Mass Eigenstate Questions [Archive]

Yi-Zen Chu; Yiren Qu

May14-04, 04:12 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi everyone,\n\nI have some newbie questions about oscillations - not necessarily\nneutrino-specific, but I guess related.\n\n1) Is mass of an elementary particle a measureable quantity? If so how\ndo we measure it?\n\n2) If the answer to 1 is yes, then when we measure the mass of say a\nneutrino we collapse its wavefunction to one of its mass eigenstates. If\nthat\'s the case does that mean mass is not conserved? For example if the\nneutron decays into a electron, proton, and an anti-electroneutrino, and\nafter a while we make a mass measurement on the anti-electroneutrino. If\nthe anti-electron-neutrino is a superposition of say 2 mass eigenstates,\nsome experiments would find the mass to be m1 and others would be m2.\nNow where does this mass difference come from? If we measure the mass to\nbe m1 does it mean the proton or the electron from the same decay would\nsuddenly lose or gain some mass to ensure mass conservation? I know mass\nis not conserved in relativity, but I wish to have some understanding of\nwhat\'s going on here.\n\n3) When we say mass in quantum mechanics - either non-relativistic or\nQFT - do we mean inertia mass or gravitational mass?\n\n4) What is the meaning of mass in quantum mechanics? In classical\nmechanics it is a property of material objects, the constant of\nproportionality between acceleration and a given force described by our\nforce theory (E&M, gravity, etc.). It is also a postulate that inertia\nand gravitational mass is the same thing. What about in QM? And, when we\nsay our particle is oscillating between its mass eigenstates, does it\nmean the gravitational force it exerts on others is oscillating or in\nsome kind of superposition? (Are there particles in a superposition of\ndifferent electrically charged states?) What about its inertia?\n\nThanks!\n\nYi-Zen\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi everyone,

I have some newbie questions about oscillations - not necessarily
neutrino-specific, but I guess related.

1) Is mass of an elementary particle a measureable quantity? If so how
do we measure it?

2) If the answer to 1 is yes, then when we measure the mass of say a
neutrino we collapse its wavefunction to one of its mass eigenstates. If
that's the case does that mean mass is not conserved? For example if the
neutron decays into a electron, proton, and an anti-electroneutrino, and
after a while we make a mass measurement on the anti-electroneutrino. If
the anti-electron-neutrino is a superposition of say 2 mass eigenstates,
some experiments would find the mass to be m1 and others would be m2.
Now where does this mass difference come from? If we measure the mass to
be m1 does it mean the proton or the electron from the same decay would
suddenly lose or gain some mass to ensure mass conservation? I know mass
is not conserved in relativity, but I wish to have some understanding of
what's going on here.

3) When we say mass in quantum mechanics - either non-relativistic or
QFT - do we mean inertia mass or gravitational mass?

4) What is the meaning of mass in quantum mechanics? In classical
mechanics it is a property of material objects, the constant of
proportionality between acceleration and a given force described by our
force theory (E&M, gravity, etc.). It is also a postulate that inertia
and gravitational mass is the same thing. What about in QM? And, when we
say our particle is oscillating between its mass eigenstates, does it
mean the gravitational force it exerts on others is oscillating or in
some kind of superposition? (Are there particles in a superposition of
different electrically charged states?) What about its inertia?

Thanks!

