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Time, clocks and the speed of Time, clocks and the speed of lightlight
Vasco Guerra and Rodrigo de Abreu
Departamendo de Física, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
email contact: [email protected]
M irror 1S ource
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The Michelson-Morley experimentThe Michelson-Morley experiment
•Time:
– is what is measured with clocks.
• Clocks:
– any periodic phenomenon may be associated with a clock
(in principle...).
• The “rest system”:
– “A coordinate system in which Newton’s equations are valid”.
– A coordinate system in which the speed of light in vacuum is c.
Time and clocksTime and clocks
Feynman’s light clockFeynman’s light clock
Mirror
Mirror
d
The “first” assumptionThe “first” assumption
•Time passes independently from the type of clocks used
to measure it.
•Time measurements of a certain clock do not depend
on its orientation!
The “second” assumptionThe “second” assumption
• Clocks measure time in the same way in different
inertial “moving” frames.
The notion of time is the same in all inertial frames.
... is true for any “moving” inertial system as well!
Two Feynman light clocksTwo Feynman light clocks
... is true for any “moving” inertial system as well!
In each inertial frame the two-way speed of light is
“constant”.
Two Feynman-like bullet clocksTwo Feynman-like bullet clocks
• In each inertial frame the two-way speed of bullets is
“constant”.
““Constancy” of speedConstancy” of speed
• In each frame the two-way speed is the same
(“constant”) in all directions.
• In all frames the two-way speed is the same
(“constant”) in all directions.
• In each frame the speed is the same (“constant”)
independently of the speed of the source.
Both for light and for bullets!
““Constancy” in all framesConstancy” in all frames
• Feynman clock with bullets in a train (S’):
– The two-way speed of bullets fired in a “moving” train is
different if measured in the train or in the station: the same
bullets travel with different speeds in different frames.
• The same Feynman clock with bullets in the station (S):
– Is the two-way speed of bullets fired in the station (“rest
system”) the same as before?
In S’: x’=v’t’ In S: x=vt
x: total distance in the round trip
v: two-way speed
v=v’
““Constancy” in all frames (continued)Constancy” in all frames (continued)
• The two-way speed of bullets is the same (“constant”)
in all frames: different bullets travel with the same two-
way speed in all frames Both for light and for bullets!
• The constancy of the two-way speed in all frames
refers to different objects!
The “third” assumptionThe “third” assumption
• There exists a limit speed in the “rest system”: no
object can travel in the rest system with a speed higher
than a certain value c.
• Objects moving with the limit speed in the rest system must do
so independently of the speed of the emitting source.
The “third” assumption (continued)The “third” assumption (continued)
• Light travels with the limit speed in the “rest system”.
• The distinction between “two” light rays is artificial.
The same light rays travel with the same two-way
speed in all inertial frames.
• Different objects, emitted from different inertial frames,
collapse into the same object if (and only if) they travel
with the (two-way) limit speed c.
ConclusionsConclusions
• All good clocks can be used to measure time, independently from
the machinery involved in their manufacturing.
The null result of the Michelson-Morley experiment and
the constancy of the two-way speed of light in vacuum
are deeply connected with the very notion of time.
• Time is measured in the same way in all inertial frames.
• A limit speed exists in the “rest system”.
