1. Jun 30, 2008

### Mykal

Hello All

This is a question from a complete physics ingnoramus, and a quick search on google brought this forum up as a good place to start! Also, apologies if I'm in the wrong bit of the forum.

Right, the question. I've been reading about the Large Hadron Collider in Cern, and it keeps making reference to the particles colliding at 99.99% of the speed of light. Why is it 99.99% of the speed of light, if they are able to accelerate them up to 99.99%, what is stopping them being accelerated to the speed of light?

Mykal

Last edited: Jun 30, 2008
2. Jun 30, 2008

### humanino

Hi Mykal, and welcome to PF
It is increasingly difficult to accelerate near the speed of light. Going from 98% to 99% requires more energy than going from 97% to 98%. You could think schematically, it will take as much energy to from 88% to 98%, than to go from 98% to 99%, or from 99.9% to 99.99%, or from 99.99% to 99.999%... So it would take infinte energy to go to 100%

3. Jun 30, 2008

Staff Emeritus
The relation between velocity and energy is:

$$v = c \sqrt{1 - \frac{m^2 c^ 4}{E^2}}$$

You can see that as E gets arbitrarily large, v gets arbitrarily close to c, but that it has to be infinite for it to equal c. You will also see that 99.99% is an underestimate: 99.999999% is closer to the mark.

4. Jun 30, 2008

### Feldoh

Basically you'd need an infinite amount of energy to have something going at the speed of light, the closest we can get is 99"-and-some-change"%

5. Jun 30, 2008

### Harut82

According to Einsteins theory of relativity. Objects gain mass as the approach the speed of light. The closer you get the more the mass increases and the harder it gets to increase the speed.

6. Jul 1, 2008

7. Jul 4, 2008

### Mykal

Excellent. Thanks for your patience and responses guys. I hope you realise that this has given me more things to read about, so be prepared for another round of educate the dummy, especially when the LHC is up and colliding!

8. Jul 8, 2008

### spyderfast

I am not qualified to provide a better solution as any of the above answers, but I would like to reflect on the trouble with understanding how something that is 99.9 or 99.99 or 99.99999 etc becomes hard to grasp in being that it seems so easy to attain the next level of higher numeric value or "wholeness/completness". I hope this graph helps. Just think of it in reverse. I don't want to confuse the discussion, but look at it by comparing the futility of trying to obtain the value of 1 to the opposite of the value of zero. I have had the opportunity to work with many radioactive materials and observe their decay rates. When you graph them out, they always show that they can never reach total decay of the amount first measured, even if the amount measured was billions of atoms or a few. Even if the time of decay (half life) was millions of years or 13 seconds. How does this apply to the question asked above? It is only an attempt to show how logarithmic changes or attempts to reach infinity in solving an observable event can seem so strange and defy common sense.

http://www.moltensalt.org/reference...nk.net/bhoglund/images/cs_137_decay_graph.gif

The graph above is not the best example, but if you could look at it close enough, the numbers curve down, but never touch the lines because you can not reach zero