Question

If i was travelling towards a light pulse in opposite direction to its velocity wouldnt length contraction and time dilation make its velocity even bigger than c, for my length measuring rods will become shorter so i will measure more distance travelled by the light and my clocks will run slower so more time for light to travel ? I get it when the distance between the pulse and observer is increasing but not the other way.

Answer 1

Answer on Question #68534, Physics / Mechanics | Relativity

If $i$ was travelling towards a light pulse in opposite direction to its velocity, wouldn't length contraction and time dilation make its velocity even bigger than $c$, for my length measuring rods will become shorter so $i$ will measure more distance travelled by the light and my clocks will run slower so more time for light to travel? I get it when the distance between the pulse and observer is increasing but not the other way.

Solution:

The velocity of the body approaches to the speed of light in vacuum. This is a special relativity.

The speed of the body is always less than the speed of light in vacuum.

Two postulates of special relativity.

First postulate (principle of relativity): The laws of physics are the same in all inertial frames of reference.

Second postulate (invariance of $c$): The speed of light in free space has the same value $c$ in all inertial frames of reference.

Time dilation (different times $t$ and $t'$ at the same position $x$ in same inertial frame):

$$t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} (1),$$

where $v$ is the speed of body.

Length contraction (different positions $x$ and $x'$ at the same instant $t$ in the same inertial frame):

$$l' = l_0 \sqrt{1 - \frac{v^2}{c^2}} (2),$$

where $v$ is the speed of body.

The laws of classical physics (e.g., $l' = vt'$) are not right for special relativity. In this way, the direction of the motion of body does not matter.

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