Fields Over Particles underly/ground Ryan Reece
[email protected] https://ucsc.academia.edu/RReece http://reece.scipp.ucsc.edu
4th International Summer School in Philosophy of Physics
July 20, 2016
Outline 1. Preface on pluralism in physics 2. Fields and symmetries - “symmetry-first physics” 3. Effective Field Theories - regime realism 4. Interacting QFT concerns - Malament/Haag/LSZ 5. Decoherence - emergence of the classical (including particles) from unitary quantum evolution 6. Summary
Ryan Reece (UCSC)
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On pluralism in physics
Feynman
“Theories of the known, which are described by different physical ideas may be equivalent in all their predictions and are hence scientifically indistinguishable. However, they are not psychologically identical when trying to move from that base into the unknown. For different views suggest different kinds of modifications which might be made and hence are not equivalent in the hypotheses one generates from them in one’s attempt to understand what is not yet understood. I, therefore, think that a good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory available to him.” -Feynman, R. (1965). “The Development of the Space-Time View of Quantum Electrodynamics.” Nobel Lecture. December 11, 1965.
Ryan Reece (UCSC)
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source: http://philosophy-in-figures.tumblr.com/post/145247040756/interpretations-of-quantum-mechanics-v2 Ryan Reece (UCSC)
my philosophy blog in figures: http://philosophy-in-figures.tumblr.com
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Assuming decoherence (largely) explains the appearance of collapse, and that consciousness plays no special role in QM, let’s explore the tension between popular no-collapse positions. Rather than debate these interpretations in full, let’s focus on discussing the more basic ontological commitments in QM. source: http://philosophy-in-figures.tumblr.com/post/145247040756/interpretations-of-quantum-mechanics-v2 Ryan Reece (UCSC)
my philosophy blog in figures: http://philosophy-in-figures.tumblr.com
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Fields and symmetries
Ontology: what there is • Detlef Dürr: “Ontology: What there is. The stuff which physics is about. Why does physics need ontology? Because that is what physics is about.” • Feynman: “It is not philosophy we are after, but the behavoir of real things.”
Central question of this talk: What is the relation between fields and particles?
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Weinberg: fields≠wavefunctions≠particles
Weinberg
“In fact, it was quite soon after the Born-Heisenberg-Jordan paper of 1926 that the idea came along that in fact one could use quantum field theory for everything, not just for electromagnetism... Although this is often talked about as second quantization, I would like to urge that this description should be banned from physics, because a quantum field is not a quantized wave function. ... In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields. In a relativistic theory the wave function is a functional of these fields, not a function of particle coordinates. Quantum field theory hence led to a more unified view of nature than the old dualistic interpretation in terms of both fields and particles.” -Weinberg, S. (1996). What is quantum field theory, and what did we think it is?
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5 .1.1 Foundations Real Foundations 5.1 of QM of QM
What in QM is fundamental?
State vReal ector in a Hilbert 5.1.1 Foundations of space QM
Orthodox QM as I see it: State vector in a Hilbert space
9 |Yi of the world, and 9 {|ni} such that hn|ni = 1 and hn|n0 i = 0
0 9 | Y i of the world, and 9 {| n i} such that h n | n i = 1 and h n | n i=0 Superposition principle:
(1)
Superposition principle:
|yi = Â an |ni n
|Yi = Â an |ni
(2)
n
Observ ables are eigenv alues of Hermitian operators: Observables are eigenvalues of Hermitian operators:
Hˆ |ni = E“eigenstate-eingenvalue n |ni
Born rule: Born rule: Ryan Reece (UCSC)
Hˆ |ni = En |ni
P(n) = |hn|Yi|2 = | an |2
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link”
R. Reece (3)
(4) 9
(4) To the orthodoxy, I would emphasize i Pˆ x =e R effects seem less 2 P(n) = |hn|Yi|2 = | an |µ surprising. Uˆ trans ( x )
µ
µ
Wigner’s theorem: (Ovrut’s retelling) (also related to Stone’s theorem of untiary groups) The generators of the representation of a transformation in a Hilbert space are the operators 1| y µn ˆ Y ( x ) = h x | n i = h 0 ( x µn i M q µn ) | n i n are ˆ 2 representing the classical Noether charges that conserved under that transformation. Urot (q ) = e i Pˆµ x µ
ˆ trans ( x µ ) = e U
TODO: also comment on and differentiate from Stone’s theorem. (5)
Y( x ) =
 a n Y n ( x ) =  a n h x | n i =  a n h0| y ( x ) | n
ˆ rot (q ) = e U µn
i
1 2
n
ˆ µn q µn M
n
Ovrut 5.1.2 Secondary properties of QM hrodinger Equation: TODO: comment on and differentiate from Stone’sintheorem. How also physical symmetries are represented the Hilbert space!
(6)
Wave function: Derivative QM concepts include: 5.1.2
Secondary properties of QM
• Schrödinger equation:
Wave function:
Wave function: • (2015).
1 Myrvold
Ryan Reece (UCSC)
i¯h ∂t |Yi = Hˆ |Yi Y ( x ) = h x | Y i = h0| y ( x ) | Y i
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Symmetry-first physics Ovrut
• Enumerate the degrees of freedom in
Correlaries are: the system. For relativistic representations, these are the familiar scalar, vector, spinor, • Schrödinger equation tensor, ... • Wave function • Quantize once: promote the dynamical • p → -i ħ ∂x variables to being opperators in a quantum • ETCR: [x, p] = i ħ Hilbert space. • Spin-statistics • Wigner/Stone: require that the generators of physical symmetries satisfy the algebras of those symmetries. Reece, R. (2006). A Derivation of the Quantum Mechanical Momentum Operator in the Position Representation. Ryan Reece (UCSC)
Reece, R. (2007). Quantum Field Theory: An Introduction.
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Symmetry-first physics
Weinberg
“Why do we enumerate possible theories by giving their Lagrangians rather than by writing down Hamiltonians? ... that symmetries imply the existence of Lie algebras of suitable quantum operators, and you need these Lie algebras to make sensible quantum theories. ... if you start with a Lorentz invariant Lag rangian density then because of Noether’s theorem the Lorentz invariance of the Smatrix is automatic.” -Weinberg, S. (1996). What is quantum field theory, and what did we think it is?
QFT is naturally relativistic if one requires that the Poincaré algebra be satisfied.
Ryan Reece (UCSC)
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⎬
planetary motion
terrestrial gravity
Unification?
Newton, Einstein
universal gravitation general relativity
Higgs mechanism
⎬
electricity
Maxwell
⎬⎬ ⎬
electromagnetism
magnetism
QED U(1)
strong force
electroweak
SU(2) × U(1)
strings?
Grand Unification
SU(5), SO(10), ... ? Z’ ? Energy
QCD SU(3) 102
Ryan Reece (UCSC)
GWS Standard Model
SUSY?
weak force
⎬
SU(3)C × SU(2)L × U(1)Y
unified quantum gravity
?
1016 ?
1019 ?
[GeV] 13
Unification = SUSY+GUTs?
heoretical situation
60
LEP (1991)
U(1)
50
malizanverse Stand the MSSM reated d be, and 7 and
SM
40 Higgs mechanism
SU(2)
SU(3)C × SU(2)L × U(1)Y
-1
α 30
10 SU(3) 0 2
Ryan Reece (UCSC)
Supersymmetry
20
4
~ 104 GeV current collider physics 6
8
10
12
unification scale ~1016 GeV
Log10(Q/GeV)
14
16
18 14
Yn ( x ) = h x |n i i== h0| y(|xn) ih |nn i |Yi = | Y a | n i n Yn ( x ) = h x |ni = h0| y( x ) |ni|Yi = |nihn|Yi = a |ni (8) n  n vsÂfield Wave function vs nstate vector
Â
Â
n
n
| Y i = | n ih discrete basis: Y ( x ) = Hilbert space  Z Z |Yi =  |nihn|Yi =  an |ni n | Yn|in= a1 |b1 i + a2 |b2 i + . . . = ( a1 , a2 , . (9) . .) |Yi =  |nnih n | Y i = a i n |Yi = 21 Âdx | x ih x |Yi = dx Y( x ) | x i Myrvold (2015). n
n
continuous Zbasis (e.g. position/spacetime): Z
|YiZ =
|Yi =
Z
dx | x ih x |dx Yi Y = ( x )dx | x|ixih x|Yi = dx Y( x) | xi ( dx Y( x ) | x i (10) local field in QFT
dx | x ih x |YiZ =
dx | x ih x |Yi = 21 Myrvold (2015). wave function: Y( x )
= h x | Y i = h0| y ( x ) | Y i
Quantum Mechanics (2015). Y ( x ) = h x | Y i = h0| y ( x ) | Y i Hilbert rule... Y(space, x ) = hsuperpositions, x |Yi = h021 |y ( xBorn ) |Yi(2015). Myrvold NRQM:
QFT: fields NR Ryan Reece (UCSC)
|YiZ =
Z
13
conserved particle 13number and trajectories
13
Y( x ) = h x |Y ( QFT is not a (11)
13 different theory from QM. It is QM applied to a field ontology.
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2nd Quantization?
Weinberg
“The wave fields φ, ψ, etc, are not probability amplitudes at all, but operators which create or destroy particles in the various normal modes. It would be a good thing if the misleading expression ‘second quantization’ were permanently retired.” -Weinberg, S. (1995). Quantum Theory of Fields,Vol. 1, p. 28.
Not cannonical quantization but a nonrelativistic heuristic.
