Half Speed

[bintang]

Is it impossible to go HALF the speed of light?

Lets say that there are three objects in space. One object (Object A) is stationary (relatively speaking). Object B takes off in one direction away from A. Object C takes off in the exact opposite direction away from A. The two objects are moving at X speed, but wouldn't they be travelling at 2X relative to each other? Wouldn't that assumption mean that if Object A saw Object B going half the speed of light, wouldn't Object C see B traveling at the speed of light? If that is the case, then shouldn't 1/2 the speed of light be just as unattainable as the speed of light itself?

[rowrrbazzle]

No.

Let's make B and C travel at .9999 light speed relative to A.

Observer A sees the separation of B and C increasing as though one of them is traveling away from the other at 1.9998 light speed. But when B or C actually does the measurement of the other's speed, it's always less than light speed.

In other words, none of the observers measure any of the others traveling at more than light speed relative to him (i.e., in his frame of reference).

[Wheelz]

Originally Posted by rowrrbazzle

No.

Let's make B and C travel at .9999 light speed relative to A.

Observer A sees the separation of B and C increasing as though one of them is traveling away from the other at 1.9998 light speed. But when B or C actually does the measurement of the other's speed, it's always less than light speed.

In other words, none of the observers measure any of the others traveling at more than light speed relative to him (i.e., in his frame of reference).

Can you expand on your answer, rowrrbazzle? Why is this so?

[Exapno Mapcase]

There's a handy List of Relativistic Equations on Wikipedia.

The one involved here is the simple Lorenz Transformation for velocity addition, near the top of the page.

Relativity is based on this. Putting any two velocities into the equation always sum to less than C.

Why?

Special relativity is based on two postulates which are contradictory in classical mechanics:

The laws of physics are the same for all observers in uniform motion relative to one another (Galileo's principle of relativity),

The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

Once you assume that the speed of light is a constant everything else follows as a consequence.

[sweeteviljesus]

The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

Is this really a postulate? I thought that this was predicted by the ToR and explained the data gained from the Michaelson-Morley experiment.

Rob

[MikeS]

The Master speaks.

[Exapno Mapcase]

Originally Posted by sweeteviljesus

Is this really a postulate? I thought that this was predicted by the ToR and explained the data gained from the Michaelson-Morley experiment.

Rob

Today we know that it is a mathematical consequence but at the time Einstein would't have been able to realize that. He had to treat it as an assumption. It's also not really clear whether he used the Michaelson-Morley experiment or not.

http://www.upscale.utoronto.ca/Gener...l/SpecRel.html

Notice that the statement also explains the null result of the Michelson-Morley experiment. However, although the evidence is not certain it seems quite likely that in 1905 Einstein was unaware of the experiment (cf. Gerald Holton, "Einstein, Michelson and the 'Crucial' Experiment," which has appeared in Thematic Origins of Scientific Thought, pg. 261. and also in Isis 60, 1969, pg. 133.).

[bintang]

Originally Posted by Exapno Mapcase

Relativity is based on this. Putting any two velocities into the equation always sum to less than C.

So this does say that half the speed of light is unattainable since any two velocities always are less than C, right?

[Telemark]

Originally Posted by bintang

So this does say that half the speed of light is unattainable since any two velocities always are less than C, right?

Not really, there's no problem reaching half the speed of light. You can't apply normal math to this. Normal math doesn't work at relativistic speeds.

[ultrafilter]

Originally Posted by bintang

So this does say that half the speed of light is unattainable since any two velocities always are less than C, right?

No, it says that as you approach the speed of light, the formula for computing relative velocities starts to deviate from simple addition.

[friedo]

Originally Posted by bintang

So this does say that half the speed of light is unattainable since any two velocities always are less than C, right?

No, what it's saying is that everything is relative. You can't say "Bob is going half the speed of light." You can only say "Bob is going half the speed of light relative to Alice"

Let's go back to the OP's example. B and C are both traveling away from A in opposite directions. From A's point of view, both B and C are traveling at 0.5C.

Similarly, from B and C's point of view, A is traveling away from them at 0.5C.

What about B's view of C? According to Newtonian physics, the apparent velocity should be exactly 1C. But Einstein postulated (and experiment later proved) that when relativistic velocities are encountered, simple Newtonian math breaks down and no longer works. To find the apparent velocity, you have to use the Lorentz equation: 1 / sqrt( 1 - ( v² / c² ) )

B is traveling away from A at (for the sake of simplicity) 150,000 km/sec. That gives us a Lorentz change factor of roughly 1.15. That means three things:

1. If A could observe B's mass, it would be 1.15 times heaver than when B was at rest.
2. If A could observe B's length in the direction of travel, it would be 1.15 times shorter than when B was at rest
3. If A could observe a clock on B, it would be going 1.15 times slower than when B was at rest.

