experimental tests of continuous symmetries gerco onderwater kvi/rijksuniversiteit groningen, the...
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Experimental Tests ofExperimental Tests ofContinuous SymmetriesContinuous Symmetries
Gerco OnderwaterGerco OnderwaterKVI/Rijksuniversiteit Groningen, The NetherlandsKVI/Rijksuniversiteit Groningen, The Netherlands
Continuous Symmetries
Are related to space and time. Translations and rotations in space, and time can take any value, hence they are continuous.
A physics law is said to be symmetric under such transformations if it does not change, i.e. the law is invariant.
Noether's Theorem
Continuous symmetry ↔ conservation law
Invariant under Conservation of
(1) time translation energy(2) space translation momentum(3) rotation angular momentum(?) boost Lorentz generators
How to Test?Two possibilities:
(1) Test that a process is the same when occuringhere and there, now and then, etc.
(2) Test the associated conservation law explicitly
Important constraint:
the trial system is isolated from external influences!
(1) Time Invariance(1) Time Invariance&&
Energy ConservationEnergy Conservation
What is Energy?
Energy can be defined as the capacity for doing work.
It may exist in a variety of forms and may be transformed from one type of energy to another.
Transformations constrained by conservation principle
One way to state this principle is "Energy can neither be created nor destroyed". Another approach is to say that the total energy of an isolated system remains constant.
E1=-E2 or E1+E2=C: this we can test!
Types of EnergyA complete test of energy conservation would require the demonstration that each of the kinds of energy below are equivalent
nuclear electric
potential kinetic thermal
mass chemical
In the end, all energy is kinetic or potential
Note that potential energy can be sub-divided according to each of the four known forces
Joule's Paddlewheel Exp't
[Philos. trans. Royal Soc. London, 140, pp. 61-82 (1840)]
Classical experiment to showequivalence of 3 types of energy
gravity – kinetic - thermal
Photoelectric EffectEmission of electrons under illumination. The electron kinetic energy increases with decreasing photon wavelength, the rate with intensity.
Demonstrates equivalence ofquantum and kinetic energy
Classic LawsOther observation-based laws, effects and relations that support continuous symmetries
Bernouilli Volt Ohm KirchhoffAmpere Biot-Savart Coulomb BraggCharles Curie-Weiss Doppler FaradayGauss Joule Keppler Le Chatelier Lenz Mach Maxwell Meissner Newton Wien Planck KelvinRayleigh-Jeans Snell Stefan-Boltzmann
and probably some ...
Watt Balance
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KnfV
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SI
UI
mgv
electrical
mechanicalz
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zv
zdt
dz
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dU
KJ
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Electrical standard of kgChange SI to QM standard
HW
When a DC voltage is applied to a Josephson junction,
an oscillation of frequency occurs at the junction.
Josephson junction standards can yield voltages with accuracies of one part in 1010. NIST has produced a chip with 19000 series junctions to measure voltages on the order of 10 volts with this accuracy.
Josephson Voltage Standard
Quantum Hall resistance standard
2/ iehRH
Quantum Hall Array Standard (QHARS)
1cm 1cm100 standard
Metrological triangle
new standard ?
Beta Decay Mystery
Beta energy expected to be mono-energetic A continuous spectrum was observed
Two explanations(1) energy non-conservation(2) new invisible particle
Did not fulfill closed system requirement
Time InvarianceSearch for time variation of reaction rate
Weak InteractionOklo natural reactor: |ĠF/GF|<1x10-11/year
EM InteractionQuasar H spectra: = -(0.7±0.2)×10-5 for 0.5<z<3.5Proton/electron mass: = (2.0±0.6)x10-5 / 12 Gyr
Strong InteractionRb/Cs = -(0.9±2.9)x10-15 /year
This will be discussed in more detail later in the course
Eur. Phys. J. A 8, 137–140 (2000) Phys. Rev. Lett. 96, 151101 (2006) Phys. Rev. Lett. 87, 091301 (2001) Phys. Rev. Lett. 92, 230802 (2004)
Energy in Quantum Mechanics
The uncertainty principle states that Et≥ħ
Does this mean energy conservation may beviolated (briefly)?
HW: wrong question
(2) Spatial Invariance(2) Spatial Invariance&&
Momentum ConservationMomentum Conservation
What is Momentum?
Momentum can be though of as the tendency ofan object to continue in its direction of travel
Classically: p = mvRelativistic: p = mvMassless: p = E/c = h/Quantum: p = -iħ
Change requires an external force
Every Day Life
Compton Effect
The increase in wavelength of a photon scattering of an electron
Demonstrates that photons carryenergy and momentum
= h/mec ( 1-cos) + 1
e+e- → 2Ps →1 : E=2me p=E/c ≠ pPs=0 FORBIDDEN
Ps →2 : E=me p+p=0 ALLOWED
Collinearity = (relativistic four) momentum conservation
Phys. Rev. 77, 205–212 (1950)
(3) Rotation Invariance(3) Rotation Invariance&&
Angular MomentumAngular MomentumConservationConservation
What is Angular Momentum?
Angular momentum is the measure of rotation around some fixed point in space(also includes spin)
Classically: L = rxpRelativistic: L = rxpMassless: L = SQuantum: L = -iħrxp
Change requires an external torque
Kepler's Second Law
A line joining a planet and its star sweeps out equal areas during equal intervals of time
Tested in solar system observations
Michelson-MorleyClassic experiment to test isotropy of c
Modern version: compare flaser,xy vs time of day (2 rotation)
c/c = (2.6±1.7)x10-15
Phys. Rev. Lett. 21, 020401 (2003)Phys. Rev. D 67, 056006 (2003)
Isotropy of -DecayMeasure differential decay rate and see if it varies with orientation w.r.t. some fixed frame (stars)
() = [ 1 + 1cos() +2cos(2) ]
< 1.6x10-7 < 2x10-6
Phys. Rev. D 14, 1 (1976)
Isotropy of MassMeasure Zeeman splitting for 3He(J=½) and 21Ne(J=3/2) (Hughes-Drever experiments)
Search for orientation-dependent binding energy = inertial mass
Lowest order: quadrupole splitting(so 3He is not sensitive)
|E/E| < 1.6x10-26
Phys. Rev. Lett. 14, 1541 (1989)Phys. Rev. Lett. 64, 2261 (1990)
Pion Decay
Best limit of angular momentum conservation in weakinteraction comes from (→e)/(→) ~ 10-4
The small factor is “unexpected” in view of (giant) phase for electron decay, but…Axial vector delivers wrong helicity (need l=1 for angular momentum conservation)
More: absence of pseudo scalar (P) coupling in WI
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