Relativistic math question.

[megaplayboy]

What is the relativistic mass for a 1kg object accelerated to the speed of light...minus 1 Planck length? That is, "c" minus 1.6 x 10^-35 m/sec?

[L. Marcus]

Almost infinite. As close so infinite can be seen on a clear day.

[Zeropoint]

I was going to calculate it for you, but it turns out that I don't have access to anything that will calculate results to 43 significant figures.

 

Edit: I found an arbitrary precision calculator online, and if I did the calculations correctly (no promises here) the answer is about 3.05 x 10^21 kg, which seems a little low, since it's about 1/1000 the mass of the Earth.

 

I've been going over the math and it looks right. I'll admit to being surprised and I would welcome a second opinion.

[megaplayboy]

I was going to calculate it for you, but it turns out that I don't have access to anything that will calculate results to 43 significant figures.

 

Edit: I found an arbitrary precision calculator online, and if I did the calculations correctly (no promises here) the answer is about 3.05 x 10^21 kg, which seems a little low, since it's about 1/1000 the mass of the Earth.

 

I've been going over the math and it looks right. I'll admit to being surprised and I would welcome a second opinion.

That...seems plausible. The "oh my god" particle had a relativistic mass about 300 billion x rest.

 

So, a human sized mass moving at (c-planck) would have a relativistic kinetic energy of 0.5 x (3.05 x 10^23)(3 x 10^8)(3 x 10^8), or about 1.5 x 10^40 joules. Or, if you compressed the universe into a fist-sized mass and accelerated it to this speed, the relativistic KE would be around 10^90 joules. Or about 300 Damage Classes!

[Zeropoint]

For a point of reference, the gravitational binding energy of the Earth is around 2.5 x 10^32 J, or a mass equivalent of 2.8 x 10^14 kg. Your one-kilogram slug has enough energy to destroy the earth 10^(21-14) = 10,000,000 times.

[Badger]

Big  numbered math!.....it burns

[Cancer]

So, a human sized mass moving at (c-planck) would have a relativistic kinetic energy of 0.5 x (3.05 x 10^23)(3 x 10^8)(3 x 10^8), or about 1.5 x 10^40 joules.

There is the minor issue of where that energy came from, how you got it all into that small mass, and what you did with all the waste heat from the process of getting all that confined in that way.

 

Perhaps just as informative, compute the energy density in that moving mass, then go to your cosmological-model-of-choice and see when the primordial fireball had that energy density. My guess is that it was Real Early On.

[Christopher]

There is the minor issue of where that energy came from, how you got it all into that small mass, and what you did with all the waste heat from the process of getting all that confined in that way.

Ask Petey. He did that at least twice. At least:

http://www.schlockmercenary.com/2004-08-20

http://www.schlockmercenary.com/2004-08-24

[Badger]

Probably enough to make my brain splode if I try to figure it out.

 

So, I am deferring to "Mortal man was not meant to know" and crawl back into my burrow.

[bigdamnhero]

...am I the only one dying to know how this came up in a Star Hero game?

[Badger]

Before you ask such a question, remember it is easier to learn than unlearn