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Imagine 1 million objects travelling in space, at a constant speed, along an imaginary line. They don't deviate from that line for the sake of this argument.

Now, object 1 has a velocity of $v_{1}=1$ km/s relative to a point in space.

Object 2 has a velocity of $v_{2,1}=1$ km/s relative to object 1, which means $v_{2}=2$ km/s when calculating the velocity related to the point in space we considered with object 1.

Object 3 has a velocity of $v_{3,2}=1$ km/s relative to object 2, which means $v_{3}=3$ km/s when calculating the velocity related to the point in space we considered with object 1.

Then I would assume that object 1 million as a velocity of $v_{1M}=1$ million km/s when calculating the velocity related to the point in space we considered with object 1. However, this goes against the principle that nothing can exceed the speed of light.

So:

1.) Where is the error in this reasoning?

2.) How can we talk about the existence of a maximum velocity when $velocity$ is actually vector-based measurement which changes with the reference we consider?

Qmechanic
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Dayman75
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1 Answers1

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As per the comments, I wasn't taking into account the relativistic addition of velocities, which is becomes relevant when designing scenarios with such high velocities.

So for a observer in the point specified in my argument, the fastest objects (object #1 million, object #999.999, ...) would appear to have velocities close to light speed, but they would never reach it.

For more information check out the Website http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

Also, this question might be a duplicate of others. If you have questions and feel this answer isn't enough, consider checking the others out: Relativistic addition of velocities of spaceships

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Dayman75
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