Ovrut Ryan Reece (UCSC)
“We take the classical theory and quantize it once by representing its dynamical variables as operators in a Hilbert space.” -My paraphrase of QFT class with Burt Ovrut at Penn. 16
wave function: Y( x ) = h x |Yi = h0| y( x ) |Yi
d (2015). Myvold
“wavefunctions of quantum mechanics are not part of the fundamental ontology of the world. They emerge, via certain approximations, in a low-energy, nonrelativistic regime. Nor are configuration spaces more fundamental than ordinary spacetime. Our quantum field theory is a theory on Minkowski spacetime. For certain states, namely, states of a definite particle number n, and for low-energy regimes, we can represent the state via a function on a 3n-dimensional space, but this representation is not available for arbitrary states. Moreover, wavefunctions, obtained in the most natural way from a quantum field theory, are not assignments of local beables to points in configuration space, even in the single-particle case. This is not to say that an advocate of separability could not, with sufficient effort, reconstrue things so as to represent quantum states via assignments of local beables to points in some appropriately constructed space, but it is clear that this would be an imposition of separability on the theory, and can by no means be regarded as the default position on the ontology of quantum theories. What quantum theory suggests is that we accept nonseparability of state descriptions.
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-Ryan Reece (UCSC)
Myrvold, W. C. (2015). What is a wavefunction?
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Effective Field Theories
Effective emergent theories have some autonomy. Physics breaks into different regimes that have different scales.
From: Flip Tanado (2009). Quantum Diaries blog: “My research [Part 2] effective theories.” Ryan Reece (UCSC)
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Effective Field Theories
Weinberg
“it is very likely that any quantum theory that at sufficiently low energy and large distances looks Lorentz invariant and satisfies the cluster decomposition principle will also at sufficiently low energy look like a quantum field theory. ... This leads us to the idea of effective field theories. When you use quantum field theory to study low-energy phenomena, then according to the folk theorem you’re not really making any assumption that could be wrong, unless of course Lorentz invariance or quantum mechanics or cluster decomposition is wrong, provided you don’t say specifically what the Lagrangian is. As long as you let it be the most general possible Lagrangian consistent with the symmetries of the theory, you’re simply writing down the most general theory you could possibly write down.” -Weinberg, S. (1996). What is quantum field theory, and what did we think it is?
QFT is a way of parametrizing effective, local degrees of freedom. Ryan Reece (UCSC)
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Ken Wilson Wilson
Effective Field Theories tell us their regime of applicability: below the ultraviolet cut-off, Λ. Slide from Sean Carroll: “Quantum Field Theory and the Limits of Knowledge” Ryan Reece (UCSC)
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Donald Rumsfeld’s
• • •
Effective Field Theory applies
known knowns known unknowns unknown unknowns
Unknown unknowns = violations of QFT itself
dynamics above the cut-off Λ
Slide from Sean Carroll: “Quantum Field Theory and the Limits of Knowledge” Ryan Reece (UCSC)
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Slide from Sean Carroll: “Quantum Field Theory and the Limits of Knowledge” Ryan Reece (UCSC)
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3000
~ 0 miss ~ g-~ g production, ~ g→qq∼ χ →qq(γ /Z)G (GGM), γ γ +E final state 1
T
SUSY
Observed limit (±1 σtheory) Expected limit (±1 σexp) Excluded at L=20.3 fb-1, s=8 TeV
ATLAS
1
Search for SUSY gluino-neutralino decays to diphoton + missing energy
mχ∼0 [GeV]
Example limits from ATLAS 2500
L = 3.2 fb-1, s=13 TeV
2000 m∼χ0 >
idden
m~g forb
1
1500
1000
All limits at 95% CL
500
0 1200
1400
1600
1800
2000
5
2200
m~g [GeV]
DM−Nucleon cross section [cm2]
Search for Higgs decaying to additional invisible modes: Higgs portal to dark matter? final states with +E .
