Sailing the Seething Sea of Quantum Uncertainty

THE FUNDAMENTALS

 SUMMER SCHOOL IN 

HIGH-ENERGY AND GRAVITATIONAL PHYSICS

16 - 20 SEPTEMBER, IN SPLIT, CROATIA

Sailing the Seething Sea of Quantum Uncertainty

Start with two fundamentals:

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• Heisenberg’s principle

of quantum uncertainty

2. Quantum vacuum contains a seething sea of virtual particles

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… and see where the wind blows us.

WHAT IS MOST FUNDAMENTAL IN PHYSICS for you?

When one tugs at a single thing in nature, he finds it hitched to the rest of the universe.�

– John Muir

Fundamental #1: Heisenberg’s Uncertainty Principle

Fundamental #2: Virtual Particles in Quantum Vacuum

Image: Malate 2017 (AIP)

Disturbing the Quantum Vacuum: Casimir Effect (1948)

← a →

Measure force gradients of μ−Newton m⁻¹ at separations of nm

Figure 3. The Casimir force gradient measured as a function of the sphere–plate separation for (a,b) 10 nm cantilever oscillations and (c,d) 20 nm cantilever oscillations [18]. The experimental data (error bars) for the force gradient and separation agree with the no-dissipation theory calculations (lines) for zero-point photon-free electron scattering for all separations shown.

Physics 2024, 6(2), 891-904

A Brief Review of Some Recent Precision Casimir Force Measurements

Madhav Dhital & Umar Mohideen

Disturbing the Quantum Vacuum

Disturbing the Quantum Vacuum

NATURE, Vol 446/1 March 2007

“We’re going to change the index of refraction of the vacuum and produce new particles.”

Gérard Mourou

Physicists are planning lasers powerful enough

to rip apart the fabric of space and time.

Ed Gerstner is impressed

Gérard Mourou

Earth surface

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Sun surface

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Sunspot

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MRI

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LHC dipoles

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Largest on Earth

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Crab pulsar

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Magnetars

Strong magnetic fields imply existence of strong electric fields.

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Many unexplained phenomena associated with pulsars, magnetars, etc.

The Skeptics Guide to the Universe

could rip the iron out of your

blood from 1,000 miles away.

MAGNETARS

Hawking (1974)

Particle creation if energy gained in acceleration from gravitational field over a Compton wavelength exceeds the particle’s rest mass.

v = c at Black Hole horizon

Disturbing the Quantum Vacuum

Particle creation if energy gained in acceleration from expansion of space over a Compton wavelength exceeds the particle’s rest mass.

Disturbing the Quantum Vacuum

Schrödinger (1939)

Particle creation if energy gained in acceleration from expansion of space over a Compton wavelength exceeds the particle’s rest mass.

Disturbing the Quantum Vacuum

Schrödinger (1939)

Schrödinger’s Alarming Times

Biographical info. from Walter Moore, Schrödinger, Life and Thought (Cambridge Univ. Press, 1992)

1926: “Quantisierung als Eigenwertproblem,” Annalen der Physik 384, 273

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1927: Schrödinger visited U.S.

Found noise and dirt of New York “shattering”

Found Chicago worse, feared “bandits who spring with loaded guns from speeding autos.” (Wife liked Chicago.)

Schrödinger departed UZH for Berlin.

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1933: Nazis came to power. Schrödinger, marked by Nazis as “politically

unreliable,” departed Berlin for “exile” in Oxford. Nobel Prize.

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1936: Schrödinger departed Oxford for Graz, Austria in a miscalculation of the

political situation that was, in his words, an “unprecedented stupidity.”

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1938: 12 March, Anschluss; 26 August, Schrödinger dismissed; 14 September, Erwin & Anny left Graz for Rome with ten Marks, three suitcases, sans Nobel medal; met in Rome by Fermi; asylum in the Vatican.

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1938: Schrödinger accepted position in Ghent, Belgium [ed. another stupidity].

Schrödinger the Cosmologist

In Belgium met big-bang cosmologist Abbé Georges Lemaître.

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In U.K. several interactions with Sir Arthur Stanley Eddington.

