I am putting here a Thought Experiment which brings out a paradox due to assumption of constant speed of light in Special Theory of Relativity with respect to all inertial observers. May be there is a simple answer but would like to know it/

1. Special Relativity - Revisited
Abhiram Modak
abhirammodak@gmail.com

2. Constancy of Speed of Light - Paradox
• Space ship and the
Observer A on the
Spaceship move
away from
Observer B
• At time TB = 0,
Spaceship passes B
• A pointed light
beam is flashed
towards the
meteorite at time
TB=0 from
Spaceship
200,000 km
A
B
Velocity of meteorite w.r.t B = 200,000 km/s
Velocity of A (and Spaceship) w.r.t B = 200,000 km/s

3. Option 1 : Speed of Light is
constant (=c) for Observers A and
B

4. Option 1 : Speed of Light is constant (=c) for
Observers A and B
•A’s version:
The light
struck the
meteorite
A
B

5. Option 1 : Speed of Light is constant (=c) for
Observers A and B
•B’s version:
The light missed
the meteorite
since the
meteorite moved
away before light
could reach it
A
B

6. Option 1 : Speed of Light is constant (=c) for
Observers A and B
• Consequences
• There is disagreement with the happening of event itself!
• This has deeper fallouts. For example from earth if we destroy a meteorite with a laser
beam, an Observer who is moving at very fast speeds with respect to earth will say that
the meteorite was never destroyed but it stays intact!
• This leads to a Universe with ‘parallel’ paths to future for the same objects with respect
to different Observers
• Special Relativity stays intact

7. Option 2 : Speed of Light is NOT
constant for Observers A and B

8. Option 2 : Speed of Light is NOT constant for
Observers A and B
•A’s version:
The light
struck the
meteorite
A
B

9. Option 2 : Speed of Light is constant NOT for
Observers A and B
•B’s version:
The light travelled
at the speed which
had a component
of Source velocity
in it and hit the
meteorite
A
B
Speed of light w.r.t B
=SQRT (3000002 + 2000002 )

10. Option 2 : Speed of Light is NOT constant for
Observers A and B
• Consequences
• Special Relativity falls apart
• There is no Time dilation nor Length shortening for moving objects
• You could travel at a speed faster than light
• There is agreement on the happening of event itself
• We may have revisit Doppler Effect for Light

11. So What is correct?
• Option 1
• Option 2
• Any other Explanation?