- #1
neopolitan
- 647
- 0
I asked this question in an earlier thread, but I have thought a bit more about it and would like to add to it, hopefully focussing more successfully on the bit the bothers me.
First some preparation: At first, I was thinking of two light clocks set in motion relative to an observer A but at rest with respect to observer B. One light clock was parallel with that motion and I call that the "longitudinal light clock". The other was perpendicular to the motion and I call that the "transverse light clock".
I am fully aware that there are simultaneity issues so "right" and "wrong" are not necessarily hard and fast terms.
As clarification, I see the "half clock" as being set up so that the "tick" is collocated with B.
The centiclock will tick one hundred times for one tick of a "normal" light clock, so long as both are at rest with respect to each other.
The initiation is based on Einstein synchronisation. The initiation of the centiclock and the longitudinal light clock will be simultaneous for B, but not for A. For the sake of the exercise, I am making the assumption that B is at the end of the longitudinal light clock which is closest to A and the centiclock is at the other end of the longitudinal light clock so that, according to A, the longitudinal light clock initiates before the centiclock.
I can break up the inertial journeys like this:
According to A, the period that centiclock is in operation (between the time the initiation photon hits the centiclock and the time the longitudinal light clock photon hits the tock mirror) is determined by the lengths of the journeys. The journey the longitudinal light clock photon takes between tick and tock mirror is twice that of the initiation photon from start point to centiclock.
I think they do.
The centiclock stops emitting photons when the longitudinal light clock's photon hits the tock mirror, according to both A and B.
According to A, the centiclock starts emitting photons after the longitudinal light clock's photon starts its journey from the tick mirror.
So, according to A, there are three phases:
According to A, the phases during which the centiclock is not in operation, when combined, equal the phase during which the centiclock is operation.
I really think I have answered my own question, but confirmation would be great.
cheers,
neopolitan
First some preparation: At first, I was thinking of two light clocks set in motion relative to an observer A but at rest with respect to observer B. One light clock was parallel with that motion and I call that the "longitudinal light clock". The other was perpendicular to the motion and I call that the "transverse light clock".
neopolitan said:If there was one more synchronised clock (orientation unimportant) which was half the length of the other two and at rest with respect to B, B would assume/calculate that whenever the "half clock" ticks, the photons in other clocks would be bouncing off one mirror or the other.
Would he be right or wrong, according to A?
If I understand correctly (and JesseM gave some useful figures https://www.physicsforums.com/showpost.php?p=2147892&postcount=10"), then according to A, B would be "right" in the case of the tranverse light clock and "wrong" in the case of the longitudinal light clock.
I am fully aware that there are simultaneity issues so "right" and "wrong" are not necessarily hard and fast terms.
As clarification, I see the "half clock" as being set up so that the "tick" is collocated with B.
Because we are talking about photons, B can only know that a photon has hit a distant mirror (call it a "tock mirror") when the photon that hit the tock mirror hits the "tick" mirror where he is nominally located. It's difficult to split up the two way journey into two meaningful legs for B who can only be in one place at a time.
However, say we had a "centiclock", one hundredth the length of a standard light clock, attached to the "tock mirror" of the longitudinal light clock. With each tick of the centiclock (where the tick is collocated with the longitudinal light clock's "tock mirror"), a photon is transmitted towards B. However, this only happens until until the photon of the longitudinal light clock hits the "tock mirror".
The action of both the centiclock and the longitudinal clock would be initiated by a photon emitted from the centre of the longitudinal clock's length (ie the photons from the centiclock would start being emitted simultaneously with the first tick of the longitudinal clock, according to B).
The centiclock will tick one hundred times for one tick of a "normal" light clock, so long as both are at rest with respect to each other.
The initiation is based on Einstein synchronisation. The initiation of the centiclock and the longitudinal light clock will be simultaneous for B, but not for A. For the sake of the exercise, I am making the assumption that B is at the end of the longitudinal light clock which is closest to A and the centiclock is at the other end of the longitudinal light clock so that, according to A, the longitudinal light clock initiates before the centiclock.
I can break up the inertial journeys like this:
- initiation photon leaves centre of longitudinal clock towards "tick mirror" - a quicker journey according to A (because the tick mirror is moving towards the start point)
- initiation photon leaves centre of longitudinal clock towards "tock mirror" and "centiclock" - a slower journey according to A (because the tock mirror is moving away from the start point)
- clock photon leaves longitudinal light clock's tick mirror towards tock mirror - a slower journey according to A.
According to A, the period that centiclock is in operation (between the time the initiation photon hits the centiclock and the time the longitudinal light clock photon hits the tock mirror) is determined by the lengths of the journeys. The journey the longitudinal light clock photon takes between tick and tock mirror is twice that of the initiation photon from start point to centiclock.
B would have these facts to hand:
As far as I can tell, B should get 50 photons from the centiclock in half the time it takes for the clock photon to complete one full circuit. Assume then that those photons pass by B and reach A. Like B, A will also see 50 photons, in half the time it takes the clock photon in the longitudinal clock to complete a full circuit.
- a photon arrived from initiator and the clock photon left "tick mirror",
- photons started arriving from the centiclock,
- a certain number of photons arrived and
- photons stopped arriving from centiclock at the same time as the clock photon arrived back from the "tock mirror".
Or do they?
I think they do.
The centiclock stops emitting photons when the longitudinal light clock's photon hits the tock mirror, according to both A and B.
According to A, the centiclock starts emitting photons after the longitudinal light clock's photon starts its journey from the tick mirror.
So, according to A, there are three phases:
- Longitudinal light clock in operation (photon on way from tick mirror to tock mirror), centiclock not yet in operation
- Longitudinal light clock in operation (photon on way from tick mirror to tock mirror), centiclock in operation
- Longitudinal light clock in operation (photon on way back from tock mirror to tick mirror), centiclock no longer in operation
According to A, the phases during which the centiclock is not in operation, when combined, equal the phase during which the centiclock is operation.
I really think I have answered my own question, but confirmation would be great.
cheers,
neopolitan
Last edited by a moderator: