廣義相對論課堂一課件

廣義相對論課堂17不變性原理、相對論電磁學(xué)、1Einstein等效原理決定度規(guī)理論2012.11.13NATURE

PHYSICS

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LETTER2Quantum

non-locality

basedonfinite-speed

causal

influencesleads

to

superluminalsignallingJ-D.Bancal,S.Pironio,A.Acín,Y-C.

Liang,V.Scarani

&

N.

GisinWe

derive

our

results

assuming

that

the

speed

of

causal

influences

v

isdefined

with

respect

to

aprivileged

reference

frame

(or

a

particular

foliationof

spacetime

intospace-like

hyperplanes).

It

should

be

stressed

thatalthough

the

assumption

of

a

privileged

frame

is

not

in

line

with

the

spirit

ofrelativity,

there

is

also

no

empirical

evidence

implying

its

absence.

In

fact,even

in

a

perfectly

Lorentz-invariant

theory,

there

can

be

naturalpreferredframes

owingtothenon-Lorentz-invariantdistributionofmatter—awell-known

example

of

this

is

the

reference

frame

in

which

the

cosmic

microwave

background

radiation

seems

to

be

isotropic

(see,

for

example,ref.

17).

Moreover,

note

that

there

do

exist

physical

theories

that

assume

aprivileged

reference

frame

and

are

compatible

with

all

observed

data,

suchas

Bohmian

mechanics18,

19,

the

collapse

theory

of

Ghirardi,

Rimini

andWeber20

and

its

relativistic

generalization21.

Although

both

of

these

theories

reproduce

all

tested

(non-relativistic)

quantum

predictions,

theyviolate

the

principle

of

continuity

mentioned

above

(otherwise

they

wouldnotbe

compatible

with

no-signalling

as

our

result

implies).3不變性原理4以廣義坐標(biāo)變換為例Kretchmann

1917方程協(xié)變covariant5形式不變covariance（Galileo、Lorentz、廣義）協(xié)變性原理無約束6物理上

實(shí)驗(yàn)結(jié)果7動力學(xué)量=幾何體方程不變invariance不但形式而且內(nèi)容絕對體～常數(shù)純粹數(shù)學(xué)常數(shù)、物理學(xué)常數(shù)函數(shù)（坐標(biāo)變換函數(shù)、Jacobian）分量（閔氏度規(guī)）動力學(xué)體——物理變量——依賴物質(zhì)狀態(tài)（條件）：粒子位置、動量、場強(qiáng)、能量密度......8例牛一律：V=常數(shù)？a=0進(jìn)化到狹義相對論第一定律詰問Rosser第434頁——定律和具體運(yùn)動方程Rahilly

三維空間中光線球面——橢球面例Galilei

徑向自由下落vs拋物9維基百科10The

relationship

between

general

covarianceand

general

relativity

may

be

summarized

byquoting

a

standard

textbook:[2]–

Mathematics

was

not

sufficiently

refined

in

1917

tocleave

apart

the

demands

for

"no

prior

geometry"

andfor

a

geometric,

coordinate-independentformulationof

physics.

Einstein

described

both

demands

by

asingle

phrase,

"general

covariance."

The

"no

priorgeometry"

demand

actually

fathered

general

relativity,but

by

doing

so

anonymously,

disguised

as

"generalcovariance",

it

also

fathered

half

a

century

ofconfusion.The

essential

idea

is

that

coordinates

donot

exist

a

priori

in

nature,

but

are

onlyartifices

used

in

describing

nature,

andhence

should

play

no

role

in

theformulation

of

fundamental

physical

laws.類似AB

effect——potential11動力學(xué)方程12不變性原理決定共動系中：四力、四動量、固有時(shí)四力的時(shí)間分量是共動系LB到實(shí)驗(yàn)室系13EEP決定度規(guī)理論14Einstein

Equivalence

Principle=EEP15WEPLLI=Local

Lorentz

InvarianceLPI=Local

Position

InvarianceWEP

The

trajectory

of

a

pointmass

in

agravitationalfield

depends

only

on

its

initial

positionandvelocity,

and

is

independent

of

its

composition.–運(yùn)動學(xué)——力學(xué)——》其他物理LLI–點(diǎn)質(zhì)量——SEP–FFF——preferred——對應(yīng)原理LIF16LLI=Local

Lorentz

InvarianceThe

outcome

of

any

local

non-gravitational

experiment

is

independent

ofthe

velocity

of

the

freely-falling

referenceframe

in

which

it

isperformed.local非引力=失重自由下落——FFFSEP例：電磁——精細(xì)結(jié)構(gòu)常數(shù)測量速度——相對性原理SR17LPI=Local

Position

InvarianceThe

outcome

of

any

localnon-gravitational

experiment

is

independentof

where

and

when

in

the

universe

it

isperformed.局域非引力同LLI——EEP

vs

SEP何地——引力紅移實(shí)驗(yàn)GRE何時(shí)——物理學(xué)常數(shù)上兩者合起來——時(shí)空posit