1. PHYS344 Lecture 8 Problem set 2 due on Wednesday the 16 th in class. Krane, Chapter 2: Problems 25, 26, 32, 33, 37, 39, 40, 41, 42 Finish Relativity today, start prelude to Quantum Theory

2. The Doppler Effect A similar change in sound frequency occurs when the source is fixed and the receiver is moving. But the formula depends on whether the source or receiver is moving. The Doppler effect in sound violates the principle of relativity because there is in fact a special frame for sound waves. Sound waves depend on media such as air, water, or a steel plate in order to propagate. Of course, light does not! Christian Andreas Doppler (1803-1853) The Doppler effect for sound yields an increased sound frequency as a source such as a train (with whistle blowing) approaches a receiver and a decreased frequency as the source recedes.

3. Waves from a source at rest Viewers at rest everywhere see the waves with their appropriate frequency and wavelength.

4. Recall the Doppler Effect A receding source yields a red-shifted wave, and an approaching source yields a blue-shifted wave. A source passing by emits blue- then red- shifted waves.

5. The Relativistic Doppler Effect So what happens when we throw in Relativity? Consider a source of light (for example, a star) in system K ’ receding from a receiver (an astronomer) in system K with a relative velocity v. Suppose that (in the observer frame) the source emits N waves during the time interval T ( T 0 ’ in the source frame). In the observer frame: Because the speed of light is always c and the source is moving with velocity v, the total distance between the front and rear of the wave transmitted during the time interval T is: Length of wave train = cT + vT cTvTvT

6. The Relativistic Doppler Effect Because there are N waves, the wavelength is given by: And the resulting frequency is: In the source frame: and Thus: Use a + sign for v/c when the source and receiver are receding from each other and a – sign when they’re approaching. So: Source frame is proper time.

7. Using the Doppler shift to sense rotation The Doppler shift has a zillion uses.

8. Relativity and Electromagnetism Einstein’s belief that Maxwell’s equations describe electromagnetism in any inertial frame was the key that led Einstein to the Lorentz transformations. Maxwell’s result that all electromagnetic waves travel at the speed of light led Einstein to his postulate that the speed of light is invariant in all inertial frames. Einstein was convinced that magnetic fields appeared as electric fields when observed in another inertial frame. That conclusion is the key to electromagnetism and relativity.

9. But how can a magnetic field appear as an electric field simply due to motion? Electric field lines (and hence the force field for a positive test charge) due to positive charge. Magnetic field lines circle a current but don’t affect a test charge unless it’s moving. Wire with current How can one become the other and still give the right answer?

10. A Conducting Wire Suppose that a positive test charge and negative charges in a wire have the same velocity. And positive charges in the wire are stationary. The electric field due to charges in the wire will be zero, so the force on the test charge will be magnetic: The magnetic field at the test charge will point into the page, so the force on the test charge will be up.

11. A Conducting Wire 2 The electric field will point radially outward, and at the test charge it will point upward, so the force on the test charge will be up. The two cases can be shown to be identical. Now transform to the frame of the previously moving charges. Now it’s the positive charges in the wire that are moving. And they will be Lorentz-contracted, so their density will be higher. There will still be a magnetic field, but the test charge now has zero velocity, so its force will be zero. The excess of positive charges will yield an electric field, however:

12. 3.1 Discovery of the X-Ray and the Electron 3.2Determination of Electron Charge 3.3Line Spectra 3.4Quantization 3.5Blackbody Radiation 3.6Photoelectric Effect 3.7X-Ray Production 3.8Compton Effect 3.9Pair Production and Annihilation Prelude to Quantum Theory CHAPTER 3 Prelude to Quantum Theory Max Karl Ernst Ludwig Planck (1858-1947)

13. Discovery of the X-Ray and the Electron In the 1890s scientists and engineers were familiar with “cathode rays.” These rays were generated from one of the metal plates in an evacuated tube with a large electric potential across it. It was surmised that cathode rays had something to do with atoms. It was known that cathode rays could penetrate matter and were deflected by magnetic and electric fields. J. J. Thomson (1856-1940) Wilhelm Röntgen (1845-1923)

14. Observation of X Rays Wilhelm Röntgen studied the effects of cathode rays passing through various materials. He noticed that a phosphorescent screen near the tube glowed during some of these experiments. These new rays were unaffected by magnetic fields and penetrated materials more than cathode rays. He called them x-rays and deduced that they were produced by the cathode rays bombarding the glass walls of his vacuum tube. Wilhelm Röntgen

15. Röntgen’s X-Ray Tube Röntgen constructed an x-ray tube by allowing cathode rays to impact the glass wall of the tube and produced x-rays. He used x-rays to make a shadowgram the bones of a hand on a phosphorescent screen.

16. Thomson’s Cathode-Ray Experiment Thomson used an evacuated cathode-ray tube to show that the cathode rays were negatively charged particles (electrons) by deflecting them in electric and magnetic fields.

17. Thomson’s method of measuring the ratio of the electron’s charge to mass was to send electrons through a region containing a magnetic field perpendicular to an electric field. Thomson’s Experiment: e/m J. J. Thomson

18. An electron moving through the electric field is accelerated by a force: Electron angle of deflection: Then turn on the magnetic field, which deflects the electron against the electric field force. The magnetic field is adjusted until the net force is zero. Charge to mass ratio: Calculation of e/m  << 1, so v x ≈ v 0

19. Millikan’s oil-drop experiment Determination of Electron Charge Robert Andrews Millikan (1868 – 1953) Millikan was able to show that electrons had a particular charge.

20. Calculation of the oil drop charge Millikan used an electric field to balance gravity and suspend a charged oil drop: e = 1.602 x 10 -19 C Thousands of experiments showed that there is a basic quantized electron charge: Turning off the electric field, Millikan noted that the drop mass, m drop, could be determined from Stokes’ relationship of the terminal velocity, v t, to the drop density, , and the air viscosity,  : and Drop radius: