A presentation on the connection between classical and quantum descriptions of NMR and MRI with a focus on visualization.

1. The ups and downs of classical and
quantum MR descriptions
Lars G. Hanson
Danish Research Centre for MR and
Technical University of Denmark
Speakable and unspeakable in basic spin ½ NMR
2017

2. Concerns the connection between
classical and quantum descriptions of
Magnetic Resonance used for NMR and MRI
Practical part: Advice for avoiding repetition
of common misunderstandings.
Paraphrasing Bell:

3. Visualization of basic NMR
 A basic understanding of NMR is crucial for
both MRI users and developers.
 Challenging to explain & understand.
 Take home messages:
 Classical and QM are more similar
than they first appear.
 This helps intuition.
 Basic NMR is relatively simple to
explain and understand.
 Don’t repeat myths.

4. Why visualize?
 Math says it all, but is not very intuitive.
Intuitive insight is needed for conducting science.

5. Why visualize?
 Math says it all, but is not very intuitive.
Intuitive insight is needed for conducting science.
 Excellent example of graphics supporting MR math:
 Malcolm Levitt, ”Spin Dynamics”, Wiley

6. Why visualize?
 Math says it all, but is not very intuitive.
Intuitive insight is needed for conducting science.
 Excellent example of graphics supporting MR math:
 Malcolm Levitt, ”Spin Dynamics”, Wiley

7. Why visualize?
 Math says it all, but is not very intuitive.
Intuitive insight is needed for conducting science.
 Excellent example of graphics supporting MR math:
 Malcolm Levitt, ”Spin Dynamics”, Wiley
What are the
limits of MR
visualization
from a QM
perspective?

8. Why visualize?
 Math says it all, but is not very intuitive.
Intuitive insight is needed for conducting science.
 Excellent example of graphics supporting MR math:
 Malcolm Levitt, ”Spin Dynamics”, Wiley
What are the
limits of MR
visualization
from a QM
perspective?
And which visualizations are acceptable?

9. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Back to Basics

10. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Back to Basics
This picture is has severe flaws…

11. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Back to Basics
This picture is has severe flaws…
…that are not important for NMR. I’ll go with it.

12. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Back to Basics
This picture is has severe flaws…
…that are not important for NMR. I’ll go with it.
Actually, I really like this picture…

13. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Back to Basics
This picture is has severe flaws…
…that are not important for NMR. I’ll go with it.
Actually, I really like this picture…
because of the predictive power it gives you,
despite the fact that the picture is wrong.

14. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
Back to Basics

15. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

16. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

17. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

18. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

19. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

20. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

21. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
Back to Basics

22. Nuclei have spin that makes them magnetic.
In absense of field, the directional distribution is isotropic.
Common explanation of MR based on QM:
 Nuclei can only point near parallel or anti-parallel to the field:
 This explanation is largely wrong (interpretation unsuported by
quantum mechanics). It opens more questions than it answers.
Back to Basics

23. Why?
 Why would nuclei align anti-parallel to the field?

24. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?

25. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?
 Strength of field required for this to happen?

26. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?
 Strength of field required for this to happen?
 Can radio waves change the magnetization size?
It seems so.

27. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?
 Strength of field required for this to happen?
 Can radio waves change the magnetization size?
It seems so.

28. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?
 Strength of field required for this to happen?
 Can radio waves change the magnetization size?
It seems so.
 Why don’t spin flips just equalize populations?

29. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?
 Strength of field required for this to happen?
 Can radio waves change the magnetization size?
It seems so.
 Why don’t spin flips just equalize populations?
 Why doesn’t an inversion pulse maximize signal?

30. Why?
 Why would nuclei align anti-parallel to the field?
 Are nuclei forced into ”cone states” instantly?
 Strength of field required for this to happen?
 Can radio waves change the magnetization size?
It seems so.
 Why don’t spin flips just equalize populations?
 Why doesn’t an inversion pulse maximize signal?
Good questions that are not well-answered
unless you know QM sufficiently well to
recognize the provided explanation as being wrong.
It does not qualify as a simplification (no predictive power).

31. Origins of common misconception

32. Origins of common misconception
Well-known aspects of QM:
 Microscopic systems such as atoms can
only exist in discrete states with specific
energies.
 Transitions between these states happen
in sudden “quantum jumps” and involve
exchange of energy.
 The timings of the jumps are truly
unpredictable.

33. Origins of common misconception
Well-known aspects of QM:
 Microscopic systems such as atoms can
only exist in discrete states with specific
energies.
 Transitions between these states happen
in sudden “quantum jumps” and involve
exchange of energy.
 The timings of the jumps are truly
unpredictable.
Sorry, this is highschool QM. So 1913. Go modern!

34. Definition
 Definition: In this talk…
”Magnetic Resonance” is Magnetic Resonance

35. Definition
 Definition: In this talk…
”Magnetic Resonance” is Magnetic Resonance
 …in contrast to every effect worth knowing about
when dealing with magnetic resonance
 e.g. spin, J-coupling, relaxation,…

36. Definition
 Definition: In this talk…
”Magnetic Resonance” is Magnetic Resonance
 …in contrast to every effect worth knowing about
when dealing with magnetic resonance
 e.g. spin, J-coupling, relaxation,…
 These effects all require elements of QM to be
understood in detail,

37. Definition
 Definition: In this talk…
”Magnetic Resonance” is Magnetic Resonance
 …in contrast to every effect worth knowing about
when dealing with magnetic resonance
 e.g. spin, J-coupling, relaxation,…
 These effects all require elements of QM to be
understood in detail,
 …but maybe less than you think.

38. Definition
 Definition: In this talk…
”Magnetic Resonance” is Magnetic Resonance
 …in contrast to every effect worth knowing about
when dealing with magnetic resonance
 e.g. spin, J-coupling, relaxation,…
 These effects all require elements of QM to be
understood in detail,
 …but maybe less than you think.
 Additional important limitation:

39. Definition
 Definition: In this talk…
”Magnetic Resonance” is Magnetic Resonance
 …in contrast to every effect worth knowing about
when dealing with magnetic resonance
 e.g. spin, J-coupling, relaxation,…
 These effects all require elements of QM to be
understood in detail,
 …but maybe less than you think.
 Additional important limitation:
 Only spin 1/2, and only simple NMR as used in MRI.

40. Equilibrium pittfalls
 In equilibrium, nuclei are not aligned parallel or
anti-parallel to B0.

41. Equilibrium pittfalls
 In equilibrium, nuclei are not aligned parallel or
anti-parallel to B0.
 These are acceptable illustrations of eigenstates,
…but equilibrium orient. dist. is near isotropic.

42. Equilibrium pittfalls
 In equilibrium, nuclei are not aligned parallel or
anti-parallel to B0.
 These are acceptable illustrations of eigenstates,
…but equilibrium orient. dist. is near isotropic.

43. Origin of common misconception

44. Origin of common misconception
 Quantum Mechanics:
 When a measurement is performed, the
system ”collapses” into an eigenstate.

45. Origin of common misconception
 Quantum Mechanics:
 When a measurement is performed, the
system ”collapses” into an eigenstate.
 Apparent consequence:
 If the polarization is measured, each
nucleus is left in an eigenstate.

46. Origin of common misconception
 Quantum Mechanics:
 When a measurement is performed, the
system ”collapses” into an eigenstate.
 Apparent consequence:
 If the polarization is measured, each
nucleus is left in an eigenstate.
 In fact not:
 The ensemble as a whole is left in an
eigenstate. This is very different.

47. Origin of common misconception
 Quantum Mechanics:
 When a measurement is performed, the
system ”collapses” into an eigenstate.
 Apparent consequence:
 If the polarization is measured, each
nucleus is left in an eigenstate.
 In fact not:
 The ensemble as a whole is left in an
eigenstate. This is very different.
 Technically a projection onto an enourmous
subspace, which has little effect.

48. Role of eigenstates: Forms a basis

49. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:

50. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)

51. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.

52. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.
 |Ψ› = C↑ |↑› + C↓ |↓› note: up/down are orthogonal!

53. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.
 |Ψ› = C↑ |↑› + C↓ |↓› note: up/down are orthogonal!
 For each direction in 3D space,
there is one (C↑, C↓) except for an arbitrary phase

54. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.
 |Ψ› = C↑ |↑› + C↓ |↓› note: up/down are orthogonal!
 For each direction in 3D space,
there is one (C↑, C↓) except for an arbitrary phase
 Coordinate systems are connected by unitary
transformations (rotations).

55. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.
 |Ψ› = C↑ |↑› + C↓ |↓› note: up/down are orthogonal!
 For each direction in 3D space,
there is one (C↑, C↓) except for an arbitrary phase
 Coordinate systems are connected by unitary
transformations (rotations).

56. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.
 |Ψ› = C↑ |↑› + C↓ |↓› note: up/down are orthogonal!
 For each direction in 3D space,
there is one (C↑, C↓) except for an arbitrary phase
 Coordinate systems are connected by unitary
transformations (rotations).
 What is along x in one system may be along y in
another. Interpretations may be affected.

57. Role of eigenstates: Forms a basis
The concept of basis vectors is well-known:
 A velocity expressed in terms of x and y components:
 v = vx x + vy y (e.g. horizontal and vertical velocity of thrown stone)
 A spin QM state is conveniently split in up/down comp.
 |Ψ› = C↑ |↑› + C↓ |↓› note: up/down are orthogonal!
 For each direction in 3D space,
there is one (C↑, C↓) except for an arbitrary phase
 Coordinate systems are connected by unitary
transformations (rotations).
 What is along x in one system may be along y in
another. Interpretations may be affected.
 Choosing a basis is a matter of convenience.

58. Role of the eigenstates
 The single spin eigenstates do not correspond to
physical reality in NMR.
 Spectra are often interpreted as jumps between
eigenstates, which is not true.
 The eigenstate basis is a mathematical convenience.
One basis out of many.
 The up/down states are not even eigenstates of
our measurement operator.
 Eigenstates are not specific for QM:
 Both classic physics and QM predict oscillation at
eigenfrequencies, and resonances.

59. Equilibrium from QM and
classical perspectives

60. Equilibrium from QM and
classical perspectives
Unlike this:

61. Equilibrium from QM and
classical perspectives
 The field causes precession and alignment,..
 …but nuclear interactions randomize orientations

62. MR reconciliation
 The relation between the descriptions?

63. MR reconciliation
 The relation between the descriptions?
 Solution:
 For simple NMR, the two descriptions can
be made very similar. Both are valid…
 …after repair.

64. MR reconciliation
 The relation between the descriptions?
 Solution:
 For simple NMR, the two descriptions can
be made very similar. Both are valid…
 …after repair.

65. MR reconciliation
 The relation between the descriptions?
 Solution:
 For simple NMR, the two descriptions can
be made very similar. Both are valid…
 …after repair.

66. MR reconciliation
 The relation between the descriptions?
 Solution:
 For simple NMR, the two descriptions can
be made very similar. Both are valid…
 …after repair.

67. QM description of MR

68. QM description of MR
General state is a superposition:

69. QM description of MR
General state is a superposition:
Any basis will do.
Please ignore inconsistent notation on this slide:
• The up/down states are the same as the ±½ eigenstates of Sz

70. The Bloch vector
 Rewrite any single-spin superposition as follows:

71. The Bloch vector
 Rewrite any single-spin superposition as follows:
 i.e. a parametrization with the arbitrary phase fixed.

72. The Bloch vector
 Rewrite any single-spin superposition as follows:
 i.e. a parametrization with the arbitrary phase fixed.
 Any superposition can be represented by a unit
vector with polar/azimuthal angles (θ,φ).

73. The Bloch vector
 Rewrite any single-spin superposition as follows:
 i.e. a parametrization with the arbitrary phase fixed.
 Any superposition can be represented by a unit
vector with polar/azimuthal angles (θ,φ).
 This is the Bloch vector.
 It evolves like a classical magnetic dipole.

74. The Bloch vector
 Rewrite any single-spin superposition as follows:
 i.e. a parametrization with the arbitrary phase fixed.
 Any superposition can be represented by a unit
vector with polar/azimuthal angles (θ,φ).
 This is the Bloch vector.
 It evolves like a classical magnetic dipole.
 Eigenstate for S θ,φ:

75. The Bloch vector
 The Bloch vector:
 Introduced by Feynman, Vernon & Hellwarth, 1957.
 Showed that QM two-level dynamics can generally
be understood in terms of classical MR.

76. The Bloch vector
 The Bloch vector:
 Introduced by Feynman, Vernon & Hellwarth, 1957.
 Showed that QM two-level dynamics can generally
be understood in terms of classical MR.
 The Bloch vector is a QM property inspired by
classical MR.

77. The Bloch vector
 The Bloch vector:
 Introduced by Feynman, Vernon & Hellwarth, 1957.
 Showed that QM two-level dynamics can generally
be understood in terms of classical MR.
 The Bloch vector is a QM property inspired by
classical MR.
 A vector in an abstract space that moves as the
magnetization vector in real space.

78. The Bloch vector
 The Bloch vector:
 Introduced by Feynman, Vernon & Hellwarth, 1957.
 Showed that QM two-level dynamics can generally
be understood in terms of classical MR.
 The Bloch vector is a QM property inspired by
classical MR.
 A vector in an abstract space that moves as the
magnetization vector in real space.
 Points up for the up state, down for the down state,
and can point in any other direction.

79. The Bloch vector
 The Bloch vector:
 Introduced by Feynman, Vernon & Hellwarth, 1957.
 Showed that QM two-level dynamics can generally
be understood in terms of classical MR.
 The Bloch vector is a QM property inspired by
classical MR.
 A vector in an abstract space that moves as the
magnetization vector in real space.
 Points up for the up state, down for the down state,
and can point in any other direction.
 Bottom line: Basic ”classical MR” is quantum mechanics,
 but not for spin > ½, J-coupling, entanglement,…

80. Predictive power?

81. Predictive power?
This is mostly meaningful, if you know the Schrödinger
equation well enough to realize that the picture
describes vector dynamics: Precession around B0 and
around an orthogonal rotating B1.

82. Predictive power?
This is mostly meaningful, if you know the Schrödinger
equation well enough to realize that the picture
describes vector dynamics: Precession around B0 and
around an orthogonal rotating B1.
For most, the educational value is low until the classical
picture is understood.

83. Magnetic Resonance
 Spins precess around B0 and around…
 …a weak field B1-field that rotates around B0.
QM understanding of arrows:
• Illustrating a distribution (the QM density matrix)

84. But wait a minute…
Why is the spherical distribution more correct
than the cone picture ???
 Two distributions with the same density matrix:
 Observations depend only on the density matrix, so
aren’t the descriptions equally good?

85. But wait a minute…
Why is the spherical distribution more correct
than the cone picture ???
 Two distributions with the same density matrix:
 Observations depend only on the density matrix, so
aren’t the descriptions equally good?

86. Magnetic resonance made
complicated
 Also, if you accept cone states as describing
thermal equilibrium, you also have to accept
rotated versions after excitation:

87. Magnetic resonance made
complicated
 Also, if you accept cone states as describing
thermal equilibrium, you also have to accept
rotated versions after excitation:
Homogenous fields cannot change relative orientations!

88. Magnetic resonance made
complicated
 Also, if you accept cone states as describing
thermal equilibrium, you also have to accept
rotated versions after excitation:
Homogenous fields cannot change relative orientations!

89. Magnetic resonance made
complicated
 Also, if you accept cone states as describing
thermal equilibrium, you also have to accept
rotated versions after excitation:
Homogenous fields cannot change relative orientations!

90. Magnetic resonance made
complicated
 Also, if you accept cone states as describing
thermal equilibrium, you also have to accept
rotated versions after excitation:
Homogenous fields cannot change relative orientations!

91. Dirt under the carpet…
 Ignored so far:
 The overall spin state is not a product state.
Entanglement/decoherence would soon occur.
 Bloch vectors can then no longer be assigned.
 The nuclei are not in pure states.
 Thermal equilibrium is a mix of classical uncertainty and
quantum indeterminism.

92. Dirt under the carpet…
 Ignored so far:
 The overall spin state is not a product state.
Entanglement/decoherence would soon occur.
 Bloch vectors can then no longer be assigned.
 The nuclei are not in pure states.
 Thermal equilibrium is a mix of classical uncertainty and
quantum indeterminism.
 Bottom line:
 Individual spins in thermal equilibrium do not have
a direction, not even an unknown direction!

