I recently came across this paper http://arxiv.org/abs/physics/0504110v2 by Oas that is a semi-rant about how pedagogically evil relativistic mass is. He gives the following sample question:
From the context, it appears that the students are expected to have little or no background in relativity other than reading a paragraph that introduces relativistic mass in special relativity. It seems from the context that they do *not* know the equivalence principle (or anything about GR). The correct answer is stated to be that in both cases, a and b, the reading equals 200 lb. He takes the students' failure to give the right answer as indicating that relativistic mass has corrupted their brains.
My reaction on reading the question is that there's no reason to expect students to be able to construct an elementary argument if all they know is minimal SR and not the e.p. Am I missing some such elementary argument?
If you know the e.p., then I suppose you could reason that both A and B are being accelerated upward by a force from underneath their feet. Since they see each other as being at rest, and their displacement from each other is horizontal, their upward accelerations are equal, and must be caused by an equal force. This is all a little tricky because it does depend on the geometry. If A and B were displaced vertically from one another rather than horizontally, then I think the answer would be different. (This would be similar to the Bell spaceship paradox.)
Another approach would be to transform the earth's stress-energy tensor into A's frame -- obviously these students are not being expected to do that.
Am I missing some elementary argument that provides the correct answer? It seems to me that Oas's question is one that students at this level should not know the answer to, and that it's completely bogus to blame the result on relativistic mass.
Quote:
...the students were queried about two identical twins, one of which (Al) is aboard a rapidly moving train car while the other (Bob) watches from the ground. Given that Bob sees his own scale to read 200 lbs, the students were asked; a) As Bob looks at Al’s scale what does he see it to indicate?; b) As Al looks at his own scale what does he see it to in- dicate? The choice of response consisted of less than, greater than, or equal to, 200 lbs. |
From the context, it appears that the students are expected to have little or no background in relativity other than reading a paragraph that introduces relativistic mass in special relativity. It seems from the context that they do *not* know the equivalence principle (or anything about GR). The correct answer is stated to be that in both cases, a and b, the reading equals 200 lb. He takes the students' failure to give the right answer as indicating that relativistic mass has corrupted their brains.
My reaction on reading the question is that there's no reason to expect students to be able to construct an elementary argument if all they know is minimal SR and not the e.p. Am I missing some such elementary argument?
If you know the e.p., then I suppose you could reason that both A and B are being accelerated upward by a force from underneath their feet. Since they see each other as being at rest, and their displacement from each other is horizontal, their upward accelerations are equal, and must be caused by an equal force. This is all a little tricky because it does depend on the geometry. If A and B were displaced vertically from one another rather than horizontally, then I think the answer would be different. (This would be similar to the Bell spaceship paradox.)
Another approach would be to transform the earth's stress-energy tensor into A's frame -- obviously these students are not being expected to do that.
Am I missing some elementary argument that provides the correct answer? It seems to me that Oas's question is one that students at this level should not know the answer to, and that it's completely bogus to blame the result on relativistic mass.
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