The twin “paradox” Speedo Nogo 20 yrs 20 yrs Star 20 lt-yrs away
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The twin “paradox”
Speedo Nogo
20 yrs 20 yrs 42 yrs 62 yrs
Star 20 lt-yrs away
The twin “paradox”
Speedo Nogo
20 yrs 20 yrs 42 yrs 62 yrs
v = 0.95c
Star 20 lt-yrs away
The twin “paradox”
Speedo Nogo
20 yrs 20 yrs 42 yrs 62 yrs
v = 0.95c
Star 20 lt-yrs away
The twin “paradox”
Speedo Nogo
20 yrs 20 yrs 42 yrs 62 yrs
v = 0.95c
Speedo experiencedaccelerations, Nogo didn’t.
Star 20 lt-yrs away
General relativity (Einstein—1916)
General relativity (Einstein—1916)
2gravgrav
gravr
mmGF
⋅= amF inertialinertial ⋅=
General relativity (Einstein—1916)
2gravgrav
gravr
mmGF
⋅= amF inertialinertial ⋅=
mgrav = minertial ? Yes, ~ a few parts in 1012.
General relativity (Einstein—1916)
2gravgrav
gravr
mmGF
⋅= amF inertialinertial ⋅=
mgrav = minertial ? Yes, ~ a few parts in 1012.
All the laws of nature have the same form for observers in any frame of reference, whether accelerated or not.
General relativity (Einstein—1916)
2gravgrav
gravr
mmGF
⋅= amF inertialinertial ⋅=
mgrav = minertial ? Yes, ~ a few parts in 1012.
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.
Gravity&
no acceleration
No gravity&
uniformacceleration
The principle of equivalence
Light bentby gravity
Gravity&
no acceleration
No gravity&
uniformacceleration
The principle of equivalence
Light bentby gravity
Gravity&
no acceleration
No gravity&
uniformacceleration
The principle of equivalence
Light bentby gravity
No experiment can be devised to tellthe difference.
Gravity&
no acceleration
No gravity&
uniformacceleration
The principle of equivalence
Light bentby gravity
No experiment can be devised to tellthe difference.
Test of general relativity: during eclipse of the sun in 1919
Test of general relativity: during eclipse of the sun in 1919
5×10-4 °
Clocks run slower in a gravitational field.
Black holes trap light.
Gravitational lensing.
Test of general relativity: during eclipse of the sun in 1919
5×10-4 °
Quantum Physics
Quantum Physics
Blackbody radiation and Planck’s hypothesis
Quantum Physics
Blackbody radiation and Planck’s hypothesis
All bodies with T > 0 K emit thermal radiation
Blackbody: perfect absorber of radiation ⇒ efficient radiator
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 buildingduring daytime, as seen from outside
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 buildingduring daytime, as seen from outside
T
Blackbody spectrum
λmax
Blackbody spectrum
λmax
Wien’s displacement law
Km 109.2T 3max ⋅×=λ −
Blackbody spectrum
λmax
Wien’s displacement law
Km 109.2T 3max ⋅×=λ −
Sun’s surface: T ≈ 5000 K∴λmax ≈ 580 nmVisible spectrum: 400 → 700 nm
Blackbody spectrum
λmax
Wien’s displacement law
Km 109.2T 3max ⋅×=λ −
Sun’s surface: T ≈ 5000 K∴λmax ≈ 580 nmVisible spectrum: 400 → 700 nmStill significant emission in infrared(tinted windows to reflect infrared)
Blackbody spectrum
λmax
Wien’s displacement law
Km 109.2T 3max ⋅×=λ −
Sun’s surface: T ≈ 5000 K∴λmax ≈ 580 nmVisible spectrum: 400 → 700 nmStill significant emission in infrared(tinted windows to reflect infrared)
Imaging warm animals: T ≈ 300 Kλmax ≈ 10 µm
Blackbody spectrum
λmax
Wien’s displacement law
Km 109.2T 3max ⋅×=λ −
Sun’s surface: T ≈ 5000 K∴λmax ≈ 580 nmVisible spectrum: 400 → 700 nmStill significant emission in infrared(tinted windows to reflect infrared)
3-K background blackbody radiationin universe—big bang residue:λmax ≈ 1 mm
Imaging warm animals: T ≈ 300 Kλmax ≈ 10 µm
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
Max Planck (1858-1947)
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
Max Planck (1858-1947)
Hypothesis in 1900
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
Max Planck (1858-1947)
Hypothesis in 1900Walls of blackbody have billions of small “resonators” whose energy is quantized.
