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Hot Stuff Sourendu Gupta Wednesday Colloquium TIFR Mumbai October 3, 2012

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Hot Stuff Sourendu Gupta Wednesday Colloquium TIFR Mumbai October 3, 2012 Saumen Datta, Rajiv Gavai, Nikhil Karthik, Xiaofeng Luo (CCNU), Nilmani Mathur, Pushan Majumdar (IACS), Bedangadas Mohanty (NISER), M. Padmanath, Hans-Georg Ritter (LBL), Nu Xu (LBL)

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1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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A hot big bang

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The baby universe was very nearly in thermal equilibrium

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Choice of units

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k =1 c =1 =1

temperature is energy length is time, mass is energy energy is frequency

Energy is the only dimensionful quantity

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Relativity and particle production

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In thermal equilibrium particles have kinetic energy typically equal to their temperature: T . If two particles collide, their total kinetic energy is of order T . If the mass of the particles is M, and the kinetic energy in a collision is much larger (T M), then particles can be produced. So the Lorentz factor E /M T /M is much larger than 1 when particles are easily produced in a thermal medium. Maxwell, Boltzmann, Einstein

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quantum mechanics and field theory

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Quantum mechanics perfectly fine for problems with fixed number of particles. Say, spectrum of acetylcholine, information transfer through entangled states, transport in nanowires ... Quantum mechanics fails when particle Number Changes: H H + . Then need quantum field theory. Thermal matter with M T requires relativistic quantum field theory. All matter that we know of obeys the Standard Model. So standard model at finite temperature. Pauli, Dirac, Bethe (1930s) ... Weinberg (1972)

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The Discovery of the Strong Interactions

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The atomic nucleus discovered in the scattering of and particles by matter. Positively charged nucleus unstable unless there is a new force to keep it together: the strong interactions. Rutherford (1911) Half a century of discoveries of mesons and baryons. All attempts to understand strong interactions failed. Realization that the true constituents of matter were quarks and gluons. Nambu (1960); Gell-Mann, Ne'eman (1961) Forces between quarks and gluons hundred times stronger than electrodynamics; forces between nucleons is a shadow of these.

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The Discovery of the Theory of Strong Interactions

A relativistic quantum field theory of quarks developed. Initially faced technical difficulties similar to electrodynamics, but problems resolved. Theory has an intrinsic momentum scale, 200 MeV. Well tested for log(p/) 1: perturbative QCD. Gross, Wilczek, Politzer (1973) Three "flavours" of quarks: light flavours up, down (mu, md ), strange (ms ). Later three heavy flavours discovered (m ). Quarks and gluons confined, seen together only in combinations of mesons and baryons. Remained a theoretical mystery; until a radically new approach developed. Strong interactions: 30 Nobel Prizes to about 50 people

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Particle content

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Little bangs

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Recreate the conditions of the big bang in controlled experiments in a lab: relativistic collisions of heavy ions. Create a fireball which thermalizes at high temperature, then expands and cools. Size of the fireball 10 femto meters. Detectors placed 10 meters away. See only the late stages of the bang. Similar to today's telescopes looking back for traces of the big bang. Main difference: small bangs can be repeated. Statistical accuracy as high as you want. CERN SPS 1980s, BNL RHIC 2000s, CERN LHC 2010s, GSI FAIR 2020s ...

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A typical experiment

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1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science

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Post-colonial quantum field theory

xi , ti |xf , tf

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time

space

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Post-colonial quantum field theory

xi , ti |xf , tf

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time

space

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Post-colonial quantum field theory

xi , ti |xf , tf

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time

space

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Post-colonial quantum field theory

xi , ti |xf , tf

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time

space

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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space

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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space

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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space

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

time

space

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

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Post-colonial quantum field theory

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xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm

space

time Sum over all paths: path integral Dirac (1933), Feynman (1948)

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The grand synthesis

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Notice a relation between quantum evolution operator (transition matrix) and the thermal density operator exp(iHt) and exp(-H/T ), Wick rotation t it. Makes path integral real; then use Monte Carlo to do the integral. Fisher, Kadanoff; Wilson (1974), Creutz, Jacobs, Rebbi (1979)

Opens the door to the study of almost any quantity in a field theory. Applied to the study of hadron masses and widths, hadron Form Factors, decay constants, weak matrix elements, muon g - 2, rare decays of hadrons, exotics and glueballs, nucleon-nucleon scattering, nuclear structure, equation of state of neutron stars, phase transitions at finite temperature ...

