Il paradosso dei gemelli - Fisica

<strong>Il</strong> <strong>paradosso</strong> <strong>dei</strong> <strong>gemelli</strong><br />

Luca Gammaitoni

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La storia (P. Langevin, 1911)<br />

Ci sono due <strong>gemelli</strong>...<br />

Quando Jane torna a terra trova che Joe<br />

è invecchiato più di lei

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Paradosso?<br />

simmetria apparente della situazione<br />

asimmetria <strong>dei</strong> sistemi: uno è inerziale<br />

uno no.

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elementi di Relatività Speciale<br />

A. Einstein, 1905<br />

postulati della R.S.<br />

Principio di relatività:<br />

Tutte le leggi della fisica sono le stesse per gli osservatori che<br />

si muovono di moto rettilineo uniforme.<br />

Principio di costanza della velocità della luce:<br />

La luce si propaga nel vuoto a una velocità "c" che è<br />

indipendente dal moto della sorgente.

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Background...<br />

Trasformazioni di Lorentz<br />

Dilatazione <strong>dei</strong> tempi

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Dilatazione <strong>dei</strong> tempi<br />

Time dilation is the phenomenon whereby an<br />

observer finds that another's clock which is physically<br />

identical to their own is ticking at a slower rate as<br />

measured by their own clock.<br />

This is often taken to mean that time has "slowed<br />

down" for the other clock, but that is only true in the<br />

context of the observer's frame of reference.<br />

Locally, time is always passing at the same rate. The<br />

time dilation phenomenon applies to any process that<br />

manifests change over time.

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Verifiche sperimentali<br />

1971, un orologio atomico ha viaggiato a<br />

bordo di un jet attorno al globo a 966<br />

Km/h. Verifica su pochi miliardesimi di<br />

secondo di ritardo.<br />

vita media delle particelle elementari<br />

(muoni)<br />

Funzionamento sistema GPS

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vita media delle particelle elementari (muoni)<br />

Rossi and Hall (1941)<br />

compared the population of cosmic-ray produced muons<br />

at the top of a mountain to that observed at sea level.<br />

Although the travel time for the muons from the top of the<br />

mountain to the base is several muon half-lives, the muon<br />

sample at the base was only moderately reduced.<br />

This is explained by the time dilation attributed to their<br />

high speed relative to the experimenters. That is to say, the<br />

muons are decaying about 10 times slower than they<br />

would in a rest frame (that is, for "stationary observers").

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Funzionamento sistema GPS<br />

•The in-orbit clocks are corrected for both special and<br />

general relativistic time-dilation effects so they run at the<br />

same (average) rate as clocks at the surface of the Earth.<br />

•In addition, but not directly time-dilation related, general<br />

relativistic correction terms are built into the model of<br />

motion that the satellites broadcast to receivers.<br />

• Uncorrected, these effects would result in an<br />

approximately 7-metre oscillation in the pseudo-ranges<br />

measured by a receiver over a cycle of 12 hours.