You lost me. I don't see how the running-on-the-train issue is resolved; why wouldn't he be running faster than c? (I know he can't, that thought experiment has just confused me.) Also I lol'd
No, he wouldn't be going faster than c because of the time dilation. Relative to the observer, nothing can exceed the speed of light, so to counter any discrepancies (such as someone running along a train moving at c) time dilates. Remember speed = d/t; the distance travelled is the same so the time alters to keep the speed relative to the observer at c or below it. Did that sort of explain it?
Sort of, but...well, no What I can't get past is this: the guy is moving down the train. To the observer, the train is moving faster than the guy. So the guy can't be moving forwards down the train - if anything he should be moving backwards, if the train is perceived to be going faster than him. I know it makes sense on paper, I just can't make it line up in my head. I don't think I'm imagining it in the right way, I've gotten something wrong.
The special relativity formula for adding velocities is: u + v --------- 1 + uv/c^2 equals the total velocity, for this example relative to the ground.(I found this via Google.) I used Wolfram Alpha and this formula to add the velocity of a train moving at the speed of light to the velocity of a passenger moving at 4 meters/second onboard the train in the direction of its travel. The end result was a velocity of the speed of light for the passenger. (c+4 m/s) + c --------------------------- 1 + ((c+4 m/s)(c)/c^2) = c Nifty. Notice that this equation will yield the correct result for low velocities, ie. 4 m/s + 5 m/s = 9 m/s, but has a limit at the speed of light, c, so that velocities can't add up to be faster than the speed of light (according to the math). BUT since this is just a theory and math; things might be able to travel faster than light.
I find this very interesting but it does hurt my brain. I thought that physicists were now speculating that Einstein's theory of relativity was incorrect? Is it his theory which dictates that faster than light travel is impossible?
Relativity is the whole shebang - all of the mechanics related to travelling at a significant fraction of the speed of light. There are certain issues, for sure. In 1900, Maxwell and Newton had completed their work, and most members of the scientific community thought it was over. They thought that no natural phenomena existed which could not be modeled by either Maxwell's equations or Newton's laws. Then, in 1905, Einstein just blew it away. He created a scientific revolution with Relativity, and he created another scientific revolution with the photoelectric effect (which proved quantization of energy) Clearly, it is both naive and foolish to assume that Einstein's theory is perfectly correct, as those physicists in the four decades between Maxwell''s equations and Special Relativity believed about Newton and Maxwell. The biggest issue in the theory is resolving between Relativity and Quantum Mechanics. Relativity is great for astrophysics and other stuff that's big and fast. Quantum Mechanics is great for subatomic particles and stuff. But there's a fundamental difference between the two, which is part science and part philosophy. Quantum Mechanics deals with probability functions. Everything there has to do with probability. A particle can be in a superposition of several possible states, which can be modeled by a probability function. When the particle is observed or interacts with another particle, the probability function collapses and the particle falls into a single state. Now, Relativity does NOT have any probability. There is only one possible result of a given action. What this ties into is the question: Is the universe random? With Relativity, the universe is not random. If something happens, then something else will happen as a result. The universe isn't random. With Quantum Mechanics, the universe is random. If something happens, then several other things could happen as a result. The universe is random. Einstein (the father of relativity) is quoted as telling Bohr (one of the founding fathers of quantum mechanics): "God doesn't play dice" (that the universe isn't random). Bohr is quoted as responding "Don't tell God what to do". So this is a big question that's been around for about a century. Most research in Physics is an attempt to resolve that question. However, that doesn't mean that Relativity is a load of crap. It can't explain things on a subatomic level, and there are some quantum phenomena that would contradict Relativity. Quantum Entanglement is often brought up as a phenomenon that is impossible by Relativity. However, there is some debate on this, and it's far from being resolved. That does not mean that you can travel above the speed of light.
Can I recommend Steven Hawkins Universe it explains this in great detail, the reasons for time dilation etc etc. Clicky *Also Available from other shops put "Steven Hawkings Universe" into your favourite search engine. Definately worth the purchase.
Stephen Hawking has been quoted as saying: "Not only does God play dice, but he sometimes throws them where they cannot be seen."