93. Dirt under the carpet…
 Ignored so far:
 The overall spin state is not a product state.
Entanglement/decoherence would soon occur.
 Bloch vectors can then no longer be assigned.
 The nuclei are not in pure states.
 Thermal equilibrium is a mix of classical uncertainty and
quantum indeterminism.
 Bottom line:
 Individual spins in thermal equilibrium do not have
a direction, not even an unknown direction!
 But we can experimentally assign them one,
consistent with the density operator.

94. A gedanken experiment

95. A gedanken experiment
 Take a sample in thermal eq, for example.

96. A gedanken experiment
 Take a sample in thermal eq, for example.
 For each nucleus:
 Measure its spin direction using a Stern-Gerlach
apparatus oriented randomly.
 This assigns a Bloch vector to each nucleus
randomly, and consistently with the density
operator. Plot it.

97. A gedanken experiment
 Take a sample in thermal eq, for example.
 For each nucleus:
 Measure its spin direction using a Stern-Gerlach
apparatus oriented randomly.
 This assigns a Bloch vector to each nucleus
randomly, and consistently with the density
operator. Plot it.
 The resulting spin distribution:

98. A gedanken experiment
 Take a sample in thermal eq, for example.
 For each nucleus:
 Measure its spin direction using a Stern-Gerlach
apparatus oriented randomly.
 This assigns a Bloch vector to each nucleus
randomly, and consistently with the density
operator. Plot it.
 The resulting spin distribution:
 This can be experimentally
verified to evolve classically:
 New Stern-Gerlach measurements oriented
along classically expected spin orientations
give certain measurement outcomes.

99. A gedanken experiment
 Take a sample in thermal eq, for example.
 For each nucleus:
 Measure its spin direction using a Stern-Gerlach
apparatus oriented randomly.
 This assigns a Bloch vector to each nucleus
randomly, and consistently with the density
operator. Plot it.
 The resulting spin distribution:
 This can be experimentally
verified to evolve classically:
 New Stern-Gerlach measurements oriented
along classically expected spin orientations
give certain measurement outcomes.
 Conclusion: The picture has QM meaning.

100. QM and classical descriptions
 QM is not classical mechanics. Differences:
 Interference (e.g., cancellation of possibilities)
 Entanglement (non-factorizable states)
 QM is probabilistic at the most fundamental level.
 …

101. QM and classical descriptions
 QM is not classical mechanics. Differences:
 Interference (e.g., cancellation of possibilities)
 Entanglement (non-factorizable states)
 QM is probabilistic at the most fundamental level.
 …
 However, QM and classical formulations need
not be very different for basic NMR.
 Mathematical differences are deceptive.
 Similar superpositions, eigenstates, correlations,
spectral structures, for example.
 Worth pointing out in education, but don’t stay
classical for NMR education! (sufficient for MRI)

102. Limits of classical MR

103. Limits of classical MR
 Spin itself is a quantum phenomenon.

104. Limits of classical MR
 Spin itself is a quantum phenomenon.
 Nuclear interactions:
 J-coupling:
 Nuclear interaction mediated by electrons (intramolecular effect)
 Causes spectral splitting which is not unexpected classically.
 Not surprising that nuclei couple through electronic cloud, but QM is
needed to get it right.
 ”Exchange interaction” is an important contribution
that does not exist classically.

105. Limits of classical MR
 Spin itself is a quantum phenomenon.
 Nuclear interactions:
 J-coupling:
 Nuclear interaction mediated by electrons (intramolecular effect)
 Causes spectral splitting which is not unexpected classically.
 Not surprising that nuclei couple through electronic cloud, but QM is
needed to get it right.
 ”Exchange interaction” is an important contribution
that does not exist classically.
 Relaxation mediated by dipolar interaction is expected clasically,
 but QM is needed for a quantitative description.
 The general behaviour is consistent with classical mechanics.

106. Limits of classical MR
 Spin itself is a quantum phenomenon.
 Nuclear interactions:
 J-coupling:
 Nuclear interaction mediated by electrons (intramolecular effect)
 Causes spectral splitting which is not unexpected classically.
 Not surprising that nuclei couple through electronic cloud, but QM is
needed to get it right.
 ”Exchange interaction” is an important contribution
that does not exist classically.
 Relaxation mediated by dipolar interaction is expected clasically,
 but QM is needed for a quantitative description.
 The general behaviour is consistent with classical mechanics.
 For spectroscopy, a quantum description is highly recommended.
 The operator formalism is really convenient.

