Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] velocity-dependent mass (or not)



--- On Tue, 6/30/09, WC Maddox <maddox@physics.Auburn.EDU> wrote:


From: WC Maddox

"Relativistic mass just won't go away. In the article by Gary Oas (On the
abuse and use of relativistic mass) arguing against the use of
relativistic mass there is a question that students were asked. It
amounts to weighing yourself on a spring scale at rest with respect to
the Earth and then weighing yourself using the same scale while moving
relative to the Earth. Would you, at least in principle, detect a change
in the scale reading? The answer in the article was no on the grounds
that mass does not increase with velocity.

In an article by Bernhard
Rothenstein (Relativistic velocity
transformation as a genitor of transformation equations) there is a
setup involving a two pan balance. The pans are on those frictionless
rods found in introductory physics texts. There are given equal speeds
(V) in opposite directions. At time t (center observer time) equal
masses are placed on the pans which are equal distances from the center.
The apparatus will remain balanced from the point of view of an observer
in the center. What about from the point of view of an observer (A)
traveling with one of the masses? According to the article, if A uses
the relativistic velocity addition formula to calculate the speed of the
other mass (B) and uses this to find the length of arm B, then observer
A finds arm B is shorter than arm A. According to the article A finds
that B is moving from the center with a speed less than V so distance
traveled by B is less than distance
traveled by A. To remain alanced,
mass B would have to be larger by an amount given by the relativistic
mass formula.

Did one author make a mistake? Does it matter whether it is a spring
balance or a two pan balance? Are both authors wrong by not bringing in
general relativity?"

    I did not read the second author, and therefore will only comment on the first one. He made more than one mistake. The first one was that the problem was poorly stated, and this is already a promising beginning. The conditions do not specify your trajectory relative to the Earth in the second trial. If it is perpendicular to the Earth's radius but coincident with the surface of the Earth, then the scale would record DECREASE of the normal force since part of it would go to create centripetal force. Already at v = 8.2 km/s (far from relativistic domain needed for experimental detection of the velocity-dependence of mass)  the
scale will read zero, indicating weightlessness. Not a very good procedure for detecting the existence of relativistic mass.
  In order for the suggested experiment to be meaningful, the considered part of the trajectory must be a straight line, which would be equivalent to riding on a flat horizontal support. But in this case the outcome, whatever it is, would be, under condition, not indicative in principle to existence of relativistic mass: you can detect it if you measure it first in its rest frame, and second, from some other frame in which this mass is moving. In Gary Oas' suggestion both measurements
are performed in the rest frame of the measured mass (which is yours, and you are standing on the same scale, so in both trials you measure your weight remaining in your own rest frame.) This is his second mistake showing not a very good understanding of the subject of his own article.
  Now, what IS the actual outcome? Oas'
statement that there will be no difference is downright wrong. Since in the first trial you are stationary and in the second one you are moving relative to Earth, the normal force measured by your scale will be DIFFERENT in these two cases. Namely, in the second trial it will increase by a factor gamma^2. The first gamma is due to relativistic mass of the Earth which is now moving with respect to you, and the second factor is due to retardation effects similar to those producing increase of the transverse electric field of a moving charge. Already from this result one could deduce the existance of relativistic mass - that of the Earth. Ignoring these two well-known effects is Oas' third mistake. I think this says all there is to say about his renowned paper.

  BTW, the discussion of the experiments in gravitational field reminded me about    the relevant message of Brian Whatcott a few days ago:



From:
"Brian Whatcott" <betwys1@sbcglobal.net>
Add sender to Contacts



To:
"Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>


How interesting that you used electromagnetic deflection of a high speed
particle, rather than the gravitational deflection of a photon i.e. by
angular displacement of the path of a photon beam at glancing solar
incidence during a solar eclipse! The latter setup whispers to adherents
of the current view of gravitational displacement, only about 
space-time distortion, but the former seems to bring less baggage to the
party!

Brian W

Brian is totally right that the gravitational experiments are less straightforward in terms of their interpretation. But if we really want to get a deeper insight into the origin of the space-tame geometry, then the experiments with light deflection in gravitational field.also provide us with a compelling evidence in favor of relativistic mass. Suppose we launched a bunch of photons with different frequencies but all in one horizontal direction. A photon's energy is
h*w, but all of them are deflected from their originally horizontal direction equally regardless of w, that is, regardless of their energy. Therefore we can talk about equal transverse acceleration a = g (here g is local acceleration due to gravity at the place of the launch). This acceleration is the ratio of gravitational force h*w*g/c^2 to mass of the photon (under conditions, this relation holds in relativity as well). The only way to obtain the experimentally observed result (frequency-independent deflection) is to accept that a photon possesses mass equal to h*w/c^2, which is definition of relativistic mass. This can be considered as the extreme version of the Oas' thought experiment, but performed by Nature, and the result also tells us something about the validity of Oas' conclusion.
   We can of course say that the whole thing is just space-time geometry. But one should not forget that the mere possibility to describe this in terms of geometry is based on the equivalence principle, which in turn rests on the fundamental fact of the fixed local acceleration a=g for all masses, and the latter only holds because
g = weight/m(rel) = weight/m0*gamma, NOT weight/m0. (In the latter case all photons, as having weight=h*w*g/c^2 and m0 = 0, would go directly towards the gravitational center wiih infinite acceleration) .
  Summarizing, we find the concept of relativistic mass at the origin of one of the most elegant theories - GR. And if we are thoughtful enough, this thing at the bottom reminds us (especially in non-stationary situations!) about dynamical underpinnings of geometry.

Moses Fayngold,
NJIT
 
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l