The twin paradox. Star 20 lt-yrs away. 20 yrs 20 yrs 42 yrs 62 yrs

Transcription

1 The twin paradox Star 20 lt-yrs away Speedo Nogo 20 yrs 20 yrs 42 yrs 62 yrs

2 The twin paradox Star 20 lt-yrs away v = 0.95c Speedo Nogo 20 yrs 20 yrs 42 yrs 62 yrs

3 The twin paradox Star 20 lt-yrs away v = 0.95c Speedo Nogo 20 yrs 20 yrs 42 yrs 62 yrs

4 The twin paradox Star 20 lt-yrs away Speedo experienced accelerations, Nogo didn t. v = 0.95c Speedo Nogo 20 yrs 20 yrs 42 yrs 62 yrs

5 General relativity (Einstein 1916)

6 General relativity (Einstein 1916) F grav mgrav mgrav = G F m a 2 inertial = inertial r

7 General relativity (Einstein 1916) F grav mgrav mgrav = G F m a 2 inertial = inertial r m grav = m inertial? Yes, ~ a few parts in

8 General relativity (Einstein 1916) F grav mgrav mgrav = G F m a 2 inertial = inertial r m grav = m inertial? Yes, ~ a few parts in All the laws of nature have the same form for observers in any frame of reference, whether accelerated or not.

9 General relativity (Einstein 1916) F grav mgrav mgrav = G F m a 2 inertial = inertial r m grav = m inertial? Yes, ~ a few parts in All the laws of nature have the same form for observers in any frame of reference, whether accelerated or not. In the vicinity of any given point, a gravitational field is equivalent to an accelerated frame of reference without a gravitational field the principle of equivalence.

10 The principle of equivalence Gravity & no acceleration No gravity & uniform acceleration Light bent by gravity

11 The principle of equivalence Gravity & no acceleration No gravity & uniform acceleration Light bent by gravity

12 The principle of equivalence Gravity & no acceleration No gravity & uniform acceleration No experiment can be devised to tell the difference. Light bent by gravity

13 The principle of equivalence Gravity & no acceleration No gravity & uniform acceleration No experiment can be devised to tell the difference. Light bent by gravity

14 Test of general relativity: during eclipse of the sun in 1919

15 Test of general relativity: during eclipse of the sun in

16 Test of general relativity: during eclipse of the sun in Clocks run slower in a gravitational field. Black holes trap light. Gravitational lensing.

17 Quantum Physics

18 Quantum Physics Blackbody radiation and Planck s hypothesis

19 Quantum Physics Blackbody radiation and Planck s hypothesis All bodies with T > 0 K emit thermal radiation Blackbody: perfect absorber of radiation efficient radiator

20 Quantum Physics Blackbody radiation and Planck s hypothesis All bodies with T > 0 K emit thermal radiation Blackbody: perfect absorber of radiation efficient radiator Like darkened windows of a building during daytime, as seen from outside

21 Quantum Physics Blackbody radiation and Planck s hypothesis All bodies with T > 0 K emit thermal radiation Blackbody: perfect absorber of radiation efficient radiator T Like darkened windows of a building during daytime, as seen from outside

22 Blackbody spectrum λ max

23 Blackbody spectrum λ max Wien s displacement law λ max T = m K

24 Blackbody spectrum λ max Wien s displacement law λ max T = m K Sun s surface: T 5000 K λ max 580 nm Visible spectrum: nm

25 Blackbody spectrum λ max Wien s displacement law λ max T = m K Sun s surface: T 5000 K λ max 580 nm Visible spectrum: nm Still significant emission in infrared (tinted windows to reflect infrared)

26 Blackbody spectrum λ max Wien s displacement law λ max T = m K Sun s surface: T 5000 K λ max 580 nm Visible spectrum: nm Still significant emission in infrared (tinted windows to reflect infrared) Imaging warm animals: T 300 K λ max 10 µm

27 Blackbody spectrum λ max Wien s displacement law λ max T = m K Sun s surface: T 5000 K λ max 580 nm Visible spectrum: nm Still significant emission in infrared (tinted windows to reflect infrared) Imaging warm animals: T 300 K λ max 10 µm 3-K background blackbody radiation in universe big bang residue: λ max 1 mm

