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*To*: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)*Subject*: Engineering Newsletter*From*: Steve VanDevender <stevev@efn.org>*Date*: Sat, 25 Nov 1995 01:02:48 -0800*Cc*: KellySt@aol.com, hous0042@maroon.tc.umn.edu, stevev@efn.org, rddesign@wolfenet.com, RUSSESS@cellpro.cellpro.com, jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl*In-Reply-To*: <199511221718.AA11651@student.utwente.nl>*References*: <199511221718.AA11651@student.utwente.nl>

Timothy van der Linden writes: > ReplyTo : Steve and Kevin > ReplyFrom: Timothy > > >I say that "relativistic mass increase" is a misnomer and that > >you are better off treating mass as invariant. > > Both methods are valid to use. The difference is more a physical matter than > a mathematical. I was used to working with the "wrong" formulas and Steve > was used working with the "right" formulas. > The so called "wrong" formulas look a bit more like the classic formulas so > they may be easier to understand. > > Both methods are being taught at universities and both are valid. I think we'd both agree that, for example, p(v) = m * v / sqrt(1 - v^2). What I have learned to be suspicious of is interpreting this as (m/sqrt(1 - v^2)) * v, as if the mass somehow increases with velocity. What I find to be a more intuitive and less misleading interpretation is that mass is invariant (m^2 = E^2 - p^2) but that energy and momentum can increase without limit as the moving object accelerates. When doing more elaborate kinematics problems it's also easier to just keep track of the conserved E and p components, then sort out the resultant masses of the reaction products. Often in math there is more than one way to the right answer. I happen to find that concentrating on conservation of energy and momentum and keeping track of invariant quantities makes it easier to get the right answer and to prove that it's right. If you can do it the "wrong" way, get the right answer, and prove that it's right, then fine. > I've always looked at is as follows: When you move faster and faster, part > of the energy is transformed into mass, the other part is used to get the > extra momentum. I used to look at it this way, but Taylor and Wheeler talked me out of it (see chapter 8 of _Spacetime Physics_ for a lengthy, careful discussion on "Use and Abuse of the Concept of Mass"). The problem here is that relative velocity or acceleration do not cause any fundamental changes in the structure of the moving object. Where is this extra mass? If it's really stashed on the ship somewhere then the people on the ship could measure it. But they don't feel the ship getting heavier or see any increase in the mass of the ship in their frame. You also seem to be falling into the same trap that Kelly did earlier, in not treating energy and momentum as separate components. Most of the counterintuitive results of relativistic kinematics problems come from failing to understand that the conserved quantity in a reaction is a _vector_ quantity, and that the magnitude of that vector is calculated using Lorentz rather than Euclidean geometry. Taylor and Wheeler's wisdom on the subject is that the definition of mass is sqrt(E^2 - p^2); then every observer sees the same mass for the same object, no matter what their relative motion. The quick treatment in many physics texts is that mass is sort of like E, but they do a lot of tapdancing to keep everything consistent. This appears to be motivated by trying explain the famous "E = m * c^2", which turns out to be a lot less profound an observation than some of the other implications of relativistic physics. Taylor and Wheeler look at "E = m * c^2" as a mere matter of unit conversion; it's only really true if you are at rest relative to the mass in question, and they consider the use of Lorentz geometry for spacetime and invariance of spacetime interval as more fundamental and revealing concepts. > Now I only wonder, does such a fast moving particle excert greater > gravitation on a non-moving observer? This I can't answer with certainty. Offhand, I'd say "no." If the particle's mass doesn't change, then how could its gravitation change? > Steve if the answer is yes, how do you explain that not using "relativistic > mass increase"? If, on the other hand, a moving object did exert greater gravitation than a stationary object of the same mass, I'd probably be looking for a relation to a quantity that did change, like the object's total energy.

**Follow-Ups**:**Re: Engineering Newsletter***From:*Kevin C Houston <hous0042@maroon.tc.umn.edu>

**References**:**Engineering Newsletter***From:*T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)

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