spacetime approach

[JohnDenker]

Consider the following:

• The concept of «time dilation» as introduced in section 14.3 on page 345ff and repeated in lots of other places, including the chapter summary (aka «glossary») on page 373.
• The concept of «length contraction» as introduced on page 349ff and repeated in lots of other places, including the chapter summary (aka «glossary») on page 373.
• The whole idea of velocity-dependent mass as discussed in item #199 and item #200.

These are all archaic (pre-1908) concepts. They make sense to people who think Einstein's 1905 paper was the last word on relativity. Well, it wasn't. Physics has moved on. Even Einstein moved on, shortly after Minkowski's epochal Raum und Zeit (1908) paper. Without spacetime, Einstein would never have been able to work out general relativity.

The idea of clocks that can't be trusted, rulers that can't be trusted, N different incompatible notions of velocity-dependent mass ... it's madness. It was the state of the art for about 3 years, more than 100 years ago.

Pedagogical issues:

This is one of the many reasons why I say you have to write two books: One for the students, and one for the teachers. The teachers are part of the team, and we need to meet their needs. Teachers and students are not coming from the same place. The teachers have been poisoned by a bunch of paradoxical, weird, archaic ideas, whereas students have not. It's harder to teach relativity to high-school teachers than to high-school students, but still it has to be done.

Suggestions:

• When presenting the topic to students, do not mention ridiculous archaic ideas at all. Rip them out of the book, without mercy:
  • «time dilation»
  • «length contraction».
  • «velocity-dependent mass».
• Adopt the spacetime approach exclusively:
  • Spacetime diagrams
  • four-vectors
  • proper time
  • invariant mass
  • constant speed of light as a consequence of the geometry (not a postulate)
• Emphasize that relativity is not weird or paradoxical.
• Special relativity is the geometry and trigonometry of spacetime; nothing more and nothing less.
• Relativity makes students' life easier, not more complicated. It provides a unified view of a whole bunch of things that otherwise would have to be learned separately.

Meanwhile ... we owe teachers an explanation. They need to know that certain concepts are more than 100 years out of date, and that's why they are missing from the students' book. They need to know how to reconcile the archaic viewpoint with the modern viewpoint. Emphasize that this is for the teachers' edification only, and is not to be inflicted on the students.

Also explain to teachers that this is the spiral approach in all its glory. It is an opportunity to review, reinforce, and extend everything the students ever knew about trigonometry, geometry, vector spaces, et cetera. Even if students never get much use out of relativity directly, this reinforcement is useful.

For the next level of detail on this, see https://www.av8n.com/physics/spacetime-welcome.htm which is supplemented by (and contrasted with!) https://www.av8n.com/physics/spacetime-dirty-laundry.htm

See also item #201 for a catalog of issues related to special relativity.

[JohnDenker]

It has been suggested that "some" incoming students have taken AP physics and been exposed to archaic (pre-1908) ideas of rulers that can't be trusted, clocks that can't be trusted, velocity-dependent mass, et cetera ... and that therefore we need to address these topics. I am not convinced, for multiple reasons:

• Not all of them have been exposed. Mentioning the archaic ideas will -- on average -- cause more problems than it solves.
• Even among those who were exposed, very few were seriously infected. Many have already forgotten it. Those who haven't forgotten will forget more quickly if we don't mention it. Given them a viable alternative, and let the archaic ideas die from neglect.
• For the exceptional student who insists on some actual critical reasoning, who insists on reconciling the new information with what he was told previously, we can explain as follows: The shadow of a ruler may be longer or shorter than the ruler, but that does not change "the" length of the ruler. The thing you are calling the contracted length is not "the" length but rather just a projection. The real thing -- i.e. the thing you should be using as your conceptual basis -- is not necessarily the thing that is easiest to measure in the lab frame ... which is an idea that goes back all the way to Plato if not earlier.
• I would turn the argument around and point out that the vast majority of the students have at least heard of the four-dimensional spacetime continuum. We are much better off using that as our springboard.