Yi-Zen

Matthew A. Nobes

May17-04, 06:23 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <c81fql\\$l23\\$1@news.wss.yale.edu>, Yi-Zen Chu; Yiren Qu wrote:\n> Hi everyone,\n>\n> I have some newbie questions about oscillations - not necessarily\n> neutrino-specific, but I guess related.\n>\n> 1) Is mass of an elementary particle a measureable quantity? If so how\n> do we measure it?\n\nThe lepton masses are directly measurable. You can, for example, extract\nthe muon mass from muon decay (formula 10.39 in Griffith\'s book). There\nare ways of directly looking for neutrino masses, but it\'s a lot harder.\n\nThe W and Z boson masses can also be measured. The Z0 is "easy" to get\nfrom the peak observed at LEP (easy in quotes, since you need LEP to begin\nwith). The W is harder to get, I think the best measurements of it\'s mass\ncome from Fermilab.\n\nQuark masses are not directly measurable. You have to infer them from\nthe properties of hadronic states. And even then, there is some\nambiguity.\n\n> 2) If the answer to 1 is yes, then when we measure the mass of say a\n> neutrino we collapse its wavefunction to one of its mass eigenstates. If\n> that\'s the case does that mean mass is not conserved? For example if the\n> neutron decays into a electron, proton, and an anti-electroneutrino, and\n> after a while we make a mass measurement on the anti-electroneutrino. If\n> the anti-electron-neutrino is a superposition of say 2 mass eigenstates,\n> some experiments would find the mass to be m1 and others would be m2.\n> Now where does this mass difference come from? If we measure the mass to\n> be m1 does it mean the proton or the electron from the same decay would\n> suddenly lose or gain some mass to ensure mass conservation? I know mass\n> is not conserved in relativity, but I wish to have some understanding of\n> what\'s going on here.\n\nI actually touched on this several years ago in a long sci.physics.particle\npost. The short answer is that you have to account for the energy and\nmomentum of the particles the neutrino interacts with. So if the\nneutrino hits a proton, the recoil velocity will be differant if it\nwere in mass eigenstate m1 or m2. This differance is way to small to\nactually be observed though.\n\n[snip]\n> 4) What is the meaning of mass in quantum mechanics?\n\nThat\'s much to deep a question for me :)\n\n> In classical\n> mechanics it is a property of material objects, the constant of\n> proportionality between acceleration and a given force described by our\n> force theory (E&M, gravity, etc.). It is also a postulate that inertia\n> and gravitational mass is the same thing. What about in QM?\n\nWell, operationally in quantum field theory, I think of mass as the\namount of energy needed to create a certian type of particle.\n\n> And, when we\n> say our particle is oscillating between its mass eigenstates, does it\n> mean the gravitational force it exerts on others is oscillating or in\n> some kind of superposition? (Are there particles in a superposition of\n> different electrically charged states?) What about its inertia?\n\nTo answer those sorts of questions in QM it\'s useful to think of a\nspecific situation, rather than a general one. (At least, I find\nit useful). So, for example, you can ask what happens to the initial\nparticles in the neutrino creation? If the nuetrino is in a superpostion\nyou\'d expect them to be. Until they\'re measured, they\'re in a superpostion\nof states of differant recoil momentum. Like I said above, in\npractice it would be impossible to distinguish those states, but\nconsidering them resolves any "paradoxical" issues. Apart from\nthe general "wierdness" of QM in general that is.\n\n--\nmanobes@sdf.lonestar.org\nSDF Public Access UNIX System - http://sdf.lonestar.org\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <c81fql$l23$1@news.wss.yale.edu>, Yi-Zen Chu; Yiren Qu wrote:
> Hi everyone,
>
> I have some newbie questions about oscillations - not necessarily
> neutrino-specific, but I guess related.
>
> 1) Is mass of an elementary particle a measureable quantity? If so how
> do we measure it?

The lepton masses are directly measurable. You can, for example, extract
the muon mass from muon decay (formula 10.39 in Griffith's book). There
are ways of directly looking for neutrino masses, but it's a lot harder.

The W and Z boson masses can also be measured. The Z0 is "easy" to get
from the peak observed at LEP (easy in quotes, since you need LEP to begin
with). The W is harder to get, I think the best measurements of it's mass
come from Fermilab.

Quark masses are not directly measurable. You have to infer them from
the properties of hadronic states. And even then, there is some
ambiguity.

> 2) If the answer to 1 is yes, then when we measure the mass of say a
> neutrino we collapse its wavefunction to one of its mass eigenstates. If
> that's the case does that mean mass is not conserved? For example if the
> neutron decays into a electron, proton, and an anti-electroneutrino, and
> after a while we make a mass measurement on the anti-electroneutrino. If
> the anti-electron-neutrino is a superposition of say 2 mass eigenstates,
> some experiments would find the mass to be m1 and others would be m2.
> Now where does this mass difference come from? If we measure the mass to
> be m1 does it mean the proton or the electron from the same decay would
> suddenly lose or gain some mass to ensure mass conservation? I know mass
> is not conserved in relativity, but I wish to have some understanding of
> what's going on here.

I actually touched on this several years ago in a long sci.physics.particle
post. The short answer is that you have to account for the energy and
momentum of the particles the neutrino interacts with. So if the
neutrino hits a proton, the recoil velocity will be differant if it
were in mass eigenstate m1 or m2. This differance is way to small to
actually be observed though.

