The twin “paradox” - Michigan State University › courses › 2003spring › PHY232 › ... · The twin “paradox” ... Quantum Physics Blackbody radiation and Planck’s hypothesis

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