Lecture 28: TUE 04 MAY 2010 Ch. 37 Einstein’s Theory of Relativity Ch. 38: Photo

Lecture 28: TUE 04 MAY 2010 Ch. 37 Einstein’s Theory of Relativity Ch. 38: Photo www.phwiki.com

Lecture 28: TUE 04 MAY 2010 Ch. 37 Einstein’s Theory of Relativity Ch. 38: Photo

Puig, Claudia, Film Critic has reference to this Academic Journal, PHwiki organized this Journal Lecture 28: TUE 04 MAY 2010 Ch. 37 Einstein’s Theory of Relativity Ch. 38: Photons in addition to Matter Waves Chapter 37 Relativity Relativity is an important subject that looks at the measurement of where in addition to when events take place, in addition to how these events are measured in reference frames that are moving relative to one another. In this chapter we will explore the special theory of relativity (which we will refer to simply as “relativity”), which only deals with inertial reference frames (where Newton’s laws are valid). The general theory of relativity looks at the more challenging situation where reference frames undergo gravitational acceleration. In 1905, Albert Einstein stunned the scientific world by introducing two “simple” postulates with which he showed that the old, commonsense ideas about relativity are wrong. Although Einstein’s ideas seem strange in addition to counterintuitive, e.g., rate at which time passes depends on the speed of reference frame, these ideas have not only been validated by experiment, they are also being used in modern technology, e.g., global positioning satellites. (37-1) The Postulates Both postulates tested exhaustively, no exceptions found! (37-2)

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The Relativity of Time (37-8) The Relativity of Time, cont’d Lorentz factor: Speed Parameter: (37-9) Lorentz factor g as a function of the speed parameter b The Relativity of Time, cont’d (37-10)

2. Macroscopic Clocks. Super precision atomic clocks (large systems) flown in airplanes b~7×10-7 (Hafele in addition to Keating in 1977 within 10%, in addition to U. Maryl in addition to a few years later within 1% of predictions) repeated the muon lifetime experiment on a macroscopic scale If the clock on the U. Maryl in addition to flight registered 15.00000000000000 hours as the flight duration, how much would a clock that stayed on earth (lab frame) have measured as long as the duration More or less Does it matter whether airplane returns to same place Two Tests of Time Dilation, cont’d (37-12) Twin Paradox The Relativity of Length (37-13)

Does a moving object really shrink You must measure front in addition to back of moving penguin simultaneously to get its length in your frame. Let’s do this by having two lights flash simultaneously in the rest frame when the front in addition to back of the penguin align with them. In penguin’s frame, your measurements did not occur simultaneously. You first measured the front end (light from front flash reaches moving observer first as in slide 37-7) in addition to then the back (after the back has moved as long as ward), so the length that you measure will appear to be shorter than in the penguin’s rest frame. (37-14) A New Look at Energy Mass energy or rest energy (37-25) A New Look at Energy , cont’d Total energy (37-26)

Experiment by Bertozzi in 1964 accelerated electrons in addition to measured their speed in addition to kinetic energy independently. Kinetic energy as speed c The Ultimate Speed Ultimate SpeedSpeed of Light: (37-3) Chapter 38 Photons in addition to Matter Waves The subatomic world behaves very differently from the world of our ordinary experiences. Quantum physics deals with this strange world in addition to has successfully answered many questions in the subatomic world, such as: Why do stars shine Why do elements order into a periodic table How do we manipulate charges in semiconductors in addition to metals to make transistors in addition to other microelectronic devices Why does copper conduct electricity but glass does not In this chapter we explore the strange reality of quantum mechanics. Although many topics in quantum mechanics conflict with our commonsense world view, the theory provides a well-tested framework to describe the subatomic world. (38-1) Quantum physics: Study of the microscopic world Many physical quantities found only in certain minimum (elementary) amounts, or integer multiples of those elementary amounts These quantities are “quantized” Elementary amount associated with this quantity is called a “quantum” (quanta plural) Analogy example: 1 cent or $0.01 is the quantum of U.S. currency. Electromagnetic radiation (light) is also quantized, with quanta called photons. This means that light is divided into integer number of elementary packets (photons). The Photon, the Quantum of Light (38-2)