28 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission ultraviolet catastrophe

29 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission Max Planck ( ) ultraviolet catastrophe

30 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission Max Planck ( ) Hypothesis in 1900 ultraviolet catastrophe

31 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission ultraviolet catastrophe Max Planck ( ) Hypothesis in 1900 Walls of blackbody have billions of small resonators whose energy is quantized. E = n h f where n is an integer and h is Planck s constant. h = J s = ev s

32 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission ultraviolet catastrophe Max Planck ( ) Hypothesis in 1900 Walls of blackbody have billions of small resonators whose energy is quantized. E = n h f where n is an integer and h is Planck s constant. h = J s = ev s Resonators emit and absorb radiation energy in discrete units: E = h f.

33 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission ultraviolet catastrophe Max Planck ( ) Hypothesis in 1900 Walls of blackbody have billions of small resonators whose energy is quantized. E = n h f where n is an integer and h is Planck s constant. h = J s = ev s Resonators emit and absorb radiation energy in discrete units: E = h f. For low λ (high f ), E >> thermal energy, so no emission.

34 Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ higher acceleration more emission ultraviolet catastrophe Max Planck ( ) Hypothesis in 1900 Walls of blackbody have billions of small resonators whose energy is quantized. E = n h f where n is an integer and h is Planck s constant. h = J s = ev s Resonators emit and absorb radiation energy in discrete units: E = h f. For low λ (high f ), E >> thermal energy, so no emission. Agrees with experimental data!

35 Planck did not assume that energy of E-M radiation was quantized.

36 Planck did not assume that energy of E-M radiation was quantized. Einstein (1905): energy of E-M radiation is quantized: photon

37 Planck did not assume that energy of E-M radiation was quantized. Einstein (1905): energy of E-M radiation is quantized: photon Example: red photon emitted by atom: λ 600nm 15 hc (ev s) 3 10 m / s Eph = hf = = = λ m ev

38 Planck did not assume that energy of E-M radiation was quantized. Einstein (1905): energy of E-M radiation is quantized: photon Example: red photon emitted by atom: λ 600nm 15 hc (ev s) 3 10 m / s Eph = hf = = = λ m ev

39 Planck did not assume that energy of E-M radiation was quantized. Einstein (1905): energy of E-M radiation is quantized: photon Example: red photon emitted by atom: λ 600nm 15 hc (ev s) 3 10 m / s Eph = hf = = = λ m ev

40 Planck did not assume that energy of E-M radiation was quantized. Einstein (1905): energy of E-M radiation is quantized: photon Example: red photon emitted by atom: λ 600nm 15 hc (ev s) 3 10 m / s Eph = hf = = = λ m ev

41 Planck did not assume that energy of E-M radiation was quantized. Einstein (1905): energy of E-M radiation is quantized: photon Example: red photon emitted by atom: λ 600nm 15 hc (ev s) 3 10 m / s Eph = hf = = = λ m ev So atom must have lost 2.07 ev of energy in creating photon.

42 Photoelectric effect Emitter Collector - DV +

43 Photoelectric effect Emitter for fixed l Collector - DV + DV

44 Photoelectric effect Emitter for fixed l Collector stopping potential - DV + DV

45 Photoelectric effect Emitter for fixed l Collector stopping potential independent of intensity - DV + DV

46 Photoelectric effect Emitter for fixed l Collector stopping potential independent of intensity - DV + DV Electrons have a maximum KE, independent of intensity.

47 Photoelectric effect for fixed l Emitter Collector stopping potential independent of intensity - DV + DV Electrons have a maximum KE, independent of intensity. KE = e max V s

48 Photoelectric effect for fixed l Emitter Collector stopping potential independent of intensity - DV + DV Electrons have a maximum KE, independent of intensity. KE = e max V s Electron emission is instantaneous.

49 Photoelectric effect for fixed l Emitter Collector stopping potential independent of intensity - DV + DV Electrons have a maximum KE, independent of intensity. KE = e max V s Electron emission is instantaneous. Cannot be explained by classical physics