}+k^{2}). Do you mean that the equation you wrote is the one valid for photons only? I'm just trying to understand.Quote If we ask how fast a particle goes, with this equation here ω^{2}=m^{2}+k^{2} then we need to compute the group velocity ∂ω/∂k=k/√m^{2}+k^{2}. And this tells us the velocity of a wave.Yes, certainly, infact is the inverse of the phase velocity (their product is c^{2} for a free particle, but here c =1).QuoteHow did you get this from the Dirac equation? Can you explain?Do you know anything about partial derivates?Yes.Quote Ψ = e^{i(kx-ωt)} is what we need. ∂Ψ_{R}/∂ x + ∂Ψ_{R}/∂ t = 0 whenever you take a wave form like thisAh, yes, certainly. Only that I haven't understood why "you take a wave form like this".

Quote from: lightarrow on 31/12/2010 21:21:49Sorry, but I haven't understood. I don't know anything about Dirac eq., so what ω stands for? And k? Because, if they had the same meaning they have in non-relativistic QM, the phase velocity cannot be just 1 or -1 (case of photons), but it is (1/k)*sqrt(m^{2}+k^{2}). Do you mean that the equation you wrote is the one valid for photons only? I'm just trying to understand.Then you might be really interested when I tell you that k and ω are actually 2 by 2 matrices?

Sorry, but I haven't understood. I don't know anything about Dirac eq., so what ω stands for? And k? Because, if they had the same meaning they have in non-relativistic QM, the phase velocity cannot be just 1 or -1 (case of photons), but it is (1/k)*sqrt(m^{2}+k^{2}). Do you mean that the equation you wrote is the one valid for photons only? I'm just trying to understand.

Ah, yes, certainly. Only that I haven't understood why "you take a wave form like this".Oh well, this is just a matter of rewriting equations where our terms are equivalent.

In itself it's not (delusional I meant) I agree QC. Although some conclusions following might be, if compared to our SpaceTime. Like parallel tracks always meeting. Saying that it could be true 'somewhere' becomes a philosophical question, and possible too. If that was the truth though it would still make those tracks meeting a impossibility inside SpaceTime. If we are right in assuming that they don't

Mathematics is not dilusional; it's logical.

Quote from: QuantumClue on 01/01/2011 19:46:07Mathematics is not dilusional; it's logical.Mathematics is an abstract philosophy that is based on idealised axioms that require spiritual faith to maintain their apparent immutability.(For example its a mistake to lump numeracy and mathematics into the same basket. Only one of these is abstract)

Quote from: Foolosophy on 02/01/2011 11:45:36Quote from: QuantumClue on 01/01/2011 19:46:07Mathematics is not dilusional; it's logical.Mathematics is an abstract philosophy that is based on idealised axioms that require spiritual faith to maintain their apparent immutability.(For example its a mistake to lump numeracy and mathematics into the same basket. Only one of these is abstract)It's not clear to me what you mean with your statement. Can you make a better example? Because there isn't, IMHO, so much difference with physics: physics too must have theories based on postulates (and definitions); you can't make a single statement without them.

Did anyone have any other ideas for any more writeups... I was thinking about doing one now on the Klein-Gordon equation.

Quantum Mechanics is another very good example of a THeory that makes accurate predictions and can be supported by experiment and observations BUT in essence is a collection of insane probability functions that have been arrogantly applied to the microscopic world by its high priests because they are not clever enough at this time to think of a deterministic theory

Quote from: Foolosophy on 11/01/2011 05:55:03Quantum Mechanics is another very good example of a THeory that makes accurate predictions and can be supported by experiment and observations BUT in essence is a collection of insane probability functions that have been arrogantly applied to the microscopic world by its high priests because they are not clever enough at this time to think of a deterministic theory[Emphasis mine]Foolosophy, You're railing against quantum mechanics a lot, which is fine, but your arguments against it make it clear that you don't understand how it's formulated, that you're basing your arguments on emotion and that you have some grudge against those who don't agree with your views. Do you have any scientific reasoning behind your grudge against QM?

If you don't have a scientific reason for disliking it, that doesn't leave much to discuss on a science forum.

String Therory is a good example of this.ST is a mathematical philosophy. At this point you cant validate the theory via experimentation or observation.

Any theory that is PURELY based on mathematical axioms and cannot be verified by observation and/or experimentation, is simply a philosophy - a Religious doctrine

Quantum Mechanics is another very good example of a Theory that makes accurate predictions and can be supported by experiment and observations BUT in essence is a collection of insane probability functions that have been arrogantly applied to the microscopic world by its high priests because they are not clever enough at this time to think of a deterministic theory

Quote from: Foolosophy on 11/01/2011 05:55:03String Therory is a good example of this.ST is a mathematical philosophy. At this point you cant validate the theory via experimentation or observation.String theory is not a "proper" physics theory, yet.QuoteAny theory that is PURELY based on mathematical axioms and cannot be verified by observation and/or experimentation, is simply a philosophy - a Religious doctrine If it wants to be a physical theory, yes. If it wants to be a mathematical theory it's another story.QuoteQuantum Mechanics is another very good example of a Theory that makes accurate predictions and can be supported by experiment and observations BUT in essence is a collection of insane probability functions that have been arrogantly applied to the microscopic world by its high priests because they are not clever enough at this time to think of a deterministic theoryNo, it's simply because "the world" IS NOT deterministic.

Perhaps you claim that the world is non deterministic because of your literal interpretation of the conclusions that QED generates?

Quote from: Foolosophy on 11/01/2011 13:09:19Perhaps you claim that the world is non deterministic because of your literal interpretation of the conclusions that QED generates?Even, but not only for this. The determinism we are discussing here is related, for example, to the fact that a quantum system as an elementary particle had an exact position in space before being measured. Do you agree with it?

Quote from: JP on 11/01/2011 06:19:41If you don't have a scientific reason for disliking it, that doesn't leave much to discuss on a science forum.I said that I dont dislike QM - I use it often in my professional work environment.

Quote from: Foolosophy on 12/01/2011 06:45:22Quote from: JP on 11/01/2011 06:19:41If you don't have a scientific reason for disliking it, that doesn't leave much to discuss on a science forum.I said that I dont dislike QM - I use it often in my professional work environment.Out of curiosity, what work do you do that you use QM often?

Quote from: JP on 12/01/2011 06:47:32Quote from: Foolosophy on 12/01/2011 06:45:22Quote from: JP on 11/01/2011 06:19:41If you don't have a scientific reason for disliking it, that doesn't leave much to discuss on a science forum.I said that I dont dislike QM - I use it often in my professional work environment.Out of curiosity, what work do you do that you use QM often?Why the sudden interest in how my pay is generated?

Quote from: lightarrow on 11/01/2011 18:33:49The determinism we are discussing here is related, for example, to the fact that a quantum system as an elementary particle had an exact position in space before being measured. Do you agree with it?This is precisely the Quantum point and only half the Heisenberg story.You may well claim that an elementary particle has an exact position before being measured, but the Heisenberg uncertainty principle dictates that if you know a particles position with infinite accuracy then its velocity can NEVER be known or measured.Can you extract these nuerotic conclusions from the insane stochastic based quantum depiction of the atomic world and apply them to the real world of flesh and bones, stars and planets, galaxies and nebulae??

The determinism we are discussing here is related, for example, to the fact that a quantum system as an elementary particle had an exact position in space before being measured. Do you agree with it?