[1606.09150]
ypical production and decay-chain processes for the gluino-pair production GGM model for which the -37 ATLAS σZH ,SM 10 limits Higgs-portal Model ATLAS Figure 3: Exclusion in the neutralino–gluino mass plane at 95% CL. The observed limits are exhi bino-like neutralino. -38 -1 Ldt=4.5 fb-1 ssection = 7 TeV, 10 ∫ the nominal SUSY model cross section, as well as for a SUSY cross increased and lowered by o s = 7 TeV, ∫ L dt = 4.5 fb Observed 95% CL limit -39 fb -1 as well a s = 8isTeV, ∫ Ldt=20.3limit, ard deviation of10 the cross-section systematic uncertainty. Also shown the expected -1 0 ˜ -40 s = in 8 each TeV,of∫ the L dttwo = 20.3 fb in a GGM event would be predominantly ˜ ! + G, final decay cascades → ℓℓ of + inv. 1 because the low count expected. Expected 95% CL limit standard-deviation 10range of the expected limit, which is asymmetricZH miss
q¯ → ℓℓ T+ inv. ZH
χ
-41 the background 10 expectation is close to zero and the observed number of events is zero, the expected and ± 1 σ nearly overlap. n to the bino-like ˜ 01 NLSP, a degenerate octet of gluinos (the SUSY partner oflimits the SM gluon) is 10-42The previous limit from ATLAS using 8 TeV data [3] is shown in grey. 0 -43 e potentially accessible with 13 TeV pp collisions. ±2Both σ the gluino and ˜ 1 masses are considered 10 parameters, with the ˜ 01 mass constrained to be less than that of the gluino. All other SUSY 10-44 χ requirements associated with the SR, as well as the NLO (+NLL) GGM cross section [20–24 h 13 TeV pp collisions. This results in a SUSY -45 e set to values that preclude their production in 10 varies steeply with-46gluino mass, 95% CL lower limits may be set on the mass of the gluino as a fun n process that proceeds through theZcreation of pairs of gluino states, each of which subsequently mass of the10 lighter a a virtual squark (the 12 squark flavour/chirality eigenstates are taken to bethe fully degenerate) -47 bino-like neutralino, in the context of the GGM scenario described in Sect 10 –antiquark pair plus the NLSP neutralino. Other SM objects (jets, leptons, photons) may be -48 DAMA/LIBRA 3σ as a function CRESST 2σ observed limit on the gluino mass is exhibited, of neutralino mass, in F 10 in these cascades. The ˜ 01 branching fractionZto + G˜ is 100% 0 andresulting approaches !−for m ˜ 01 ! The CDMS 95% CL CoGeNT -49 the purpose `⌫) + background XENON10 limits, the W(! XENON100 10of establishing these model-dependent ˜ For all ˜ 0For r m ˜0 mZ , with the remainder of the ˜ 01 sample decaying to Z + G. LUX ATLAS, scalar DM 1 masses, then, the -50 1
[1402.3244]
and the limit on 10the possible number of events from new physics are extracted from a simultaneo
ATLAS, vector DM ATLAS, fermion DM fraction is dominated by the photonic decay, leading to the diphoton-plus-ETmiss signature. For -51 the SRproduction and W(! 10 `⌫) + control region, although for a gluino mass in the range of the observ with a bino-like NLSP, a typical production and decay channel for strong (gluino) 3 q + valu ! 350relevant400 102than 0.03 events for 10any 1in the W(! `⌫) + 10control sample is less d in Figure 1. Finally, it should be250 noted that the phenomenology tothe thissignal searchcontamination has a 150 200 300 Ryan Reece (UCSC) DM Mass [GeV]and24bac neutralino mass. its statistical dependence on the ratio tan of the two SUSY Higgs-doublet vacuum expectation values; for Also shown for this figure is the expected limit, including
Accepting the empirical adequacy or structural realism of QFT in a regime does not commit one to any “fundamental” ontology. Slide from Sean Carroll: “Quantum Field Theory and the Limits of Knowledge” Ryan Reece (UCSC)
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Interacting QFT
No particles in interacting theory Several important theorems in QFT by Haag (1992), Malament (1996), Halvorson & Clifton (2002), and others, point out the difficuluties in decomposing an interacting field theory into what could be called “particle” states.
“For a free system, special relativity and the linear field equation conspire to produce a quanta interpretation. For an interacting system, the combination of special relativity and the nonlinear field equation is not so fortuitous; as a result, there is no quanta interpretation and there are no quanta.”
Fraser
-Fraser, D. (2008). The fate of ’particles’ in quantum field theories with interactions.
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Asymptotic LSZ “particle” states are still ok! “First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implications of Haag’s theorem.”
Bain
3
s
-Bain, J. (2000). Against particle/field duality: Asymptotic particle states and interpolating fields in interacting R. Reece QFT, or Who’s afraid of Haag’s theorem? Erkenntnis, 53, 375–406.
LSZ reduction formula ˆ Sf i = hf |S|ii
˜ (n) ( pf , . . . , pi ) = G
Y⇣
˜ (2) (pf ) G
f
⌘
=
iM
i M (2 ⇡)
4
4
Ryan Reece (UCSC)
⇣X
pi
X
pf
⌘
Y⇣ i
⇥
=
=
1
n Y i,f
˜ (2) (pi ) G
⌘
1
!
1
Asymptotic particle states that appear in the LSZ formalism of interacting field theory are still definiable, and asymptotically related to the free fields, and form a Fock space.
,
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Field-particle duality?
Haag
proton
“Yet the belief in field-particle duality as a general principle, the idea that to each particle there is a corresponding field and to each field a corresponding particle has also been misleading and served to veil essential aspects. The role of fields is to implement the principle of locality. The number and the nature of different basic fields needed in the theory is related to the charge structure, not to the empirical spectrum of particles. In the presently favoured gauge theories the basic fields are the carriers of charges called colour and flavour but are not directly associated to observed particles like protons.” -Haag, R. (1992). Local Quantum Physics: Fields, Particles, Algebras. p. 46.
