FTL Question

ccb056 · Post by **ccb056** » Wed May 05, 2004 5:45 pm

If this equation is true:
V=(V1+V2)/(1+(V1*V2)/c^2)

Then why is it when you plug in c^2 for both V1 and V2 you get the total velocity as 2m/s

Lothar · Post by **Lothar** » Wed May 05, 2004 6:12 pm

If you plug in c^2 for your velocities, that doesn't make much sense... what are the units on c^2?

If you plug in c, you get:
V = ( c + c ) / (1 + c*c/c^2)
= ( 2*c ) / (1 + 1)
= 2c / 2
= c (which is what you should get)

If you plug in c^2 (but fix the units), you get:
V = ( 2 * c^2 ) / (1 + c^2 * c^2 / c^2)
= ( 2 * c^2 ) / (1 + c^2)
= 2 + 2/c^2 + 2/c^4 + ...
~= 2

The reason you get a nonsense result is that you plugged in a value outside of the range of the equation. It's like, if you plug in a temperature of -26 K into just about any equation, you're going to get some really strange results. You can't get a sensible result if you use a velocity larger than c.

ccb056 · Post by **ccb056** » Wed May 05, 2004 6:36 pm

but, if you bent spacetime then your apparent speeds could be faster than c, right?

and if the apparent speeds are faster than c, then why is the apparent answer only 2?

Lothar · Post by **Lothar** » Wed May 05, 2004 6:56 pm

My assumption would be that if you bend spacetime to the point where you can have velocities above c, you're no longer operating within a model where v = (v1 + v2)/(1 + v1*v2/c^2) is a valid equation.

What is that equation, anyway? Where does it come from? It's not something I recognize.

ccb056 · Post by **ccb056** » Wed May 05, 2004 7:20 pm

that's an equation I was given in physics class

In general newtonian physics, if youre riding in a bus traveling at 10 mph and you throw a ball forward at 5 mph, then the ball relative to the ground travels at 15mph

so, according to newton, if you were traveling at .9c and threw a ball at .9c the ball would go 1.8c

but, the formula is flawed so it was Einstein who created the
V=(V1+V2)/(1+(V1*V2)/c^2)
formula

Lothar · Post by **Lothar** » Wed May 05, 2004 7:46 pm

oh, I see that... yes, it's a formula for adding velocities in a relativistic frame. Neither velocity can be larger than c, though -- if either velocity is larger than c, the whole thing falls apart.

ccb056 · Post by **ccb056** » Wed May 05, 2004 7:52 pm

well, if you graphed it with the V1 and V2 equal and from 0 to "past c", wouldn't it be a parabola?

Lothar · Post by **Lothar** » Wed May 05, 2004 8:14 pm

No, it's not a parabola. The graph would be

v(x,x) = 2x / (1+(x/c)^2)

X is small, this graph increases like a line. As x approaches c, v levels off to c, and then as x grows larger than c (which is physically impossible) v begins to drop, but always remains positive. You already mentioned that for x = c^2, v is about 2. For x = c^3, v is just a tiny bit above zero. For x = c^100, v is an even smaller bit above zero. In the limit as x -> infinity, v -> zero.

Mobius · Post by **Mobius** » Thu May 06, 2004 12:24 am

ccb - you don't understand relativity.

If you are travelling at .99C and fire a laser beam from the front of the craft, it will only travel away from you at the speed of .01C.

However, to YOU, it will *appear* as if it is travelling away at light speed. This is relativity.

Newtonian motion means dick at relativistic velocites.

There are some excellent resources on the web which use simple examples to explain how relativity works.

As to exceeding C: unless Einstein was wrong (and it seems unlikely) then you can't travel faster than light in this universe.

However, it *may* be possible to shorten the distance you require to travel, by bending space time to bring two objects separated by great distance into very close proximity in an area of warped space time.

Whether there is enough energy in the universe to allow this to happen is unknown however.

Worm holes are a favourite idea too - but the energy required to open one large enough for a ship to fit through exceeds the output of our sun by several orders of magnitude.

fliptw · Post by **fliptw** » Thu May 06, 2004 12:42 am

Mobius wrote: Newtonian motion means dick at relativistic velocites.

no, it doesn't mean dick.

Conservation of momentum doesn't depend on velocity.
Neither does action = equal reaction.

Relativity doesn't happen only at near the speed of light either.

Avder · Post by **Avder** » Thu May 06, 2004 12:44 am

The answer is 42.

[spoiler]If you dont get it, well....YOURE STUPID!!![/spoiler]

Dedman · Post by **Dedman** » Thu May 06, 2004 10:50 am

220, 221 whatever ti takes.

woodchip · Post by **woodchip** » Thu May 06, 2004 7:43 pm

The problem I have here is the whole relativity theory is based on the speed of light (hope I'm not sticking my foot in my mouth). So what happens when a different form of energy is discovered where its basic particle moves faster than light?
Secondly if we can slow the speed of a photon of light in a special medium, would it be logical to assume there may be a medium where light can be sped up?

ccb056 · Post by **ccb056** » Thu May 06, 2004 7:54 pm

the speed of light is constant, so only the aparent speed of light can be changed

because e=mc^2 as you approach the speed of light, the required energy approaches infinity and your mass increases withou bounds

DCrazy · Post by **DCrazy** » Thu May 06, 2004 8:27 pm

Chipper, don't forget particle-wave duality. Light is a form of electro-magnetism, and in actuality it is more accurate to say that c = the speed of any electromagnetic wave. Since a wave is not a particle (and thus has no mass), it transcends the typical notion of speed. As far as waves go, Velocity = frequency * wavelength for any wave, physical or electromagnetic, NOT distance/time.

