It’s a clever idea, but these sorts of things don’t actually work out because relativistic velocities are not linearly additive. The only intuitive reference we have is newtonian mechanics, in which velocities are linearly additive, so a lot of things that make intuitive sense in our slow moving world don’t work out for velocities close to C.
The velocity addition issue is the key, but you can rework most of the “common” equations using the relativisitic velocity addition formula. I can’t quote it to you off the top of my head (been far too many years), but I’m sure a web search would turn it up.
threemae:
Sounds like you are paying enough attention to get your head messed with. That’s the fun part for me.
Ah, but that’s just the thing! No one ever observes a change in the speed of light travelling in a vacuum! The detector on the bus and the detector on the sidewalk (pretending this is a vacuum rather than Earth air) are going to determine that the speed of light is that familar constant.
Re the emitter/detector diagram. Very good example. You are so ready for a course in special relativity.
Lemme modify the example a bit to illustrate the point.
Suppose we have a light beem that is passing between two mirrors. The mirrors are positioned so that it takes the light exactly 1 second to get from mirror A to mirror B (i.e. they are 1 light-second apart).
Now, suppose we have mister observer C. Mister C sees the mirrors moving perpendicular to their flat surfaces at a high speed. According to Mister C, this bouncing light is not simply going back and forth. To Mister C, the light is travelling in a zig-zag pattern. He observes the distance between mirror A and mirror B to be one light second, but since A and B are moving, and the speed of light is constant, he observes that it takes the light longer than one second to get from A to B. Let’s say he sees the trip to take 1.5 seconds.
Lovely. We have a contradiction here right? Nope. Because from C’s perspective, time has slowed down for A and B. From C’s point of view, in the time that 1.5 seconds has passed, only 1 second has passed for A and B.
Umm, yes, you can slow light down. You don’t need a doctorate, either. You need a glass of water and a pencil. Oooooooh. Wasn’t that cool?
1 light year is the distance it takes for light to travel in one year. Right, we know that. Stuff can slow light down, like glass, water, other particals, or gravity. So the speed of light is not constant. That’s why I’m not sure I buy the whole relativity thing. Why would it take infinate energy to send a rocket at or past the speed of light? And why does your mass become infinate? This is what we call Theoretical Physics, which cannot be proven. At least not yet. Al was a smart guy, but I’m holding my breath for proveable science.
Umm. Babar? I guess perhaps you haven’t been keeping up with physics for the past 50 years or so…
In high-energy physics experiments, it is quite commonplace to accelerate particles to very near the speed of light. The effects of increased mass and time dilation are have been very well demonstrated.
At one time, Star Trek’s “Warp Factor” was translated as c*w[sup]3[/sup]. However, I believe that was obviated as of TNG.
As to light, here’s the skinny. It is a known, observed fact that every observer sees light moving at c relative to him. All the weird stuff that comes out of Relativity is just the result of Einstein (and others) working out the equations so that this known fact fits.
For example, you don’t have to bring in relativistic mass and all that to explain why you can’t go faster than light. All you have to do is realize that no matter how fast you go to chase light, it will always be going exactly c faster than you are. Space and time twist themselves around to force this always to be true.
John W. Kennedy
“Compact is becoming contract; man only earns and pays.”
– Charles Williams
That was precisely my point. That’s what I meant by the chicken/egg thing. Photons generated by electric/magnetic forces generated by photons. See what I mean now? I was pointing out that describing the speed of light in terms of the nature of the fields isn’t the most fundamental description. The nature of the fields is dependent on the nature of photons.
Well, that’s one way of looking at it, but massless particles are kinda a special case. They do have momentum, and you can calculate their energy, but then if you try to plug that energy back into an equation that determines its (relativistic) mass, it doesn’t fit with any of the other relativistic mechanics equations. For one thing, you would now be describing an object that has finite mass at the speed of light. Technically, the only intuitive way to determine the mass of a photon is inaccurate. In E = mc<super>2</super>, m is specifically rest mass, and E is specifically rest energy. For a moving body, the equation is E = gamma * mc<super>2</super>, which gives you infinity times zero.
Conceptually speaking, I have heard of light referred to as having relativisic mass, but no rest mass. However, the photon is generally referred to as a massless particle, I have never seen an equation to determine that mass of a photon directly, and, come to think of it, the last teacher who described photons as having relativistic mass was my high-school teacher.
I’ve always thought that a good (if simplistic-that’s the way I can deal w/it) way to get a grasp of what happens to mass, acceleration and all that other happy stuff is–to go back 2500 years. One of Zeno’s paradoxes is that you can’t really get anywhere because you have to get halfway there first, and to get halfway, you have to get half of that, etc. ad infinitum. Of course, it doesn’t hold up walking across the room, but when you get to about .99999…c, I can see a parallel.
–Alan Q
You are correct, the warp-x-equals-x-cubed-times-the-speed-of-light warp speed formula was never canonized by Paramount/Roddenberry, and was formally abandoned in the TNG Scriptwriter’s Bible the first year. It has been replaced with, of all things, a graph on one page of the ST:TNG Technical Manual. A footnote claims this graph was based on “Warp X = X^3.33333… times c UP TO WARP NINE”, and the graph appears to match this formula. So at least in the ST:TNG days of Trek, warp 1 is 1c, warp 2 is about 10c, all the way out to warp 9 which is around 1000c. Past warp 9, your warp-speed asymptotically approaches warp 10 as your acutal speed approaches infinity.
Now, in the series finale (“All Good Things…”), one possible future showed an aging Beverly Picard commanding her starship to go to “Warp Thirteen”. However, this was many years after the main timeline of the show – perhaps Star Fleet got sick of splitting hairs between warp 9.9 and warp 9.95 and decided to recalibrate the warp speed scale – and they made it clear at the end of the episode that this future need not even happen at all.
We now return you to your regularly-scheduled program on special relativity, already in progress.
I’d say that the QM version is the more precise (electric/magnetic forces arise from interactions of virtual photons). The Maxwell version (photons arise from a chain reaction of chaging electric and magnetic fields) is an effective and useful classical approximation, but does not represent physical reality as much as the QM version.
In the late 17th Century astronomers noticed that the eclipses of Io, one of Jupiter’s large moons, were coming as late as 16 2/3 minutes after they should have. Someone finally realized that this was caused by the time it took for Io’s reflected light to reach Earth, and that the farther away Earth got from Jupiter, the longer it would take for the light to reach us. The distance from Earth to the Sun had recently been calculated as 93 million miles, so the Earth’s orbit is 186 million miles across. Since the “error” in the eclipses of Io were coming was 16 2/3 minutes, the astronomers concluded that it took light 16 2/3 minutes to travel the distance of 186 million miles, or 186,000 miles per second.
