# Infinite Accelatation

Before I ask my question, let me just say, I know very little about particle physics and general relativity, so I may ask a obvious question or a question that makes little or no sense.

Now, what would stop this object accelerating to the speed of light:

If an object was in a perfect vacuum (no matter at all, except the objects, and particles couldn't 'appear'), and there was another object which was attracting, via gravity, the first object, but the second object was moving away (irrelevant how it does it) so it will always be ahead of the first object.

I understand forces are carried using bosons? So perhaps if there wasn't any other particles the gravity couldn't be carried. A proposed force carrier for gravity is the gravitiron, but this is still hypothetical. If the gravitiron does exist, and was in the vacuum, would it slow down the object when coming in contact?

I know this seems vague, but I will happily accept any answer.

• while there's this hypothetical thing known as negative mass that can do this when you have a pair of mass and negative mass of the same mass (a "mass dipole") placed side by side, it is considered highly speculative as so far we have no experimental evidence for the existence of negative mass . People sometimes talked about negative energy densities in general relativity, however I am not good enough at General relativity to comment on that any further Aug 17 '15 at 11:03
• Possible duplicates: physics.stackexchange.com/q/24319/2451 , physics.stackexchange.com/q/170502/2451 , physics.stackexchange.com/q/172786/2451 , and links therein. Aug 17 '15 at 11:32

A simple answer is that there is no point at which you are close to the speed of light, you might be close to the speed of light relative to other objects however you can keep trying to accelerate, and your slow relative to other objects. Your both fast and slow.

From the point of view of an object looking at you, they may see you travelling close to the speed of light but you can keep trying to accelerate, nothings going to stop you from trying, and you will accelerate a little, but not as much as you did when you were "stationary" (relatively at the same speed as at the point you started at).

The reason is that your "high speed" has made your time slow down relative to the place you started off accelerating from. So now it takes you longer to try to do anything, so you can't accelerate as quickly as before. Its going to take you longer to throw something out the back of your spaceship. As you keep going faster, your time gets slower.

Does that make any sense?

But all of this is just words and doesn't do justice what equations would do, and equations don't "explain" it as far as I'm concerned, they just show what really happens. Knowing what happens is not an explanation.

Knowing the equations of motion and being able to predict gravity's effect on a ball falling down doesn't explain gravity, but its useful, also that's the case with relativity, they give you the equations, they don't give you an explanation. (I think I'm right on that).

• You should make it clear that when your "high speed makes time slow down" is only true from the point of view of the observer. You do not yourself see time slow down and acceleration getting harder. i.e. it doesn't take you longer to do anything, as measured by the clock you carry. Aug 17 '15 at 12:17
• Yes correct, but I think there's also more errors in what I wrote, its a gross over-simplification. Its not easy to express in English language.
– Phil
Aug 17 '15 at 12:19
• Thanks for this explanation, and I sort of worked out that in would take infinite energy to accelerate to the speed of light, from an stationary observer. Aug 17 '15 at 21:28

Many things stop you.

Firstly, it turns out forces do not cause accelerations. Forces increase momentum, and for slow speeds when you double the momentum you almost double your speed, and it is so close to doubling that for hundreds of years we thought it was doubling.

But now that we've learned how to make things go fast and how to measure their momentum we've found out that it is an empirical fact that doubling the momentum makes the speed get less than doubled.

So what happens is a force can be applied and your momentum gets larger and larger but your speed is always less than c.

Here is how speed is related to energy and momentum: $v=c^2p/E$ and for a massive particle $E>pc$ so $v<c.$ How do we know $E>pc$? This is how energy is related to mass and momentum $E=\sqrt{(mc^2)^2+(pc)^2}$ so we know how speed depends on momentum and mass: $v=c^2p/\sqrt{(mc^2)^2+(pc)^2}.$

Now we can talk about why it took hundreds of years to notice this. When momentum is small, much less than $mc$ then $E\approx mc^2$ so $v\approx c^2p/(mc^2)=p/m.$

So for slow speeds $p\approx mv$ but in general the momentum is larger than that, but since everyday momentum is so much smaller than $mc$ we didn't notice the deviations. So the momentum is actually a bit larger than you'd think for the speed, or the other way around the speed is a bit smaller than you'd think for the momentum.

So specifically as your momentum goes to infinity $E\approx pc$ so $v\approx c$ but $E$ is a tiny bit bigger so $v$ is a tiny bit smaller. So you never get to the speed of light. Applying a force can't make you go the speed of light because all it actually does is change your momentum.

Now if you have a mass of zero then $E=pc$ and you have to go the speed of light and changing your momentum won't change your speed. Mass tells you how much bigger your energy is than you momentum ($E=\sqrt{(mc^2)+(pc)^2}$) and since your speed is $v=c^2p/E$ you either go less than $c$ if you have mass, or at $c$ if you have zero mass.