Ok, it was Indiana, and apparently the law never actually passed, although it did come close: http://www.straightdope.com/columns/read/805/did-a-state-legislature-once-pass-a-law-saying-pi-equals-3
I think that the best and most concise explanation I've ever heard for that happening is "Physics gets weird when you get close to the speed of light."
I don't have the formulas memorized, but they don't simply add the way you would expect from Newtonian mechanics. At normal speeds, the Relativity formulas for adding velocities are essentially the same as the Newtonian formulas. The error is so small it can safely be ignored, and in fact is too small to measure except under very special circumstances. But as you get closer to the speed of light, the formulas add less and less to the measuresd sum. What happens, depending on where you observe from, is that the rate of flow of time changes, or the distance along the line of travel changes, or a combination of both. I haven't looked at the actual equations in years, and even then didn't do a lot of real calculations with them. But they do work, and they aere actually not huge formulas. at least in the straightforward cases (observer near the collision point, observer on one particle or the other).
When you try to add them at higher speeds, you have to do a transformation because you have to take into account frames of reference. Instead of simply adding the velocities, I believe you have to subtract them and then divide that by some factor which I don't have memorized. So, if particle A is traveling .75c (75% the speed of light) and particle B is also traveling .75c, in particle A's point of view, it will look like particle B is moving at 0c, not 1.5c.
Oh things get really weird near the event horizon. From an outside view, the falling object begin to slow down and compressalong the line of travel as it approaches the EH. The light itself is slowed, so the apparand to the outside observer is that the distanace to the center of the holoe is infinite, and the object accelerates to nearly the speed of light. But it never reached the "bottom". and if you travel in a halfcircle to the other side, the circumference is finite even though the radius in infinite. From the falling object, the universe begins to recede behind you. You know you will reach the center in a matter of seconds, but time slows so that last second never occurs. That's ignoring the tidal forces that will rip you apart before you gett anywhere near the actual EH. A rod alined toward the center of the hole is accelerating faster at the near end than the far end, because it is that much closer to the gravitational center. That difference in acceleration builds to a force of many tone per linear inch, to the point where no piece of matter can hold together.
I see where you're coming from with the precesion and accuracy thing. But I really hope you see where I'm coming from. I mean, lets say for the sake of arguement that the speed of light is 120 miles an hour. We know it's not, but lets just say it is. So, let's say there's a car traveling at 120 miles an hour hit a wall. You'd say something about the collision being around 120 miles and hour. Now, let's say we have two cars traveling at 65 miles an hour (this is our particle accelerator). If those two cars hit, wouldn't the collision be considered 130 miles an hour? All fourmulas and theroys aside, that's porpotinatly faster than the speed of light. You can't just discard that 10 miles an hour. That is impossible. Unless it's being discharge somehow. Now, if that's the case, I want to know where it went and why.
If you accelerate with an energy of 200 Newton seconds to reach a speed of 120 MPH, then you expect that an additional 200 Newton-seconds woul accelerate you to 240 MPS (no air resistance or friction) But what happens is that the car at 120 MPH becomes more massive, so you only get 200 MPH out of it instead of 240. From outside the car at the "motionless" vantage point, the car is shorter from front to back. From inside the car the distance ahead of you has stretched out. You seem to be going 240 MPH, but because you and everything in the car along the direction of travel is shortened (from the outside perspective) your miles are shorter than the external observer's miles. But time also enters into it all. A key poin that all the calculations depenf on is that no matter how fast you are travelling relative to another observer, a beam of light - the SAME beam of light, will be travelling at the same speed, approximately 186,000 mps. Time and distances will adapt to make this true.
Stupid light, why does it get priority huh? You'd think that the big boys like time and distance would be the ones to define everything, but instead they all get the shaft and light is king of the universe.
That's what is really worrying me. The faint possibility that we might turn the rest of the universe into the same cesspit we have this little corner of it. But it ain't gonna happen. We're too thick on this planet, to do something that stupid!
The universe is incomprehensibly more vast than our tiny speck of rock. No matter how sloppy and wasteful we are, we could not possibly amount to a blight over any significant portion of it. In the grand scheme, you could look away from our entire galaxy and be hard-pressed to find it again. And I refuse to take such a pessimistic view of humankind's potential.
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/velocity.htm Read this link, it answers your question far better than I could.
One thing the link doesn't show is a visual diagram of what's going on. Imagine a normal x-y coordinate system. As Cogito mentioned earlier, the speed of light is constant in any frame of reference. So, it doesn't matter if you are walking down a street or traveling at .99c, if a light beam passes you, you will see it traveling at the speed of light. So, in order to take this into account for all frames of reference, you have to tilt the x-y axis. This tilting is what gives us the mathematical formula you see in that link. Here's a picture I found of what I'm talking about: http://gregegan.customer.netspace.net.au/FOUNDATIONS/01/Fig09.gif
Agreed, but if you have never seen one of these diagrams before, it's not rasy to understand its meaning. Then again. I'm probably a bit strange in finding the raw formulas far more enlightening.
Ok sorry had to work missed the discusion. But my new point is science is always disproving it's old laws, or at least "adjusting" them. So instead of it saying 1 + 1 = 2, it's more like 1 + 1 =2 unless a chicken flies past and releases a burst of gas into a camp fire that proceedes to burn down a forest exactly 20 acres square. (LOL that's my interpritation of when they change laws.) Science is constantly correcting itself, i just hope it doesn't correct itself as time slows by the increase of gravity (Not sure what law but heard something about that.) "Hmmm, looks like we were wrong." Says scientist prior to being sucked into a black hole, which is fine because it turns out it just sent him to a new dimionsion were he is god and gets to create the universe.
Einstein didn't adjust Newton's physics. They are different ones. Newtonian physics are fine for the macro-world, but both Einstein's and Newton's fall under the micro-sized world (quantum). Really, Einsteinian and Newtonian physics are but the closest aproximation we have. Physics is the weirdest part of science and doesn't always make sense unless you study it deeply. Besides, "adjusting" falls under the scope of science. The scientific process goes like this (mostly): -Fomulate hypothesis. -Find evidence. -If evidence supports hypothesis, then hypothesis becomes theory. -If evidence doesn't support hypothesis change hypothesis. -If new evidence contradicts theory, reformulate theory to accommodate new evidence. Or that's at least how I understand it. Wouldn't that be awesome? If the multiple-worlds theory turns out to be right and in some dimension I could fly by flapping two cats with my feet, that would just make me feel good about living in this reality.
Call me simple-minded, but I don't understand why we have to go around and experiment with various parts of existence. It really does puzzle me how annoyingly curious the human race naturally is. It's going to be our downfall one way or another. We need to stop bothering with the natural order of some things and accept life as it is. I guess that would be too boring.