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July 1939 Nature of the Nebular Red-Shift

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August 1939 The Proper Vibrations of the Expanding Universe

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1956 Expanding Universes, Cambridge Univ. Press

Schrödinger’s Alarming Times

1926: “Quantisierung als Eigenwertproblem,” Annalen der Physik. 384, 273

​

1927: Schrödinger visited U.S.

Found noise and dirt of New York “shattering”

Found Chicago worse, feared “bandits who spring with loaded guns from speeding autos.” (Wife liked Chicago.)

Schrödinger departed UZH for Berlin.

​

1933: Nazis came to power. Schrödinger, marked by Nazis as “politically

unreliable,” departed Berlin for “exile” in Oxford. Nobel Prize.

​

1936: Schrödinger departed Oxford for Graz, Austria in a miscalculation of the

political situation that was, in his words, an “unprecedented stupidity.”

​

1938: March, Anschluss; 26 August Schrödinger dismissed; 14 September, Erwin & Anny left Graz for Rome with ten Marks, three suitcases, sans Nobel medal; met in Rome by Fermi; asylum in the Vatican.

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1938: Schrödinger accepted position in Ghent, Belgium [another stupidity].

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1939: October, Schrödinger departed Belgium for Dublin.

Biographical info. from Walter Moore, Schrödinger, Life and Thought (Cambridge Univ. Press, 1992)

THE PROPER VIBRATIONS

OF THE EXPANDING UNIVERSE

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by ERWIN SCHRÖDINGER

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Physica VI, 899 (1939)

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Received 21 August 1939

Published October 1939

No author affiliation listed

Cited 325 times (Google Scholar)

If start with pure incoming or outgoing waves, in and out will become mixed.

Outstanding importance. The universe creates particles merely by expansion!

This alarms me [ed. why?], so I wrote a paper.

Schrödinger found the phenomenon “alarming”

In 1939 Schrödinger was alarmed by creation of a single particle

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per Hubble time (H₀⁻¹ ~ 10¹⁰ yr)

per Hubble volume (H₀⁻³ ~ 10⁵⁷ km³)

with Hubble energy (H₀ ~ 10⁻³³ eV)

Of all the circumstances faced by Schrödinger in 1939, this alarmed him?

Schrödinger’s Alarming Phenomenon

Why was Schrödinger alarmed?

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• Appearance of particles from the vacuum sounds crazy.

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• Technical issues with calculation:

Quantum mechanical calculation (requires quantum field theory).

Only create particles with mass less than expansion rate H (today H₀ ~ 10⁻³³ eV).

Only create particles if violate Weyl Conformal Invariance (don’t create photons).

Would Schrödinger still have been alarmed?

• Schrödinger looked for (and found) a cosmological solution (Milne) without mutual adulteration (not a very physical solution).

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• Perhaps he thought it was conceptual challenge to Quantum Mechanics or General Relativity.

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• (Sometimes should just follow the equations).

Cosmological Gravitational Particle Production (CGPP)

• In Minkowskian QFT, a particle is an IR of the Poincaré group.
• But, expanding universe not Poincaré invariant.
• Notion of a “particle” is approximate.

Schrodinger (1939); Parker (1965, 68); Fulling, Ford, & Hu; Zel’dovich; Starobinski; Grib, Frolov, Mamaev, & Mostepanenko; Mukhanov & Sasaki, Birrell & Davies…

cosmological expansion ⇒

time-dependent background ⇒

time-dependent Hamiltonian for spectator fields

covariant action

field rescaling

in a spatially flat FRW background : ds² = a²(η)[dη ² − dx ²] (η is conformal time)

action for canonically-normalized field

time-dependent effective mass

Gravity enters the picture

Scalar field in FRW background

Expansion of the universe causes explicit time dependence in action for “spectator” fields. Initial State ~ Minkowski (early-time) vacuum may not evolve to

Final State ~ Minkowski (late-time) vacuum, but to an excited state populated by particles.

Spring constant varied

abruptly (nonadiabatically)

x

Schrödinger’s Alarming Phenomenon

V

Initial State

ψ

x

x

Spring constant varied

slowly (adiabatically)

V

V

ψ

ψ

covariant action

no symmetry forbids it, from EFT point of view should include it

furthermore, it should not be constant: there should be an RGE

in general, ξ should be a free parameter. ξ = 1/6 is an enhanced (classical) conformal symmetry point.

