Riepiloghiamo quanto affermato nel precedente scritto. Ciò che percepiamo con l’udito è la sorgente sonora; ciò che percepiamo con la vista è la sorgente luminosa. La percezione uditiva è mediata dalle onde sonore. Senza queste onde l’informazione proveniente dalla sorgente sonora non potrebbe giungere alle nostre orecchie. La percezione visiva è mediata dalle onde elettromagnetiche. Senza queste onde l’informazione proveniente dalla sorgente visiva non potrebbe giungere ai nostri occhi. L’onda sonora non può essere al contempo “ente percepito” e “veicolo” d’informazione percettiva. Analogamente l’onda elettromagnetica non può essere contemporaneamente “ente percepito” e “veicolo” d’informazione percettiva. Se potessimo percepire con l’udito un’onda sonora a dieci metri di distanza, come potrebbe quest’informazione giungere alle nostre orecchie? Avremmo bisogno di un’altra onda sonora che trasmette quest’informazione. Analogamente se potessimo percepire un’onda elettromagnetica a cento metri di distanza, come potrebbe quest’informazione giungere ai nostri occhi? Avremmo bisogno di un’altra onda elettromagnetica che trasmette queste informazioni.
Si presuppone che le leggi fisiche siano valide a prescindere dall’osservatore. La luna, infatti, continuerebbe a girare attorno alla terra, anche se nessuno la guardasse. Nella fisica classica e nella fisica relativistica spesso si utilizza l’osservatore come riferimento, al fine di rendere più comprensibile quanto esposto. Utilizzare l’osservatore come riferimento consente di interpretare i fenomeni studiati in modo più intuitivo.
Il punto di vista dell’osservatore, utilizzato come riferimento, è un punto di vista soggettivo. L’osservatore compartecipa alla relazione riferimento/riferito. Gli eventi avvengono rispetto al proprio soma. Il punto di vista dell’osservatore esterno, invece, è oggettivo. L’osservatore non compartecipa alla relazione riferimento/riferito ma osserva quanto accade tra il riferimento e il riferito che sono esterni.
Nella fisica galileiana i due punti di vista, soggettivo e oggettivo, sono interscambiabili, danno cioè gli stessi risultati.
Osserviamo l’immagine in basso (figura 1).
Mettiamoci dal punto di vista del soldato romano a terra. Si tratta di un punto di vista soggettivo, nel quale il riferimento è l’osservatore, mentre il riferito è la lancia. Egli percepisce la velocità della lancia scagliata dal cavaliere. Ipotizziamo tre ipotesi: Il cavallo è fermo; il cavallo galoppa in direzione del sondato romano; il cavallo galoppa allontanandosi dal soldato romano. Il soldato romano percepisce che la velocità della lancia è maggiore quando il cavaliere galoppa nella sua direzione ed è minore quando galoppa in direzione opposta. Col cavallo fermo la velocità è intermedia.
Mettiamoci dal punto di vista di un osservatore esterno, cioè oggettivo. Il riferito è la lancia, mentre il riferimento è lo scudo. L’osservatore esterno percepisce questa relazione. Se il cavallo galoppa in direzione del soldato romano, la lancia penetra nello scudo di 20 cm (velocità maggiore); se il cavallo è fermo, la lancia penetra nello scudo di 10 cm (velocità intermedia); se il cavallo si allontana dal soldato romano, la lancia penetra nello scudo per 2 cm (velocità minore).
L’interazione scudo/lancia avendo come riferimento lo scudo dà gli stessi risultati dell’interazione cavaliere romano/lancia, avendo il cavaliere romano come riferimento. Da ciò si evince che, nella fisica galileiana, i due punti di vista, soggettivo ed oggettivo, sono interscambiabili.
Osserviamo l’immagine in basso (figura 2)
Ivan può assumere il punto di vista soggettivo. Egli percepisce la velocità del treno rispetto al proprio soma. Ivan, però, può assumere anche un punto di vista oggettivo. In questa circostanza percepisce la velocità del treno rispetto alle rotaie. I due punti di vista sono interscambiabili, danno cioè lo stesso risultato. Il treno si sposta rispetto al proprio soma e rispetto alle rotaie sempre alla stessa velocità.
Questa intercambiabilità tra i due punti di vista dipende da un assunto implicito: l’interazione riferimento/riferito è istantanea. Se si modifica quest’assunto, l’interscambiabilità viene meno.
Riconsideriamo il punto di vista soggettivo nel quale Ivan assume il proprio soma come riferimento. Ivan percepisce se stesso (riferimento) col sistema propriocettivo e percepisce il treno (riferito) col sistema visivo. La percezione propriocettiva avviene nell’istante “T”; la percezione visiva è mediata dall’onda elettromagnetica che impiega un infinitesimo di secondo per giungere agli occhi di Ivan. La percezione del treno avviene nell’istante “T ⁱ”. L’interazione riferimento/riferito non è istantanea, ma prima/dopo.
Riconsideriamo il punto di vista oggettivo nel quale Ivan assume le rotaie come riferimento. L’interazione tra le rotaie e il treno è istantanea. Ivan percepisce istantaneamente le rotaie (riferimento) e il treno (riferito) col sistema visivo. Le due percezioni avvengono nell’istante “T ⁱ”. Il tempo dall’onda elettromagnetica che impiega un infinitesimo di secondo per giungere agli occhi di Ivan concerne l’interazione tra le rotaie e il treno.
La contemporaneità dell’interazione oggettiva si riscontra anche nell’esempio dello scudo (riferito) e la lancia (riferimento). Questa interazione è istantanea. Il tempo che l’informazione impiega per giungere agli occhi dell’osservatore concerne l’interazione non le due singole percezioni.
Se prendiamo in considerazione il tempo che l’informazione visiva proveniente dalla sorgente visiva (treno) impiega per giungere agli occhi dell’osservatore (assunto come riferimento), il punto di vista soggettivo non è interscambiabile col punto di vista oggettivo. Ciò significa che i due punti di vista danno risultati diversi.
Einstein propose il seguente esperimento mentale per aiutare il lettore disorientato a formarsi un’intuizione di come anche la simultaneità sia un concetto relativo. Osserviamo l’immagine in basso (figura 3)
Seguiamo l’esperimento mentale attraverso la descrizione dello stesso Einstein, tratta dall’esposizione divulgativa della teoria della relatività (1916):
Allorché diciamo che i colpi di fulmine A e B sono simultanei rispetto alla banchina, intendiamo: i raggi di luce provenienti dai punti A e B dove cade il fulmine s’incontrano l’uno con l’altro nel punto medio M dell’intervallo A→B della banchina. Ma gli eventi A e B corrispondono anche alle posizioni A e B sul treno. Sia M’ il punto medio dell’intervallo A→B sul treno in moto. Proprio quando si verificano i bagliori del fulmine, questo punto M’ coincide naturalmente con il punto M, ma esso si muove verso la destra del diagramma con la velocità v del treno. Se un osservatore seduto in treno nella posizione M’ non possedesse questa velocità, allora egli rimarrebbe permanentemente in M e i raggi di luce emessi dai bagliori del fulmine A e B lo raggiungerebbero simultaneamente, vale a dire si incontrerebbero proprio dove egli è situato. Tuttavia nella realtà (considerata con riferimento alla banchina ferroviaria), egli si muove rapidamente verso il raggio di luce che proviene da B, mentre corre avanti al raggio di luce che proviene da A. Pertanto l’osservatore vedrà il raggio di luce emesso da B prima di vedere quello emesso da A. Gli osservatori che assumono il treno come loro corpo di riferimento debbono perciò giungere alla conclusione che il lampo di luce B ha avuto luogo prima del lampo di luce A. Perveniamo così al seguente importante risultato:
Gli eventi che sono simultanei rispetto alla banchina non sono simultanei rispetto al treno e viceversa (relatività della simultaneità). Ogni corpo di riferimento (sistema di coordinate) ha il suo proprio tempo particolare; una attribuzione di tempo è fornita di significato solo quando ci venga detto a quale corpo di riferimento tale attribuzione si riferisce.
In questo esperimento mentale Einstein utilizza come riferimenti due osservatori posti uno sul treno e l’altro nella panchina. La simultaneità è soggettiva, cioè concerne la percezione del primo e del secondo osservatore.
L’osservatore sul treno pone una relazione riferimento/riferito tra due sue percezioni separate, si tratta della propria percezione del primo fulmine (riferimento) e la propria percezione del secondo fulmine (riferito). La relazione riferimento/riferito non concerne il tempo dell’interazione (riferimento/riferito) tra i due fulmini, ma il tempo dell’interazione tra due percezioni.
Anche l’osservatore a terra pone una relazione riferimento/riferito tra due sue percezioni separate, si tratta della propria percezione del primo fulmine (riferimento) e la propria percezione del secondo fulmine (riferito). La relazione riferimento/riferito non concerne il tempo dell’interazione (riferimento/riferito) tra i due fulmini ma il tempo dell’interazione tra due percezioni.
Per rendere la simultaneità oggettiva occorrono due strumenti posti in M e in M’ che misurino i tempi di arrivo dei due raggi verificandone la contemporaneità e/o il prima/dopo. Possiamo usare, per esempio, due interferometri (l’interferometro è lo strumento utilizzato nell’esperimento di Michelson e Morley). L’interferometro registra l’interazione tra i due fulmini verificandone con estrema precisione il tempo. Osservando l’interferometro si può constatare se i due fulmini arrivano contemporaneamente oppure uno prima e uno dopo.
L’interferometro registra la relazione riferimento/riferito tra l’arrivo del primo fulmine e l’arrivo del secondo. Questa registrazione è oggettiva. L’interferometro, infatti, non è un osservatore che guarda il primo raggio e il secondo. L’interferometro, quindi, non registra l’interazione tra due osservazioni, ma tra due eventi.
Se utilizziamo questi strumenti, verifichiamo che sia i raggi di luce della prima coppia sia i raggi di luce della seconda coppia arrivano contemporaneamente nel punto M (i primi) e nel punto M’ (i secondi). La velocità della luce, infatti, è sempre la stessa e non dipende dal sistema di riferimento che può essere in moto o immobile.
Nell’esperimento mentale di Einstein s’ipotizza che l’osservatore possa percepire l’onda elettromagnetica. Abbiamo dimostrato che ciò è illogico. Ci vorrebbe, infatti, una seconda onda elettromagnetica che trasporta l’informazione della prima verso gli occhi dell’osservatore. Utilizzando due interferometri si elimina l’illogicità. Dobbiamo quindi accettare che la contemporaneità oggettiva, cioè quella registrata dagli strumenti è reale mentre la non contemporaneità soggettiva si fonda su un presupposto illogico.
Dal punto di vista fisico, cioè oggettivo, esiste la contemporaneità e può essere verificata con un esperimento. Dal punto di vista soggettivo, cioè di due osservatori, la contemporaneità viene meno. Questa non contemporaneità, però si basa su un presupposto illogico.
Dal punto di vista soggettivo la non contemporaneità concerne l’interazione (riferimento/riferito) tra due osservazioni di eventi. Dal punto di vista oggettivo la contemporaneità concerne l’interazione (riferimento/riferito) tra due eventi.
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