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Q theory, Relativistic Mass and Einstein 
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#1
Dec1804, 07:02 AM

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In another thread dextercioby posted the comment
dextercioby  What's Q theory? I assume that it pertains to quantum mechanics?? I thought you made a good point, one I'm quite familiar with. But there is something I wanted to comment on regarding this point. When someone speaks of the mass of a particle (i.e. what you refered to as relativistic mass) they are speaking about classical particle dynamics. Not all of classical particle dynamics carries over to quantum mechanics (which I assume Q theory pertains to). Many often used concepts in relativity can't be used in the quantum domain. For instance, there is no concept of a worldline in quantum theory (or at least its quite different than in classical relativity). I don't believe that there is even a 4velocity in quantum theory. These are imporant points to keep in mind when applying relativity to quantum mechanics. Einstein never used the term relativistic mass so one can't say for sure. He simply referred to "mass", or "inertial mass". In his text TMR he spoke of the inertial mass of a particle as being altered when there is a gravitational field present. What he was refering to was the quantity [itex]m = m_0 dt/d\tau[/itex] when v << c. This is not the same quantity as [itex]m_0[/itex] since [itex]dt/d\tau[/itex] does not equal one when v << c and there is a gravitational field present. Pete 


#2
Dec1804, 12:57 PM

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As to Einstein, he seems to have had many different views over the years on how to interpret his theories. You can usually find any (reasonable) viewpoint from Einstein's writings if you look hard enough. 


#3
Dec1804, 01:28 PM

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I guess (maybe Einstein's formula,again) the other formula is more useful to QFT:[tex]E^{2}=m_{0}^{2} c^{4}+ \vec{p}^{2}c^{2} [/tex] and with the last 2 formulas we're given the explanation why QFT teachers never use the concept of 'relativistic mass'.Neither in their research,nor in their teaching. As for 'poor' Mr.Einstein,he discovered some formulas as part of his theories that people found useful in other theories (like QFT) with which A.Einstein had nothing to do (e.g.QFT).Whether he liked those concepts he introduced,that's relevant only for history of physics,but not for physics and its evolution. Daniel. 


#4
Dec1804, 01:39 PM

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Q theory, Relativistic Mass and Einstein
One can speak of 4momentum in quantum theory because energy and momentum are compatible observables so that proper mass is a well defined quantity. However since speed/velocity is not a well defined quantity one can't defined m = p/v. If one always means "proper mass" then its best so make that clear and stick to it. Otherwise it can get tedious. Pete 


#5
Dec1804, 01:46 PM

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Pete 


#6
Dec1904, 10:54 AM

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PF Gold
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I'm not kind of authority of relativstic QM, but there is a fourvelocity operator (as indeed there is a velocity operator in bogstandard QM) as it is one of the postulates of QM that operators have the same functional relationship to the momentum operator as the observables they represent have to momentum in classical physics, so it is fairly obvious how to define a velcoity operator. Mass in relativstic quantum mechanics is not a dynamical quantity (I think tho' that's not true in quantum flavordynamics) so really it's exactly the same as it is in classical mechanics i.e. it's simply the inertial mass of the particle in it's rest frame.



#7
Dec1904, 11:59 AM

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Do you know of an online source so I can see the definition of such a quantity? Thanks. Here's a list of of the postulates of quantum mechanics http://www.upei.ca/~physics/polson/c.../notes/ch9.pdf Which one are you referring to? In any case that doesn't sound right since you're assuming that all quantities have corresponding operators and I don't see that as being true. Pete 


#8
Dec1904, 12:40 PM

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#9
Dec1904, 01:23 PM

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Daniel. 


#10
Dec1904, 01:27 PM

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Recall what I was saying  If it were basically the same then they'd have the same value in all possible cases. dextercioby was talking about an equality, i.e. E = mc^{2}. I was pointing out that this is an equality (in some cases) between m and E and not a definition of m given E. When the object is a point particle (i.e. zero dimensions, no internal structure) then the equality holds. Question: The energy E of a photon is related to its frequency f by E = hf. Since this holds in all cases do you consided E and f to be the "same thing"? Pmb 


#11
Dec1904, 01:32 PM

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Daniel. PS.It really makes me sick when somebody mocks at the Postulates of QM. 


#12
Dec1904, 01:35 PM

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PF Gold
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http://www.lns.cornell.edu/spr/200008/msg0027589.html http://wwwec.njit.edu/~venanzi/chem.../notes_Ch3.pdf 


#13
Dec1904, 01:52 PM

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The first link doesn't work for me by the way. Pete 


#14
Dec1904, 02:03 PM

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#15
Dec1904, 02:05 PM

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Daniel. 


#16
Dec2004, 05:01 AM

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I'm going to make a web page on this point soon to illustrate this point. Meanwhile if you have Rindler's Intro to SR text he explains this in the chapter in his chapter on relativistic mechanics of continua. Schutz also mentions something to this effect in his new text. Meanwhile this page illustrates the point quite nicely http://www.geocities.com/physics_wor...rd_paradox.htm Griffiths wrote an article sometime ago which illustrated a nice point  that the momentum of a (nonisolated) body is not always parallel to the velocity of the body. Tolman mentions this in his text but does not illustrate it. Of course the total momentum of a closed isolated system is always parallel to the velocity of the system. (more later; system problem and must reboot) [itex]\frac{d}{dt}\hat{X}_H(t) = \frac{1}{m}\hat{P}_H(t)[/itex] where [itex]\hat{X}_H(t) = U^{+}(t,t_0)\hat{X}_S U(t,t_0)[/itex] I guess if you want you can measure a momentum eigenvalue and then divide by m and call that "velocity". But if you do that with a photon then the "m" has to be relativistic mass. Pete 


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