Scalar field in FRW background

Forgotten in 40s, 50s, 60s (by Schrödinger also).

Schrödinger’s Alarming Phenomenon

Schrödinger 1939: “Generally speaking this is a phenomenon of outstanding importance. With particles it would mean the production or annihilation of matter, merely by the expansion.” [why would that be of “outstanding importance”?]

Leonard Parker Thesis 1966. In 1968 paper: “…for the early stages of a Friedmann expansion it [particle creation] may well be of great cosmological significance, especially since it seems inescapable if one accepts quantum field theory and general relativity.” [no speculation as to the “great cosmological significance”]

“Outstanding importance”?

“Great Cosmological Significance”?

Lull in 40s, 50s:

Interest in 1960s (mostly regarded as a curiosity):

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US: Parker, Ford, Fulling, Allen, Friedman, Wald, …

Soviet Union: Zel’dovich, Starobinski, Grishchuk, Grib, Mostepanenko, Lukash, …

Some in UK: Bunch, Davies, Birrell, Hawking, …

Schrödinger’s Alarming Phenomenon

Great cosmological significance in the 1980s (inflation):

Mukhanov & Chibisov, Sasaki, Kodama, Vilenkin, Linde, Abbott, Wise, Lyth, Salopek, Bond, …

Inflation

• Scalar field has potential energy V(φ) and kinetic energy

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• Potential energy (zero-momentum mode of φ) dominates ⇒ acceleration

Usual picture of inflation:

Universe dominated by potential

energy of a scalar field, the inflaton

Particle creation if energy gained in acceleration from expansion of space over a Compton wavelength exceeds the particle’s rest mass.

Disturbing the Quantum Vacuum

Schrödinger’s Alarming Phenomenon applies to inflaton field - Mukhanov-Sasaki equation

Inflation

• Scalar field has potential energy V(φ) and kinetic energy

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• Potential energy (zero-momentum mode of φ) dominates ⇒ acceleration

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• Schrödinger’s Alarming Phenomenon produces inflaton particles

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• Particles produced with non-zero momentum (finite length scales) Δφ → Δρ → ΔT

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• Particles produced when they cross Hubble radius during inflation → fluctuations on all scales with approximately same amplitude (Harrison—Zel’dovich)

Usual picture of inflation:

Universe dominated by potential

energy of a scalar field, the inflaton

A pattern

of vacuum

quantum

fluctuations

→ 0

→ 0

You are the result of

quantum uncertainty and virtual particles!

A (highly) nonlinear amplified quantum fluctuation

• (Schrödinger’s alarming phenomenon)

• and rapid expansion ripped particles out of the quantum vacuum

• produced 10⁻³⁵ seconds after the bang during primordial inflation

• producing primordial seeds of structure that grew to all we see

• when the universe was dominated by vacuum energy

• The map of CMB ΔT/T is a map of quantum fluctuations

• and encoded in it is the imprint of fundamental physics.

• (you are an amplified quantum fluctuation),

Particle creation if energy gained in acceleration from expansion of space over a Compton wavelength exceeds the particle’s rest mass.

Disturbing the Quantum Vacuum

Schrödinger’s Alarming Phenomenon applies to graviton field

Inflation

Big Bang plus 10^-35? seconds

Big Bang plus 380,000 Years

Big Bang plus 14 Billion Years

CMB fluctuations

density perturbations

gravitational waves

Schrodinger’s Alarming Phenomenon

Leaves Imprint of GPP

Schrödinger’s Alarming Phenomenon

Great cosmological significance in the 1980s (inflation):

Sasaki, Kodama, Mukhanov & Chibisov, Vilenkin, Linde, Abbott, Wise, Lyth, Salopek, Bond, …

Could there be more?

Gravitational Particle Production universal

Gravitational Particle Production not a large effect (cf., CMB perturbations ≈ 10⁻⁵)

What else could be observable?

Dark matter (DM)

CMB Isocurvature perturbations

CMB Nongaussianities

Baryon asymmetry

Schrödinger’s Alarming Phenomenon

Great cosmological significance in the 1980s (inflation):

Sasaki, Kodama, Mukhanov & Chibisov, Vilenkin, Linde, Abbott, Wise, Lyth, Salopek, Bond, …

Could there be more?