[snip]
> 4) What is the meaning of mass in quantum mechanics?

That's much to deep a question for me :)

> In classical
> mechanics it is a property of material objects, the constant of
> proportionality between acceleration and a given force described by our
> force theory (E&M, gravity, etc.). It is also a postulate that inertia
> and gravitational mass is the same thing. What about in QM?

Well, operationally in quantum field theory, I think of mass as the
amount of energy needed to create a certian type of particle.

> And, when we
> say our particle is oscillating between its mass eigenstates, does it
> mean the gravitational force it exerts on others is oscillating or in
> some kind of superposition? (Are there particles in a superposition of
> different electrically charged states?) What about its inertia?

To answer those sorts of questions in QM it's useful to think of a
specific situation, rather than a general one. (At least, I find
it useful). So, for example, you can ask what happens to the initial
particles in the neutrino creation? If the nuetrino is in a superpostion
you'd expect them to be. Until they're measured, they're in a superpostion
of states of differant recoil momentum. Like I said above, in
practice it would be impossible to distinguish those states, but
considering them resolves any "paradoxical" issues. Apart from
the general "wierdness" of QM in general that is.

--
manobes@sdf.lonestar.org
SDF Public Access UNIX System - http://sdf.lonestar.org

Andr? Michaud

May18-04, 03:45 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Yi-Zen Chu; Yiren Qu" <y#i#-#z#e#n#.#c#h#u#@#y#a#l#e#.#e#d#u> wrote in message news:<c81fql\\$l23\\$1@news.wss.yale.edu>...\n> Hi everyone,\n>\n> I have some newbie questions about oscillations - not necessarily\n> neutrino-specific, but I guess related.\n>\n> 1) Is mass of an elementary particle a measureable quantity? If so how\n> do we measure it?\n\nIt is directly measurable in the case of charged elementary particles\nthat can move freely, like electron, positron (stable) and their\nunstable siblings, muons and taus.\n\nLong ago, the precise mass of electrons and positrons has been\ndirectly measured in Wilson chambers by measuring the deflection\nof their trajectory by a transverse magnetic field.\n\nAt velocities well below relativistic, the precision is very high.\n\nFor scatterable massive particles (quarks up and down) captive of more\ncomplex systems, like protons and neutrons, the situation is more\nproblematic.\n\nOnly estimations can be made through scattering other particles\non them, typically, electrons or positrons.\n\nIn the Review of Particle Physics 2000 edition:\n\n1 to 5 MeV/c^2 for the up quark\n3 to 9 MeV/c^2 for the down quark\n\nIn the 2004 edition of the Handbook of Chemistry and Physics\n\n1.5 to 5 MeV/c^2 for the up quark\n3 to 9 MeV/c^2 for the down quark\n\nI won\'t get into the so-called "masses" of virtual particles.\nThey all are calculated from observed energy levels.\n\nAndré Michaud\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Yi-Zen Chu; Yiren Qu" <y#i#-#z#e#n#.#c#h#u#@#y#a#l#e#.#e#d#u> wrote in message news:<c81fql$l23$1@news.wss.yale.edu>...
> Hi everyone,
>
> I have some newbie questions about oscillations - not necessarily
> neutrino-specific, but I guess related.
>
> 1) Is mass of an elementary particle a measureable quantity? If so how
> do we measure it?

It is directly measurable in the case of charged elementary particles
that can move freely, like electron, positron (stable) and their
unstable siblings, muons and taus.

Long ago, the precise mass of electrons and positrons has been
directly measured in Wilson chambers by measuring the deflection
of their trajectory by a transverse magnetic field.

At velocities well below relativistic, the precision is very high.

For scatterable massive particles (quarks up and down) captive of more
complex systems, like protons and neutrons, the situation is more
problematic.

Only estimations can be made through scattering other particles
on them, typically, electrons or positrons.

In the Review of Particle Physics 2000 edition:

1 to 5 MeV/c^2 for the up quark
3 to 9 MeV/c^2 for the down quark

In the 2004 edition of the Handbook of Chemistry and Physics

1.5 to 5 MeV/c^2 for the up quark
3 to 9 MeV/c^2 for the down quark

I won't get into the so-called "masses" of virtual particles.
They all are calculated from observed energy levels.

André Michaud