# Is it realy true that nothing can travel faster than light? if so, why?

1. Aug 16, 2009

How do the movement of a particle relate to the speed of light

2. Aug 16, 2009

### DaveC426913

Re: Is it realy true that nothing can travel faster than light?if so,y?

Special Relavitiy does not specifically state that nothing can travel faster than the speed of light. SR does state that nothing can start off at slower than c and reach or exceed c.

Hypothetical particles called tachyons travel faster than c. They cannot slow down to or below c. They are forever cut off from interaction with our sub-c universe.

3. Aug 16, 2009

### Fredrik

Staff Emeritus
Re: Is it realy true that nothing can travel faster than light?if so,y?

For starters, we can show (see post #15 here) that the work required to accelerate an object of mass m from speed 0 to speed v is $(\gamma-1)mc^2$, where

$$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

Note that $\gamma\rightarrow\infty$ when $v\rightarrow c$. This means that there's no amount of work that can accelerate the particle to speed c.

The above is at least a valid way of looking at it, but I wouldn't call this "the reason" why massive particles can't reach c. A better answer is that the combination of special relativity and quantum mechanics severely restricts what types of particles can exist. Any particle must have the property that $$E^2-\vec p^2c^2$$ is the same in all inertial frames. If this quantity is =0, the particle must always move at c. If it's >0, the particle must always move at speeds <c. (Edit: After reading Dave's post, I think I should add that the third possibility, i.e. that the quantity is <0, corresponds to tachyons. I didn't mention that at first because they aren't believed to exist. They have never been observed, and it's hard to even write down a theory with tachyons in it that doesn't contradict itself). We now define the "mass" of the particle by setting this quantity equal to $m^2c^4$, and choosing m to be positive when it's not zero.

In other words, it's a consequence of the definition of "mass" (and "particle"), and there's no easy way to see why this is so. It requires some fairly advanced mathematics. (Chapter 2 of Weinberg's QFT book covers this pretty well).

Last edited: Aug 16, 2009
4. Aug 18, 2009

Re: Is it realy true that nothing can travel faster than light?if so,y?

what is it that prevents it to travel faster than c?

5. Aug 18, 2009

### DaveC426913

Re: Is it realy true that nothing can travel faster than light?if so,y?

To summarize Fredrik's post:

As a mass approaches relativistic velocities, its mass increases. This requires more energy to accelerate it further. At a speed arbitrarily close to c, its mass approaches infinity, so the energy requires to accelerate it further approaches infinity.

6. Aug 18, 2009

### DrGreg

Re: Is it realy true that nothing can travel faster than light?if so,y?

It's kind of built into the postulates of relativity. The second postulate says that all observers measure the speed of light to be the same value. If it were possible for you to gradually accelerate up to the speed of light and then overtake it, you would have to measure the speed of light gradually decreasing to zero, relative to yourself, and then going backwards. That can't happen because you always measure it as constant.

As to why the Universe behaves like this, we can't really say, we just know it does.

7. Aug 18, 2009

### Count Iblis

8. Aug 18, 2009

### Darryl

Re: Is it realy true that nothing can travel faster than light?if so,y?

Would it be correct to say that due to time dilation, as a particle increases in speed towards c then that particle's own time slows.

So given a constant force applied to the particle, the force seen by that partical as it approaches c will reduce to zero and its own time frame of reference approaches.

So it's not so much you need infinate energy (you may do) to accelerate a particle to c, you also need infinate time to do so.

That also implies to me, that a photon of light never experiences time, distance of space it simply starts to exist and in zero (it's own time) time ceases to exist.

A Photon can only exist at c as soon as it deviates from c it experiences time and annialates itself.

A very interesting subject though

9. Aug 19, 2009

### VKint

Re: Is it realy true that nothing can travel faster than light?if so,y?

This is correct, except that to speak sensibly of an object "experiencing time" (or "experiencing" anything, for that matter), one needs to be able to refer to the rest frame of the object. A photon, however, has no rest frame. Thus, saying that it "experiences no time" is slightly illusory, as a photon doesn't have a "vantage point" from which to experience things.