American International J ournal of Contem porar y Research
Vol. 4, No. 10; Octoer !014
The Fallacy Regarding Newton’s First Law: Its Non Axiomatic
Nature
Luis E. Acevedo !me"# $. %. University of Puerto R ico ico Faculty of General Studie udiess Department of Physical Scien ciences ces Río Piedras Campus San Juan, Puerto R ico ico
A&stract "his paper in#esti$ates if Ne%ton&s first la% of inertia fulfills the re'uirements in or(er to e consi(ere( as an a)iom of Ne%tonian mechanics as presente( in the *rincipia. "he fact that it (oes not fulfill its alle$e( purpose of pro#i(in$ an error+free error+free %ay of empirically empirically i(entifyin$ i(entifyin$ inertial inertial reference reference frames, its inaility inaility to pro#i(e pro#i(e a((itional information apart from that %hich is alrea(y pro#i(e( y the secon( la% alone an(, the fact that it may e (e(uce( from the secon( la% lo$ically (is'ualifies (is'ualifies it as an a)iom of Ne%tonian mechanics. mechanics. refere nce frame, fictitious 'eywords: e!ton"s la!s, a#iom, theory, la!, definition, inertia, inertial reference force
1. Newton’s First Law as an Axiom Since the presentation of the *rincipia in $%&7, e!ton"s first la! has 'een accepted as one of the fundamental la!s or a#ioms in the theory of e!tonian mechanics( )his idea has rooted so deeply that even today"s te#t'oo*s on physics present the la! a s one of these funda mental principles or a #ioms( +o!ever, !hen the nature of $ a#iom" as a lo-ical independent statement is e#amined, it is dou'tful that this la! may 'e considered such 'ecause it provides no additional information inf ormation to the theory than the t he one provided 'y the second sec ond la! alone a lone as !e shall see in this paper( .t is typical to find in -eneral physics te#t'oo*s statements li*e this one/ 0Reference frames !here the la! of inertia does not hold 1 are called non inertial reference frames( +o! can !e 'e sure a reference frame is inertial or not2 3y chec*in- to see if e!ton"s first la! holds( )hus e!ton"s first la! serves as the definition of inertial reference frames4 5Giancoli6( )he first la! is associated !ith the concept of inertia and !ith the identification of inertial reference frames in the conte#t of e!t on"s classical mechanics in many discussions in !hich it is pr esented( .t is ar-ued that the empirical confirmation of this la! in a certain reference frame, that is, the confirmation of the fact that an o'ect maintains a constant velocity !hen no forces act on it, is a !arranty that the frame is an inertial one( +o!ever, . claim that this empirical confirmation is no !arranty that the frame considered is an inertial one in the conte#t of e!tonian mechanics unless it is a fact that all the forces actin- on the system have 'een identified and included in the analysis( +o!ever, as . shall sho! in section 8 of this essay, e#perience does not assure this fact(
2. The Role of Fictitious Forces in the Identification of Inertial Reference Frames )he idea that fictitious forces arise in accelerated reference frames has 'een reco-ni9ed as the criteria for cate-orically identifyin- the de-ree of inertial motion of reference frames in the conte#t of e!tonian mechanics( +o!ever, more than 8:: years a fter the pu'lication of the the *rincipia there is still some confusion re-ardin- the conditions under !hich these fictitious forces !ill arise( )hese ideas re-ardin- the -eneration of fictitious forces in accelerated frames have 'een discussed deeply( ;et"s clarify ho! this *ind of forces sho! up in accelerated frames su--estin- that the frame is non inertial in the e!tonian mechanics sense( 7
© C ent er f or *r om oti n$ I (e as , -A
$
%% %. a i cr ne t. c om
.n a closed lo-ical system the lo-ical independence of the fundamental principles is !hat ma*es them a#ioms in that lo-ical system( .n other !ords the fact that an a#iom may not 'e deduced from another a#iom is !hat -ives them this status in the system(
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American International J ournal of Contem porar y Research
Vol. 4, No. 10; Octoer !014
