If a a object is falling in a gravity field with infinitly long radius. can it eventually travel faster than the speed of light?
"Why" is not a question that physics answers. "What does it do" and "how does it work" are the kind of questions physics answers. "Why questions" just lead to more "why questions" at which point religious folks say "god" and physicists say "damned if I know". Warp drives do not exist.
OK... how does the object do not go beyond the speed of light given that there is infinite lengths for acceleration?
If the acceleration is caused by a constant force then one reason is that the resulting acceleration becomes less and less as the accelerating object gets nearer and nearer to light speed. In the realm where special relativity applies, F = ma and p = mv are no longer accurate. Instead, F = dp/dt and p = m gamma v. Where gamma is given by 1/sqrt(1-v^{2}/c^{2}) If you want to contrive a constant acceleration by something like a uniform gravity field then you get different complexities that I am not competent to explain. Things like a Rindler horizon.
Yes, that's one of my favorites and has been referenced on this site many times. There is an abbreviated version (cropped from this one) that is only a minute or so long, where he is JUST discussing the "why".
I was brought up in Scotland, where "how" is often used instead of "why". I only noticed it when I moved to England. So, for me, "how" and "why" don't have the same linguistic difference that they may for others. In Scotland you could say something like "how are you not going?". Which means "why are you not going?"! Or, of course, "how can you not travel faster than light?"!
Yeah, this kind of translation issue, or difference in dialects, is something I've noticed in many situations. For example, my wife is from Pennsylvania and says (Pennsylvania Dutch style) "let it outside" when she means what the rest of us would mean if we said "leave it outside" (talking about something that is already outside). So I would say, "let the dog outside and then leave it outside" and she would say "let the dog outside and then let it outside". Very confusing. I once had a German teacher who, when I told him I was going on a trip, said "what are you going with?" when he meant "what are you taking with you?". This kind of stuff just goes on and on.
Did you meet a lot of people in Scotland with the monniker 'henrywang' who were also interested in 'wrap drives'?
In my personal experience, "why does it happen?", and "how does it happen" are physics questions. "Why does it happen?", is usually a metaphysics question. Perhaps you should read some Aristotle for that. Actually, an object can go faster than c. If you're talking about an object in a gravitational field with an infinitely long radius, I would think that you would be talking about an alternative universe. Surely, the same laws of physics might not apply.
If you are launched from the surface of a planet at escape velocity, your speed would reach 0 at infinity. If you freely fall toward a mass from an infinite distance--with an initial v=0--you would impact the surface at escape velocity.
There's a number of reasons. 1. An infinite length of acceleration is easy to think about. Just look at escape velocity. It is the velocity an object needs in order to escape the Earth's gravitational pull. In other words, it is how fast an object needs to go to get from the Earth's surface to an infinite distance. But how is this possible if gravity is pulling on it the whole way? The answer lies in the fact that the force of gravity falls off with distance. So if you launch an object away from the Earth fast enough, gravity won't be able to slow it down fast enough to keep up with how quickly the force falls off. Its speed will continue to decrease as it gets further and further away, but it will never hit zero. So any realistic situation in which you would have an infinite distance to accelerate would be subject to the same laws. An object attracted to another object through gravity will never reach an infinite velocity because of how weak the attraction is at great distances. Note that there is no realistic scenario in which you could apply a steady force for an infinite distance or time. 2. Even in a situation where you could apply a steady force for an infinite amount of time, the rules of special relativity show us that this still wouldn't result in a velocity equal to c. That's simply not the way the universe works.
If you constantly push on an object you are always putting in a finite amount of energy given the amount of time that you've pushed it is finite. Special relativity gives: Kinetic Energy = T = mc^{2}(γ-1) = [itex]\frac{mc^2}{\sqrt{1-v^2/c^2}} - mc^2[/itex] If we get close to the speed of light, then that's the limit as v approaches c. If you take that limit v→c, then K→∞. So to get to lightspeed we need infinite energy. There's no way to give an object infinite energy with a finite amount of force. So you would need to run your experiment for an infinite amount of time to reach light speed. Alternatively, you can look at the addition formula for velocities. If v is our original velocity, u the velocity we add to v, and u' the final velocity, we have: [itex] u' = \frac {u-v} {1-\frac {uv}{c^2}} [/itex] If I apply a force for some finite interval of time and start below the speed of light, then u' will never be equal to or greater than c. You can repeat this addition as many times as you want and you'll never get to c. So, say I take the amount of velocity that the gravitational field adds every second and keep adding it to the velocity using this formula, the sequence will look like .99, .999, .9999, .99999, but it'll never get to or above 1 for any finite number of additions. Both of these break down if you have an infinite time in which to perform the experiment, but this isn't a realistic scenario, so don't expect physics to answer such a question.
I am in agreement with the first answer; Nothing (energy or matter) can travel faster than the speed of light, period. But then you asked "Why?" Well, there's a much better answer to that follow-up question, ever since July 4, 2012. Nothing made of atoms can travel faster than the speed of light because the Higgs mechanism provides mass to electrons, positrons, quarks, anti-quarks, W and Z bosons, without which, atomic structure is not possible. The Higgs mechanism does this without violating conservation of energy by slowing these particles down (from the speed of light). The Higgs boson also imparts mass to itself, but decays into photons in about 10^-21 seconds in the LHC. Energy itself cannot travel faster than the speed of light. Give it up. Nothing material or energy in this universe is ever going to exceed c. Heck, the LHC couldn't even have been designed without E=mc^2, and that particular derivation by Einstein has only one assumption. It is that the speed of light is invariant and cannot be exceeded by matter or energy.
Then by that same analogy we can say that the higgs boson is able to travel at the speed of light right? BTW: Not about the subject in question but I wonder if two higgs boson can actually collide and wonder what would happen? Super fast telecommunications maybe, anyone?
No, the higgs boson has mass and is not able to reach c. Given the extremely short lifetime of a higgs boson before it decays, two of them colliding is very unlikely. However, if it happened we'd just get a shower of new particles like all particle collisions.
Awesome, btw i missunderstood the concept of the higgs boson then, since i understood it did not had a mass since is all around the universe dispersed. Probably completely wrong... lol anyhow thanks