01. Pre-20th Century Physics Topics 1.Aristotelian Physics 1 ...faculty.poly.edu/~jbain/philrel/philrellectures/01.Pre20...1.Aristotelian Physics 2.Newton's Theory of Motion 3.Maxwell's

1.AristotelianPhysics 4thcenturyB.C.- 17thcentury

Aristotle'sTheoryofMotionI. Nomotionwithoutamoverincontactwithmovingbody.II. Distinctionbetween:

(a) Naturalmotion: moverisinternal tomovingbody(b) Forcedmotion: moverisexternal tomovingbody

3TypesofNaturalMotion(i) Instraightline towardscenterofthecosmos: earth,water(ii) Instraightline awayfromcenterofthecosmos: fire,air(iii) Incircle aboutcenterofthecosmos: aether

01.Pre-20thCenturyPhysics Topics:1. AristotelianPhysics2. Newton'sTheoryofMotion3. Maxwell'sElectrodynamics

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TheCelestialRealm(betweenthesphereofthemoonandthesphereofthefixedstars).

Eachdottedcirclereallyrepresentsasetofnestedspheres...

Thespheresofthesunandplanets.Inorder:MoonSunVenusMercuryMarsJupiterSaturnfixedstars

Aether

Fire,Air,Water,Earth

TheTerestrialRealm(insidethesphereofthemoon).

2

Earth

planet

3

Earth

4

Earth

5

Earth

6

Earth

7

Earth

8

Earth

9

Earth

• Explainsretrogrademotion.

• Aristotlerequiresadditionalspherestocounteractsomeofthemotionsoftheplanetaryspheres.- Theseadditionalspheresareplacedbetweentheoutermostsphereofagivenplanetandtheinnermostsphereofthenextplanetandareonelessthanthenumberofspheresofthelatter.

Howmanyspheres?Eudoxus Callippus Aristotle

Moon 3 5 5Sun 3 5 5+ 4Venus 4 5 5+ 4Mercury 4 5 5+ 4Mars 4 5 5+ 4Jupiter 4 4 4+ 3Saturn 4 4 4+ 3fixedstars 1 1 1

27 34 56

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2.Newton'sTheoryofMotion MathematicalPrinciplesofNaturalPhilosophy(1686)

3LawsofMotion

• Describes naturalmotion ("kinematics")forNewton:uniformmotion(restorconstantvelocity)inastraightline.- ReferredtoasThePrincipleofInertia.- inertia =tendancyinanobjecttoobeyLawI.- inertialmotion =restorconstantvelocityinastraightline.

LawI. Everybodycontinuesinitsstateofrest,orofuniformmotioninarightline,unlessitiscompelledtochangethatstatebyforcesimpresseduponit.

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• Describes forcedmotion ("dynamics")forNewton.- acceleratedmotion = non-uniformmotion(non-constantvelocity).- inertialmass =m=measureofamountofinertia.

LawII.Thechangeofmotionisproportionaltothemotiveforceimpressed;andismadeinthedirectionoftherightlineinwhichthatforceisimpressed.

LawIII.Toeveryactionthereisalwaysopposedanequalreaction;or,themutualactionsoftwobodiesuponeachotherarealwaysequal,anddirectedtocontraryparts,andtakesplaceinthedirectionofthestraightlinealongwhichtheforceisimpressed.

OR: Theforceneededtoaccelerateanobjectisproportionaltotheacceleration. 𝐹 = 𝑚𝑎 = 𝑚

𝑑!𝑥𝑑𝑡!

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NewtonianRelativityPrinciple

Thelawsofmotionarethesameinallinertialreferenceframes

Whatthismeans:

• InertialreferenceframescannotbedistinguishedbyNewton'slawsofmotion.• Anyexperimentinvolvingmovingobjectsperformedinoneinertialreferenceframewillproducethesameresults asinany otherinertialreferenceframe:

Ex:Throwaballstraightupinsideaconstantlymovingtraincar.- Whathappens?

• Howareinertialframesrelated,accordingtotheNewtonianRelativityPrinciple?- NeedtodeterminethecoordinatetransformationsthatleaveNewton'sLawsofMotionthesame(i.e.,"invariant").

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WhatthismeansmathematicallyIfyousubstitutex' forx andt' fort inthe2ndLaw,youdon'taffectitsform.

GalileanTransformationsx↦ x' = Rx − v0t + x0t↦ t' = t + t0

R = (componentsof)3×3rotationmatrixv0,x0,t0= constants

• Thesearethe"symmetries"ofNewton's2ndLawF =ma =md2x/dt2.

WhatthismeansphysicallyIfyourlabisinitiallyinaninertialframeatrest,thenanyorallofthefollowingwillhavenoaffectonexperimentswithmovingobjectsgovernedbyNewton'sLaws:(a) Rotatingit(byR).(b) Puttingitintouniformmotion(atspeedv0).(c) Movingitadistanceinspace(byamountx0).(d) Waitingagivenamountoftime(t0).

