The Development of Quantum Mechanics 383

12.1 The development of quantum 384 mechanics

12.1.1 From oscillators to photons 384 to other things

12.1.2 The planetary model of the 385 atom

12.1.3 The quantum enters the picture 385

12.1.4 Quantum jumps — light comes 386 out of the atom

12.1.5 The lowest orbit 387

12.1.6 The demise of determinism 387

12.1.7 A new way of thinking 388

12.1.8 The Copenhagen interpretation 389

12.2 Matrix mechanics 389

12.2.1 Heisenberg's approach 389

12.2.2 Light from the hydrogen atom 390

12.2.3 A matrix for everything 390

12.2.4 Rules of the game 391

12.2.5 The laws of nature 392

12.2.6 An example of the Heisenberg 392 method

12.2.7 Matrices do not commute! 393

12.2.8 Laws of nature must be built 394 into the matrices

12.3 Order does matter 395

12.3.1 One measurement disturbs 395 the other

12.3.2 A 'table top' experiment with 395 polaroids

12.3.3 Experimenting with a series 397 of polaroids

12.3.4 The uncertainty principle 400

12.4 Wave mechanics 402

12.4.1 The Schrodinger approach 402

12.4.2 De Broglie's original idea 402

12.4.3 Adapting de Broglie waves 405

12.4.4 Uncertainty from another 406 aspect

12.5 Generalised quantum mechanics 407

12.5.1 A wider view 407

12.5.2 Relativity and quantum 408 mechanics

12.5.3 Triumph out of difficulty 409

12.5.4 Antimatter 410

12.5.5 Positron emission tomography 410

12.5.6 Antiprotons and antihydrogen 412

12.6 Quantum reality 413

12.6.1 Critics of the Copenhagen 413 interpretation

12.6.2 Bell's theorem 414

12.6.3 A precursor of quantum reality 415 A historical interlude: Niels Bohr 416 (1885-1963)

Appendix 12.1 Calculating the radius of 421 atomic orbits for hydrogen

Chapter 13 Atoms of Light Acting as Particles 423

13.1 The photoelectric effect 424

13.1.1 Evidence for the particle 424 nature of light

13.1.2 Short sharp shocks 424

13.1.3 An accidental discovery 425

13.1.4 How long would we expect 426 to wait? An order-of-

magnitude calculation

13.1.5 The 'lucky' electron 427

13.1.6 Einstein's photoelectric 428 equation

13.1.7 Millikan's Experiment 429

13.1.8 Current flowing uphill 431

13.1.9 The photoelectric work function 433

13.1.10 Practical applications 434

13.2 The Compton effect — more evidence 436 for the particle nature of light

13.2.1 Real bullets have momentum 436

13.2.2 The Compton effect 437

13.2.3 Collision dynamics revisited 437

13.2.4 Collision of X-ray photons 438

13.2.5 The photon loses energy but 438 does not slow down

13.2.6 Experimental verification 440 A historical interlude: Robert A. Millikan 441 (1868-1953)

Appendix 13.1 Mathematics of the 446 Compton effect

Chapter 14 Atoms of Light Behaving as Waves 451

14.1 Photons one at a time 452

14.1.1 The human eye 452

14.1.2 Detecting a single photon 452

14.1.3 The long thin line 454

14.1.4 Single slit diffraction 454

14.1.5 Double slit diffraction and 455 interference

14.1.6 Measuring 'clicks' as photons 456 arrive one by one

14.1.7 Separating the possible paths 459

14.1.8 'Delayed choice' 461 14.2 Feynman's 'strange theory of 461

the photon'

14.2.1 Partial reflection 461

14.2.2 The strange theory of the 464 photon

14.2.3 A 'sum over histories' 465

14.2.4 The rotating amplitude vector 465

14.2.5 How can we believe all this? 468

14.2.6 It all comes together 469

14.2.7 Quantum electrodynamics 470 A historical interlude: Richard Feynman 472 (1918-1988)

Chapter 15 Relativity Part 1: How It Began 479

15.1 Space and time 480

15.1.1 Space and the ancient 480 philosophers

15.1.2 Space — the intuitive view 482

15.1.3 Space and time — according 482 to Isaac Newton

15.2 'Dogmatic rigidity' 483

15.2.1 Starting with a clean slate 483

15.2.2 Frames of reference — defining 484 a point of view

15.2.3 Specifying the prejudices 486

15.3 Looking for the ether 488 15.3.1 The Michelson-Morley 488

experiment

15.3.2 Timing the ferry 489

15.3.3 Details of the experiment 491

15.3.4 A powerful conclusion 492

15.4 Symmetry 493

15.4.1 Space is uniform 493

15.4.2 The new model 493

15.4.3 Postulates of special relativity 494

15.5 The first postulate 494

15.5.1 Nature does not discriminate 494

15.5.2 Galileo had the right idea! 496

15.5.3 The Galilean transformation 497

15.5.4 The speed of a bullet 498

15.6 The second postulate 500

15.6.1 The courage of one's convictions 500

15.6.2 An imaginary experiment 500 with light

15.6.3 A paradox? 501

15.6.4 'The impossible' in 502 mathematical form

15.6.5 The Lorentz transformation 504

15.6.6 The gamma factor 506

15.6.7 Addition of velocities — a 507 classical example

15.6.8 Addition of velocities when 508 the speeds are relativistic

15.6.9 Playing with the formula 509

15.7 The fourth dimension 510

15.7.1 Definition of an 'event' 511

15.7.2 The invariant interval 512

15.7.3 Pythagoras revisited 512

15.7.4 Time as a fourth dimension 514

15.7.5 The smoking astronaut 515

15.8 A philosophical interlude 516 A historical interlude: Hendrik A. Lorentz 517 (1852-1928)

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