Particle states emerge from a QFT depending on the structure and strength of the couplings among its fields. But fields and particles are not dual; not one-to-one. 1. If a particle has a field in the Lagrangian, it is (effectively) fundamental. 2. If it is a boundstate of energy in multiple of such fields, it is composite. Ryan Reece (UCSC)
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Decoherence
Decoherence
ian may rotate instantaneous pointer states into erpositions. These very likely complications will gated in specific models below. Decoherence caused by a premeasurement-like rence is causedisby a premeasurement - like pro-process carried ! environment ε: #|A ed out outbybythethe environment αj |s (27) −→ j E: j #|εj # = |ΦSAE # system/apparatus/environment ! j αj |sj #|Aj #)|ε0 # |ΨSA #|ε0 # = (
Eq. (4.1
j
!to einselection when the states of the oherence leads Eq. (4.18), this tran αj |sj #|Aj #|εj # = |ΦSAE # (27) −→ ronment |εj # corresponding to different pointer states j ! meDecoherence orthogonal: ρP leads to einselection when the states of the SA =
ecoherence leads|εj⟩to corresponding einselection when the states of thestates environment to different pointer vironment |εj # corresponding pointer states (4.19) become orthogonal: $εi |εj #to=different δij come orthogonal:
!
−→ Einselec i
shows how a quantum system interacting n the SchmidtDecoherence decomposition of the state vector $ε |ε # = δ (4.19) i j ij with an environment with many degrees of freedom rapidly Einselection is acco subsystem SA and E yields AE # into a composite moves from being in a pure quantum state—in general a hen the Schmidt decomposition of of thethe state vector duct states |sj #|A orthogonal envi- ∆H(ρ coherent superposition—to being in an incoherent mixture j # as partners )= SAby and subsystem SA and E yields SAE # into a composite of these states, the appearance of describing collapse! ment states. The decohered density matrix measure oduct states |sj #|Aj # as partners of the orthogonal enviand by the disappe Zurek pair is then diagonal in product states: For simplicity W.H. (2003). Decoherence, quantum origins of the nment states. The Zurek, decohered density matrixeinselection, describingand themeasured ence the1 (Zurek, classical. Mod. Phys. 715.For http://arxiv.org/abs/quant-ph/0105127 Ryan Reece 31 hall often reference to75,the object that A pair is (UCSC) thendiscard diagonal in Rev. product states: simplicity
Pointers einselection
+1 0 -1
pointer
“in physics the only observations we must consider are position observations, if only the positions of instrument pointers.”
Bell Ryan Reece (UCSC)
-Bell, J. (1982). On the Impossible Pilot Wave. Foundations of Physics, 12, 989. 32
QM of everything Zurek
Lipid bilayer
“[Quantum mechanics] has been nevertheless convincingly verified in experiments stimulated by the EPR paradox. Furthermore, if one denies any special role to consciousness, there is seemingly nothing that could keep one from describing an arbitrary system, no matter how large, by a state vector and Schrödinger equation. After all, there is nothing in the laws of physics that would make quantum mechanics applicable to a few-body system but render it invalid for a truly many-body system, even if it contains 1025 or more atoms as long as it remains isolated.” -Zurek, W. (1981). Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? Phys.Rev. D, 24, 1516.
Even the largest systems are, in principle, quantum systems.
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Minimal QM (+Decoherence) → ≈Everett
Schlosshauer
“Decoherence adherents have i typically µ been inclined towards ˆ µ P x µ ˆ U trans ( x ) = epresumably because the Everett relative-state interpretations a pproach ta kes unita ry qua ntum mecha nics essentially “as is” with a minimum of added interpretive elements. This matches well the spirit of the decoherence program, which attempts to explain the emergence of classicality purely from the formalism ofµn basic quantum mechanics. 1 ˆ µn i M q µn ˆ 2 It mayUalso (q natural ) = to e identify the decohering components of rotseem the wave function with different Everett branches.”
-Schlosshauer, M. (2004). Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev.Mod.Phys., 76, 1267–1305.
Uˆ (t ) = e
ment
i Hˆ t
Decoherence, having fully unitary evolution, makes no-collapse interpretations of QM very tennable. on and differentiate from Stone’s theorem.
Ryan Reece (UCSC)
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Emergence of particles
Wallace
Wallace argues that particles in QFT may be thought of as emergent in a way analogous to how quantized phonon quasiparticles emerge from the dynamics of an underlying crystaline latice.
phonon modes of excitation
Wallace, D. (2001). Emergence of particles from bosonic quantum field theory. Ryan Reece (UCSC)
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Decoherence → particles “All particle aspects observed in measurements of quantum fields (like spots on a plate, tracks in a bubble chamber, or clicks of a counter) can be understood by taking into account this decoherence of the relevant local (i.e., subsystem) density matrix.”
Zeh
-Zeh, H. (1993). There are no quantum jumps, nor are there particles! Phys.Lett.A, 172, 189.
