# Particle Accelerator Vmax

Discussion in 'Physics & Math' started by ZMacZ, May 9, 2014.

1. ### ZMacZRegistered Senior Member

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Ellos tech peeples...

Since this is so far beyond my personal knowledge I need to ask you something:

"What is the highest speed of a regular particle (proton, neutron) ever achieved using a particle accelerator ?"

- it needs to be actual proton or neutron or even larger...like Helium...
- it doesn't matter how much energy it took..only the highest speed achieved ever..

Thanx..I guess Google has it's limits when it comes to that kinda stuff..

3. ### ZMacZRegistered Senior Member

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I'm just going to tell you why...

In my post about space travel well..I kinda got stuck..
Even with ionthrusters....although even a ten fold would only allow thrust up to maybe 300KM per sec..on a cosmic scale..not quite fast enough..
So..
Gievn linear particle acceleration..(ion thrusters)..I'd figure the only way to increase fuel/thrust ratios..well..non-linear particle acceleration..
Given that an accelerator might be able to increase the speed of a particle in a circle...the speed buildup before release might be that much higher..
So...hence the question...since an actual ionthruster (yes..here and now..can build up release of about 50Km/sec..I wanna know what the maximum speed is ever achieved..)
And also..if that can be achieved and what exactly the boundaries are that keep the accelerators from increasing that speed even further ?

Once again..thanx..

Last edited: May 9, 2014

5. ### OnlyMeValued Senior Member

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The LHC accelerates lead and gold ions to 99% the speed of light... http://arstechnica.com/science/2012...r-at-lhc-and-more-hints-about-early-universe/.

Protons likely reach velocities estimated at 99+% the speed of light.

Just google LHC and ion speeds... Play around with the search and you should find more references. But keep in mind that these are all going to be estimates, no stop watches to time this sort of thing...

7. ### ZMacZRegistered Senior Member

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Ah..
Well.. did they also get a mass readout on that ion ?
I mean according to certain theories..the mass of the ion oughta have been much greater than if standing still no ?
Has that been proven/disproven ?

Also..what were the quantities involved ? Like only two ions ? or like a couple thousand ?

Last edited: May 9, 2014
8. ### lpetrichRegistered Senior Member

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Special relativity to the rescue:
$E = \gamma mc^2 = \frac{mc^2}{\sqrt{1-v^2/c^2}}$
with solution
$v = c \sqrt{1 - \left(\frac{mc^2}{E}\right)^2} \sim c \left(1 - \frac12 \left(\frac{mc^2}{E}\right)^2 - \dots\right)$

The all-time champion is the electrons in the LEP, the former occupant of the LHC's tunnels:
E = 104.5 GeV, γ = 205,000, 1 - v/c = 1.20*10[sup]-11[/sup]

The champion for protons is the LHC:
E = 4 TeV, γ = 4300, 1 - v/c = 2.71*10[sup]-8[/sup]

9. ### OnlyMeValued Senior Member

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I think you are confusing mass or rest/inertial/gravitational mass with the old concept of relativistic mass. The rest mass of an iron or gold ion is known. It is the mass of the atom less the mass of the electrons.

Relativistic mass associated with the kinetic velocity of a massive particle is more accuratelty thought of as the particle's momentum.., or the product of its rest mass and speed relative to another object. In a very flawed analogy, a bullet does not weight more while moving from a gun to a target, than is does after hitting the target, barring any loss of matter scraped away as it is fired from a gun and then hits the target. But it has far more momentum while moving between the gun and target, than is does before being fired from the gun or after hitting the target, and comming to rest. Momentum is a combination of mass and speed or velocity and is a relative measurement based on another frame of reference.., the speed and/or velocity of both, in the earlier example bullet and the target, play a role in the relative momentum, but neither has any affect on the rest mass, or simplistically the bullet's weight.

And lastly particle accelerators are almost always dealing with groups of protons or ions not single particles.

