- Absolute Newtonian simultaneity – gravity is instantaneous.
- Everyday simultaneity:
- Under what conditions do our normal judgements of simultaneity get made, and compared?
- What about under very different conditions? Very distant events or for people with very fast relative speeds?
- Einstein's relativity of simultaneity is not (merely) the trivial point that different people hear/see the same events in different orders.
- It is that the same events really occur in different orders depending on their motions.
Suppose two guns (at the points marked 'bang') are fired simultaneously (absolutely if space is absolute, or relative to 2 in relativity), and suppose 6 passes 2 as the light from the muzzle flashes arrives, 5 when the bullets arrive, and 6 when the sound of the firing arrives.
- Consider two guns fired simultaneously at each other, observed by six observers, each with different positions and/or motions – with or without relativity they will have the following experiences:
- 1 hears the left gun before 2 who hears it before 3.
- 3 hears the right gun before 2 who hears it before 1.
- 1 hears the left gun before the right gun – and v.v. for 3, while 2 hears them simultaneously.
- Ditto for the arrival of the bullets and seeing the muzzel flash.
- 4 hears the bangs simultaneously.
- Both bullets arrive simultaneously at 5.
- 6 sees both muzzle flashes at once.
- In other words:
- The different order in which signals arrive is not relativity.
- Even in relativity, two observers that meeting at a time and place will perceive exactly the same events at that time.
- Generally, relativity is about how things are, not (just) how they
'seem' to people.
3. (Non-relativistic) Bullets:
- They have different speeds relative to different frames!
- Suppose a gun mounted at the center of a train car is fired at a target fixed to the end, Lm away: if it taskes Ts then its speed is L/T m/s.
- If the train moves at Vm/s relative to the ground then the bullet Ts to travel (L + TV)m to the target. Why? So its speed is (L + TV)/T m/s = L/T + V m/s – the speed relative to the train, plus the speed of the train.
- I.e., the bullet travels a different distance in each 'frame', but at different speeds, so it takes the same time.
- If they arrive simultaneously in one frame then they do in all frames!
- Suppose a second gun at the center simultaneously fires at a target Lm away at the other end: assuming this bullet travels at the same speed as the first, then they will arrive simultaneously.
- Relative to the ground:
- the forward travelling bullet has speed L/T + V m/s, while by similar reasoning the speed of the second is L/T - V m/s.
- the distance to the forward target is (L + TV)m so the time to reach it is (L + TV)/(L/T + V) = Ts.
- the distance to the rear target is (L - TV)m so the time to reach it is (L - TV)/(L/T - V) = Ts.
- That is, relative to the train and relative to the ground, the bullets reach their targets simultaneously – although the distances to be covered are different, so are the speeds, by just the right amount.
- Completely unlike
bullets, all light has the same speed (300,000,000 m/s) in all directions
in all frames regardless of its source – the constancy of the speed of
light
- Experimental fact.
- Fact about the laws of physics.
- How is this possible? Suppose different frames are in disagreement,
not just about how far light travels from source to target, but how long it
takes…
5. Relativity of Simultaneity