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A sample result

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M[MeV]

2000 1500 1000 500 0

K p

K* r

X S L N

O X* S* D experiment width input QCD

Durr, Fodor, Katz, et al (2009)

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The sign problem

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When there are Fermions in the external states, then the integrand of the path integral is complex. Monte Carlo method fails. Examples: QCD at non-zero particle density, high temperature superconductors, · · ·

Proposed workaround, use the Maclaurin expansion:

P(µ) = P(0) +

n

µn n!

n

1 is mean particle number, 2 is a particle number susceptibility, 3, · · · are non-linear susceptibilities. Developed methods to compute the coefficients n. Gavai, SG (2002)

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The QCD critical point

1.1

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T/Tc

1

0.9

30 GeV 18 GeV (CERN SPS)

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10 GeV

Freezeout curve

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1

2

3

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µB/T

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The QCD critical point

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1.1 Critical point estimates: 1

T/Tc

0.9

30 GeV

Mumbai Nt=4

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10 GeV

Freezeout curve

0.70

1

2

3

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µB/T

Critical point for the onset of confinement and chiral symmetry breaking; note unspecified scale Tc Gavai, SG (2005, 2008), Datta, Gavai, SG (2012)

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The QCD critical point

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1.1

1

0.9

30 GeV

Critical point estimates: Mumbai Nt=6 Mumbai Nt=4

T/Tc

0.8

10 GeV

Freezeout curve

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1

2

3

4

5

µB/T

Critical point for the onset of confinement and chiral symmetry breaking; note unspecified scale Tc Gavai, SG (2005, 2008), Datta, Gavai, SG (2012)

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The QCD critical point

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1.1

1

0.9

30 GeV

Critical point estimates: Mumbai Nt=8 Mumbai Nt=6 Mumbai Nt=4

T/Tc

0.8

10 GeV

Freezeout curve

0.70

1

2

3

4

5

µB/T

Critical point for the onset of confinement and chiral symmetry breaking; note unspecified scale Tc Gavai, SG (2005, 2008), Datta, Gavai, SG (2012)

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1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science

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Relativistic Collisions of Nuclei

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At relativistic energies if two heavy nuclei (Au, Pb, etc) collide, then produced particles interact and form a dense hot fluid, which cools as it expands. The particles in the fluid are strongly interacting, matter is opaque: no knowledge of the early stages of the collision. When fluid becomes dilute then particles freeze out, and observations can be made. Fluctuations of conserved quantities possible, between one event and another. Asakawa, Heinz, Muller -- Jeon, Koch (2000)

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Thermodynamic Fluctuations

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Since there are 1028 molecules of gas in this room, the pressure, entropy, heat content, etc can be accurately determined. Limits on our knowledge are due to instrumental limitations. If the number of molecules was 106 then there would be inherent limits on the accuracy. Repeated accurate measurements would not give the same value but would reveal a distribution of values. Fluctuations give physical information. Gaussian distribution of energy; width give specific heat. Specific heat can be computed from molecular properties. Carnot (1824), ... Einstein (1905)

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Observed fluctuations

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Number of Events text STAR arxiv:1004.4959

106 Au+Au 200 GeV

105

0.4

|y|<0.5

104

103

102

0-5% 30-40% 70-80%

10

1 -20 -10 0 10 20 Net Proton (Np)

Central rapidity slice taken. Protons accepted with pT of 400800 MeV.

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Shape of distribution

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placeholder STAR: QM 2009

Shape of distribution captured in cumulants [Bn]. Cumulants change with volume (proxy: Npart ), by Central Limit Theorem.

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QCD predictions needed at finite µB

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Shape variables: [Bn] = (VT 3)T n-4n(T , µ). Ratios of cumulants are thermodynamic state variables:

m0 :

[B 2 ] [B ]

=

T 2 1

m1 :

[B 3 ] [B 2 ]

=

T 3 2

m2 :

[B 4 ] [B 2 ]

=

T 24 2

m3 :

[B 4 ] [B 3 ]

=

T 4 3

SG, 2009; Athanasiou, Rajagopal, Stephanov, 2010

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Checking the match

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S

79 140 (A) 720 420 2 m1 1.5 1 0.5 0 (B) 2 m2 1 0 -1 -2 4 5 6 10

T (MeV)

160

165

µ (MeV)

210 B

54

166 20 10

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Lattice QCD

HRG

20 30

100 200

sNN (GeV)

2

Gavai, SG (2010) -- STAR (2010)

T2 (4)/(2)

T (3)/(2)

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Tuning lattice scale to match data

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/S 2 placeholder text GLMRX (2011)

(A) 10

Lattice QCD Tc=165 MeV Tc=170 MeV Tc=175 MeV Tc=180 MeV Tc=190 MeV

5

Exp. Data

(B) Tc =175-+71 (MeV) 30

20

0

5 10 20

100 200

sNN (GeV)

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2 min

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1

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160 170 180 190 Tc (MeV)

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Conclusions

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Thermalization After 1 parameter tuning agreement of thermodynamic predictions with data for 2 ratios at 3 energies. Indicates thermalization of the fireball at freezeout. Tc Comparison of lattice and data along the freezeout curve gives Tc = 175+-71 MeV, in agreement with other scale settings on the lattice. Indicates that non-perturbative phenomena in single hadron physics and strong interaction thermodynamics are mutually consistent through QCD.

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Implications for QCD

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T=0 lattice T>0 lattice Hadron properties Bulk matter

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Implications for QCD

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step (a)

T=0 lattice T>0 lattice Hadron properties Bulk matter

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Implications for QCD

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step (b) T=0 lattice T>0 lattice

step (a)

Hadron properties Bulk matter

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Implications for QCD

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step (b) T=0 lattice T>0 lattice

step (a)

Hadron properties Bulk matter step (c)

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Implications for QCD

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step (a)

step (b) T=0 lattice T>0 lattice Tc Hadron properties Bulk matter step (c)

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Implications for QCD

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step (a)

step (b) T=0 lattice T>0 lattice Tc Hadron properties Bulk matter step (c)

step (d)

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Implications for QCD

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step (a)

step (d)

step (b) T=0 lattice T>0 lattice Tc Hadron properties Bulk matter step (c) Beginning of quantitative theory for hot relativistic matter. Extend this method to the search for the critical point of QCD.

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1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science

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The beginning of experimental sciences

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Usually attributed to Galileo, often dated to 1609, but could be a little earlier.

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The start of mathematical sciences

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Usually attributed to Newton and dated to the establishment of the inverse square law of gravity in 1686.

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The founding of Computational Sciences

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Often attributed to Alan Turing, and traced to his 1937 proof that the behaviour of computer programs is observable but not mathematically predictable.

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The computational mode is a conceptual revolution

Quantum mechanics was the first revolution of modern science. Conceptual unification of physically totally different fields: atomic spectroscopy, chemistry, Solid State Physics, etc.

Today the computational aspects of very large scale problems creates a methodological unification of lattice gauge theory with fermions, Google search and data mining, extraction of sky maps from noisy radio telescopes, atomic spectroscopy, Fluid Dynamics of nanorobots, ... Conceptual advances in one can cross fertilize other problems.

Similar methodological unification also occurring elsewhere within the computational mode of doing science.

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A pedagogical shortcoming

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Work in every area of science today involves an interplay of these three modes of science.

The science training programs developed in the 1920s and 30s still persists in Our country today with updated content but little structural change. Not a problem earlier since the founding generations of the computational mode of doing science grew up with the subject.

This is a problem because a new generation is entering the sciences now. We need to train them in the computational mode of doing science: new course work, new text books. Computatiion must be embedded into course work.

Dramatization of Tea in British Novels and Short Stories in the First Half of the Twentieth Century, 42 pages, 0.37 Mb

Have you seen that movie yet?'-A qualitative methodological research paper about the, 85 pages, 1.64 Mb

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