OK--here is my question about starting with momentum and force = delta-p/delta-t.
When asked something like: "What is the necessary average force needed to stop a 1000 kg car from a speed of 30 m/s in 10 seconds?" aren't you forced to return to p = mv? Once there, introducing the relativistic observations that the momentum of a given object (an electron for example) is not linear in velocity since both the velocity and momentum can be measured experimentally, isn't there a very strong temptation to look at something going on with the mass? That is, if one almost always pulls momentum apart into mass and velocity at low speeds, why not at high speeds?
Related, I think, is the notion of how WE would experience and the 'logically' explain relativistic phenomena. To the point--the twins. In my presentation we have twin brothers, Harlie and Charlie. Harlie gets hungry and wants a pizza. He knows a great pizza joint on Alpha Seti 6, a mere 30 light years away, and dashes off at relativistic speeds. He returns with the pizza (still hot). Charlie is now 60 years older, whereas Harlie has experienced an hour's time. Harlie KNOWS that Alpha Seti 6 is 30 light years away (and he knows he has undergone a bunch of accelerations). He knows Charlie is now 60 years older--which basically precludes a conclusion that he has been traveling much faster than light (he knows that rule too). He might consider that the distance to AS-6 somehow shrunk considerably, but with his knowledge of the universe, he knows that can't really be true and besides Charlie has been measuring that distance each year using parallax techniques. Isn't the only thing Harlie is left with as a workable conclusion is that HIS CLOCK has been running slower than Charlie's. I don't see how 'geometry' can help here--he is 1 hour older, Charlie is 60 years older, Harlie is holding the pizza box clearly marked with an Alpha Seti 6 address that required a 60 light-year round trip. Slow clocks seem the only way for Harlie to resolve this puzzle. ??
Rick
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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
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