# Why can't we accelerate objects past the speed of light? [duplicate]

Is there any intuitive reasoning behind why there would be this universal speed limit? It just seems so arbitrary. I know that there must be things that are unknown, but what reasoning is there behind the existence of some limiting speed?

Edit: I really was asking more abstractly, why it makes sense for there to be a limit. It really is a question that can't be answered, but this isn't a duplicate.

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## marked as duplicate by Ben Crowell, Mark Eichenlaub, dmckee♦May 6 '13 at 23:13

Hi Anthony, and welcome to Physics Stack Exchange! Questions like this have been asked frequently on this site; take a look at this, this, this, this, this, and other related questions and see if they help you out. –  David Z May 6 '13 at 21:36
Basically it's because it would require infinite energy physics.stackexchange.com/a/1558/3948 –  ChrisF May 6 '13 at 21:42
@Anthony initially it's just based on experimental evidence. In particular, we cannot accelerate the speed of light. Mounting a laser on a cart that moves with 1 m/s does not make the laser light move with c + 1m/s. So, you start from the assumption that the speed of light is the same in all inertial frames of reference. This is really the only starting point you need to derive special relativity. And it tells you that adding velocities $v_1$ and $v_2$ does not give you $v_1 + v_2$. –  Martin Büttner May 6 '13 at 22:21
If you are not questioning the mathematical reasoning, but just the overall universal fact that there is a speed limit... I think the question might be pointless. Because you could think of it as not there being a speed limit, but of us having a wrong perception of velocity addition. After all, you can accelerate something further and further. And for someone travelling at the $0.99c$ there can still be something $0.99c$ faster. It is just that in our non-relativistic environment we are used to velocities adding up normally - but that's just not how the universe works with velocities. –  Martin Büttner May 6 '13 at 22:24
why it makes sense for there to be a limit - There wouldn't be any disaster in theoretical physics if there weren't such a limit. Some phenomena would go differently, but no mathematical contradictions would arise (as far as it is known today). So universes with and without limit are both possible, and it is just an experimental fact that we live in the first kind. –  firtree May 12 '13 at 8:33

Yes, the answer is actually very simple:

While you increase the speed, the required amount of energy increases - because with the speed, the objects mass increases. And, to get to the light speed, you'd need infinite amount of energy, and the object itself would have an infinite mass.
You may know that photons, which do move with lightspeed, have zero invariant mass. Now look up this equation:
$$m=\frac{m_0}{\sqrt{1-v^2/c^2}}$$ As you can see, the real mass of the object is the object's invariant mass $m_0$ divided by the $1-speed^2/lightspeed^2$ all squared. Now if we say that speed of the object is lightspeed ($v=c$), we get this:

$$m=\frac{m_0}{\sqrt{1-c^2/c^2}}$$ $$m=\frac{m_0}{\sqrt{1-1}}$$ $$m=\frac{m_0}{0}$$

In complex number system number larger than zero divided by zero equals to infinity, thus $m=\infty$.
Pure mathematic, no dogmas.

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This didn't actually answer the fundamental underlying question which is essentially "Why is the speed of light the ultimate speed limit?" Yes your formulas are correct however they are results from relativity, not reasons for relativity. –  Brandon Enright May 7 '13 at 5:56
Question "Why does relativity exists" or "Why are things as they are" is a question that belongs on religious forums, not physical forum. The reason why photons can achieve the speed of light is because they have zero invariant mass. –  Tomáš Zato May 7 '13 at 6:29
Normally I'd agree with you but relativity was not born out of philosophy. It was born out of the need for the speed of light to be constant in all reference frames per the Michelson Morley experiment. Why nothing can go faster than the speed of light is a consequence of relativity which in turn is a consequence of all inertial references frames being equal. –  Brandon Enright May 7 '13 at 6:32