The energy of light with frequency f must be an integer multiple of hf. In the previous chapters we dealt with such large quantities of light that individual photons were not distinguishable. Modern experiments can be per as long as med with single photons. So what aspect of light is quantized Frequency in addition to wavelength still can be any value in addition to are continuously variable, not quantized: The Photon, the Quantum of Light, cont’d However, given light of a particular frequency, the total energy of that radiation is quantized with an elementary amount (quantum) of energy E given by: where the Planck constant h has a value: where c is the speed of light 3×108 m/s (38-3) When short-wavelength light illuminates a clean metal surface, electrons are ejected from the metal. These photoelectrons produce a photocurrent. First Photoelectric Experiment: Photoelectrons stopped by stopping voltage, Vstop. The kinetic energy of the most energetic photoelectrons is The Photoelectric Effect Kmax does not depend on the intensity of the light! single photon ejects each electron (38-4) The Photoelectric Effect, Einstein’s Analysis! Second Photoelectric Experiment: Photoelectric effect does not occur if the frequency is below the cutoff frequency f0, no matter how bright the light! single photon with energy greater than work function F ejects each electron (38-5)

The Photoelectric Effect, Einstein’s Analysis Photoelectric Equation The previous two experiments can be summarized by the following equation, which also expresses energy conservation: Using equation as long as a straight line with slope h/e in addition to intercept –F/e Multiplying this result by e: (38-6) Photons Have Momentum (38-7) Photons Have Momentum, Compton shift Conservation of energy Since electrons may recoil at speeds approaching c we must use the relativistic expression as long as K: where g is the Lorentz factor Substituting K in the energy conservation equation Conservation of momentum along x: Conservation of momentum along y: (38-8)

Loose end: Compton effect can be due to scattering from electrons bound loosely to atoms (m = me peak at q 0) or electrons bound tightly to atoms (m matom >>me peak at q 0). Photons Have Momentum, Compton shift cont’d Want to find wavelength shift: Conservation of energy in addition to momentum provide 3 equations as long as 5 unknowns (l, l’, v, f, in addition to q ), which allows us to eliminate 2 unknowns, v in addition to q. l, l’, in addition to f can be readily measured in the Compton experiment. is the Compton wavelength in addition to depends on 1/m of the scattering particle. (38-9) How can light act both as a wave in addition to as a particle (photon) Light as a Probability Wave St in addition to ard Version: Photons sent through double slit. Photons detected (1 click at a time) more often where the classical intensity: is maximum. Light is not only an electromagnetic wave but also a probability wave as long as detecting photons. (38-10) Light as a Probability Wave, cont’d Single Photon Version: Photons sent through double slit one at a time. First experiment by Taylor in 1909. 1. We cannot predict where the photon will arrive on the screen. 2. Unless we place detectors at the slits, which changes the experiment ( in addition to the results), we cannot say which slit(s) the photon went through. 3. We can predict the probability of the photon hitting different parts of the screen. This probability pattern is just the two-slit interference pattern that we discussed in Ch. 35. The wave traveling from the source to the screen is a probability wave, which produces a pattern of “probability fringes” at the screen. (38-11)

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Light as a Probability Wave, cont’d Conclusions from the previous three versions/experiments: 1. Light is generated at source as photons. 2. Light is absorbed at detector as photons. 3. Light travels between source in addition to detector as a probability wave. (38-13) If electromagnetic waves (light) can behave like particles (photons), can particles behave like waves Electrons in addition to Matter Waves where p is the momentum of the particle (38-14) In the previous example, the momentum (p or k) in the x-direction was exactly defined, but the particle’s position along the x-direction was completely unknown. This is an example of an important principle as long as mulated by Heisenberg: Measured values cannot be assigned to the position r in addition to the momentum p of a particle simultaneously with unlimited precision. Heisenberg’s Uncertainty Principle (38-21)

As a puck slides uphill, kinetic energy K is converted to gravitational potential energy U. If the puck reaches the top its potential energy is Ub. The puck can only pass over the top if its initial mechanical energy E> Ub. Otherwise the puck eventually stops its climb up the left side of the hill in addition to slides back. For example, if Ub = 20 J in addition to E = 10 J, the puck will not pass over the hill, which acts as a potential barrier. Barrier Tunneling (38-22) What about an electron approaching an electrostatic potential barrier Due to the nature of quantum mechanics, even if E< Ub there is a nonzero transmission probability (transmission coefficient T) that the electron will get through (tunnel) to the other side of the electrostatic potential barrier! Barrier Tunneling, cont’d (38-23)

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