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Announcements

Announcements. Exam 3 is Thursday April 11 Tentatively will cover Chapters 7, 8 & 9 Sample questions have been posted. The main equations of special relativity. Time Dilation:. Length Contraction:. A bit about terminology.

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Announcements

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  1. Announcements • Exam 3 is Thursday April 11Tentatively will cover Chapters 7, 8 & 9 Sample questions have been posted

  2. The main equations of special relativity Time Dilation: Length Contraction:

  3. A bit about terminology Proper Time: time measured stationary relative to the “event” Your watch always tells proper time for you Proper length: length measured stationary relative to the “event” A meter stick you carry always measures the proper length of objects that are stationary with respect to you Rest mass: mass measured stationary with respect to the object A scale you carry always measures the rest mass of objects that are stationary with respect to you Boost factor (G) from the Lorentz transformation. Check out links on Special Relativity at http://www.apsu.edu/astronomy/cosmology-links-and-applets

  4. Other Equations of Relativity Relativistic Momentum Relativistic Mass Relativistic Energy

  5. The Classic Doppler Effect The classical Doppler Effect is only radial: only motion away or towards the observer affect the observed frequency

  6. The Relativistic Doppler Effect The relativistic Doppler Effect includes the stretching or contracting of waves due to relative motion and time dilation due to the relative motion. Note that the relativistic Doppler Effect occurs even perpendicular to the direction of motion

  7. Space-time Diagrams Anything inside your light cone could influence you (below you) or you could influence it (above you). Anything outside your light cone cannot affect you

  8. The Space-time Interval is invariant. i.e.: it is the same for all inertial reference frames Note the minus sign difference from the Pythagorean theorem. This means Ds2can be negative (space-like) Play with Applets on Special Relativity

  9. The Twin Paradox. The paradox goes away if you consider that the traveler is in two different inertial reference frames Terence stays at home while Stella makes a trip to Alpha Centauri. See the Twin Paradox Website

  10. The “Special” of Special Relativity was constant velocity How do we deal with situations where there isn’t constant velocity? What about near the surface of the Earth where there is gravity? What about the general case? It took Einstein 10 years to figure out General Relativity

  11. The problem with Newton’s gravity: the anomalous precession of the perihelion of Mercury The observed precession is 5600 arcseconds per century. 5025 arcseconds is due to the Precession of the Equinoxes of Earth, 532 is due to the effects of Venus, Earth, Jupiter and all the other planets on Mercury. That leaves 43 arcseconds per century unaccounted for by Newtonian gravitation and mechanics.

  12. Newton’s Universal Gravity is a force law with no propagation speed There is nothing in the force equation that says how fast it is transmitted. In fact, it assumes an instantaneous transmission of the force. An instantaneous transmission is in direct violation of Special Relativity

  13. Special Relativity was for “inertial” reference frames. What about accelerating reference frames?

  14. The Weak Equivalence Principle Any acceleration is indistinguishable from gravity

  15. Is “freefall” an inertial reference frame?

  16. On Earth’s surface we are not in an inertial reference frame

  17. The two “fictitious” forces we feel are the Coriolis force and the centrifugal force The fictitious forces are invoked to explain the observed accelerations when we are in a non-inertial reference frame

  18. The Strong Equivalence Principle All inertial and freely falling reference frames are equivalent Recall from Special Relativity: All laws of physics are the same in all inertial reference frames

  19. A consequence of the equivalence principle is the bending of light by massive objects

  20. Time is changed by gravity Gravity slows time. The stronger the gravity, the slower time flows. Unlike Special Relativity, you can tell whose clock is slow. The one that is deeper in the gravity well is the slower one.

  21. Gravitational Redshift is another consequence of equivalence Light loses energy as it “climbs” out of a gravity well. This results in the light being redshifted by gravity.

  22. General Relativity deals with geometry

  23. Euclidian Geometry: Flat

  24. Spherical Geometry

  25. Hyperbolic Geometry

  26. The Metric is the formula for the distance between two points Spherical geometry Euclidian geometry Hyperbolic geometry

  27. So what kind of geometry do we use in General Relativity? Riemannian geometries are locally flat. On a small enough scale they are Euclidian

  28. The Earth is a good example of a Riemannian Geometry The mathematics of Riemannian geometry had been worked out in the mid 1800’s by Georg Friedrich Bernhard Riemann

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