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The Stern-Gerlach Effect for Electrons*. Herman Batelaan Gordon Gallup Julie Schwendiman TJG Behlen Laboratory of Physics University of Nebraska Lincoln, Nebraska 68588-0111 * Work funded by the NSF – Physics Division. Electron Polarization. example : P = 0.3: 65% spin-up - PowerPoint PPT Presentation
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The Stern-Gerlach Effect for Electrons
Herman BatelaanGordon Gallup
Julie SchwendimanTJG
Behlen Laboratory of PhysicsUniversity of Nebraska
Lincoln Nebraska 68588-0111
Work funded by the NSF ndash Physics Division
Electron Polarization
σρtrP spin
)N()N(
)N()N(PP
example
P = 03
65 spin-up
35 spin-down
Atomic Collisionsσ
cosθgfA
(from GDFletcher et alii PRA 31 2854 (1985))
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Electron Polarization
σρtrP spin
)N()N(
)N()N(PP
example
P = 03
65 spin-up
35 spin-down
Atomic Collisionsσ
cosθgfA
(from GDFletcher et alii PRA 31 2854 (1985))
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Atomic Collisionsσ
cosθgfA
(from GDFletcher et alii PRA 31 2854 (1985))
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
Feasibility