Similarly, an observer on B would notice the same thing about A. Because of this time and length dilation, any observations that B makes about C would be likewise affected. The net result is that to an observer on B, C appears to be traveling away at something less than the speed of light.

[bintang]

Thanks so much! Especially Friedo. You guys really cleared that up for me!

[Exapno Mapcase]

Originally Posted by bintang

So this does say that half the speed of light is unattainable since any two velocities always are less than C, right?

And to third it, particles are known that travel at .99 many nines % C.

If you do the math, two particles moving away from one another at .99 C have a relative velocity of .999949 C. Any speed short of C is attainable in theory.

[Chronos]

On the other hand, you can't really say that you can approach the speed of light, since no matter how fast you're going, you're always just as far away from c as when you started.

[Exapno Mapcase]

Originally Posted by Chronos

On the other hand, you can't really say that you can approach the speed of light, since no matter how fast you're going, you're always just as far away from c as when you started.

Oh, c'mon, don't confuse the poor sod.

[Reply]

People can actually understand this sort of stuff?!

[Chronos]

Relativity, sure, that's easy once you get used to it. Now, quantum mechanics, nobody actually understands that.

[friedo]

Originally Posted by Chronos

Relativity, sure, that's easy once you get used to it. Now, quantum mechanics, nobody actually understands that.

At least people know what quantum mechanics is, though. Nobody can even define string theory.

[DSYoungEsq]

Why bother? Definitions just get in the way.

[Crafter_Man]

Originally Posted by Chronos

On the other hand, you can't really say that you can approach the speed of light, since no matter how fast you're going, you're always just as far away from c as when you started.

That makes my brain hurt.

[Stranger On A Train]

Originally Posted by Chronos

Relativity, sure, that's easy once you get used to it. Now, quantum mechanics, nobody actually understands that.

"We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct." -- Niels Bohr to Wolfgang Pauli.

Stranger

[sailor]

In special relativity the formula for adding speeds is:

               u + v
         w =  ---------
              1 + uv/c2

It is just that at our low everyday speeds the term uv/c2 can be neglected and the formula taken as w = u + v but that is only an approximation.

[Chessic Sense]

Ok, look people...some of us here are rather dumb about this stuff. You can´t just say "Here´s an equation for this stuff" and just bank on us knowing what the hell those variables are.

[Santo Rugger]

u is the speed of B relative to A, v is the speed of C relative to A, and W is the speed of C relative to A.

The part I don't understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not?

[Exapno Mapcase]

Originally Posted by Chessic Sense

Ok, look people...some of us here are rather dumb about this stuff. You can´t just say "Here´s an equation for this stuff" and just bank on us knowing what the hell those variables are.

That's the equation I used to calculate what would happen if both speeds were .99C. So I set u = .99 and v = .99 and C = 1.

You can set u to any value and v to any value to calculate the outcome. I used .99 because it's the most dramatic and least obvious that w will still be less than 1.

If you use half light speed, then u = v = .5 and w = .8.

If u = .99 and v = .5, w = .9966.

But if u = v = .000001 (or 670 mph, around the speed of sound), then w = .000002 just as you'd expect. And sound is much faster than any normal human process.

The equation is amazingly simple and straightforward. You can calculate it by putting the terms into the Google search bar.

And to explain Chronos' joke. You can never achieve infinity. So any finite number, no matter how large, is essentially 0% of infinite. Extremely loosely speaking. For all real world purposes, a few nines in the .999 expansion is pretty damn close.

[ultrafilter]

Chronos wasn't quite joking, though. No matter how fast you're going relative to another observer, you will both measure the speed of light as the same value. If you plug in c for one of the terms in the equation, you get (v + c)/(1 + v/c), which rearranges to c(v + c)/(v + c), or c. Note that this happens regardless of the value of v, so even if v = c, the relative velocity is still c.

[Stranger On A Train]

Originally Posted by Santo Rugger

The part I don't understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not?

They'll be 1 ly from each other, as measured by an observer at A. What B and C see as distance to each other (or any other point) is dependent upon the relative velocity.

