Scenario of Crossing the speed limit of our Universe

Question

One of Important conclusions of Einstein's Theory of Relativity is that we cannot cross or break the speed limit set by the laws of physics that is the speed of causality

consider this scenario:

suppose I somehow built a spaceship and is able to reach 99.99.......% the speed of light. After achieving this much speed i somehow turned on the boosters on my shuttle.

will I be able to cross the limit by turning on the boosters if no what will actually happen to spaceship and where will the work-done by the boosters go. can expect to be in another universe having different laws and speed limits.

Answer 1

You would get one very little bit closer to the speed of light.

One of the important conclusions of the Theory of Special Relativity is, that 'The faster you go, the more inertial mass you get' (but your invariant mass doesn't change.) If something (other than massless particles ) would reach c, it's mass would be infinite, so the energy needed to accelerate this mass to c would be infinite too. So the work of your thrusters would go 'in the shuttle's mass, instead off it's velocity.'

With different approach, on such extreme velocities, the velocities don't add like in our everyday world. The sum of 0.9c and 0.7c, is not 1.6c, but slightly below c.

You could read this:

https://en.wikipedia.org/wiki/Mass_in_special_relativity

https://en.wikipedia.org/wiki/Velocity-addition_formula

for a brief, but more precise explanation, and exact formulas.

Answer 2

The Lorentz transformations are $$ dt'~=~\gamma(dt~+~vdx/c^2) $$ $$ dx'~=~\gamma(dx~+~vdt) $$ where $\gamma~=~1/\sqrt{1~-~(v/c)^2}$ and the velocity $u~=~dx/dt$. We now compute $dx'/dt'$ that results from the addition of the velocity $u$ with $v$, $$ \frac{du'}{dt'}~=~\frac{\gamma(dx~+~vdt)}{\gamma(dt~-~vdx/c^2)} $$ which leads to $$ \frac{du'}{dt'}~=~\frac{u~+~v}{1~-~uv/c^2}. $$ If is clear that no additional $u$ on the velocity $v$ is going to make $du'/dt'$ equal to $c$ the speed of light.