# Why cant an object travel faster than the speed of light?

What is the reason for this?

## Answers and Replies

mathman
Science Advisor
It is a fundamental part of the theory of special relativity. One simple part is that it takes an infinite amount of energy to accelerate anything with mass to the speed of light.

it would need infinite energy to do so.

Why would it take infinite energy?

I mean the speed of light is a fixed number so is there not a fixed number of energy unit that can reach this speed.

ghwellsjr
Science Advisor
Gold Member
Do you understand and believe that every observer, no matter how much they have accelerated in the past will still measure the speed of light to be that same fixed number? So let's say that you have an infinite amount of energy in your rocket and you turn it on for a certain period of time and change your speed by one-half the speed of light. When you make another measurement of the speed of light, it's the same as it was before. You can repeat this process as many times as you wish and you will be no closer to achieving the speed of light than you were before you started. Do you understand this? If this were not the case, then there would be some states of rest that are different than others making them preferred.

But why would you go one half the speed of light If I want to go 100 percent the speed of light?

Most people can see the difference between 1/2 and 100 percent.

I mean light goes 365,000 km/s according to observations.

Force is mass times acceleration
Therefore
acceleration is Force/mass
If a strong enough force is applied an object could accelerate faster than the speed of light.

It's hard to understand because it doesn't match anything that a human being can experience in everyday life. But there a are a few reasons why you can't reach the speed of light. For one, as you go faster and faster, your mass increases (weird, but that's just how it works)...making it harder to go faster and faster. The result it that you can keep getting closer to the speed of light, but the harder you try the harder it gets...and you will NEVER actually reach it. Not even if god himself pushed your spaceship.

Another thing that stops you is that as you go faster, time slows down for you. Again, weird, but it just does. Literally...your watch will show one hour has passed, while on earth perhaps a year or century has passed. The result is that you can be close to the speed of light and hit the gas and feel a huge surge of acceleration....BUT, in fact if someone on earth measured your acceleration it might be close to zero, because what was a second for you might be a thousand years on earth.

So then you might try to measure your speed, perhaps against a light beam. Well...that's useless, because light ALWAYS travels at the speed of light away from you. Even if you yourself are going at 99.9999% the speed of light. Again, doesn't make sense but that's how it is. Trying to catch a light beam would be like trying to reach the horizon.

So basically, the universe doesn't allow you to reach this speed. Your mass rises, your energy rises, your time slows, bunch of other things happen. In order for you to get to the speed of light, your mass would have to be infinity, your energy infinity, and time would be zero. Not even the mathematics allow you to do this, as you'd end up multiplying by infinity and dividing by zero and, well, good luck with that....

russ_watters
Mentor
I mean light goes 365,000 km/s according to observations.

Force is mass times acceleration
Therefore
acceleration is Force/mass
If a strong enough force is applied an object could accelerate faster than the speed of light.
Well, perhaps the easiest way to explain is that it turns out that equation is wrong. It works pretty well at low speed, but fails at high speed. Newton didn't have access to a particle accelerator, so he didn't know.

How can this instrument "particle accelerator" provide evidence an object cannot accelerate to the speed of light?

According to Newton, today's particle accelerators are so powerful that they should be able to F=ma the hell out of a particle waaaaaaaaaay past the speed of light, but yet they still can't reach it.

We keep making particle accelerators multiple times more powerful than the ones before them, and yet all they can do is add another 9 to the 99.9......9% the speed of light that the particles actually reach.

All we have to do is to somehow convert a material object to light, then send the light to a destination. Problem solved. :) Then convert back to the material object.

ghwellsjr
Science Advisor
Gold Member
All we have to do is to somehow convert a material object to light, then send the light to a destination. Problem solved. :) Then convert back to the material object.
It still won't be faster than the speed of light.

ghwellsjr
Science Advisor
Gold Member
Do you understand and believe that every observer, no matter how much they have accelerated in the past will still measure the speed of light to be that same fixed number? So let's say that you have an infinite amount of energy in your rocket and you turn it on for a certain period of time and change your speed by one-half the speed of light. When you make another measurement of the speed of light, it's the same as it was before. You can repeat this process as many times as you wish and you will be no closer to achieving the speed of light than you were before you started. Do you understand this? If this were not the case, then there would be some states of rest that are different than others making them preferred.

But why would you go one half the speed of light If I want to go 100 percent the speed of light?

Most people can see the difference between 1/2 and 100 percent.

I mean light goes 365,000 km/s according to observations.

Force is mass times acceleration
Therefore
acceleration is Force/mass
If a strong enough force is applied an object could accelerate faster than the speed of light.
With low velocities, the formula for calculating the velocity, v, after an acceleration, a, for a time, t, is:
$$v = a t$$
So this says you could apply any acceleration for a long enough time and get v to exceed c. Or if you had a high enough acceleration, for a shorter time, it says you could get v to exceed c.

But this formula is only an approximation where the velocities end up being very small compared to c.

The correct formula is:
$$v = \frac{a t}{\sqrt{1+(a t/c)^2}}$$

If you look carefully at this formula you will see that when $$a t$$ is very small, the formula approximates to:
$$v < \frac{a t}{\sqrt{1}}$$
$$v < a t$$
This is similar to the original formula.

But when $$a t$$ is very large, the formula approximates to:
$$v < \frac{a t}{\sqrt{(a t/c)^2}}$$
$$v < \frac{a t}{(a t/c)}$$
$$v < \frac{1}{(1/c)}$$
$$v < c$$
So in reality, no matter how much you accelerate, or how long you accelerate, you can never reach c.

Now to answer your other question about going one half the speed of light, I was trying to show you that since it is possible to accelerate to that speed, then you should be able to get to 100%c in two accelerations and even faster in three, correct? The only problem is that after each step, if you measured the speed of light, you will still measure it as c and you will be no closer than you were before you started. You could repeat this as many times as you wished and still not get any closer to the speed of light.

its all in the details! The required energy to move an object to the speed of light becomes infinity as you get near the speed of light with Einsteins' field equations. And if you think that's weird, check out Time Dilation and Length Contraction. Try those out for fun! Happy Travels!