107. Summary of typical myths

108. Summary of typical myths
 Nuclei can only be in the spin-up or the spin-
down state (cone picture). The Bo field is
somehow responsible.

109. Summary of typical myths
 Nuclei can only be in the spin-up or the spin-
down state (cone picture). The Bo field is
somehow responsible.
 RF brings the precessing spins in phase, thus
creating coherence.

110. Summary of typical myths
 Nuclei can only be in the spin-up or the spin-
down state (cone picture). The Bo field is
somehow responsible.
 RF brings the precessing spins in phase, thus
creating coherence.
 Quantum jumps play a significant role in MR.

111. Summary of typical myths
 Nuclei can only be in the spin-up or the spin-
down state (cone picture). The Bo field is
somehow responsible.
 RF brings the precessing spins in phase, thus
creating coherence.
 Quantum jumps play a significant role in MR.
 In particular, the spectra reflect sudden
jumps between energy eigenstates.

112. Summary of typical myths
 Nuclei can only be in the spin-up or the spin-
down state (cone picture). The Bo field is
somehow responsible.
 RF brings the precessing spins in phase, thus
creating coherence.
 Quantum jumps play a significant role in MR.
 In particular, the spectra reflect sudden
jumps between energy eigenstates.
 Magnetic Resonance is a quantum phenomenon,
i.e. necessitates a QM explanation.

113. What is a quantum phenomenon?

114. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.

115. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.
 Example: ”Atom formation”

116. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.
 Example: ”Atom formation”
 Only QM correctly predicts that atoms are stable.

117. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.
 Example: ”Atom formation”
 Only QM correctly predicts that atoms are stable.
 Hirarchical definition:

118. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.
 Example: ”Atom formation”
 Only QM correctly predicts that atoms are stable.
 Hirarchical definition:
 Though atoms require QM to be understood,
 …not all phenomena involving atoms are quantum.

119. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.
 Example: ”Atom formation”
 Only QM correctly predicts that atoms are stable.
 Hirarchical definition:
 Though atoms require QM to be understood,
 …not all phenomena involving atoms are quantum.
 Similarly: MR is a classical phenomenon…

120. What is a quantum phenomenon?
 A quantum phenomenon is…
 a phenomenon where understanding requires QM.
 Example: ”Atom formation”
 Only QM correctly predicts that atoms are stable.
 Hirarchical definition:
 Though atoms require QM to be understood,
 …not all phenomena involving atoms are quantum.
 Similarly: MR is a classical phenomenon…
 …relying on spin, which is a quantum-relativistic
phenomenon.

121. Facts contradicted by the myths
Important truths that can be derived from QM:

122. Facts contradicted by the myths
Important truths that can be derived from QM:
 MR is a classical phenomenon,

123. Facts contradicted by the myths
Important truths that can be derived from QM:
 MR is a classical phenomenon,
 in contrast to spin, exchange coupling,…

124. Facts contradicted by the myths
Important truths that can be derived from QM:
 MR is a classical phenomenon,
 in contrast to spin, exchange coupling,…
 Homogeneous magnetic fields (including RF) can only
rotate the spin-distribution as a whole.

125. Facts contradicted by the myths
Important truths that can be derived from QM:
 MR is a classical phenomenon,
 in contrast to spin, exchange coupling,…
 Homogeneous magnetic fields (including RF) can only
rotate the spin-distribution as a whole.
 Quantum jumps play little, if any, role in NMR.

126. Facts contradicted by the myths
Important truths that can be derived from QM:
 MR is a classical phenomenon,
 in contrast to spin, exchange coupling,…
 Homogeneous magnetic fields (including RF) can only
rotate the spin-distribution as a whole.
 Quantum jumps play little, if any, role in NMR.
 The near spherical spin distribution is only perturbed
weakly by the Bo field.

127. Facts contradicted by the myths
Important truths that can be derived from QM:
 MR is a classical phenomenon,
 in contrast to spin, exchange coupling,…
 Homogeneous magnetic fields (including RF) can only
rotate the spin-distribution as a whole.
 Quantum jumps play little, if any, role in NMR.
 The near spherical spin distribution is only perturbed
weakly by the Bo field.
 Field-assisted T1-relaxation is the true source of
coherence.