One way to think about this is that you have velocity along four orthogonal directions; x, y, z, and t. Your total scalar of velocity is alwaysc. If you are fixed (relative to an inertial reference frame), your velocity is <0,0,0,c>. If you are moving at half the speed of light in the x direction, your velocity is <0.5c,0,0,√(0.75)·c> and so forth. And of course as your direction along the t-axis changes, all of your measurements that pertain to intervals of time (i.e. how long it takes to go from here to there, and how far that makes it) also change.

Fundamentally, all Special Relativity really says is that c is the invariant ruler of the space-time plenum against which all other scales are measured. When you adjust the length of c in a given direction, you have to adjust everything else accordingly to make the math come out. General Relativity--now that stuff's a bit more tricky. It's the same basic concept, but now it factors in the effect of mass on time and the interval you travel in space, which requires a far more complex model.

I dub the o.p.'s apparent (fallicious) paradox Zeno's Relativity Paradox, and for his next trick he needs to show why the tortoise is both ahead of and behind Achilles, but the group velocity of his decoherence quantum probability cloud is always just a little bit ahead.

Stranger

[Chronos]

The part I don't understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not?

After one year in whose reference frame? And distances measured in whose reference frame?

[Malacandra]

Now I'm all at c.

[Exapno Mapcase]

Originally Posted by Santo Rugger

u is the speed of B relative to A, v is the speed of C relative to A, and W is the speed of C relative to A.

The part I don't understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not?

B and C are moving at opposite directions to one another. If we were on earth, we'd say that one moves a half-mile west from A and the other a half-mile east from A so at the end they are one mile apart.

B < = 1/2 light year < A > 1/2 light year => C

B <= 1 light year => C

[Ring]

I personally think Einstein must have been one conceited SOB.

I mean who else thinks their theory a is a special theory?

Did Schrodinger call his equation The Special Wave Equation”?

What about Heisenberg, did he think his Uncertainty Principle should be called “The Special Uncertainty Principle”?

What about Pauli? Etc. etc. etc. (Say this with a Cary Grant accent)

No! Only big Al was pompous enough to think his damn theory was special.

Screw you Al. Poincare almost beat you to it anyway

[sailor]

Originally Posted by Ring

I personally think Einstein must have been one conceited SOB.

I mean who else thinks their theory a is a special theory?

Did Schrodinger call his equation The Special Wave Equation”?

What about Heisenberg, did he think his Uncertainty Principle should be called “The Special Uncertainty Principle”?

What about Pauli? Etc. etc. etc. (Say this with a Cary Grant accent)

No! Only big Al was pompous enough to think his damn theory was special.

Screw you Al. Poincare almost beat you to it anyway

I once knew a German girl who said the Brits were so conceited to call their country "Great Britain". I had to explain to her the origin and meaning of the name.

[Stranger On A Train]

Originally Posted by Ring

I personally think Einstein must have been one conceited SOB.

I mean who else thinks their theory a is a special theory?...Screw you Al. Poincare almost beat you to it anyway

Actually, Special Relativity is "special" in the short bus sense of the word; it is the retarded little brother of the more jingoistic "General Relativity".

Poincare really did beat Albert to the punch in terms of developing the theory, but he was a little too scattered to publish. It's the whole Newton and Liebniz thing all over again.

Stranger

[Ring]

Actually, Sailor, now that I think about it all physicists must be pompous asses.

It’s not the Wave Equation, it’s the “Schrodinger Wave Equation”. It’s not the Uncertainty Principle it’s the “Heisenberg Uncertainty Principle”, and then there’s “Feynman Diagrams”, and the ‘Pauli Principle”, and on and on.

Pretty soon we’ll be hearing about “Chronos’ General Theory of Nano Dongers” or something or other.

BTW what does the Great in Great Britain stand for? A sop to Scotland and Wales?

Stranger, I knew that - I was just being a silly ass.

[DSYoungEsq]

Originally Posted by Ring

Actually, Sailor, now that I think about it all physicists must be pompous asses.

It’s not the Wave Equation, it’s the “Schrodinger Wave Equation”. It’s not the Uncertainty Principle it’s the “Heisenberg Uncertainty Principle”, and then there’s “Feynman Diagrams”, and the ‘Pauli Principle”, and on and on.

Pretty soon we’ll be hearing about “Chronos’ General Theory of Nano Dongers” or something or other.

BTW what does the Great in Great Britain stand for? A sop to Scotland and Wales?

Stranger, I knew that - I was just being a silly ass.

"Great" Britain as opposed to Lesser Britain, as in what we now call Brittany, a part of France.