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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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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