128.  Relevance of basis choice for NMR:
 The basis choice affects interpretation.
 Population differences and coherences are equivalent:
 A unitary transformation turns density operator off-diagonal
elements into population differences, so they are formally the same.
Coherence

129.  Relevance of basis choice for NMR:
 The basis choice affects interpretation.
 Population differences and coherences are equivalent:
 A unitary transformation turns density operator off-diagonal
elements into population differences, so they are formally the same.
 The real source of coherence is T1-relaxation.
Coherence

130.  Relevance of basis choice for NMR:
 The basis choice affects interpretation.
 Population differences and coherences are equivalent:
 A unitary transformation turns density operator off-diagonal
elements into population differences, so they are formally the same.
 The real source of coherence is T1-relaxation.
 Coherence is generally correlations,
Coherence

131.  Relevance of basis choice for NMR:
 The basis choice affects interpretation.
 Population differences and coherences are equivalent:
 A unitary transformation turns density operator off-diagonal
elements into population differences, so they are formally the same.
 The real source of coherence is T1-relaxation.
 Coherence is generally correlations,
 non-random phase-relations, e.g. polarization.
Coherence

132.  Relevance of basis choice for NMR:
 The basis choice affects interpretation.
 Population differences and coherences are equivalent:
 A unitary transformation turns density operator off-diagonal
elements into population differences, so they are formally the same.
 The real source of coherence is T1-relaxation.
 Coherence is generally correlations,
 non-random phase-relations, e.g. polarization.
 Unfortunate: Coherence is in the MR community often
understood as describing transversal phase relations only.
Coherence

133.  YouTube movie:
 Coupled pendulums
Classical eigenstate example

134.  YouTube movie:
 Coupled pendulums
 Two eigenmodes: in-phase, opposite-phase, oscillating
at different frequencies. A superposition is excited…
Classical eigenstate example

135.  YouTube movie:
 Coupled pendulums
 Two eigenmodes: in-phase, opposite-phase, oscillating
at different frequencies. A superposition is excited…
 Relevance:
Classical eigenstate example

136.  YouTube movie:
 Coupled pendulums
 Two eigenmodes: in-phase, opposite-phase, oscillating
at different frequencies. A superposition is excited…
 Relevance:
 NMR itself: Energy is transferred back and forth between
field and magnetic dipole.
Classical eigenstate example

137.  YouTube movie:
 Coupled pendulums
 Two eigenmodes: in-phase, opposite-phase, oscillating
at different frequencies. A superposition is excited…
 Relevance:
 NMR itself: Energy is transferred back and forth between
field and magnetic dipole.
 J-coupling: The oscillating nuclei are coupled via
the electronic cloud. Peak splitting is expected.
Classical eigenstate example

138.  YouTube movie:
 Coupled pendulums
 Two eigenmodes: in-phase, opposite-phase, oscillating
at different frequencies. A superposition is excited…
 Relevance:
 NMR itself: Energy is transferred back and forth between
field and magnetic dipole.
 J-coupling: The oscillating nuclei are coupled via
the electronic cloud. Peak splitting is expected.
 Notice: No jumps between states despite peaked spectrum.
Classical eigenstate example

139. Concluding remarks
 Basic NMR can be explained by QM but the
interpretation is often problematic.
 Only QM gives the full picture. It is particularly
convenient for interpreting spectra.
 Even your parents can understand NMR, off-
resonance effects, coherence and couplings, for
example. Most aspects are as expected classically.
 Tool: http://drcmr.dk/CompassMR
 A classical introduction to MR can provide intuition
and predictive power.
 There are excellent reasons to teach QM formalism
to those who need it. By far, QM takes you furthest.

140. Further interest?
 Myths and alternative explanations.

141. Sequel
 Book chapter on classical/QM connection:
 Appears in ”Anthropic Awareness - The Human Aspects of Scientific
Thinking in NMR Spectroscopy and Mass Spectrometry”
Editor: Csaba Szántay. See chapter at http://drcmr.dk/MR

142. Educational MRI software
 Interactive MR simulators for browser:
 Linked via http://drcmr.dk/MR
 Demonstration videos are available on YouTube.