DOC.

47 265

It follows further that the addition of the light

velocity

c

and

a

"sublightvelocity" yields

again

the light velocity

c.

The

addition

theorem

of velocities also

yields

the interesting

conclusion

that there

cannot

exist

an

effect that

can

be used

for arbitrary

signaling and

that is

propagated

faster than light in

vacuum.

For

example,

[27]

let

there be

a

material

strip

stretched

along

the x-axis of

S,

relative

to

which

a

certain effect

(viewed

from

the material

strip)

propagates

with

velocity

W,

and

let there

be

two

observers,

one

in the point

x

=

0

(point

A)

and

one

in

the point

x

= X

(point

B)

of the x-axis,

who

are

at rest

relative

to

S. Let the observer

in

A

send

a

signal

by means

of the

[28]

above-mentioned effect

to

the

observer in

B

through

the material strip,

which

shall

not

be

at rest

but

shall

be

moving

in the

negative

x-direction

with velocity

v (

c).

As

a

consequence

of the first of

equations

(3),

the

signal will

then

be

transmitted

from

A

to

B

with

velocity

W-u/1-Wv/c2.

The

time

T

necessary

for this is then

¥v

T=*-irir-7?"11-

The

velocity

v can

assume any

value smaller than

c.

Hence,

if,

as we

have

assumed,

W

c, one can

always

choose

v

such

that

T

0.

This

result

means

that

we

would have

to

consider

as

possible

a

transfer

mechanism

whereby

the achieved effect

would precede

the

cause.

Even

though

this

result,

in

my

opinion,

does not

contain

any

contradiction

from

a

purely logical

point of

view,

it

conflicts

with the

character

of

all

our

experience

to such

an

extent

that this

seems

sufficient

to

prove

the

impossibility

of the

assumption

W c.

§6.

Application of

the

transformation equations

to

some

problems

in optics

[29]

Suppose

the light

vector

of

a

plane

light

wave

propagated

in

vacuum

is

proportional

to

sin u

i

_

ix

+

mv

+ nz

[30]

with

respect

to

the

system

S,

and to