marcus wrote
Rindler, who got his PhD back in 1956, is in a tiny minority of hold-outs.
What evidence do you have to support that conclusion? I don't see it that way in the literature. One notable example is Alan Guth at MIT. In his class notes he writes
http://www.geocities.com/physics_world/guth-mass.htm
(
http://web.mit.edu/8.286/www/)
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We are perhaps not used to thinking of electromagnetic radiation as having mass, but it is well-known that radiation has an energy density. If the energy density is denoted by u, the special relativity implies that the electromagnetic radiation has a mass density
(7.3) rho = u/c^2
To my knowledge nobody has ever "weighed" electromagnetic radiation in any way, but the theoretical evidence in favor of Eq. 7.3 is overwhelming - light has mass. (Nonetheless, the photon has zero rest mass, meaning that it cannot be brought to rest). The general relation for the square of four-momentum reads p^2 = -(mc)^2, and for the photon this becomes p^2 = 0. Writing out the square of the four-momentum leads to the following relation for photons:
p^2- E^2 = 0, or E = cp.
In this set of notes we will examine the role which the mass of
electromagnetic radiation plays in the early stage of the universe.
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I'd hardly say that Guth was out of touch. And this is what he's teaching students at MIT.
>Is he still teaching in Texas or is he emeritus?
I think he's emeritus.
>It is a really confusing phrase in general
> discussion---at least as you use it Pete
When you say "confusing" do you find it confusing or is it you think that others are confused? If you find it confusing then in what sense are you confused?
>Everytime on PF I have pointed out that the righthand side of
>the Einstein eqn is an *energy* density----which is the normal
> view----you automatically answer back "oh no! you misunderstand!
> it is a "relativistic mass" term!
They differ by a constant. So you can write that equation either way. But if you follow the actual usage in, say, the American Journal of Physics, or Peebles text on cosmology then they tend to be more precise when they use terms like "mass" - it can mean one of 3 things
(1) proper mass
(2) inertial mass (i.e. relativistic mass = This is how Schutz uses it)
(3) active gravitational mass
(4) passive gravitational mass
Einstein's equation is the general relativity equation that replavced Poisson's equation - and in that equation it's mass. and yes mass density =- but I thought it was obvious that it was density.
And I realize that you think it's out of use by all "up to date" folks. Fine - believe that. I'm not trying to force you to believe anything. But I will state my opinion and what I see relativists doing.
By the way. Rindler is just *one* example. There are others. E.g.
"Basic Relativity," Richard A. Mould
"Introducing Einstein's Relativity," Ray D'Inverno
"Understanding Relativity: A Simplified Approach to Einstein's Theories," Leo Sartori
And then there is my astronomy text 'Perspectives in Astronomy' I think it's callled (It's somewhere around here. Ref furnished upon request)
Then there are the articles from the literature, i.e. physics jorunals written in support of relativistic mass and others who disagree with the con-relativistic mass people.
However I question the reason that its becoming porpular. I don't think its based on pure logic and for purely physics oriented reasons. I think some authors wrote in their text that relativistic mass is "old fashioned" when it really wasn't. Students eager to learn relativity and who want to impress their friends with it surely want to learn the "up to date" physics. Reading that relativistic mass is "old fashioned" then leads them to think "Gee! I certainly don't want to be old fashioned and the guy who wrote my, very expensive, text must surely know what he's talking about. They must have done an experiment that proved it wrong. etc."
When the fact is that some of the articles in the physics literature had some highly misleading arguements as well as some which were just plain wrong! In actuality there is nothing wrong with the notion. In fact it best fits the notion of what mass is.
After all. The student is in no position to fully understand such broad sweeping statements as are made in their texts. And the physics I, II, III course barely scratch the surface of relatvity.
Physicists for the last (almost) 100 years have been studying and testing these ideas. Some have gone through great pains to cover all the intricate ideas and notions that go into such statements such as m = E/c^2 with all of its implications.
To dimsiss the notion as "old fashioned" is extremely misleading. Some of these claims of old fashioned were made when relativistic mass was IN fashion. Something of this magnitude of an idea doesn't become olf fashioned over night. It'd take many decades of complete non-use. And that can hardly be said for current physics today. Intro Physics texts (For physics I, II and III) are not written by cosmologists and GR-experts in general. And these are the greatest users of the idea.
marcus - Pick up the Peebles' cosmology text and look under (1)inertial mass (2) active gravitational mass and (3) passive gravitational mass
Also look under cosmic strings and vacuum domain walls. The former has zero active g-mass and the later negative active g-mass
Pete