“In a universal quantum field theory, spatial fields (rather than particle positions) do not only form the fundamental configuration” space on which the wave function(al) is defined as a general superposition. Time-dependent quantum states may also describe apparently discontinuous “events” by means of a smooth but rapid process of decoherence.” Ryan Reece (UCSC)
-Zeh, H. (2003). There is no “first” quantization. Phys.Lett. A, 309, 329–334.
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Fundamental particles? “so decoherence alone does not necessarily make Bohm’s particle concept superfluous. But it suggests that the postulate of particles as fundamental entities could be unnecessary, and taken together with the difficulties in reconciling such a particle theory with a relativistic quantum field theory, Bohm’s a priori assumption of particles at a fundamental level of the theory appears seriously challenged.”
Schlosshauer
-Schlosshauer, M. (2004). Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev.Mod.Phys., 76, 1267–1305.
It is not to claim that particles do not exist, but they are reducible to emergent effects of a more fundamental field theory.
Ryan Reece (UCSC)
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Bohmian trajectories 6
A. S. Sanz, F. Borondo: A quantum trajectory description of decoherence
(b) 5
(a)
Several recent calculations make arguments supporting the plausibility that Bohmian trajectories could be Fig. 1. (a) Comparison between experiin some sense the (semi-classical) mental data (◦) and the intensity obtained from quantum trajectory (•) and SQM (full limiting case of post-decoherence. line) calculations for a double–slit experi-
Z (m)
Measured intensity
4 3 2 1
-500
-250
0 X (µm)
250
500
0 -200
-100
0 X (µm)
100
200
ment with cold neutrons [20]. (b) Sample of trajectories illustrating the dynamics of the results shown in part (a).
time τc = 2.26×10−2 s, slightly smaller than the time–of– jectories (right) are displayed. Notice that, despite null coflight. Appleby, D. M. (1999). Bohmian trajectories herence (see Figure 2(b)), the trajectories do not cross the post-decoherence. Foundations of Physics, 29, The reduced quantum trajectories were integrated ac- symmetry axis that separates the regions covered by each 1885–1916. cording to equation (18) at the same time that the par- slit, as in the case of total coherence (see Figure 2(a)). This tial waves were propagated. To obtain the statistical re- is a manifestation of the contextual character of quantum sults, about 5,420 trajectories were used in each calcu- trajectories, which remains even under these conditions. of interference prevents description the particles from of decoherence. lation Sanz, shown below, them in spaceF.intervals of The A.S.,binning & Borondo, (2007). A absence quantum trajectory 20 µm, which coincides with the experimental scanning undergoing the typical “wiggling” motion that leads to TheEuropean Physical Journal D, 44, 319–326. the different diffraction channels [14], but not from beslit width [20]. These trajectories were initially distributed according to the probability density ρ(0) , thus ensuring the ing non–locally correlated with particles coming from the other slit. Thus, within the approach proposed here we agreement with SQM calculations through equation (3). can see that decoherence leads to a suppression of quanRomano, D. (2016). Bohmian Classical Limit in Bounded Regions. http://arxiv.org/abs/ tum interference, but not to loss of memory on the initial 1603.03060 context information (i.e., the existence of two slits). This 3.2 Numerical results is somehow similar to what happens in BM when trying In Figure 1(a) the results obtained from the statistics of to reach the classical limit without appealing to any decotrajectories (•) are plotted together with the experimental herence mechanism [32]; classical–like statistical patterns values (◦). Also to compare, we have included the results emerge, but contextuality does not disappear.
Ryan Reece (UCSC)
from SQM (solid line), as given by equation (15). The ex-
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Reductionism coarse-graining, approximation, emergence of ontologies
causation
renormalization
classical mechanics
fine-graining, reduction, completion of ontologies
decoherence nonrelativistic quantum mechanics
≈Bohmian trajectories?
nonrelativistic regime
(effective) quantum field theory ? the bottom of physics (if it exists)?
≈Everettian universal quantum mechanics what ontology?
Is Bohmian mechanics an emergent nonrelativistic property of an underlying effective field theory obeying universal quantum mechanics? adapted from my figure here: http://philosophy-in-figures.tumblr.com/post/93712656521/reductionism Ryan Reece (UCSC)
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Summary • Reviewed orthodox quantum mechanics • Emphasized a symmetry-first approach, with Wigner’s theorem as a cornerstone. • Particle states are definable through canonical quantization of fields once, without 2nd quantization. Multi-particle states and wave functions, and their properties from NRQM, can be seen as derivative from the low-energy regime of QFT. • QFT can be made relativistic by construction by respecting the Poincaré group. Extending to additional symmetries in SUSY and GUTs is natural. • Despite the concerns of Malament/Haag/others about defining consistent particle states in interacting relativistic QFT, asymptotic particle states through the LSZ formalism are definable and enable the remarkably precise and experimentally verified predictions of scattering theory. But they are not fundamental; they are asymptotic approximations! • Decoherence naturally produces particle-like states through interactions of a system with the environment. • Perhaps there is a unified view, semi-Everettian/Bohmian, giving Bohmian trajectories as the NR classical limit. Ryan Reece (UCSC)
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Back up slides
Against Bohr’s classical-quantum duality “As it is well known, Bohr has repeatedly insisted on the fundamental role of classical concepts. The experimental evidence for superpositions of macroscopically distinct states on increasingly large length scales counters such a dictum. Superpositions appear to be novel and individually existing states, often without any classical counterparts. Only the physical interactions between systems then determine a particular decomposition into classical states from the view of each particular system. Thus classical concepts are to be understood as locally emergent in a Schlosshauer relative-state sense and should no longer claim a fundamental role in the physical theory.” -Schlosshauer, M. (2006). Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics. Annals of Physics, 321, 112–149.
