## Faster than light

Post any maths and/or physics related questions here.

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When I say that we have physicists, astronomers and so on, I should actually say that we have former physicists, former astronomers and so on. I was a geometrist in my previous life, but now I work there as a programmer/software engineer. Some of the other guys I mentioned are also programmers, while some others so research (basically statistics).

Alvaro
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--The speed limit is the speed of light in vacuum, c. In a medium in which light travels slower, a particle can travel faster than light (but not faster than c).--
So they can't go faster than c? I thought they could...

And WHY does space-time bend because of matter? Don't tell me it explains things so we take it that way.

And what would happen if someone broke the light barrier. Would you get a blast of dazzling light like we now get a large BOOM with the sound barrier?

You can't conquer the game if you can't conquer yourself.

Jetru

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When you have false begining you may have (most?) any ending. (like if you would say that 1=2, you could 'prove' that whole math is wrong). So you may imagne anything, and mabye prove it . But remember that you started with a sentence thats false.
Generaly you shouldn't to ask 'if..?' to much , becauose it wont give you anything.
frea

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Alvaro wrote:When I say that we have physicists, astronomers and so on, I should actually say that we have former physicists, former astronomers and so on. I was a geometrist in my previous life, but now I work there as a programmer/software engineer. Some of the other guys I mentioned are also programmers, while some others so research (basically statistics).

Ah... I see. Thank you very much.
"Given enough time, man can do anything with a bit of string and some Tinker toys." Bruce Bolden, Senior Instructor at the University of Idaho.

leas5040

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Eh... C'mon something special must happen. Just don't say, it's not possible, so we should not think about it.

You can't conquer the game if you can't conquer yourself.

Jetru

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like i said everything may happen .
frea

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GeekDog wrote:
Safari wrote:Okey, c = fastest. Heat = particles "moving/shaking". Can you then say that when atoms are moving in the speed of light, c, thats the hottest anything can get?

-273,15 °C is when they're not moving at all.

No, there is no 'hottest' (as far as we know). What prevents things going faster than light, and arises from special relativity (and has incidentally been observed a lot in particle physics experiments, if you believe that sort of thing) is that when you accelerate something, it becomes heavier. Thus, by inertia, the next time you want it to accelerate, putting the same amount of impulse (impulse = force x time) will give you a smaller increase in speed.

This is very closely linked to E = mc^2, which you must have heard of. It's basically saying that when you make something go faster, you increase its kinetic energy. An increase in energy is equivalent to an increase in mass.

As an aside, special relativity is founded on the assumption that c (speed of light in a vacuum) is equal in all inertial reference frames. Once you've made that assumption, it's easy to work out for yourself. No calculus required! The reason people believe this to be true is that assuming c is the maximum speed leads to all kinds of interesting consequences, all of which (so far) appear to occur in reality.

I do not quite understand what you mean here.
If there is a maximum speed then there is a maximum heat... Safari was right.

Invictus

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leas5040 wrote:
Alvaro wrote:Errr, not exactly. These physicists and I (and astronomers, and experts in speech recognition...) write programs to model financial markets and invest in them automatically. I work for a hedge fund that uses quantitative methods.

I'm somewhat curious. How do the other people factor in to how you make investments? Are there certain patterns in nature (i.e. celestials movements as studied by the astronomers) that correlate to market fluctuations, and that's how you base predictions, or what? [...]

If there was, sure someone would tell you

Zen

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Zen wrote:
leas5040 wrote:
Alvaro wrote:Errr, not exactly. These physicists and I (and astronomers, and experts in speech recognition...) write programs to model financial markets and invest in them automatically. I work for a hedge fund that uses quantitative methods.

I'm somewhat curious. How do the other people factor in to how you make investments? Are there certain patterns in nature (i.e. celestials movements as studied by the astronomers) that correlate to market fluctuations, and that's how you base predictions, or what? [...]

If there was, sure someone would tell you

Sounds like the movie "PI".
The black and white REALLY hurt my eyes..
Last edited by Invictus on Wed Dec 15, 2004 2:22 pm, edited 1 time in total.

Invictus

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X-ecute wrote:If there is a maximum speed then there is a maximum heat... Safari was right.

I don't see the connection. You can give a particle arbitrary ammounts of energy (no limit), and will acquire arbitrarily large temperatures (no limit). No matter how much energy the particle has, though, it will never go faster than c. I don't see any problem with this picture.

Alvaro
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Alvaro wrote:
X-ecute wrote:If there is a maximum speed then there is a maximum heat... Safari was right.

I don't see the connection. You can give a particle arbitrary ammounts of energy (no limit), and will acquire arbitrarily large temperatures (no limit). No matter how much energy the particle has, though, it will never go faster than c. I don't see any problem with this picture.

But energy itself is speed. The faster the molecules are moving the more energy it has and heat is energy.

Invictus

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X-ecute wrote:But energy itself is speed. The faster the molecules are moving the more energy it has and heat is energy.

The thing is that the relation between speed and energy is not E=1/2*m*v^2 as Newton thought. There is a correction term that makes energy go to infinity as v approaches c.

I think the correct relativistic formula is
Kinetic Energy = m*c^2*(-1+1/sqrt(1-v^2/c^2))

If we use units in which c=1 and we consider an object of mass 1, the kinetic energy would be
-1+1/sqrt(1-x*x)
A plot of that function will show that we can give a particle as much kinetic energy as we want, but the speed never gets to c.

If you plot x*x/2 next to it, you will see that for values under .1*c, Newton's formula is a great approximation.

Alvaro
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Alvaro wrote:
X-ecute wrote:But energy itself is speed. The faster the molecules are moving the more energy it has and heat is energy.

The thing is that the relation between speed and energy is not E=1/2*m*v^2 as Newton thought. There is a correction term that makes energy go to infinity as v approaches c.

I think the correct relativistic formula is
Kinetic Energy = m*c^2*(-1+1/sqrt(1-v^2/c^2))

If we use units in which c=1 and we consider an object of mass 1, the kinetic energy would be
-1+1/sqrt(1-x*x)
A plot of that function will show that we can give a particle as much kinetic energy as we want, but the speed never gets to c.

If you plot x*x/2 next to it, you will see that for values under .1*c, Newton's formula is a great approximation.

Can you define the variables in those formulas please?
I got c is speed and m is mass but what are v and x?

Invictus

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m is the mass of our object.
c is the speed of light in vacuum.
v is the speed of our object.

x:=v/c is a handy way of representing speed, where 1 means the speed of light in vacuum. Sorry I forgot to mention this. I just called it x so it is easy to plot the formulas in gnuplot.

Alvaro
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Newton never thought of energy. He was a force guy.

You can't conquer the game if you can't conquer yourself.

Jetru

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