E = n·h·fwhere n is an integer and h is Planck’s constant.
h = 6.63×10-34 J·s= 4.14×10-15 eV·s
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
Max Planck (1858-1947)
Hypothesis in 1900Walls of blackbody have billions of small “resonators” whose energy is quantized.
E = n·h·fwhere n is an integer and h is Planck’s constant.
h = 6.63×10-34 J·s= 4.14×10-15 eV·s
Resonators emit and absorb radiation energy in discrete units: ∆E = h·f .
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
Max Planck (1858-1947)
Hypothesis in 1900Walls of blackbody have billions of small “resonators” whose energy is quantized.
E = n·h·fwhere n is an integer and h is Planck’s constant.
h = 6.63×10-34 J·s= 4.14×10-15 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.
ultravioletcatastrophe
Classical theory: thermal agitation accelerates electrons causing emission over many frequencies, shorter λ ⇒ higher acceleration⇒ more emission
Max Planck (1858-1947)
Hypothesis in 1900Walls of blackbody have billions of small “resonators” whose energy is quantized.
E = n·h·fwhere n is an integer and h is Planck’s constant.
h = 6.63×10-34 J·s= 4.14×10-15 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!
Planck did not assume that energy of E-M radiation was quantized.
Planck did not assume that energy of E-M radiation was quantized.
Einstein (1905): energy of E-M radiation is quantized: “photon”
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
eV 07.2m10600
s/m103)seV(1014.4hchE 9
815
ph =×
××⋅×=
λ== −
−f
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
eV 07.2m10600
s/m103)seV(1014.4hchE 9
815
ph =×
××⋅×=
λ== −
−f
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
eV 07.2m10600
s/m103)seV(1014.4hchE 9
815
ph =×
××⋅×=
λ== −
−f
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
eV 07.2m10600
s/m103)seV(1014.4hchE 9
815
ph =×
××⋅×=
λ== −
−f
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
eV 07.2m10600
s/m103)seV(1014.4hchE 9
815
ph =×
××⋅×=
λ== −
−f
So atom must have lost 2.07 eV of energy in creating photon.
Photoelectric effect
∆V +-
Emitter
Collector
Photoelectric effect
∆V
for fixed λ
+-
Emitter
Collector
∆V
Photoelectric effect
∆V
for fixed λ
stoppingpotential
+-
Emitter
Collector
∆V
Photoelectric effect
∆V
for fixed λ
stoppingpotential
independent of intensity
+-
Emitter
Collector
∆V
Photoelectric effect
∆V
for fixed λ
stoppingpotential
independent of intensity
Electrons have a maximum KE,independent of intensity.
+-
Emitter
Collector
∆V
Photoelectric effect
∆V
for fixed λ
stoppingpotential
independent of intensity
smax VeKE ∆⋅=
Electrons have a maximum KE,independent of intensity.
+-
Emitter
Collector
∆V
Photoelectric effect
∆V
for fixed λ
stoppingpotential
independent of intensity
smax VeKE ∆⋅=
Electrons have a maximum KE,independent of intensity.
Electron emission is instantaneous.
+-
Emitter
Collector
∆V
Photoelectric effect
∆V
for fixed λ
stoppingpotential
independent of intensity
smax VeKE ∆⋅=
Electrons have a maximum KE,independent of intensity.
Electron emission is instantaneous.
Cannot be explained by classical physics
+-
Emitter
Collector
∆V
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