Gravitational Particle Production universal

Gravitational Particle Production not a large effect (cf., CMB perturbations ≈ 10⁻⁵)

What else could be observable?

Dark matter (DM)

CMB Isocurvature perturbations

CMB Nongaussianities

Baryon asymmetry

Dark Matter:

25%

Dark Energy:

70%

Stars:

0.8%

H & He:

4%

Chemistry (elements other than H & He):

0.025%

Neutrinos:

0.17%

Radiation:

0.005%

ν_e

ν_μ

ν_τ

?

?

For 40 Years, Leading DM Candidate: “Weak-Scale” Cold Thermal Relic

• Mass: GeV – TeV
• “Weak-scale” interaction strength with SM No self-interactions
• Produced by “freeze-out” from primordial plasma.
• “Detectable” by direct detection, indirect detection, decay products, production at colliders

But WIMPs (and SUSY) have stubbornly evaded detection!

Dark Matter: if not a WIMP

• If DM not a WIMP, many other possibilities:
• Axions
• Asymmetric DM
• Sterile neutrino DM (e.g., 7 keV sterile neutrino producing 3.5 keV X-ray line.
• Axino (7 keV axino) DM
• Self-interacting DM
• Inelastic DM
• Q-balls or other solitonic DM
• Dark photons
• Quark nuggets
• Hidden-sector DM

• What if DM interacts only gravitationally?

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• Gravity must play a role in its cosmological production
• But gravity weak!
• CGPP capable of producing dark matter (WIMPzilla!)

• Inflation indicates a new mass scale

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• In most models, m_inflaton ≈ H_inflation ≈ 10¹² − 10¹⁴ GeV?

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• H_inflation detectable via primordial gravitational waves in CMB

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• (I, at least) expect other particles with mass ≈ m_inflaton

WIMPzillas

Chung, Kolb, Riotto; Kuzmin, Tkachev; …. Kolb & Long

WIMPzilla^© is a very massive dark-matter candidate produced via GPP

Dark Matter From Schrödinger’s Alarming Phenomenon

Chung, EWK, Riotto (1998); Kuzmin & Tkachev (1999)

My collaborators:

Ivone Albuquerque

Edward Basso

Christian Capanelli

Daniel Chung

Patrick Crotty

Michael Fedderke

Gian Giudice

Lam Hui

Leah Jenks

Siyang Ling

Andrew Long

Evan McDonough

Guillaume Payeur

Toni Riotto

Rachel Rosen

Leo Senatore

Alexi Starobinski

Keyer Thyme

Igor Tkachev

Mark Wyman

Inner Space/Outer Space Interface

Also, limits from cosmological gravitational particle production

Quantum Field Theories in the Early Universe

1. Well-behaved QFTs in Minkowski space can develop pathologies when promoted to FRW.
2. This is especially acute for “higher-spin” QFTs (1, 3/2, 2, …).
3. And some funny business for spin-0.
4. Is there a swampland of Minkowskian QFTs?
5. Or should we just accept restrictions on parameters of the QFTs (mass, couplings, etc.).
6. I will not have time to review EFT cutoffs, strong-coupling limits, nonlinearities, etc.

More complete treatment in

Cosmological gravitational particle production

EWK and Andrew Long

Reviews of Modern Physics (to appear) 2312.09042

Minimal coupling: Graham, Mardon, & Rajendran (2016); Ahmed, Grzadkowski, & Socha (2020); EWK & Long (2020)

Non-minimal coupling: Capanelli, Jenks, EWK, McDonough (2024)

7^th Duc de Broglie—Proca field (dark photon) in FRW background

Two possible nonminimal dimension−4 terms: and

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Gauge invariance broken by mass term and by nonminimal terms, can fix via trick of

Baron Ernst Carl Gerlach Stueckelberg von Breidenbach zu Breidenstein und Melsbach (Abelian Higgs mechanism)

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In FRW

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Α₀ is not dynamical and will be integrated out.

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Two time-dependent mass terms m_t² and m_x² can be positive or negative!

