Transcript How to Test?

Experimental Tests of
Continuous Symmetries
Gerco Onderwater
KVI/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
of
(1) time translation
(2) space translation
(3) rotation
(?) boost
Conservation
energy
momentum
angular momentum
Lorentz generators
How to Test?
Two possibilities:
(1) Test that a process is the same when occuring
here 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
&
Energy 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 Energy
A complete test of energy conservation would require the
demonstration that each of the kinds of energy below are
equivalent
nuclear
potential
electric
kinetic
mass
thermal
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
Classical experiment to show
equivalence of 3 types of energy
gravity – kinetic - thermal
[Philos. trans. Royal Soc. London, 140, pp. 61-82 (1840)]
Photoelectric Effect
Emission of electrons under illumination. The
electron kinetic energy increases with decreasing
photon wavelength, the rate with intensity.
Demonstrates equivalence of
quantum and kinetic energy
Classic Laws
Other observation-based laws, effects and
relations that support continuous symmetries
Bernouilli
Ampere
Charles
Gauss
Lenz
Newton
Rayleigh-Jeans
Volt
Biot-Savart
Curie-Weiss
Joule
Mach
Wien
Snell
and probably some ...
Ohm
Kirchhoff
Coulomb
Bragg
Doppler
Faraday
Keppler
Le Chatelier
Maxwell
Meissner
Planck
Kelvin
Stefan-Boltzmann
HW
Watt Balance
d
dz 

U 

 v z
dt
dt z
z

Fz  mg   I
z
mechanical mgv
{SI }

 2
electrical
UI {V / }
V  nf / K J
  RK / i
K J2 RK  (2e / h) 2 (h / e 2 )  4 / h
Electrical standard of kg
Change SI to QM standard
Josephson Voltage Standard
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.
Quantum Hall resistance standard
RH  h / ie
2
Quantum Hall Array Standard
(QHARS)
1cm  1cm
100  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 Invariance
Search for time variation of reaction rate
Weak Interaction
Oklo natural reactor: |ĠF/GF|<1x10-11/year
EM Interaction
Quasar H spectra: a/a = -(0.7±0.2)×10-5 for 0.5<z<3.5
Proton/electron mass: m/m = (2.0±0.6)x10-5 / 12 Gyr
Strong Interaction
mRb/mCs = -(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 Et≥ħ
Does this mean energy conservation may be
violated (briefly)?
HW: wrong question
(2) Spatial Invariance
&
Momentum Conservation
What is Momentum?
Momentum can be though of as the tendency of
an object to continue in its direction of travel
Classically: p = mv
Relativistic: p = gmv
Massless:
p = E/c = h/l
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 carry
energy and momentum
l2 = h/mec ( 1-cosq ) + l1
+
e e
Ps →1g : Eg=2me
Ps →2g : Eg=me
→ 2g
pg=Eg/c ≠ pPs=0
pg1+pg2=0
FORBIDDEN
ALLOWED
Collinearity = (relativistic four) momentum conservation
Phys. Rev. 77, 205–212 (1950)
(3) Rotation Invariance
&
Angular Momentum
Conservation
What is Angular Momentum?
Angular momentum is the measure of
rotation around some fixed point in space
(also includes spin)
Classically: L = rxp
Relativistic: L = rxp
Massless:
L=S
Quantum:
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-Morley
Classic experiment to test isotropy of c
Modern version: compare flaser,xy vs time of day (2p rotation)
qc/c = (2.6±1.7)x10-15
Phys. Rev. Lett. 21, 020401 (2003)
Phys. Rev. D 67, 056006 (2003)
Isotropy of b-Decay
Measure differential decay rate and see if it
varies with orientation w.r.t. some fixed frame
(stars)
G(q) = G0 [ 1 + e1cos(q) +e2cos(2q) ]
|e1| < 1.6x10-7
Phys. Rev. D 14, 1 (1976)
|e2| < 2x10-6
Isotropy of Mass
Measure Zeeman splitting for 3He(J=½) and
21
Ne(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 weak
interaction comes from G(p→en)/G(p→mn) ~ 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)
n
m+
p+
More: absence of pseudo scalar (P) coupling in WI