10. ### eramSciengineerValued Senior Member

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Not directly measuring the relativistic mass, but the relativistic energy. The Bertozzi experiment does prove it.

http://en.wikipedia.org/wiki/File:BertozziExp.svg

11. ### BalerionBannedBanned

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Every time I see a particle accelerator mentioned, part of me hopes for another "Supernova from experimentation at Fermilab" thread.

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13. ### JJMRegistered Senior Member

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Howdy.....Hello.....cross section of 10^21, travelling at 99.99999c means each particle would have as much mass as one forth of a ton of mass, iron. So (10^21)(500lb.).......I like tonnage, for all objects and accelerated mass.......cross section is the amount of individual particles.....

Last edited: May 19, 2014
14. ### rpennerFully WiredValued Senior Member

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• what particles are you talking about when you mention the cross section?
• what units is the cross section of 10^21 in?
• When you write "99.99999c" do you mean (100 - 10^-5)c or (1 - 10^-7)c
• when you write "man as fourth of a short ton of mass" do you mean rest mass?
• what's iron got to do with anything?

$(100 - 10^{-5})c$ is an unphysical speed for any particle. Assuming the relative speed is $v = (1 - 10^{-7})c$ it follows that the time dilation factor is $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{1}{\sqrt{1 - \left(1 - 10^{-7} \right)^2}} = \frac{10^7}{\sqrt{ 2*\times 10^7 -1 }} \approx \frac{10^7}{2000\sqrt{5} } = 1000 \sqrt{5} \approx 2236.068$

A lead-208 nucleus has a mass of about 207.93 amu or 193.69 GeV/c^2 so even at the above speed it only has an energy of about 433 TeV = 4.33 × 10^14 eV so I still haven't found your source for 10^21? Starting in November 2010, the LHC reached somewhat higher speeds and achieved 574 TeV / nucleus or $v = (1 - 0.57 \times 10^{-7})c$. This is usually reported as 2.76 TeV/nucleon.

15. ### ZMacZRegistered Senior Member

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hmm..

I'll try and reformulate..

If
Condition 1:there's a particle A, standing still..(in space..no gravitation..or any other significant forces applied..), and it would take an energy amount E1 to accelerate it from 0 m/s to 1 m/s..
Condition 2:Same particle A..now moving at 90% of the speed of light..and an amount of energy E2 to accelerate it one more m/s.

Question: Would E2 > E1 ? (and by how much if so ?)

16. ### OnlyMeValued Senior Member

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This goes way past the limited question you ask and involves some speculation based on theoretical work suggesting that inertia is an emergent characteristic...

Yes E2 > E1. This is one of the apparent paradoxes of an EMPTY space ideology.

When within the context of SR, it is postulated that the laws of physics are the same for all inertial frames of reference, it does not mean that the force or forces associated with acceleration will be equal. In SR space is conceptually truly EMPTY. However, within the context of both GR and QM, space is no longer conceptually empty. GR gives to space an undefined substance and labels it spacetime.., a dynamic counterpart to matter... Within the context of QM or quantum field theory, space is filled with constant fluctuations of zero point energy, which can and is conceptually modeled in different ways by different disciplines within QM, two major examples being QED & SED.

Still the basic principle associated with the postulate, that the laws of physics are the same for all inertial frames of reference holds. In the case you present it does not mean that E2 = E1, it means that for an observer at rest in either frame of reference the force required to equally accelerate (or decelerate depending upon one's frame of reference) will be equivalent.

It is important to put the observer in the same frame of reference as the particle being accelerated. From that frame of reference the laws governing acceleration are equal between inertial frames. Once a particle has been accelerated relative to an observer and then either accelerated (or decelerated) the particle is no longer inertial.., from the frame of reference of the observer.