;et"s consider the motion of an o'ect that moves under the influence of the force of -ravity !ith respect to a certain frame of reference that is fi#ed to the =arth( .f a 'all is released from a certain hei-ht, it descri'es a vertical traectory !ith respect to this frame( .f the same o'ect is then released from the same hei-ht a second time 'ut from a car that is movin- hori9ontally !ith constant velocity !ith respect to the =arth, then the o'served traectory in the car"s reference frame loo*s the same as the vertical fall o'served from the reference frame fi#ed to the =arth !hen the 'all !as released the first time( )his time, in the =arth"s reference frame, the o'served traectory is a para'ola( Since the second la! is confirmed no matter !hich frame is considered, and since there is no criteria to determine !hich of the t!o frames is at rest !ith respect to a'solute space, if any, then it should 'e concluded that 'oth are e!tonian mechanics inertial reference frames( )hese frames are also characteri9ed as e>uivalent frames( o! suppose that the 'all is released from a car that is movin- hori9 ontally !ith a constant acceleration !ith respect to the =arth( .n the frame of the =arth the o'served traectory is the same para'ola already considered, 'ut in the frame of the accelerated car, apart from the vertical accelerated free fall motion, !hich is due to the action of the force of -ravity, there is an o'ser ved acceleration in the hori9ontal direction pointin 'ac*!ards( )o e#plain this, e!ton"s s econd la! is invo*ed( Since the only identified force is the -ravitational vertical pull do!n!ards, the 'ac*!ards hori9ontal acceleration forces the introduction of a fictitious force actin- in this direction on the fallin- o'ect so that the vector addition of the t!o forces, or net force actin- on the 'all, may 'e invo*ed to e#plain the o'served curved path( )his fictitious force leads to the introduction of the concept of non inertial reference frames as ones in !hich e!ton"s second la! doesn"t hold( ?n these -rounds !e identify the accelerated frame of the car as a non inertial one( .n the e!tonian mechanics conte#t a non inertial reference frame is a frame that is acceleratin- !ith respect to a'solute space( .n summary, it is alle-ed that in the conte#t of @ e!tonian mechanics non inertial reference frames are identified 'ecause, in them, fictitious forces arise( .t is interestin- to o'serve that every e!tonian mechanics non inertial reference frame has an acceleration that is not 9ero !ith respect to a'solute space 'ein- this acceleration the same !hen calculated !ith respect to any inertial reference frame( )hat is, the accelerations are a'solute( )his is the reason !hy it can 'e said that velocities are relative to the inertial frame selected for the analysis 'ut accelerations are a'solute !ith respect to them(
3. The Arument )his ar-ument sho!s that in the conte#t of e!tonian mechanics the empirical confirmation of e!ton"s la! of inertia is no !arranty that the frame is a e!tonian Aechanics inertial frame( ;et us -ive thou-ht to the follo!in- /e(anen e#periment( Suppose that a -roup of o'servers are inside a la'oratory room 'i- enou-h to carry out e#periments for the purpose of testin- e!ton"s first and second la!s and have no !ay of loo*in- out( For e#ample, suppose that they are in a room that ha s no !indo!s so that there is no !ay of identifyinanythin- outside, for e#ample, a massive 'ody in case there is one( ;et"s define this room and all the o'ects inside it as our system( o! suppose that the room is movin- !ith a constant velocity as illustrated in fi-ure $, for e#ample, let"s say it is movin- throu-h space in the a'sence of all e#ternal forces( .n this case it is not difficult to sho! that inside the room everyone !ill a-ree on the fact that e!ton"s first la! is confirmed( .f no forces a re e#erted on the 'ody 'ein- e#perimented !ith, it !ill move !ith a constant velocity( So the conclusion in this case, since e!ton"s first la! is confir med, is that the frame of the room is a e!tonian mechanics inertial frame( 8