Covariant action:

1742

Standard procedure:

• Decompose action in terms of mode functions
• Integrate out
• Introduce orthonormal set of transverse and longitudinal mode functions
• Action separates into two pieces, transverse and longitudinal
• Transverse mode action that of conformally-coupled scalar with mass (which can be positive or negative)
• Longitudinal mode action more “interesting”

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• Since is time-dependent and not necessarily positive definite, a ghost can be propagated
• If demand ghost-free for arbitrarily large k, must have during evolution
• This will place limits on and as a function of m.
• Longitudinal frequency “interesting”

Minimal coupling: Graham, Mardon, & Rajendran (2016); Ahmed, Grzadkowski, & Socha (2020); EWK & Long (2020)

Non-minimal coupling: Capanelli, Jenks, EWK, McDonough (2024)

7^th Duc de Broglie—Proca field (dark photon) in FRW background

Minimal coupling: Graham, Mardon, & Rajendran (2016); Ahmed, Grzadkowski, & Socha (2020); EWK & Long (2020)

Non-minimal coupling: Capanelli, Jenks, EWK, McDonough (2024)

1. In high-momentum limit (large k ) the first term dominates
2. Have established that to be ghostless, if then will be negative
3. Leading to an instability to particle production for arbitrarily large k modes.
4. Require and
5. Depends (a little) on inflation model

runaway ⟶

7^th Duc de Broglie—Proca field (dark photon) in FRW background

Minimal coupling: Graham, Mardon, & Rajendran (2016); Ahmed, Grzadkowski, & Socha (2020); EWK & Long (2020)

Non-minimal coupling: Capanelli, Jenks, EWK, McDonough (2024)

For “large” m/H_e , not very restrictive

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But for small m/H_e , as in dark photon models, very restrictive

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Breakdown of EFT? Discussed in Capanelli et al.

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Strong coupling? A. Hell

7^th Duc de Broglie—Proca field (dark photon) in FRW background

How should one regard QFTs, perfectly healthy in Minkowski spacetime, but have issues in a non-pathological, classical gravitational background?

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1. (H_e–dependent, T_RH –dependent, and spin –dependent) limits on stable particles masses from Ω.

Is that an issue with the QFT, or just a result like m_ν ≲ eV?

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2. Stable, minimally-coupled scalars have infrared issues unless m ≳ H_e.

Is that an issue with the QFT, or just “not in our universe”?

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3. Dark photons have issues with runaway production if non-minimally coupled.

Shared with massive Kalb-Ramond fields.

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4. Massive Rarita-Schwinger fields can have catastrophic production unless m ≳ H_e.

SUGRA people should pay attention.

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5. Massive Fierz-Pauli fields can develop ghosts and gradient instabilities unless m ≳ H_e.

Is there a better formulation of massive gravity?

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6. Do we have to look at different gravity theories at high-energy.

Torsion, contorted geometry, disformal gravity.

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7. Is there a Flatland Swampland?

Quantum Field Theories in the Early Universe

Sailing the Seething Sea of Quantum Uncertainty

THE FUNDAMENTALS

 SUMMER SCHOOL IN 

HIGH-ENERGY AND GRAVITATIONAL PHYSICS

16 - 20 SEPTEMBER, IN SPLIT, CROATIA

Schrödinger ̶ Fermi

Dublin

February 10, 1951

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Dear Fermi,

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….. I beg you to help me remove once and for all, a remorse that I cannot help associating with my memory of you at our last meeting, namely that I still owe you Lire 400 val. Sept 1938. To re-calculate this sum to date, now that all money-value has gone down is very difficult, but I think something like 200 Swedish Crowns would be a modest estimate for re-payment. If you agree and if you still have an account at Stockholm, this would be very simple. If the later is not the case, please indicate me your bankers’ account at Chicago, and I hope to manage even so.

…..

Yours very sincerely,

E. Schrödinger

Chicago

February 27, 1951

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Dear Shrodinger [sic],

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….. As to the old debt that you mention, I believe that you are estimating the value of 400 lire too high. At that time the lire was worth about one twentieth of one dollar and it seems therefore a $20.00 settlement would be correct. I no longer have an account in Sweden. My bank here in Chicago is the University National Bank, 1354 East 55^th Street, Chicago 15. Please however, be sure if there are any difficulties whatsoever about transferring this amount not to worry about it because it is certainly not worth it.

…..

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Yours very sincerely, Enrico Fermi

Schrödinger ̶ Fermi