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| | :A footnote goes on to say that "In a complicated or contrived series of calculations that most physics majors cannot duplicate even after learning them, the theory of general relativity's fundamental formula, <math>G_{\mu\nu} = 8 \pi K T_{\mu\nu}\,</math>, was conformed to match Mercury's then-observed precession of 5600.0 arc-seconds per century. Subsequently, however, more sophisticated technology has measured a different value of this precession (5599.7 arc-seconds per century, with a margin of error of only 0.01) ..." | | :A footnote goes on to say that "In a complicated or contrived series of calculations that most physics majors cannot duplicate even after learning them, the theory of general relativity's fundamental formula, <math>G_{\mu\nu} = 8 \pi K T_{\mu\nu}\,</math>, was conformed to match Mercury's then-observed precession of 5600.0 arc-seconds per century. Subsequently, however, more sophisticated technology has measured a different value of this precession (5599.7 arc-seconds per century, with a margin of error of only 0.01) ..." |
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| | :Considering only the ''anomalous'' precession, that is, the precession that remains after all known other factors (other planets and asteroids, solar oblateness) have been accounted for, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values are: | | :Considering only the ''anomalous'' precession, that is, the precession that remains after all known other factors (other planets and asteroids, solar oblateness) have been accounted for, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values are: |
| | ::: 43.11 ± 0.21 (Shapiro et al., 1976) | | ::: 43.11 ± 0.21 (Shapiro et al., 1976) |
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| | 9: ''The discontinuity in momentum as velocity approaches "c" for infinitesimal mass, compared to the momentum of light.'' | | 9: ''The discontinuity in momentum as velocity approaches "c" for infinitesimal mass, compared to the momentum of light.'' |
| − | :You have to take them going to 0 at the same time! It's nonsense for a massive particle to travel at c! | + | :The formulas for velocity, momentum, and mass can in fact be written in such a way that they appear to have discontinuities, just as the tangent function has discontinuities while the underlying sine and cosine functions do not. But they can also be written in a form that does not show discontinuities. |
| | + | :All particles, with or without mass, can have any value of momentum. The formula for the velocity of a particle, in terms of its mass and momentum, is |
| | + | :::<math>v = \frac{pc}{\sqrt{m^2c^2+p^2}}</math> |
| | + | :For a particle with mass, this means that momentum of zero gives a speed of zero, and, as the momentum approaches infinity, the speed approaches c. |
| | + | :For a massless particle, the speed is always c. |
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| | + | 33: ''Based on Relativity, Einstein claimed in 1909 that the aether does not exist, but in order to make subatomic physics work right, theorists had to introduce the aether-like concept of the Higgs field, which fills all of space and breaks symmetries.'' |
| | + | Quantum field theory abounds with fields. The Higgs particle has a Higgs field. It has nothing to do with the "luminiferous aether". |
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