I began with the qualification of empty space, because the concepts of the origins of both mass and inertia are not yet fully understood and/or defined. Both are historically and to a large extent remain thought of as intrinsic properties. But there is some theoretical work that suggests that both may actually be emergent, and the result of an interaction between the particle and zero pint energy or more specifically the associated zero point field (ZPF)... Should this be the case that same ZPF would by necessity have to be incorporated into the concept of spacetime, within the context of GR... And thus in neither case could space be thought of as truly empty and the isotropic character of the ZPF as explored within the context of QM would become dynamic within the context of GR.., the affects that the existence and dynamics of massive objects, and their interaction with the ZPF, would result in dynamic changes in the ZPF background, at the scales associated with GR and gravitation... And explain why the force (E2) required to accelerate a particle with an inertial velocity of 0.9c would be greater than the force (E1) required to accelerate a similar particle with a classical relative velocity. While F = ma would hold for both cases, F would be determined by the particle's acceleration with respect to the local ZPF dynamics.

This assumes the particles are massive charged particles, not photons and that when you say 0.9c it is as observed from a preferred (not absolute) frame of reference associated with an observer. It is also possible that two particles one inertial and at rest relative to an observer and the other inertial and with a velocity of 0.9c relative to the observer, could both be inertial relative to the dynamics of the local ZPF with respect to their own frames of reference. E2 would then be equal to E1, but it would also be assuming a flat spacetime and the limited conditions consistent with SR.

17. ### rpennerFully WiredValued Senior Member

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I think you misunderstand that Energy and velocity are both frame-dependent quantities.

In the assumed coordinate frame we have $v_0 = 0, \quad \Delta v_0 = 1 \textrm{m} / \textrm{s}, \quad v_1 = \frac{9}{10} c, \quad \Delta v_1 = 1 \textrm{m} / \textrm{s}$ and relative energies given by $\Delta E = \frac{m c^2}{\sqrt{1 - \frac{(v + \Delta v)^2}{c^2}}} - \frac{m c^2}{\sqrt{1 - \frac{v^2}{c^2}}}$

In another coordinate frame we might have $v'_0 = -\frac{9}{10} c , \quad \Delta v'_0 = \frac{2848028351}{14989622855} \textrm{m} / \textrm{s}, \quad v'_1 = 0, \quad \Delta v'_1 = \frac{7494811450}{1424014153} \textrm{m} / \textrm{s}$ and relative energies given by $\Delta E' = \frac{m c^2}{\sqrt{1 - \frac{(v' + \Delta v')^2}{c^2}}} - \frac{m c^2}{\sqrt{1 - \frac{v'^2}{c^2}}}$

But perhaps the most physically natural quantity for comparing moving objects is not velocity, but rapidity, $r = c \tanh^{-1} \frac{v}{c}$

In such a case $r_0 = 0, \quad \Delta r_0 \approx 1 + 3.7088 \times 10^{-18} \textrm{m} / \textrm{s}, \quad r_1 = 299792458 \ln \sqrt{19} \textrm{m} / \textrm{s}, \quad \Delta r_1 \approx \frac{100}{19} \textrm{m} / \textrm{s}$ and $\Delta E = mc^2 \left( \cosh \frac{r + \Delta r}{c} - \cosh \frac{r}{c} \right) = 2 mc^2 \, \sinh \frac{2 r + \Delta r}{2 c} \, \sinh \frac{\Delta r}{2 c}$

And $r'_0 = -299792458 \ln \sqrt{19} \textrm{m} / \textrm{s}, \quad \Delta r'_0 \approx 1 + 3.7088 \times 10^{-18} \textrm{m} / \textrm{s}, \quad r'_1 = 0, \quad \Delta r'_1 \approx \frac{100}{19} \textrm{m} / \textrm{s}$

18. ### OnlyMeValued Senior Member

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True, but the question was framed with respect to the same particle, which implies a common relative frame of rest.

So instead of two completely unrelated inertial frames, you have a comparison of E1 the energy (or force) required to accelerate a particle from rest to 1 m/s and E2 the energy (or force) required to accelerate the same particle from 0.9c to 0.9c + 1 m/s. Both accelerations being with respect to the particle's original rest frame. It takes more force or energy to accelerate a particle from 0.8c to 0.9c than it does to accelerate the same particle from 0.0c to 0.1c. And within a particle accelerator does it not require a constant addition of energy just to keep a particle at a constant relativistic velocity?

