DaveKillens wrote:But doesn't mass decrease as velocity increases?
DaveKillens, I am impressed by you reading my post. I did not think anybody would. You are probably, like me, on vacation.
This is why I decided to break my own record for a long post. Who knows, maybe somebody will read it some day...
I am afraid you are wrong. As you approach c (speed of light, around 300.000 km/second) your mass increases exponentially.
The equation that gives you the mass increase is this:
m = m0/square root(1-(v^2/c^2))
Where m0 is your mass at rest, or mass when your speed is zero, v^2 is the square of your current velocity and c^2 means c (the speed of light) squared.
I do not have my Buck Rogers slide rule at hand either but, for example, if you are going at 225.000 km/sec, which is 3/4 of the speed of light, your mass increases by:
m = m0/square root (1-(225.000^2/300.000^2))
m = m0/square root (1-(50,625,000,000/90,000,000,000))
m = m0/square root (1-0.562)
m = m0/square root (0.44) = m0/0.661 = 1.51 m0
Your mass increases a little over 50%.
As I explained, this does not mean that you grow or something like that. You will be remain unchanged. But when you try to accelerate, you find that you need 50% more horsepower to reach the same acceleration as when your started to move. Your inertia has increased.
You can see that when you reach the speed of light, the equation converts to:
m = m0/square root (1-(c^2/c^2)) = m0/square root(1-1)
m = m0/square root (0) = m0/0 = infinity
No matter what force you apply, your mass is infinitely high, so your acceleration is zero. This is why (under special relativity) you cannot surpass the speed of light.
I have never calculate how much this effect increases the mass of an F1 car, but it will be certainly negligible.
Let's see, an F1 car reaches 350 km/hr, which is around 0.01 km/sec. This means :
m = 600 kg / square root (1-(0.01^2/90.000.000.000)
m = 600 kg / square root (1-(0.0094/90.000.000.000)
m = 600 kg / square root (1-0.000000000000105)
m = 600 kg / square root (0.999999999999894)
m = 600 kg / 0.9999999999999474
m = 600.000000000031
The increase in mass is only 0.03 millionths of a gram. This is insignificant. That is the reason why we can not notice the effects of relativity on ordinary speeds. Only when you approach the speed of light this effect becomes dominant.
Sorry for the lengthy and step by step calculations, but I have found that this gives you a quick idea of the apparently bizarre effects on your mass as you approach the speed of light, compared with the speeds we experience ordinarily.
This is the reason why it took so much time to discover relativity: only whe we started to observe particles moving at high speeds, like electrons and the such, did we notice the mass increase.
The famous equation of Einsten, e=mc^2 gives you the amount of energy that you get when you annihilate matter, for example, using an atomic bomb.
You could get the energy needed to accelerate an F1 car from the total annihilation of 0.03 millionths of a gram of matter, assuming a perfectly eficient engine. This is the reason why when you annihilate matter in an atomic bomb you get such enormous amounts of energy. Gas tanks would be minuscule if we used atomic energy instead of gasoline... You can move a giant submarine for thousands of kilometers with a few kilos of uranium, even if reactions are far from perfect efficiency.
The simmetry I find beautiful is that to reach the speed of light you should annihilate the totality of the ship, and efectively, convert it into light.
As I have never found this result of special relativity in any book, and this relation gives you certain figures and limitations about the kind of ship you need, I decided to write something about it a few years ago.
The fastes vessel humankind has created was the Apollo capsule. In 1968, Bormann, Lovell and Anderson became the fastest pilots on history, reaching around 40.000 km/hr. This is around 11 km/sec, ridiculously low compared with the speed of light.
The nearest star to Earth is Proxima Centauri. I can see it tonight from my patio, close to the Southern Cross, shining over the southern sky of Bogotá.
The light from this star takes a little less than 4 years to reach my house: the Apollo capsule would take a little over 930.000 years to get there. We clearly need something different from a rocket to reach it.
Of course, the Star Trek teletransporter is the perfect solution: you step on it and you are transported instantaneously. This, I think, is the Holy Grial of transportation science...
Cool thread 
, calls them some other dimension entities. Infact he has cured loads of stuff through them. 
