jwg@teddy.UUCP (10/28/85)
In article <536@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes: >... A direct weighing measurement would give the same result >for *any* energy delivering device, since the potential energy stored >in something CONTRIBUTES TO ITS RESTMASS. Is this true? Does the potential energy stored in a spring contribute to its rest mass? How about a battery, a capacitor, etc? -- -> Jim Galbiati, GenRad Inc, Production Test Division <- ->USmail: Mail Stop 6, 300 Baker Ave, Concord, Mass. 01742 <- ->usenet: {decvax,linus,wjh12,mit-eddie,cbosgd,masscomp}!genrad!panda!jwg <- ->tel: (617) 369-4400 x2459 <-
ins_apmj@jhunix.UUCP (Patrick M Juola) (10/31/85)
In article <1514@teddy.UUCP> jwg@teddy.UUCP (Jim Galbiati) writes: >In article <536@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes: >>... A direct weighing measurement would give the same result >>for *any* energy delivering device, since the potential energy stored >>in something CONTRIBUTES TO ITS RESTMASS. > >Is this true? Does the potential energy stored in a spring >contribute to its rest mass? How about a battery, a capacitor, etc? > >-- >-> Jim Galbiati, GenRad Inc, Production Test Division <- Yes.
js2j@mhuxt.UUCP (sonntag) (11/04/85)
> >Is this true? Does the potential energy stored in a spring > >contribute to its rest mass? How about a battery, a capacitor, etc? > >-> Jim Galbiati, GenRad Inc, Production Test Division <- > > Yes. Wow, what an informative answer! Lets consider a very simple system as a specific example. Suppose we have two electrons rather close together and very far from any other influence at T=0. They have some potential energy stored by virtue of their mutual repulsion. If we let them go, that potential energy is gradually converted to kinetic energy as they speed apart. If we could measure the mass of these electrons, would we find that the two-electron system has more than two electron rest masses? Would we find that each electron has more than one electron rest mass? If we were measuring the electron masses from the reference frame stationary w.r.t. the electrons at T=0, would the extra mass measured as T => infinity be the same as the extra mass measured due to relativistic effects, or would we have to treat that apparent mass change seperately? -- Jeff Sonntag ihnp4!mhuxt!js2j "What would Captain Kirk say?"
matt@oddjob.UUCP (Matt Crawford) (11/05/85)
The following digresses somewhat from the original question, but it is all relevant. The predominant meaning of the word "mass" among physicists is "rest mass", not mass times some velocity-dependent factor. For a single particle with energy E and momentum P (consider all P's to be vectors in this article), the mass is the square root of E^2 - P^2. This does not depend on the frame in which E and P are measured. Often physicists will talk about the mass of a pair of particles. this is just the square root of (E1 + E2)^2 - (P1 + P2)^2. If the two particle are the sole decay products of some other particle, then this is the mass of that original particle. (Side note: the combined mass of the decay products will be distributed about the mean with a standard deviation inversely proportional to the half-life of the particle that decayed to produce them. Thus one hears phrases like "the width of the Z-0".) If you compress a spring with a rock at each end, its mass will be greater than the separate masses of the rocks and uncompressed spring. The extra mass will equal the kinetic energy which the spring can give to the rocks (divided by c^2, if you like). If you separately square the total energy and total momentum of the spring and rocks, then subtract, you will get the same answer both while the system is tied together and after the rocks are sent flying. _____________________________________________________ Matt University crawford@anl-mcs.arpa Crawford of Chicago ihnp4!oddjob!matt
dgary@ecsvax.UUCP (D Gary Grady) (11/08/85)
> The predominant meaning of the word "mass" among physicists is > "rest mass", not mass times some velocity-dependent factor. For what it's worth, in high-energy physics it is not unusual to see the phrase "invariant mass" (meaning rest mass) for clarity. -- D Gary Grady Duke U Comp Center, Durham, NC 27706 (919) 684-3695 USENET: {seismo,decvax,ihnp4,akgua,etc.}!mcnc!ecsvax!dgary
tan@ihlpg.UUCP (Bill Tanenbaum) (11/12/85)
> In article <536@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes: > >... A direct weighing measurement would give the same result > >for *any* energy delivering device, since the potential energy stored > >in something CONTRIBUTES TO ITS RESTMASS. > > Is this true? Does the potential energy stored in a spring > contribute to its rest mass? How about a battery, a capacitor, etc? > -> Jim Galbiati, GenRad Inc, Production Test Division <- --------------- Yes, yes, yes, and yes. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan
tan@ihlpg.UUCP (Bill Tanenbaum) (11/12/85)
> > >Is this true? Does the potential energy stored in a spring > > >contribute to its rest mass? How about a battery, a capacitor, etc? > > >-> Jim Galbiati, GenRad Inc, Production Test Division <- > > > > Yes. > > [Jeff Sonntag] > Wow, what an informative answer! > Lets consider a very simple system as a specific example. Suppose we > have two electrons rather close together and very far from any other influence > at T=0. They have some potential energy stored by virtue of their mutual > repulsion. If we let them go, that potential energy is gradually converted > to kinetic energy as they speed apart. > If we could measure the mass of these electrons, would we find that > the two-electron system has more than two electron rest masses? Would we > find that each electron has more than one electron rest mass? If we were > measuring the electron masses from the reference frame stationary w.r.t. the > electrons at T=0, would the extra mass measured as T => infinity be the > same as the extra mass measured due to relativistic effects, or would we > have to treat that apparent mass change seperately? -------------------- 1) Yes, the 2 electron system has more than two electron rest masses. 2) I'm not sure how you intend to measure the mass of each electron separately in the above system, so I can't answer the second question. 3) The extra mass of the 2 electron system at T=0 is the same as the relativistic mass gain at T=>infinity. (This ignores the possibility that the accelerated electrons might radiate away some of their energy.) A better example: The rest mass of a deuteron (neutron-proton bound state) is about 2 Mev less than the sum of the separate rest masses of the proton and neutron. The 2 Mev deficit is just the binding energy of the attractive nuclear force. To ask whether the separate rest masses of the proton and the neutron bound in the deuteron are less than that of free protons and neutrons is to ask a meaningless question, unless you have some way of defining and measuring what you mean by it. I don't. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan