1. Time, clocks and the speed of light Vasco Guerra and Rodrigo de Abreu Departamendo de Física, Instituto Superior Técnico, 1049-001 Lisboa, Portugal email contact: vguerra@alfa.ist.utl.pt

2. The Michelson-Morley experiment

3. 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 Newtons equations are valid. –A coordinate system in which the speed of light in vacuum is c. Time and clocks

4. Feynmans light clock

5. The 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!

6. The 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!

7. Two Feynman light clocks... is true for any moving inertial system as well! In each inertial frame the two-way speed of light is constant.

8. Two Feynman-like bullet clocks In each inertial frame the two-way speed of bullets is constant.

9. Constancy 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!

10. Constancy 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=vt x: total distance in the round trip v: two-way speed v=v

11. 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!

12. The 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.

13. 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.

14. Conclusions 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.