332
30 On the Causality Problem: Particle–Tachyon Collisions
thus
t
1 =
13
16
L
c o
.
(476)
We also find
x
1 =
5
3
x 1 − v
t 1
=
5
3
L +
4
5
c o
L
2c o
=
5
3
14
10
L ,
thus
x
1 =
14
15
L .
(477)
The following observations are thus valid for event E 1 , see Fig. 30.2,
E 1 :
o : x 1 = L ,
t 1 =
1
2
L
c o
,
: x
1 = L ,
t
1 = −
1
2
L
c o
,
: x
1 =
14
15
L , t
1 =
13
6
L
c o
.
⎫
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭
(478)
Together with the corresponding coordinate origins according to (475), the quotient
of the time and space coordinates from (478) can be used to determine the velocities
of the tachyon emitted by Dr Fast as seen in all three reference systems, namely
o : u 1 =
x 1
t 1
= 2c o ,
: u
1 =
x
1
t
1
= −2c o ,
: u
1 =
x
1
t
1
=
28
65
c o .
⎫
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭
Velocities
of the first tachyon
(479)
We will assume that the tachyon emitted by Dr Fast has a positive momentum
parameter m
T
∗ . The tachyons velocity therefore has the same sign as its momentum
in both o and
. This is situation that fits into our conception based on ‘normal’
particles.
The situation however is completely different for the observer in
. The velocity
of this tachyon is negative and has the opposite direction with respect to its own
momentum. We remind the reader that the momentum of a tachyon has the same
sign in every reference system. One could therefore state that the tachyon is travelling backwards through time! This peculiarity of the tachyon being able to travel
backwards through time completely breakes our view of the world. We are however,
based on this, not allowed to come to the conclusion that tachyons do not exist. This
peculiarity only means that we must be very careful when dealing with tachyons so as
30 On the Causality Problem: Particle–Tachyon Collisions
thus
t
1 =
13
16
L
c o
.
(476)
We also find
x
1 =
5
3
x 1 − v
t 1
=
5
3
L +
4
5
c o
L
2c o
=
5
3
14
10
L ,
thus
x
1 =
14
15
L .
(477)
The following observations are thus valid for event E 1 , see Fig. 30.2,
E 1 :
o : x 1 = L ,
t 1 =
1
2
L
c o
,
: x
1 = L ,
t
1 = −
1
2
L
c o
,
: x
1 =
14
15
L , t
1 =
13
6
L
c o
.
⎫
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭
(478)
Together with the corresponding coordinate origins according to (475), the quotient
of the time and space coordinates from (478) can be used to determine the velocities
of the tachyon emitted by Dr Fast as seen in all three reference systems, namely
o : u 1 =
x 1
t 1
= 2c o ,
: u
1 =
x
1
t
1
= −2c o ,
: u
1 =
x
1
t
1
=
28
65
c o .
⎫
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭
Velocities
of the first tachyon
(479)
We will assume that the tachyon emitted by Dr Fast has a positive momentum
parameter m
T
∗ . The tachyons velocity therefore has the same sign as its momentum
in both o and
. This is situation that fits into our conception based on ‘normal’
particles.
The situation however is completely different for the observer in
. The velocity
of this tachyon is negative and has the opposite direction with respect to its own
momentum. We remind the reader that the momentum of a tachyon has the same
sign in every reference system. One could therefore state that the tachyon is travelling backwards through time! This peculiarity of the tachyon being able to travel
backwards through time completely breakes our view of the world. We are however,
based on this, not allowed to come to the conclusion that tachyons do not exist. This
peculiarity only means that we must be very careful when dealing with tachyons so as