The classical world emerges through decoherence, not an ill-defined measurement bridge between a quantum-classical dualism. Everything is always quantum. Ryan Reece (UCSC)
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Particle Physics Fundamental questions of particle physics: 1. What is matter? 2. How does it interact? Four fundamental forces at low energies: 1. Gravity 2. Electromagnetism 3. Strong force 4. Weak force Ryan Reece (UCSC)
- very weak, no complete quantum theory - binds atoms, chemistry - nuclear range, binds nuclei - nuclear range, radioactivity, solar fusion 43
The Standard Model 2. The theoretical situation
• In QFT, fields are actually what is fundamental, and particles are quantized and often localized excitations in the fields.
field content of the SM
• Gauge symmetries determine the character of the forces between fermion fields through exchanging gauge bosons.
• Bosons and chiral fermions develop mass terms that still preserve the gauge symmetries of the Lagrangian through the Higgs mechanism.
• The SM gauge group is
}
SU(3)C × SU(2)L × U(1)Y Electroweak force
Strong force
expectation value
702
〈𝜙〉
The gauge symmetry determines the gauge boson fields of the theory. Combining
Higgs mechanism, given Dirac fields describing the fermions determines the allowed interaction terms by using gauge-covariant EW symmetry breakingderivatives. In this way, the structure of the gauge sym 703 704
Electromagnetic + weak forces2.3 The Standard Model 705
Ryan Reece (UCSC)
Figure 2.2: The Standard Model.vacuum TODO. V(𝜙) Higgs potential
706
specifies the structure of its interactions.
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Unanswered problems in particle physics µ2 ⇡ (126 GeV)2/2 ⇡ 0.13
mH ⇡ 126 GeV
• Ad hoc features
neutrinos
Why SU(3)xSU(2)xU(1) ?
‣
Neutrino mixing and masses (Dirac or Majorana)
‣
Matter-antimatter asymmetry
‣
Strong CP-problem
u
GeV
MeV
keV
eV
meV
Two-loop renormalization group evolution of the inverse 1 (Q) in the Stangauge couplings ↵ a ‣ mHiggs vs mPlanck, dard Model (dashed lines) and the MSSM 10 (solid lines). 10 In9 the MSSM 5, leptons: ‣ quark masses range: case, the sparticle masses are treated a common threshold varied beFine-tuning: as tween 500 GeV and 1.5 TeV, and ↵3 (mZ ) is varied between 0.117 and problem, vacuum stability, etc. ‣ EW-scale, flatness 0.121.
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SM
49
40 SU(2) -1
α 30 20
Supersymmetry
10 SU(3) 0 2
• Why did the early universe have such low entropy? Ryan Reece (UCSC)
τ
LEP (1991)
U(1)
5% SM, 27% dark matter, 68% dark energy
• Unification? Supersymmetry?
µ
t
Figure 5: Mass range of the SM fermions (Murayama, H. 2011). For approximate va 60Table 6. masses, see
Figure 6.8: • Hierarchy problem(s)
•
b c
e
2. The theoretical situation
• Dark matter and dark energy ‣
s
TeV
‣
d
4
6
8
10
12
Log10(Q/GeV)
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Figure 2.11: TODO [195].
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18 45
Naturalness or multiverse? as
1037
where both
+
0 are complex numbers. The potential of the Higg andCERN-PH-TH/2012–134 RM3-TH/12-9
1038
V( )=µ
Higgs mass and vacuum stability in the Standard Model at NNLO
180
2
†
†
+
2
.
