In a lhc you get very near to the speed of light, but never reach it. But how could you, because there a two rivalling vectors (say x and y).
First of all, the question should be about “reaching” the speed of light, or “approaching” it. “Breaking” the speed of light is currently believed to be science fiction, and can’t have a currently factual answer.
Okay. If I understand your question, the circular motion inside the LHC (Large Hadron Collider, I presume) requires energy to divert its particles away from a straight line, and that makes it more difficult to to reach any sort of maximum speed. So wouldn’t going straight be easier?
Here’s my guess of an answer: You have a good point, but consider the fact that the particles inside the LHC are not self-propelled. The LHC accelerates them each time around the circle, so they go faster and faster and faster and faster. There’s no way to do that in a straight line unless you’re talking about something that IS self-propelled. Some sort of engine pushes and pushes and pushes, accelerating and accelerating and accelerating, so it goes faster and faster and faster. But the engine itself has mass, and that is going to make the process less efficient.
If your goal is to make something go as fast as possible, you want the thing to be as tiny as possible, and that means propelling it from the outside, and that means going in circles.
One reason the LHC is so big is to make the bends very gentle. A charged particle going around a bend radiates energy, and this is a net reduction in the efficiency of the LHC’s operation. There are however straight accelerators - SLAC - The Stanford Linear Accelerator for instance.
But the core point is that you cannot get faster then c. Going fast isn’t actually the main point of the accelerators (although that sounds silly); the main point is to get high energies. As you get very close to c the energies get large with very small increments in speed. So for most useful purposes most accelerators run at c, close enough for folk music anyway. That little margin less doesn’t affect things if you are sitting there with a stop watch. It is the energy the particles carry that matters.
NM
I can’t find it in the Wikipedia article but I thought that by passing very close to a massive rotating black hole you could exceed the speed of light relative to a point far away from the BH since the rotation of the black hole “drags” spacetime along with it, but I could be wrong.
But if I did remember correctly, then it’s easier to break the speed of light limit going circularly.
In any particle accelerator, either linear (straight) or circular, the particles are accelerated by large, powerful, expensive magnets. As the particles pass each magnet, they are given a push, increasing their speed. To reach higher speeds, they need to pass by many magnets. In a linear accelerator like SLAC, the only way to get the particles to pass by many magnets is to make the accelerator longer, with more magnets. In a circular accelerator, the particles can pass by any one magnet multiple times. Thus to reach the same energy, circular accelerators can be relatively cheaper, since you get more then one push from each magnet and you don’t need so many magnets, or such a long tube. If cost were literally no object, a linear accelerator has some advantages over a circular one, since bending particles in a circle loses some energy to synchrotron radiation.
–Mark
As Keeve said, it’s impossible to exceed light speed. But the more kinetic energy you put into the particle, the closer to c it gets.
Accelerators usually use magnetic fields to bend the path of the particle. The particle loses some energy at these bends by radiating it, but it retains enough energy (esp. if the bend is gentle) that it’s still worth making it go around in circles, adding energy to it gradually.
Though there are linear accelerators. They are more efficient, but they need to be powerful enough that the particle gets accelerated to the target energy in one pass. SLAC is the longest (2 miles) and most powerful linear accelerator in the world.
I’m going to make a pedantic point here, so please bear with me.
A sufficiently-long linear accelerator on Earth is still a circular accelerator, because the earth is (approximately) spherical. It’s just got a reeeeally gentle curvature that follows the curvature of the Earth.
Since the actual SLAC linear accelerator is only two miles long, the curvature is either negligible, or specifically engineered around (i.e., keeping the accelerator truly linear and just designing the middle to be slightly closer to the surface of the geoid.)
Googling about, I see on this reddit page that the second is occurring: the “middle” of the linear accelerator tube is several inches lower with respect to the standard surface of the earth than the ends. The SLAC is a true linear accelerator, but in a way that would require deep-tunnel excavation in the middle or tall towers for the ends if you scaled it up to 1000 miles, for instance.
So circular accelerators are a more practical way to go.
Yes, the expansion/contraction of space under GR is not constrained by the speed of light. A less arcane example than extreme frame-dragging is that the recession velocity of distant galaxies in our expanding universe increases with distance, and does eventually exceed the speed of light. This would be linear motion, albeit far less interesting than the extreme situation that you describe around a black hole, where things are potentially much closer together. But note that in neither case is there ever local motion through space that exceeds the speed of light in violation of SR.
This is an excellent accessible paper on cosmology, not entirely without math, but it explains a lot of things quite well in diagrams and words.
Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
One bizarre fact about the most distant galaxies that we can see: since the rate of expansion of the universe has changed over time, when light from those galaxies was first emitted, although it was moving through local space at the speed of light in our direction, that space itself was receding from us superluminally, so the net velocity of that light was away from us. Eventually, the light moved into space that was receding subluminally and gained net velocity toward us. There was a point in time when the light was “stationary” relative to us (although, again, not locally stationary, since light always moves locally at the speed of light).
As objects move faster, their mass increases. We don’t notice this “in the real world” because it doesn’t start to add any noticeable mass until objects are moving very, very fast. Here is a good relativistic mass calculator. If you plug in a few numbers, you will see that an object traveling at 10 meters per second (36 kilometers per hour) has a mass increase of only 1.0000000000000007. But as you start entering higher velocities, the mass increase eventually becomes significant. At 90 percent of the speed of light (269813212 meters per second) the relativistic mass becomes about 2.3 times rest mass. If you plug in a velocity of 299792457 mps (just 1 meter per second below the speed of light), the mass increase is over 12 thousand times the rest mass. Increase that to 299792457.9 mps, and the mass increase is more than 38 thousand times. 299792457.999 mps means close to 400,000 times rest mass. The highest the calculator will let you take it is 299792457.9999999 mps, which results in close to 40 million times rest mass.
For an object with any rest mass at all to reach the speed of light would require an infinite amount of energy and the object would become infinity massive, which is of course impossible. And there is a practical limit to how close you can get to the speed of light with any type of accelerator because there would be challenging technical difficulties involved in manipulating individual subatomic particles with the weight of mountain ranges.
(For a somewhat related topic, see the oh-my-god particle.)
A spaceship travelling .9c is carrying a railgun. The railgun’s capacity is .9c (for a bullet). What will be the bullet’s speed? I know that nobody is going to answer 1.8c, because it would to kindergarten math. But why it isn’t?
Relativity. Velocities don’t add that way.
Specifically, velocities add like (v1 + v2)/(1 + v1*v2/c^2).
Is this for linear motion or circular?
Linear.
Circular motion is not just velocity, it requires acceleration. Incidentally, I seem to recall an interminable crank “disproof” of SR on SDMB a couple of years ago involving relativistic rotation. I can’t find it at the moment. I do recall that it was uncontaminated by mathematics.
Your welcome.
Not really, as the thread is like trying to explain how GPS works to a particularly dumb hedgehog.
That’s the one! Also this overlapping one
I wonder what happened to mythoughts? Worryingly, in his last post
http://boards.straightdope.com/sdmb/showpost.php?p=17201767&postcount=783
Should we call somebody? I’m concerned that he may have set something up to rotate very fast, then got his shoelace caught while attempting to switch reference frames.
True, but in one particular type of circular motion, namely, an orbit around a center of gravity, no acceleration is detectable in the frame of reference of the orbiting body. ISTM that the consequence of this is that the same Lorentz transformation applies here as in linear motion, as seen here in the time correction necessary for GPS satellites due to orbital velocity. The effect of being further out from the earth’s gravity well is a different correction with the opposite sign applied independently according to general relativity.
Electric fields are used to change the speed of charged particles, not magnetic fields. In small applications this can be a static electric field, but some form of alternating electic field carefully timed with the passage of particles is used for anything beefy. Radiofrequency cavities are the main accelerating device in large accelerators.
As above, not magnets, but some electric-field-based accelerating element. But simply extending the length of the accelerator isn’t the only option. You can space the (say) RF cavities more densely, you can increase the field gradient in each, and you can increase the length of each cavity. (This is ignoring the option of changing technology entirely.) Obviously there’s an optimization to be done – R&D time, risk, cost – to decide the best approach for any given application.
Radiative losses are actually a negligible effect at the LHC. In a single loop around the ring, a 7-TeV proton loses only 10 keV of energy, which is trivially restored.
The energy at the LHC is limited by the cost and engineering of the bending magnets. Higher energy means you need stronger magnetic fields to keep the beam in the circle. And that’s hard. You could also use a bigger circle, but that’s not to keep the (already tiny) radiative losses down. It’s to keep from needing to “push” the beam around such a tight turn with the magnet technology available today.
Menlo Park, California, is rather hilly, but the beamline happily punches through the ground in a straight line. The curvature of the earth introduces no additional complexity. In fact, it would be harder to follow the curvature of the earth than to go in a straight line. To your broader point, the curvature of the earth isn’t a deciding factor between a linear or circular accelerator.