Thread: Does 0.9 repeated = 1?

Originally Posted by Xei

No, that wouldn't ever happen, because you're summing to n to infinity which is infinity.

Please elaborate.

There are an infinite amount of steps. If the runner stops for n seconds (n>0) each step, he will never catch the tortoise.

Originally Posted by Xei

There are an infinite amount of steps. If the runner stops for n seconds (n>0) each step, he will never catch the tortoise.

But there are the same infinite steps in the first scenario also. They just don't stop after each step.

Yes but the time decreases each step which is what solves the paradox. Here the time stays the same.

Originally Posted by Xei

Yes but the time decreases each step which is what solves the paradox. Here the time stays the same.

So if the stopping time got shorter and shorter every time, it would work? With eternity, there is no limit on time.

It depends. If the time was 1 then 1/2 then 1/3 then 1/4 then 1/5 etcetera, no it wouldn't. If the time is 1 then 1/2 then 1/4 then 1/8 then 1/16 (as is the case in Zeno's paradox) then it would.

http://en.wikipedia.org/wiki/Zeno's_paradoxes

I thought of something that might be a real example, you know how your weight increases exponentialy as you reach the speed of light, well it is said that you'd have to way infinite pounds to catch up with light. But light somehow goes that fast.

When you say weight, do you mean a force or do you mean mass?

Originally Posted by Kushna Mufeed

When you say weight, do you mean a force or do you mean mass?

Mass

Then that makes no sense. How can mass increase when you increase speed? You can't create matter.

Pounds is not a measure of mass, it's a measure of force.

Originally Posted by Kushna Mufeed

Then that makes no sense. How can mass increase when you increase speed? You can't create matter.

Pounds is not a measure of mass, it's a measure of force.

No, http://en.wikipedia.org/wiki/Pound_(mass)

http://www.newton.dep.anl.gov/askasc...9/phy99186.htm, curiously it says you would need no mass to catch up to the speed of light, though it does state it increases.

If you have mass, then your mass will multiply until it reaches infinity at the speed of light. According to the kinetic energy equation, 1/2mv^2, this would require infinite energy, which is impossible.

The only way to do it is if you have no mass. This means that multiplying your mass has no effect, and 1/2mv^2 does not go to infinity.

Originally Posted by Xei

If you have mass, then your mass will multiply until it reaches infinity at the speed of light. According to the kinetic energy equation, 1/2mv^2, this would require infinite energy, which is impossible.

The only way to do it is if you have no mass. This means that multiplying your mass has no effect, and 1/2mv^2 does not go to infinity.

It's not mass that increases. Einstein may have used the word mass, but that was a mistranslation. Modern physicists understand that it's momentum, not mass, that approaches infinity, and only from the perspective of an outside observer, of course.

The real fundamental reason you can't hit the speed of light is that no matter how fast you're going, the speed of light is the same. If you're going 0.9c and you turn on your headlights, you will still see light going out at 1c with respect to you. So you can never catch up because that makes no sense.

Momentum? Is that not just a consequence of your mass increasing though? Because your velocity is bounded by c.

Unless you are light, of course. Which is where LDG was having trouble.

Originally Posted by Xei

Momentum? Is that not just a consequence of your mass increasing though? Because your velocity is bounded by c.

Unless you are light, of course. Which is where LDG was having trouble.

Momentum is a fundamental physical quantity. It's not simply m*v. Take an advanced mechanics course, even classical mechanics, and you'll see this. But mass is invariant.

Momentum is a fundamental physical quantity. It's not simply m*v. Take an advanced mechanics course, even classical mechanics, and you'll see this. But mass is invariant.

Thanks. I was under the impression that when a particle moves faster it mass increases.

Originally Posted by wendylove

Thanks. I was under the impression that when a particle moves faster it mass increases.

Me as well, your a pretty smart guy I must admit.

But momentum can be calculated by the product of mass and velocity?

And hence you're saying that effectively at what we could call lightspeed, its velocity is infinite?

I haven't studied SR yet so I genuinely don't know.

Originally Posted by Xei

But momentum can be calculated by the product of mass and velocity?

No, it can't. That's a special case which only applies to large, slow moving objects not in the vicinity of a vector potential field.

Originally Posted by Xei

And hence you're saying that effectively at what we could call lightspeed, its velocity is infinite?

I haven't studied SR yet so I genuinely don't know.

There's an added factor in the SR correction. p = gamma_u*m*v, where gamma_u is the usual 1/sqrt(1-v^2/c^2). Now it's valid for large, fast moving objects not in the vicinity of a vector potential field.

Uhhh okay. I'll come back when I'm an undergrad.

...actually reading that properly it's not too bad. So neither its mass nor its velocity increases, but the new factor. Ok.

Hmmm... somebody calculate e^pi - pi.

20?

You dirty physicist.