Don't think of the energy as what's traveling in the light wave. Instead, think of the wave as a + shaped object composed of electric fields and magnetic fields traveling in perpendicular planes.

Can someone fill in details here, as I can only talk from a first-year physics perspective? I'm assuming all this talk is only about special relativity.

De Rigueur · Post by **De Rigueur** » Thu May 06, 2004 8:34 pm

ccb056 wrote:If this equation is true:
V=(V1+V2)/(1+(V1*V2)/c^2)

Then why is it when you plug in c^2 for both V1 and V2 you get the total velocity as 2m/s

I assume that c^2 is 'c squared' and V1 and V2 are velocities. Wouldn't you have a problem reconciling your units if you put in c^2 as a velocity? The units for velocity are m/s and for c^2 they are (m/s)^2.

DCrazy · Post by **DCrazy** » Thu May 06, 2004 8:35 pm

I think he meant if you are traveling at (3 x 10^8)^2 m/s.

ccb056 · Post by **ccb056** » Thu May 06, 2004 8:36 pm

DCrazy wrote:I think he meant if you are traveling at (3 x 10^8)^2 m/s.

Yes, that's what I meant

De Rigueur · Post by **De Rigueur** » Thu May 06, 2004 9:21 pm

woodchip wrote:The problem I have here is the whole relativity theory is based on the speed of light (hope I'm not sticking my foot in my mouth). So what happens when a different form of energy is discovered where its basic particle moves faster than light?
Secondly if we can slow the speed of a photon of light in a special medium, would it be logical to assume there may be a medium where light can be sped up?

As I understand it, in relativity theory, the speed of light has an absolute limit - which makes distance (or space) and time relative (given that speed is distance/time).

If something faster than the speed of light is discovered, then there will occur what is known as a scientific revolution. It's a big 'if'. I don't know if any science has ruled out the possibility.

Your second question relates to the debate between rationalists and empiricists. A rationalist may speculate that if something can slow down light, then based on some a priori principle of symmetry, balance, or whatever, there should be some way to speed it up. The empiricists (who interrogate nature rather than speculate) are usually held to have won the debate. The speed of light has been empirically verified to the point that it is considered 'established' science.

Lothar · Post by **Lothar** » Thu May 06, 2004 9:57 pm

It should be noted that Lyndon LaRouche is a rationalist. Hence, empiricism is the best ;)

woodchip · Post by **woodchip** » Fri May 07, 2004 6:25 am

Lothar you're spending too much time in E&C

Back to topic. Somewhere I was listening to a phycicist explaining dimensional space. The main conjecture on his part was that space and reality may contain up to 11 dimensions or perhaps more understandbly...11 energy levels. Boosting up to a higher level might there-by increase speed travel without the "as one approaches the speed of light, time slows down" theory. Of course the question is...how does one boost or enter a higher dimensional energy level. Sorry guys, not only am I a rationalist, I am also a generalist

De Rigueur · Post by **De Rigueur** » Fri May 07, 2004 7:38 am

I've read something about 11 dimensions in a book that tried to explain the physics that occured some fraction of a second after the big bang.

AFAIK, the only way to boost to a higher energy level is with dilithium crystals.

Wolf on Air · Post by **Wolf on Air** » Fri May 07, 2004 12:13 pm

Cut the treknobabble. Anyhow... what's usually referred to when talking about 11 dimensions is M-theory, also known as (super)string theory; a somewhat new contender for the title of Theory of Everything. Read a good book on the subject for more info; a personal favourite is Brian Greene's "The Elegant Universe" (which has also been made into a three-part TV show which imo is crap).

http://en.wikipedia.org/wiki/M-theory_( ... planation) is also a good summary.

Tricord · Post by **Tricord** » Fri May 07, 2004 3:39 pm

Wolf on Air wrote:Cut the treknobabble.

Amen to that.

If you use Einstein's relativity theory, you are using a model to describe reality. Since the relativity theory is only a gravitational theory (it ignores the other natural forces) it is flawed. But as a model it is found to be more than enough accurate for what we can possibly use it for (experiments, launching satellites, etc.)

If you decide to use a model to calculate with, and that model says that c is a constant, you're out of order when you question the value of c. You should find a new model (and thus theory that yields such model) that does not contradict the previous model, yet allows for your broadening in the sense of a variable c value.

Good luck.

DCrazy · Post by **DCrazy** » Fri May 07, 2004 3:44 pm

And so we wait for the Theory of Everything.

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