o! suppose, as sho!n in fi-ure @, that the room is su'ect to a constant -ravitational force that sets the system in a state of free fall( .n this case the o'servers inside the room are una!are of the presence of this -ravitational force actin- on the !hole system so this force is not included in the analysis as one of the forces actin- on the o'ect 'ein- e#perimented !ith( )hey are also una!are of their acceleration so inside the room the empirical confirmation of e!ton"s first la! !ill yield as a false result that their reference frame is a e!tonian mechanics inertial frame( Up to this point, ta*in- into account the results of this /e(anen e#periment, it has 'een sho!n that the empirical confirmation of e!ton"s first la! in a certain refer ence frame does not necessarily imply that the frame considered is a e!tonian mechanics inertial frame( <
© C ent er f or *r om oti n$ I (e as , -A 2
%% %. a i cr ne t. c om
.t is in fact fictitious effects an d not fictitious forces that are o'served(
8
.n this /e(anen e#periment the -ravitational force F - is assumed constant for sa*e of simplicity, 'ut it can 'e easily seen that the ar-ument is valid even con siderin- a varia'le -ravitational force that pr oduces a varia'le free fall acceleration(
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American International J ournal of Contem porar y Research
Vol. 4, No. 10; Octoer !014
.n order to assure the fact that the frame is a e!tonian mechanics inertial frame from the empirical confirmation of the la!, it is a re>uisite that all the forces actin- on the system must 'e identified, specially -ravitational ones since, as has 'een sho!n, -ravitational forces may produce free fall states in !hich fictitious effects do not sho! as they are supposed to do in accelerated frames of reference( )he reason for this lies in the fact that a state of constant velocity under the influence of no forces is empirically undistin-uisha'le from a state of free fall due to a -ravitational force( For e#ample, the only !ay of identifyin- the frame of the =arth as a non inertial e!tonian mechanics frame due to its motion around the Sun is not to o'serve arisin- fictitious effects in the frame of the =arth, 'ut to o'serve that in fact there is a 'ody that has a certain mass, the Sun, and then allude to the theory that states that there should 'e a -ravitational force actin- on the =arth( .n this system the =arth suffers the -reatest acceleration 'ecause it has a mass that is not si-nificant !hen compared to that of the Sun( Since the empirical confirmation of e!ton"s first la! does not necessarily determine the de-ree of inertial motion of reference frames in the conte#t of e!tonian mechanics as has 'een sho!n, it should 'e investi-ated if there is a !ay to determine so( Be should consider no! if the empirical test of e!ton"s second la! may serve as a !ay of identifyin- e!tonian mechanics inertial reference frames from non inertial ones( )his la! may 'e tested 'y applyin- forces Fn to an o'ect and findin- out if the o'served accelerations
a
o
are proportional to
these applied forces( o! suppose that the !hole system is a-ain set in a state of constant velocity as sho!n in fi-ure 8( .n this case it can 'e easily seen that e!ton"s second la! is confirmed empirically in the frame of reference of the room yieldin- as a correct conclusion that the frame selected is a e!tonian mechanics inertial frame( For the last part of the /e(anen e#periment the !hole system is su'ect a-ain to a state of free fall due to a -ravitational force and the o'servers loo* for the confirmation of e!ton"s second la! as illustrated in fi-ure ( Since the -ravitational force and the accelera tion it produces have not 'een identified, as in the case of the confirmation of the first la! !hen the system !as on a state of free fall 5fi-ure @6, the o'servers inside the room !ill yield a-ain confirmatory results for the second la! -ivin- as a false conclusion that the frame of reference of the room is a e!tonian mechanics inertial frame( )he failure to identify this frame as a non inertial one comes from the ina'ility to reco-ni9e the e#ternal -ravitational force and the state of free fall to !hich the !hole system is su'ect to( )he pro'lem 'ehind the identification of forces is that they are uno'serva'le >uantities( =#perience does not assure their identification(
!. Fictitious "ffects in Frames that #o$e with Free Fallin %&'ects 3ased on the precedin- analysis it follo!s that fictitious effects that need the introduction of fictitious forces in order to 'e e#plained do not sho! in frames of reference movin- !ith o'ects that are in a state of free fall( )his is also true for reference frames that move !ith constant velocity !ith respect to these accelerated frames( .f !e on planet =arth !ere una'le to identify the for ce of -ravity that the Sun e#erts on us, for !hatever reason, no fictitious effects !ill sho! in the frame of reference of the =arth, not 'ecause they are unnoticea'le, 'ut 'ecause they are not -enerated in theory( .n the video Frames of Reference 5cademic Film rchive of orth merica6 there is a discussion a'out the fact that the =arth"s reference frame is a e!tonian mechanics inertial frame 'ut only appro#imately( )his conclusion is dra!n from the fact that there is indeed a fictitious force that is a'out (8E the force of -ravity and in the opposite direction that -enerates from the fact that the =arth is rotatin-( +o!ever this force is not si-nificant in relation to the force of -ravity so the frame is for all practical purposes an inertial one( .n the video there is a statement that clashes !ith the result o'tained in the /e(anen e#periment presented in the previous section( .t is declared that 0the acceleration of the =arth in its or'it is even smaller still and produces even smaller effects4 5cademic Film rchive of orth merica6 than those produced in the fra me of the rotatin- =arth( 3ut . have sho!n that this is not the case since, !ith respect to the Sun, the =arth is in a state of free fall and hence no fictitious effects should 'e -enerated in the frame of the =arth( lmost 8:: years after the presentation of the *rincipia this misconception is still sustained(
(. )rinci*ia’s -cholium
+oo,
I $$
© C ent er f or *r om oti n$ I (e as , -A %% %. a i cr ne t. c om e!ton !as a!are of the difficulty in identifyin- inertial refer ence frames and he sho!ed his concern in the -cholium presented in the efinitiones section at the 'e-innin- of the *rincipia(
$@
+e stated/ 2otus 'ui(em #eros corporum sin$ulorum co$noscere, 3 a apparentius actu (iscriminare, (ifficillimum est; propterea 'uo( partes spati illius immoilis in 'uo corpora #ere mo#entur, non incurrunt in sensus. Causa tamen non est prorsus (esperata. Nam suppetunt ar$umenta partim e) motius apparentius, 'ui 4 sunt motuum #erorum (ifferenti, partim e) #irius 'u sunt motuum #erorum caus 3 effectus 5 Ne%tono6( +ere it is relevant to clarify !hat e!ton understood 'y true motion" and 'y apparent" or relative motion"( 0 Rursus motus #erus a #irius in corpus motum impressis semper mutatur, at motus relati#us a his #irius non mutatur necessario4 5 Ne%tono6( .t should 'e pointed here that these definitions, from !hich the e!tonian definitions of inertial and non inertial frames may 'e inferred, some!hat contrasts !ith Giancoli"s >uote in the sense that e!ton proposes the test of the second la! instead of the first( )hat is, he alludes to the a'sence or presence of a chan-e in the state of motion due to the presence or a'sence of forces( s can 'e seen from the first >uote e!ton cate-orically stated that, in order to distin-uish apparent motions from true motions, it is a fact that !e need the data related to the motion !ith respect to a certain reference frame 'ut also the information re-ardin- the forces that act on the system( .t is important to *eep in mind that the concept of a'solute space is pra-matically useless or elusive, as e!ton descri'es it, 'ecause empirically it may not 'e identified and therefore it is impossi'le to assure a'solute motion !ith respect to it( +o!ever, it may 'e useful in clarifyin- theoretically the concept of inertial reference frame and ho! it is related to it( ?nly in the case of rotational motion may a'solute motion 'e reco-ni9ed, 'ut this does not clash a-ainst the idea that the confirmation of e!ton"s first la! does not represent an errorfree !ay for the identification of e!tonian mechanics reference frames/ 0 5ffectus 'uius motus asoluti et relati#i (istin$uuntur a in#icem, sunt #ires rece(en(i a a)e motus circularis. Nam in motu circulari nu(e relati#o h #ires null sunt, in #ero autem et asoluto maores #el minores pro 7 'uantitate motus6 8Ne%tono9. )his idea is consistent !ith Aach"s conclusion that only rotational motion of a 'ody may 'e a'solutely identified as non inertial since fictitious centrifu-al effects are al!ays -enerated in this case( For e#ample, the motion of a Foucault pendulum placed at the =arth"s orth Pole !ould not s!in- in the same plane if the motion is referred to the frame of the =arth 'ut it !ould remain in the same plane of s!in- relative to the frame of the stars( ccordin- to Aach 0Bhen, accordin-ly, !e say that a 'ody preserves unchan-ed its direction and velocity in space, our assertion is nothin- more or less than an a''reviated reference to the entire universe4 5Aach6(
. The Theories
Loical
-tructure
of
Be have seen from the previous considerations that the first la! does not provide empirically any additional *no!led-e or information to the analysis from that provided 'y the second la!( o! . shall consider if from the point of vie! of lo-ics the first la!"s introduction as one of the a#ioms is ustified( .n the t!entieth century lo-ical positivists of the Hienna Circle esta'lished the fundamentals of the modern philosophy of science( )he common vie! of a scientific theory, accordin- to them, is that of a closed lo-ical system in !hich there is a relation of deduci'ility amon- the sentences that 'elon- to the system( Aany t!entieth century philosophers, includin- non positivists, accepted and promot ed this vie!( .n every lo-ical s ystem there is a set of fundamental sentences that are accepted initially and serve as premises for the deduction of the other sentences or components of the lo-ical system( )hese fundamental sentences, in the case of scientific empirical theories, are la!li*e statements that represent la!s of nature(
0.t is indeed a matter of -reat difficulty to discover, and effectually to distin-uish, the true motions of particular 'odies from the apparentI 'ecause the parts of that immova'le space, in !hich those motions are performed, do 'y no means come under the o'servation of our senses( et the thin- is not alto-ether desperateI for !e have some ar-uments to -uide us, partly from the apparent motions, !hich are the differences of the true motionsI partly from the forces, !hich are the causes and effects of the true motions4 5e!ton6( 0)rue motion suffers al!ays some chan-e from any force impressed upon the movin- 'odyI 'ut relative motion does not necessarily under-o any chan-e 'y such forces4 5e!ton6( % 0)he effects !hich distin-uish a'solute from relative motion are, the forces of recedin- from the a#is of circular motion( For there are no such forces in a circular motion purely relative, 'ut in a true and a'solute circular motion, they are -reater or
less, accordin- to the 5e!ton6(
>uantity of
motion4
.n order for these la!s to >ualify as a#ioms in a certain theory they should fulfill a set of re>uirements amon!hich there is a special property called lo-ical independence" !hich is fundamental( ;o-ical independence of a certain a#iom is simply the impossi'ility of deducin- it from other statements that 'elon- to the same lo-ical system( )his lo-ical independence is reco-ni9ed 'y the fact that the a#iom 'einconsidered provides information to the lo-ical system !hich other!ise !ould not 'e availa'le if the a#iom is left out of the lo-ical system( nother relevant aspect to 'e discussed re-ardin- the lo-ical structure of theories is the nature of a particular type of statement that is part of every lo-ical system/ the definition( Definitions are necessary in order to clarify concepts that are used !ithin the lo-ical system( For e#ample, !ithin the atomic theory the concept of atom" must 'e defined so that certain propositions related to it may 'e introduced !ith sense in the conte#t of the theory( Bithin the theory of plate tectonics the concept of plate" must 'e introduced if the theory is to present propositions a'out the !ay tectonic plates interact( t this point it is important to mention that the conceptual difference 'et!een la!s and definitions lies in the fact that la!s are su'ect to 'ein- true or false( Definitions are not su'ect to 'ein- true or false 'ecause they are accepted 'y common a-reement !ithin a community( )here is no sense in >uestionin- if they are true or false( 3rin-in- e!ton"s first la! 'ac* to the discussion, the fact that it is only valid in a certain *ind of frame of reference, that is, in inertial frames of reference, does not provide the definition of !hat an inertial frame of reference is( .f an o'ect on !hich no force is actin- is o'served to have a non 9ero acceleration then !hat proceeds lo-ically is not to conclude that the frame is not a e!tonian mechanics inertial frame 'ut to conclude that the la! does not confirm( ?nly if !ithin the conte#t of the theory the concept of inertial reference frame" is defined can !e say !e have enou-h information in order to ma*e the deduction that a certain frame is inertial or not dependin- on the result of the test of the la!( ny definition 'elon-in- to a lo-ical system must 'e presented cate-orically !ithin it 'y introducin- it as one of the premises of the syste m( ;et us analy9e the definition that can 'e inferred from Giancoli"s >uote( +e su--ests testin- e!ton"s first la! so let"s propose the follo!in- definition/ n inertial frame is one in !hich e!t on"s first la! holds( Under these conditions the deductive ar-ument is as follo!s/ (remises:
$6 'ody persists in a state of constant velocity unless there is a force that alters this motion 5e!ton"s first la!6( @6 n inertial frame is one in !hich the first la! holds 5definition proposed6( 86 e!ton"s first la! holds in the frame selected 5empirical data6( )onclusion:
)he selected inertial(
frame
is
o! let"s c onsider the follo!in- definition of inertial frame/ n inertial frame is one in !hich e!ton"s sec ond la! holds( Under these conditions the ar-ument is/ (remises:
$6 )he chan-e in the state of motion of an o'ect is proportional to the applied force actin- on it and points in the same direction 5e!ton"s second la!6( @6 n inertial frame is one in !hich the second la! holds 5definition proposed6( 86 e!ton"s second la! holds in the frame selected 5empirical data6( )onclusion:
)he selected inertial(
frame
is
.n the case of the first ar-ument, !here e!ton"s first la! is used as one of the premises, it should 'e pointed
out that the ar-ument is circular in the sense that to deter mine the de-ree of inertial motion of the reference frame the validity of the la! has to 'e supposed( 3ut the pro'lem is that this may not 'e confirmed unless one is sure that the selected frame is inertial( )he s econd ar-ument points to the same difficulty since in the determination of the de-ree of inertial motion of a certain frame the validity of the second la! must 'e supposed and, at the same time the validity of the la! depends on the proper selection of the inertial reference frame( =ven thou-h it seems that 'oth proposals are e>ually valid, there is a reason that favors the selection of the second option(
Specifically the principle of lo-ical independence of the a#iomatic 'ody of a theory is violated 'y selectinthe first option since there is no lo-ical sense in recurrin- to the first la! 'ecause it is not needed( )he first la! is a special case of the second la!( lso, the second la! is more -eneral, and thus, lo-ically more po!erful( lso, e!ton seems to ustify the use of the second la! in the determination of inertial frames as the second >uote of the Principia presented 'efore states( Aethodolo-ically he also seems to favor this option since there is, in the application of the theory to specific cases, no e#plicit use of the first la!( .n fact e!ton does not allude to it after its introduction at the 'e-innin- of the *rincipia( ?ther proposals may 'e e#amined for definin- the concept of inertial reference frame" 'y fillin- the missin premises in the follo!in- deductive ar-ument/ (remises:
$6 'ody persists in a state of constant velocity unless there is a force that alters this motion 5e!ton"s first la!6( @6 5your definition of inertial frame6 86 6 * n6 e!ton"s first la! holds in the frame selected 5empirical data6( )onclusion:
)he selected frame is inertial( =ven thou-h there is a possi'ility of findin- other definitions that may ta*e us to the conclusion, it is my hypotheses that they !ill not free the reasonin- from the violation of the principle of lo-ical independence of the a#iomatic 'ody or from circular reasonin-(
/. Final Remar,s )he fact that there is circularity in the sense that there is no !ay to confirm the la!, in 'oth cases, !ithout assumin- that the frame is a e!tonian mechanics inertial frame 'ut, at the same time there is no !ay of confirmin- that the frame is an inertial one !ithout supposin- the validity of the la!, is an e#ample of !hat happens to every empirical theory( )heories are tested in their o!n conte#t( .n this sense all !e can as* from a theory is consistency( )his methodolo-ical aspect in e!ton"s theory is validated 'y e!ton himself !hen in the -cholium presented after the efinitiones, 'efore presentin- the la!s of motion and ho! they !or* in particular cases, he declares the follo!in-/ 0 2otus autem #eros e) eorum causis, effectius 3 apparentius (ifferentis colli$ere, 3 contra, e) motius seu #eris seu apparentius, eorum causas 3 effectus, 7 (oceitur fusius in se'uentius 4 5 Ne%tono6( )hese limitations are not particularly characteristic to e!ton"s theory 'ut to ever y empirical or factual theory and reflect the hypothetical nature of all scientific theoretical *no!led-e( ?ther approaches have 'een proposed in order to ustify the a#iomatic nature of the la! of inertia( Perl declares/ 0From the evidence cited for the ;a!s, as contrasted !ith their ori-in in primitive e#perience or common sense o'servation, their mathematical character 'ecomes further confirmed( For the ;a!s are said to a-ree !ith e#perimental la!s, e#perimental theories, !ith each other, and !ith related principles4 5Perl6 . +o!ever, the fundamental nature of an a#iom, as has 'een discussed here, lies in its lo-ical independence from other statements presented in the deductive structure that is t he theory and not in their a'ility to confir m( .f the information provided 'y a la! is o'tained deductively from other statements already introduced !ithin the theory, then the deduced la! is not an a#iom 'ut a theorem in the theory( .n this paper Perl reco-ni9es that 0the first ;a! is a limitin- case of the second4 5Perl6( .t must 'e clarified that the discussion presented in this paper points to the pro'lem of ade>uate theoret ical representation of scientific theories and this aspect lies !ithin the field of philosophy( )he critic . present does
not intend to chan-e scientific methodolo-y( .n the field of science there is a series of permitted procedures that are completely ustified as part of the !or* of scientists( )his is all accepta'le( 7
0+o! are !e to collect the true motions from their causes, effects, and apparent differencesI and #ice #ersa, ho! from the motions, either true or apparent, !e may come to the *no!led-e of their causes and effects, shall 'e e#plained more at lar-e in the follo!in- tract4 5e!ton6(
)he fact that e!ton"s first la! is not an a#iom of e!tonian mechanics does not prohi'it scientists to recur to it in any !ay they desire( )here should 'e no pro'lem in acceptin- that this la! may 'e preferred, for e#ample, to -et a more clear perspective of !hat an inertial frame is or to ma*e it easier to understand the concept of inertia( +o!ever, since the pro'lem of the formal and correct representation of scientific theories lies !ithin the field of philosophy in !hich accepted methodolo-ies and conclusions differ from those in science, it is of vital importance to analy9e theory representation on these rather more strict parameters(
References Giancoli, D( Physics 5$<<&6( ( J(/ Pearson Prentice +all 5Chapter 6( cademic Film rchive of orth merica( Frames of Refer ence 5$<%:6( Retrieved from https/KKarchive(or-KdetailsKframesLofLreference( Aach, =( )he Science of Aechanics 5$<$<6( 5)( AcCormac*, )rans(6( Chica-o/ ?pen Court Pu'lishin-, 5Chapter ..6( e!ton, .( )he Principia 5$<<6( 5( Aotte )rans(6( ((/ Prometheus 3oo*s( e!tono, .( PhilosophiM aturalis Principia Aathematica 5$%&76( ;ondini/ Societatis Re-iM( Retrieved from https/KK!!!(-uten'er-( or-K e'oo*sK@&@88( Perl, A( 5$<%%6( e!ton"s Justification of the ;a!s of Aotion( Journal of the +istory of .deas, @7 586, & <@.
Figure +: Ex,erimental )on-irmation o- Newtons First Law when the /hole 0ystem is in a 0tate o- 1otion with )onstant 2elocity
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Figure 54 Ex,erimental )on-irmation o- Newtons 0econd Law when the /hole 0ystem is in a 0tate o- 1otion with )onstant 2elocity
Figure 64 Ex,erimental )on-irmation o- Newtons 0econd Law when The / hole 0ystem is in a 0tate 7- Free Fall $ue to a ravitational Force Acting on it