Gian F. Giudiced , Gino Isidorid,e , Alessandro Strumiag,h
maximum at
Pole top mass Mt in GeV
λ0 the1042TeVgives scale,degenerate then the most minima with 165115 120 125 130 Abstract important question will be to Higgs mass M in GeV 2 EW We present theconsistent first complete next-to-next-to-leading order analysis see if a and natural (in the technical sense) explanation of µ † 2 + 2 0 2 of the Standard Model Higgs potential. We computed the two-loop = | | = | | + | | = . QCD and Yukawa corrections to the relation between the Higgs breaking emerges from experimental data. But if the LHC discovers that 2 quartic coupling ( ) and the Higgs mass (M ), reducing the theoretical uncertainty the determination of theaccompanied critical value of M the Higgs boson is not by any new physics, then it will be 82in Goldstone al.Planck (1962). for vacuum stability to 1 GeV. While et at the scale is remarkably close to83 zero, absolute of the Higgs potential is much harder for stability theorists to unveil the underlying organizing principles Schwinger (1962). Anderson (1963). excluded at 98% C.L. for M < 126 GeV. Possible consequences of 84 the near vanishing ofThe at themultiverse, Planck scale,Brout includingalthough speculations of nature. being a stimulating physical concept, Englert and (1964). about the role of 85 the Higgs field during inflation, are discussed. Higgs (1964b,a). is discouragingly difficult to test from an empirical point of view. The 86 Guralnik et Higgs al. (1964). measurement of the mass may provide a precious handle to gather 87 Glashow (1961). some indirect information.” 88 Weinberg (1967). (d) CERN, Theory Division, CH–1211 Geneva 23, Switzerland
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(h) National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
Instability
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0
135
M
-st eta
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Stability
0
h
lity
abi
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Non-perturbativity
(e) INFN, Laboratori Nazionali di Frascati, Via E. Fermi 40, Frascati, Italy (g) Dipartimento di Fisica, Universit`a di Pisa and INFN Sez. Pisa, Pisa, Italy
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Top mass Mt in GeV
(c) ICREA, Instituci`o Catalana de Recerca i Estudis Avan¸cats, Barcelona, Spain
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100
150
200
Higgs mass Mh in GeV
h
h
h
Ryan Reece (UCSC) 89
Salam and Ward (1964b,a); Salam (1968).
[arxiv: 1205.6497]
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Gauge invariance is deep! Why do gauge theories work?
local U(1) phase
Internal gauge space Spacetime • Loyalty to the gauge principle motivated the Higgs mechanism. • Some have described gauge freedom as a “redundancy of description”. • But it is also a symmetry, similar to spatial rotations but in the internal space of the field. • Can be rotated locally, independently at every spacetime point. • What does it mean for the laws of nature to be describable by the continuous symmetries of Lie groups? • What does it mean that the state of the universe can be represented as an element of a complex vector space, a Hilbert space? Ryan Reece (UCSC)
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Real Patterns + J/ψ→e e
What is an electron?
candidate event e
• An excitation in a Dirac spinor field representation of SU(2)xU(1), the “Platonic electron”.
• A software object with a reconstructed track and n o calorimeter deposit, passing some r t i s selection cuts, the “pragmatist po electron”. The ATLAS Collaboration: Electron performance measurements with the ATLAS detector J/ψ m = 3.2 GeV 2000 • A set of voltages and timings 1800 ATLAS Data 2010, s=7 TeV, ∫Ldt ≈40 pb read-out from the detector, 1600 1400 the “Ramsified electron”. 1200 Events / 0.075 GeV
ele
ctr on
+ e
-1
1000 800 600 400
µ = 3080±2 MeV data µ = 3083±1 MeV MC σdata = 132±2 MeV σMC = 134±1 MeV
Data Fit J/ ψ→ee MC Background from fit
200 0 1
Ryan Reece (UCSC)
➡ Reality has a hierarchy of onion layers, but it has real patterns (Dennett 1991).
J/ψ
background 1.5
2
2.5
3
3.5 4 mee [GeV]
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Knowledge = JTB-G propositions well-formed
ill-formed no nse
good guesses
true
Gettier cases
nse
beliefs
knowledge
false
justified denial
false positives lucky denial
Ryan Reece (UCSC)
(CC-BY 4.0) 2014 Ryan Reece philosophy-in-figures.tumblr.com
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philosophy of science internal entity realism Pythagoras realism Devitt Hacking Putnam Tegmark Russell ESR Popper MUH ce n e Ladyman d n o French OSR sp
co
rre
Psillos
Maudlin Dennett Rosenberg Sellars Worrall Boyd
Quine
pessimistic meta-induction
Pragmatism Peirce Carnap
coh ere
Kuhn
Positivism
NOA
realism
Votsis
Cartwright Poincaré
nc e
anti-realism
Duhem Feyerabend Laudan Dewey van underdetermination Fraassen Fine
Naive Realism
Structural Realism
Instrumentalism
The world I see is real. What are you all arguing about?
Science has identified real patterns, relationships, and structures (at least within a regime) in nature.
Theoretical concepts may have use in predicting observations, but we have no ontological commitments to them.
Scientific Realism
Science makes real progress in describing real features of the world.
Constructive Empiricism
Relativism
Science aims to give us theories which are empirically adequate, but does not justify metaphysical claims about reality.
Social constructivism. Epistemological anarchism.
(CC-BY 4.0) 2014 Ryan Reece philosophy-in-figures.tumblr.com
metaphysically am b it
io u s
Ryan Reece (UCSC)
ap o
lo g etic
co n co n elim ser str ina uct vat tive ivis ive t
d ef ea t
ist
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