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It seems all we're capable of accelerating currently are atomic particles. Why can't we, say, accelerate a clock to relativistic speeds?

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what's so bad about this question that it deserves a down-vote? (I guess the first sentence should already include the "to relativistic speeds" since obviously a car can accelerate...) –  Tobias Kienzler Nov 12 '10 at 12:48
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The obvious answer is their mass, accelerating a subatomic particle to relativistic velocity takes many orders of magnitude less energy than accelerating a macroscopic particle.

More subtly, we can only accelerate subatomic particles that we can manipulate with electromagnetic fields, nobody has a proposed viable experiments to study relativistic neutron or neutrino reactions because we really have no way to manipulate them. What this means is that we need relatively light, charged, particles that we can accelerate to relativistic velocity in a reasonable space with reasonable amount of energy.

Which brings us to our next point. Modern accelerators use what are called "RF cavities" to accelerate charged particles like protons and electrons, these are effectively giant pulsed capacitors with the particle flying in the space between the plates. We are governed by material science and the permiativity of the vacuum and have a limit to the maxium voltage we can put across the plates, and hence the maximum energy we can impart to a particle per unit length of the cavity. For modern accelerators this is on the order of 1 MeV per cm. 1 MeV on an electron goes a long way (which is why your TV works). 1 MeV on a baseball barely does anything. If the LHC seems big, an accelerator to collide two baseballs with the same velocity would be wider than the solar system (using modern technology).

More realistically though, we accelerate particles so we can study the physics during collisions of two particles. When we collide electrons and positrons for instance, nearly 100% of the energy carried by the particle is deposited into the reaction if they collide head on, its this fact that lets us see the creation of new and exotic particles following the collision (And why LEP began seeing Z bosons as soon as they crossed the 180GeV threshold). When we move to the LHC for example, we are colliding two protons- which, roughly speaking are sacks of consisting of 3 quarks. And the momentum (and therefore the energy) of the proton is more or less evenly distributed among the three quarks. So the energy available to us in the collision is actually about 6 times less than an eqiuivalent electron-positron collider. Imagine doing this with a baseball, which is composed of trillions of trillions of particles. The energy that each particle carries is a tiny fraction of the total energy of the baseball, therefore every single collision event only has a tiny fraction of the total energy of the system, and in the end we get no useful reaction out of a collision that could not have just as easily been accomplished by putting two televisions face to face.

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Actually, the LHC is currently smashing lead atoms ;-) –  Sklivvz Nov 12 '10 at 8:47
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@Sklivvz Lead Nuclei, and the energy available in the collision (per basic particle, i.e. quark) is much smaller than in the proton collisions. Its why they are using lead to look at exotic matter forms like quark-gluon plasma (since the lead nuclei is pretty much a giant sack of quarks) and not looking for Higgs or new subatomic physics. –  crasic Nov 12 '10 at 8:50
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How about Newton's law $F=ma$? The force needed to accelerate 1 kg is 27 orders of magnitude ($10^{27}$) bigger then to accelerate a proton.

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It's not particularly hard to accelerate anything, it just requires an energy source and time. The problems are merely practical:

  • To go really fast you require a large vacuum. So in the case of particles we have a 27km underground tunnel (LHC) and in the case of space probes we have space itself.

  • In the case of probes, there's the necessity of making them self propelled, so a lot of fuel must be accelerated too, requiring even more energy.

Given the costs, we tend to accelerate stuff as little as possible. In the case of space probe, once they reach the escape velocity of the solar system, nothing more is required.

The fastest large object is currently Voyager 1, running at $5.8\times10^{-5}c$ or 0.006% of the speed of light.

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The following formula is very self-explained:

$m=\frac{m_{0}}{\sqrt{1-v^{2}/c^{2}}}$

So, as an object go faster, its mass increases, and it is more difficult to accelerate it. Mass tends to infinity when you approach to the speed of light. Thus, only massless particles can go so fast!

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that is only a formula to keep $E_{\text{kin}}=\frac12mv^2$ valid, the yet open question is whether this mass that increases is only the inertial mass or whether it is the mass (that is, the mass that is equal to the gravitational mass). The formula also only explains why no massive particle can travel with exactly $c$, but not why higher mass makes acceleration difficult –  Tobias Kienzler Nov 15 '10 at 7:55
    
In a relativistic frame, the kinetic energy is no longer given by the classical equation. Instead, you should use $E_{kin}=\sqrt{p^{2}c^{2}+m^{2}_{0}c^{4}}-m_{0}c^{2}$. The essential problem to achieve the speed of light is that your mass will tend to infinity, besides the technical problems that crasic explained. –  asanlua Nov 15 '10 at 9:32
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