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Quantum Field Theory and the Limits of Knowledge презентация
Содержание
- 1. Quantum Field Theory and the Limits of Knowledge
- 2. Two claims: 1. The laws of
- 3. “Laws of physics underlying everyday life” =
- 4. Long history of embarrassingly premature triumphalism. “[We
- 5. Perfectly obvious but necessary caveats We’re nowhere
- 6. Known particles/forces,
- 7. The Core Theory in more detail: Quantum
- 8. Measurements in Quantum Mechanics But we don’t
- 9. (Some) Observables are Quantized Standard example: Simple
- 10. Quantum Field Theory QFT is not a
- 11. Particles from fields Each mode acts like
- 12. Interactions Particle interactions are encoded in Feynman diagrams. = + + + …
- 13. Adding up virtual particles Every particle has
- 14. Ken Wilson: organize QFT by energy/length scale
- 15. Think of your theory as only describing
- 16. All diagrams with N legs contribute to
- 17. Both the field φ and the cutoff
- 18. At energies below Λ, an EFT can
- 19. “We haven’t quantized gravity,” but I’m treating
- 20. A given effective field theory with cutoff
- 21. Known particles/forces,
- 22. What about new particles/forces?
- 23. QFT puts very tight constraints on new phenomena.
- 24. Constraints on new particles As-yet-undiscovered particles
- 25. To be relevant to everyday physics, any
- 26. Strength (relative to gravity) Range [Long et
- 27. Known particles/forces,
- 28. Punchline: the laws of physics underlying everyday
- 29. Astrology is not correct. Implications of the
- 30. 3. Accessible deviations from textbook QM.
- 31. Known particles/forces,
Слайд 2Two claims:
1. The laws of physics underlying everyday life
are completely known.
2.
Слайд 3“Laws of physics underlying everyday life”
= The Core Theory
Quantum field theory
Matter (fermions): quarks,leptons.
Strong, weak, electromagnetic forces.
Gravitation = general relativity.
Higgs field.
Слайд 4Long history of embarrassingly premature triumphalism.
“[We are] probably nearing the limit
about astronomy.” – Simon Newcomb, 1888
“The more important fundamental laws and facts of physical science have all been discovered.”
– Albert Michelson, 1894
“Physics as we know it will be over in six months.”
– Max Born, 1928
There is a 50% chance that “we would find a complete unified theory of everything by the end of the century.”
– Stephen Hawking, 1980
Слайд 5Perfectly obvious but necessary caveats
We’re nowhere close to understanding the fundamental
theory
We don’t understand the non-everyday: dark matter,
quantum gravity, the Big Bang…
We don’t fully understand macroscopic aggregations:
condensed matter, chemistry, biology, economics…
Quantum mechanics or quantum field theory could
always be wrong.
Слайд 6
Known particles/forces,
general relativity
(Core theory)
Dark matter/energy,
new particles/forces,
hidden sectors
Underlying reality
(theory of everything)
Higher-level
macro-phenomena
of everyday
Astrophysics,
cosmology
Слайд 7The Core Theory in more detail:
Quantum Mechanics
Think of “configurations,”
e.g. the
Assign a complex number to
every possible configuration.
That describes a quantum state: a “wave function” Ψ(x)
that lives in a very-high-dimensional Hilbert space.
Schrödinger evolution equation:
x
x
Ψ(x)
Слайд 8Measurements in Quantum Mechanics
But we don’t “see” the wave function.
Measurements return
configuration (or other observable).
Probability of measurement outcome = |wave function|2.
After measurement, wave function “collapses” (becomes
suddenly concentrated on observed outcome).
Seems absurd. But – good enough to successfully
predict the outcome of every experiment ever done.
Слайд 9(Some) Observables are Quantized
Standard example: Simple Harmonic Oscillator.
Particle moving in a
where x is the position and ω is the frequency.
Energy is quantized
into discrete levels:
Слайд 10Quantum Field Theory
QFT is not a successor/alternative to QM; it’s just
a
Namely: “configurations” are “values of (relativistic)
fields throughout space.” E.g. φ(x).
The quantum state (wave function) is a complex
amplitude for each possible field configuration, Ψ[φ(x)].
Examples: electromagnetic field, electron field,
top quark field, gravitational field (metric), etc.
Слайд 11Particles from fields
Each mode acts like a simple harmonic oscillator!