I shall keep my life simple by not asking such questions. To remain ignorant of such things keeps me sane, as long as there is bacon, black coffee and the odd slice of cheesecake I am blissfully happy. I got my head around the whole thing that space/gravity is like a big sheet of fabric, and that masses placed upon it stretch it downwards causing attraction of smaller masses to larger masses, by also to remember that its not on one plane. Little off topic i know. Also i think one of the biggest problems with super scaling the LHC is tolerance, bigger it gets the hard its to mine and assembly with in solid bedrock. I believe its in a granite bedrock to protect it from external interference from solar activity...
This is now a Carl Sagan appreciation thread. Goddamn he's awesome. Re: the LHC, wouldn't the obvious solution to the structural problems be to put it in space? It would make things endlessly easier, once we overcome the cost and inconvenience of transporting huge component pieces into space.
At first it would seem like an obvious solution, but a lot of people fail to realize that while everything appears relatively weightless, everything still has mass. Once the International Space Station was being assembled in space, scientists started discovering second and third order effects that they never knew about. It takes an entire division of extremely intelligent (and predominantly left-handed, oddly enough) people to plan and design certain aspects of the assembly phase because the different gravitational forces that come into play while the complex orbits the Earth involves weird math that is so far above my head I think we have to do debris avoidance maneuvers just to avoid it. And all of that is just to get the thing to orbit correctly. After that, you have systems failures that require spacewalks, special flights to deliver supplies and remove trash, micro-meteoroid debris, solar radiation, and a host of other logistical nightmares. Plus, how many solar panels would it take to power the thing? For all the complex science that goes into building and operating the ISS, it's only the size of a football field. If you tried to build something the size of the LHC (or bigger), it would end up being far easier (and cheaper) to just buy a small country and build it there. Now, if we're talking hypothetical situations, with futuristic metals and plasma engines and force fields to protect against radiation and micro-meteoroid debris, then yes, an LHC in space would be cool.
Thinking of light as a particle and wave form... what if we could generate our own gravitational force (like a black hole) to pull another object towards us at a rate faster than the speed of light? Since light cannot escape a black hole, could the gravitational forces then be used to move something faster than the speed of light? btw, i am slightly drunk at this posting so please forgive me if this is retarded.
Do you really want to create a gravity well right here on Earth strong enough to trap light? Dude, listen to Burnout21 (who judging by his name is a man who knows about such matters) and get some black coffee, bacon and cheesecake down you!
got a headache just thinking about it =] what's crazy though if you approach the speed of light time slows- so exceeding the speed of light if possible I would assume time would go backwards so if you were to have a object travel that fast through space it would actually hit whatever is pulling it in the past- headache.. watch this manga called gunbuster *has flashbacks to gunbuster*
I was just thinking about that while taking a shower actually. However the problem with that is as you approach the speed of light, and since there is a limit , and assuming an accelerated motion as we know it, you have to go through that limit which makes it impossible to go faster. not to mention that it would take infinity energy to reach the speed of light because of the Lorentz factor in the E=γmc^2 equation --edit-- Just did some research and apparently there is something that hypothetically goes faster than the speed of light. Tachyons http://scienceworld.wolfram.com/physics/Tachyon.html
The equations are struggled so that it takes an infinite amount of energy to accelerate something to the speed of light, and blackholes can't. What you're thinking of is the 'event horizon' It's a demarcation line at which the escape velocity is the speed of light, and thus when light crosses it, it gets sucked in. But it doesn't speed up when it gets sucked in. Most people, when they think about blackholes, think that everything gets sucked in directly. But it doesn't. It spirals in, like the whirlpool around a drain. Your speed cannot exceed the speed of light, but the spiral you travel in will get smaller and smaller until you hit the center.
This is vastly simplified, but the easiest way to think about it is like this: We travel though space-time at the speed of light. If we are stationary we will travel through time at the speed of light, however if we travel though space we must "borrow" some of the energy that we're using to travel though time - Which is why time slows down the faster you go. The reason we cannot reach the speed of light is because, if we borrow all the energy we're using to travel through time, time stops and velocity becomes meaningless - How can you travel at 299,792,458 metres per second when a second lasts an infinite amount of time?
