30 On the Causality Problem: Particle–Tachyon Collisions
329
Fig. 30.1 Sherlock Holmes observes from his special carriage in the Mercury Express how
Dr Fast is released from prison and the sudden death of the lawyer Mr Stus. The prison is
located in the reference system o at x o = 0. Dr Fast leaves this prison at time t o = 0. This is
event E o . The reference system is realised by the Mercury Express. This reference system
moves with the positive velocity of v = 0, 8 c o with respect to o . The initial values for the time
and space coordinates in were chosen so that Holmes also registered the values x
o = 0 and
t
o = 0 for the event E o . Mr Stus’ office is at rest in o at x 1 = L. Mr Stus suddenly dies at time
t 1 = L/2c o , which, in the reference system o , is after the release of Dr Fast from prison. This is
event E 1 . Using our Eq. (151), Chap. 13, we can calculate the time and space coordinates registered
by Holmes in the Mercury Express for event E 1 . We find, see also (476) or (253), x
1 = L and
t
1 = −L/2c o (the same value for the space coordinates of the event E 1 in both reference systems
is due to our special choice of example). The time t
1 is negative! Dr Fast however leaves prison at
time t
o = 0. Holmes thus observes that Mr Stus was already dead before Dr Fast left prison and
thus proved the innocence of his client. We will keep the following in mind: The positive velocity
v of the Mercury Express with respect to o causes the event with the larger space coordinates
in o , which is registered from , to be observed to occur earlier than in o . The dotted lines
connect one and the same event
Fast, possibly sent out tachyon could not have been the cause of death of Stus, see
Fig. 30.1.
There was however a second suspect, Dr Fast’s old laboratory assistant Mr
Wacker who was also sentenced. Mr Wacker however was sent, on security reasons, to a different prison, which seen from the reference system o has the position
x 2 = 2L. Mr Wacker was too released from prison at time t 2 = 0 and was arrested
again after the death of Mr Stus, which occurred at t 1 =
1
2
L/c o . Mr Wacker was in
possession of a suspicious tachyon machine, and it was believed that this machine
may have been used to send out a second tachyon. We therefore have a second event,
E 2 , the release of laboratory assistant Mr Wacker from prison, which is described
in the reference system o as E 2 (x 2 = 2L , t 2 = 0). This event is also registered by
329
Fig. 30.1 Sherlock Holmes observes from his special carriage in the Mercury Express how
Dr Fast is released from prison and the sudden death of the lawyer Mr Stus. The prison is
located in the reference system o at x o = 0. Dr Fast leaves this prison at time t o = 0. This is
event E o . The reference system is realised by the Mercury Express. This reference system
moves with the positive velocity of v = 0, 8 c o with respect to o . The initial values for the time
and space coordinates in were chosen so that Holmes also registered the values x
o = 0 and
t
o = 0 for the event E o . Mr Stus’ office is at rest in o at x 1 = L. Mr Stus suddenly dies at time
t 1 = L/2c o , which, in the reference system o , is after the release of Dr Fast from prison. This is
event E 1 . Using our Eq. (151), Chap. 13, we can calculate the time and space coordinates registered
by Holmes in the Mercury Express for event E 1 . We find, see also (476) or (253), x
1 = L and
t
1 = −L/2c o (the same value for the space coordinates of the event E 1 in both reference systems
is due to our special choice of example). The time t
1 is negative! Dr Fast however leaves prison at
time t
o = 0. Holmes thus observes that Mr Stus was already dead before Dr Fast left prison and
thus proved the innocence of his client. We will keep the following in mind: The positive velocity
v of the Mercury Express with respect to o causes the event with the larger space coordinates
in o , which is registered from , to be observed to occur earlier than in o . The dotted lines
connect one and the same event
Fast, possibly sent out tachyon could not have been the cause of death of Stus, see
Fig. 30.1.
There was however a second suspect, Dr Fast’s old laboratory assistant Mr
Wacker who was also sentenced. Mr Wacker however was sent, on security reasons, to a different prison, which seen from the reference system o has the position
x 2 = 2L. Mr Wacker was too released from prison at time t 2 = 0 and was arrested
again after the death of Mr Stus, which occurred at t 1 =
1
2
L/c o . Mr Wacker was in
possession of a suspicious tachyon machine, and it was believed that this machine
may have been used to send out a second tachyon. We therefore have a second event,
E 2 , the release of laboratory assistant Mr Wacker from prison, which is described
in the reference system o as E 2 (x 2 = 2L , t 2 = 0). This event is also registered by