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labatrest

x

t

15

x

t

rotatedlabatrest

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labinconstantvelocity

x

t

v0

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labatrest

x

t

x0

translatedlabatrest

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labatresttomorrowattimet0

x

t

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• Restlabandrotated,spatially/temporallytranslated,movinglabareindistinguishableaccordingtoNewton'sLawsofMotion!

labatrest

x

t

x0

v0

rotated,"boosted",translatedlabatanytimet'

x'

t'

ConsequencesofNewtonianRelativityPrinciple:(1) Velocityisrelative!(Nopreferred,absolutevelocitiesinnature.)(2) Positionisrelative!(Noabsolutepositionsinnature.)(3) Orientationisrelative!(Noabsolutedirectionsinnature.)(4) Accelerationisabsolute!(Anygivenobjecthasauniquevalueof

acceleration.)

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Example: Allvelocitiesarerelativetoaninertialframeofreference.

Suppose:InA'srestframe,(a) vA = 0m/s.(b) vB = 50m/s.(c) vC = 100m/s.

A

B

C

Then:InB'srestframe,(a) vA = −50m/s.(b) vB = 0m/s.(c) vC = 50m/s.

A

B

C

And:InC'srestframe,(a) vA = −100m/s.(b) vB = −50m/s.(c) vC = 0m/s.

A

B

C

• Newton'sLawsofmotioncannotdistinguishbetweenthe(inertial)restframesofA,B andC.

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But: Accelerationisnotrelativetoinertialreferenceframes.

• Newton'sLawsofmotioncan distinguishbetweentherestframesofA andB.• Therestframethatexperiencesinertialforces istheframeundergoingacceleration(inthiscase,B).

Suppose:Bfiresit'senginesandaccelerates.InA'srestframe,Bisacceleratingtoright.

A

B

Then:InB'srestframe,Aappearstobeacceleratingtoleft...But:

A

B

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Newton's TheoryofGravityParticulartypeofforcedmotion(whenforceisduetogravity).

• Thisisauniversalforce -- actsonallobjects(inexactlythesameway).- ItthusunitesAristotles'terrestrialandcelestialrealms(the"NewtonianSynthesis").

Einstein'sAccomplishments

- ModificationofNewton's3LawsofMotion ⇒ SpecialRelativity- IncorporationofgravityintoSpecialRelativity ⇒ GeneralRelativity

F = forceofgravityonobjectofmassm duetoobjectofmassMr = distancebetweenm andMG = constantofnature(Newtoniangravitationalconstant)

𝐹 =𝐺𝑀𝑚𝑟-

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• Describemotionofelectromagneticwaves propagatingwithspeedc = 3×108m/s = 186,000mi/s

• EMwave:Producedbyanoscillatingchargedobject.

• 1860s:Aether =supposedmediumthroughwhichEMwavespropagate.

3.Maxwell'sElectrodynamics ATreatiseonElectricityandMagnetism(1873)Newtoniandynamics = theoryofmotionforunchargedmassiveobjects.Maxwell'selectrodynamics = theoryofmotionforelectricallychargedmassiveobjects(i.e.,movingelectrons).

Maxwell'sEquations(Maxwell'sLawsofMotion)

∇ ( 𝐸 = 4𝜋𝜌 ∇×𝐸 =1𝑐𝜕𝐵𝜕𝑡

∇ ( 𝐵 = 0 ∇×𝐵 =1𝑐𝜕𝐸𝜕𝑡 +

4𝜋𝐽𝑐

𝐸 = electric 5ield𝐵 = magnetic 5ield𝜌 = charge density𝐽 = 𝜌�⃗� = current density

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MathematicalExercise

• RestlabandLorentz-transformedlabareindistinguishableaccordingtoMaxwell'sLaws!

• But:Justhowexactlyaretheyrelatedtoeachotherphysically?(Storytocome!)

• Maxwell'sEquationsarenot invariantunderGalileantransformations!- WhattransformationsleaveMaxwell'sEquationsinvariant?

labatrest

x

t

• •

Lorentztransformedlab

v0

x'

t'

••

LorentzTransformationsx↦ x' = γ0(x − v0t)

Keyfeature: cisaconstantinallframesrelatedbyLorentztransformations.

• Answer (providedbyLorentz,Poincaré,andotherspriorto1905):

𝑡 ↦ 𝑡" = 𝛾# 𝑡 −𝑣#𝑥𝑐!

𝛾# =1

1 − $!"

%"

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Einstein'sInsight:Twotheorieswithdifferentsymmetries!- Thisisamessystateofaffairs!- SomethingMustbedone!

Stateofphysicsatbeginningof20thcentury:

(1) DeterminingspeedofEarththroughtheaether.Allexperimentsseemtoindicatezerospeed.

(2) Describingblack-bodyradiation-- peculiartypeofheatradiation.Alltheoreticaldescriptionsseemincoherent.

Cloud#1leadsto"RelativityRevolution":Specialandgeneralrelativity.Cloud#2leadsto"QuantumRevolution":Quantummechanics.

Claim:Newton+Maxwell= TheoryofEverything!*

*LecturedeliveredattheRoyalInstitutionofGreatBritianbyWilliamThomson,LordKelvin(1824-1907)

• TheEndofPhysics!• Only2"clouds"..."meretechnicalities":

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