I raised the ZPF reference primarily based on the work of Haisch, Rueda and Puthoff, as it relates to inertia. Where even though in their papers they are dealing with an isotropic background portion of the EM ZPF spectrum and boundary conditions (essentially a flat spacetime consistent with Newtonian dynamics and SR). Their SED approach does treat this as real photons rather than virtual photons, and suggests that that portion of the ZPF spectrum originates with the zitterbewegung motions of charged particles throughout the universe... Which suggests a possible classical or semi classical origin for inertia and the interaction between the acceleration of a charged particle and an otherwise isotropic EM ZPF background, describing a mechanism for inertia as an emergent phenomena.

Basically, while it changes nothing of our definition of an inertial frame of reference, where classical velocities are involved, the fact that inertia would, within that context be emergent and based on the particle's acceleration relative to the associated EM ZPF spectrum, would change the definition of what is inertial where relativistic velocities are involved. Following this line of reasoning (should the suggestion that), the involved EM ZPF spectrum, is composed of photons originating with the zitterbewegung motion of charged particles throughout the universe be accurate, in the real world the ZPF itself must be dynamic and the definition of inertial, consistent with the local dynamics of the ZPF background.

And yes I am speculating on the implications of theoretical work that does not itself address some of these issues and answering the question from other than the standard SR and/or GR persecutive most commonly presented in discussions such as this.

That said, again.., is it not true that in practice, in a particle accelerator it takes more energy to accelerate a particle from 0.9c to 0.99c than required to accelerate the same particle from 0.0c to 0.09c, in the accelerator's frame?

19. ### ZMacZRegistered Senior Member

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om..GAWD..

I'll put in simple terms..

Put in particle..at v=0..apply 1 Joule of energy...see how fast it goes..call that V1....then:

Same particle..accelerate to 90% speed of light..

Now apply another joule...now see an increase in speed..from 90%LS+V2..then

See if V1>V2 ? lemme know the outcome all right ?

(the only thing relevant to this experiment would be to see if there's much more energy needed to accelerate something already travelling at near LS..NOTHING else..)
.

Last edited by a moderator: Sep 1, 2014
20. ### ZMacZRegistered Senior Member

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..weird...can't remove that typo..

"accelerator"

And how come no-one ever answered ?

Last edited: Sep 1, 2014
21. ### StryderKeeper of "good" ideas.Valued Senior Member

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Fix a few spelling errors for you, however I can't start fixing the grammar or well it will be completely different. (incidentally you can't edit a post after a certain time frame purely because some dishonest people use to edit posts mid argument to call foul over who they were arguing with and what they were arguing about.)

That is one of those life long mysteries that only you can solve, you'd better stock up on scooby snacks.

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23. ### ZMacZRegistered Senior Member

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Thanx..

And for him I have an actual question, since he's into number crunching..

The speed of light is absolute right ?

Given that anything in the universe has it's own speed already (earth circling sun..sun moving away from the center of the universe..
earth rotational...etc)...it's safe to say that the everything on Earth already has a significant speed..
Anyway..

If:
Gravity uses wave characteristic..
Gravity uses the speed of light..

Then:
Would ANY object project more gravity towards the path the object is traveling or more..
AND
would ANY object project less gravity towards the path the object came from or more...?

(According to my theory..which I'd say is an unfounded one..the path towards would receive a much denser gravitic wave..)
(and mind you I'm using 'gravtic' very loosly since all stuff either get's attracted to another or repulsed..)

Also: If that is true is possible to keep stacking said wave ? (or rather..increase that wave's amplitude by overlapping ?..)

..yea yea..I know..mumbo jumbo..but after I seen this one..I'd rather know about it ?

(http://www.dailymail.co.uk/sciencet...ers-DO-work-halve-size-weight-satellites.html)