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Chazz

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- Thread starter Chazz
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Chazz

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LURCH

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russ_watters

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I'm sure someone has an exact number, but they are much faster than that: 99.999% or so. Fast enough that using %C starts to lose meaning and they just talk about energy.Originally posted by Chazz

I remenber reading something about how CERN accelerate particle to near the speed of light. 90% or even like 95% if I recall right..

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faster than a speeding... ahhh bullet doen't work.

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Chazz

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neutroncount

Originally posted by Chazz

Yep. I see no reason for an "implosion effect" as you see. Because it's going 99.999% the speed of light, it's still under c. And even at those speeds, the increase in mass is pretty "small". It's would be different if I were accelerating a 1977 Gremblin. But protons and electrons are light in the overall view of things. The same with energy. Of course you need more energy to accelerate the prontons or electrons but due to it's relative mass/energy being so small already it can be done, given the right resources (CERN).

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ahrkron

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A better measure is the energy of the particles in the lab frame. The energy of a particle moving at 99.5% of c is about 10 times its rest mass. At 99.99875% of c, the energy is 200 times its rest mass.

Fermilab accelerates protons (rest mass ~ 1 GeV) up to an energy of about a thousand times their rest mass, which corresponds to 99.99995% of the speed of light... i.e., just some 330 miles per hour short of c.

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krab

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pmb

Originally posted by Chazz

By being heavy I assume that you mean that the particle is sitting on something and its weight can't be supported. Not true for a particle accelerator. They're in the tubes for such a short time span that the amount that they fall under the acceleration of the Earth's gravitational field is negligible so they never hit the side of the tube. And there are focusing mechanisms anyway and they keep the particles on track.

As far as the increase in the intensity of the gravitational field - While that is true, i.e. the field strength increases with speed, the gravitational field even for those energies are so small as to be undetectable. Simply find the mass equivelence of the particle energy in those accelerators and you'll see that the mass is still so small as to be of no gravitational importance.

Pete

- #11

pmb

This is incorrect. Your notion that 'relativistic mass' leads one astray has led you to the incorrect notion that the gravitational mass of a particle does not increase with speed. That is wrong. It does increase with speed.Originally posted by krab

The source of gravity is not rest mass. The source of gravity is relativistic mass. aka the source of gravity is mass-energy (which is just another phrase for relativistic mass).

If you'd like to read more about this then there is an article in the Americam Journal of Physics on this topic. See

Relativistic mass is not confusing once it is properly understood.Abstract: If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic increase in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that M_rel=gamma*(1+ beta^2)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not M but is approximately 2*gamma*M.

For more on relativistic mass as the source of gravity see

Section 1 is online at

http://assets.cambridge.org/0521422701/sample/0521422701WS.pdf

The only ingredient now missing from a classical theory of relativistic gravitation is a field equation: the presence of mass

must determine the gravitational field. [...] Now, if this equation is to be covariant, T^mn must be a tensor and is known as the energy-momentum tensor (or sometimes as the stress-energy tensor). The meanings of its components in words are T^00 = c^2x(mass density) = energy density, T^12 = x-component of current of y-momentum etc. From these definitionsl the tensor is readily seen to be symmetric. Both momentum density and energy flux density are the product of a mass density and a net velocity, so T^0m = T^m0.

Pete

- #12

pmb

Originally posted by Chazz

I'm not sure what the correct formula is ..

If the rest mass of a particle is m_o and the mass is m and the speed of the particle relative to the lab is

m = m_o/sqrt[1-(v/c)^2]

This assumes the definition of mass whereby the quantity mv is a conserved quantity. Once the mass is defined in this way then one can define momentum as the product mv as momentum. I.e. mass is defined such that momentum is conserved. The 'm' defined as such is sometimes refered to as

For details and proof see --

http://www.geocities.com/physics_world/sr/inertial_mass.htm

Pete

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LURCH

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Originally posted by pmb

By being heavy I assume that you mean that the particle is sitting on something and its weight can't be supported. Not true for a particle accelerator. They're in the tubes for such a short time span that the amount that they fall under the acceleration of the Earth's gravitational field is negligible so they never hit the side of the tube. And there are focusing mechanisms anyway and they keep the particles on track.

I don't think so (Chazz, please correct me if I'm wrong about this). I think he's talking about the effect increased mass would have on momentum. Those accelerator tubes aren't straight, and a more massive partical would be more difficult to keep going "round the bend"; it would want to go straight and hit the wall of the tube. Of course, the crucial point in all this is that a proton accelerated to a couple thousand times its original mass is still lighter than a speck of dust.

PMB, regarding the relationship between relativistic mass and gravitational pull, were you one of the contributors to my

- #14

pmb

Yes. That was me. I enjoy discussing the topic of mass. Its my area of research.Originally posted by LURCH

PMB, regarding the relationship between relativistic mass and gravitational pull, were you one of the contributors to my"Relativistic Black Holes?"thread in the old PF?

Pete

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