Energy levels
Wavelength = 1/momentum.
Indeed, relativity+QM+particles QFT.
Decompose oscillating field into a sum of “modes”
of different wavelengths (Fourier transform):
=
+
+ …
+
Слайд 13Adding up virtual particles
Every particle has a
momentum, and total
is conserved at
each
Слайд 14Ken Wilson: organize QFT by energy/length scale
Remember: energy & momentum ~
IR
UV
Λ
(“cutoff”
energy
scale)
long
wavelengths/
low energies
short
wavelengths/
high energies
Слайд 15Think of your theory as only describing energies below
the ultraviolet
I.e., only include wavelengths longer than 1/Λ.
Result is an effective field theory below Λ.
Effective Field Theory
Слайд 16All diagrams with N legs contribute to an interaction
term (in Lagrangian)
There are an infinite number of terms in
EFT equations of motion…
φ4
φ8
φ6
Слайд 17Both the field φ and the cutoff Λ have units of
and the Lagrangian governing interactions is (energy)4.
So schematically we have:
Higher-order terms are negligible at low energy (<< Λ).
Only a finite number of relevant/marginal interactions.
… but only a finite number of terms matter
“relevant”
“marginal”
“irrelevant”
Слайд 18At energies below Λ, an EFT can be a complete theory.
Above
E.g. Fermi theory of weak interactions Standard Model.
Effective field theories tell us their regime of applicability:
below the ultraviolet cutoff Λ.
Fermi coupling
Слайд 19“We haven’t quantized gravity,” but I’m treating
gravity like a perfectly ordinary
Because it is – as long as gravity is weak (far from
black holes, Big Bang, etc.).
In terms of curvature parameter R, interactions look like
Here on Earth, 1st term is 1050 times bigger than 2nd.
Quantum Gravity?
Слайд 20A given effective field theory with cutoff Λ could have
many “ultraviolet
That’s why it’s hard to do experiments relevant to
quantum gravity: we expect Λ ~ Eplanck ~ 1015 ELHC.
Multiple realizability
loop quantum gravity string theory dynamical triangulations
Слайд 21
Known particles/forces,
general relativity
(Core theory)
Dark matter/energy,
new particles/forces,
hidden sectors
Underlying reality
(theory of everything)
Higher-level
emergent phenomena
of
Astrophysics,
cosmology
Underlying physics only influences us via Core Theory.
Слайд 22What about new particles/forces?
strongly
interacting
light/
long range/
low energy
heavy/
short range/
high energy
weakly
interacting
Unknown unknowns = violations
Слайд 24Constraints on new particles
As-yet-undiscovered
particles must be either:
very weakly interacting,
too heavy
too short-lived to detect.
In any of those cases, the new particle would
be irrelevant to our everyday lives.
Слайд 25To be relevant to everyday physics, any new forces
must interact with
and/or photons.
Experiments are ongoing (torsion balances) to
search for new, weak, long-range forces.
Two ways to hide:
weak interactions, or
very short ranges.
Constraints on new forces
Слайд 26Strength (relative to gravity)
Range
[Long et al. 2003; Antoniadis 2003]
Experimental limits on
new
gravitational-
strength
force
(10-36 E&M)
Слайд 27
Known particles/forces,
general relativity
(Core theory)
Dark matter/energy,
new particles/forces,
hidden sectors
Underlying reality
(theory of everything)
Higher-level
emergent phenomena
of
Astrophysics,
cosmology
New particles/forces are too heavy/weak to influence us.
Слайд 28Punchline:
the laws of physics underlying everyday experience.
Other phenomena are too massive
have any impact on the particles of which we are made.
Слайд 29Astrology is not correct.
Implications of the Core Theory
You can’t bend spoons
The soul does not survive the body.
Слайд 303. Accessible deviations from textbook QM.
(Hidden variables, spontaneous/induced
Loopholes?
2. Breakdown of QFT itself. E.g. non-local constraints/
interactions from quantum gravity (holography).
1. New forces with environment-dependent couplings.
4. Divine intervention.
Слайд 31
Known particles/forces,
general relativity
(Core theory)
Dark matter/energy,
new particles/forces,
hidden sectors
Underlying reality
(theory of everything)
Higher-level
emergent phenomena
of
Astrophysics,
cosmology
