Woo Hoo, LHC is Working

[alexander]

Mass at near c (for the bunch) :

 

(1.67262158*10^(-27)*1.15*10^(11)*2)/(sqrt(1-(299792455.00207542^2)/(299792458^2)))

 

we get .000000000002720261 or .000000000005440521kg for two bunches which is closer, but is still far too low for a miniature black hole, though that will not deter me here, now for some mass energy calculations :(

 

i corrected my energy value above, too, had a correct value, it now states collision total energy (if it happens to be an inelastic one)... say mmmmm black hole thermodynamics :cheer:

[modest]

Mass at near c (for the bunch) :

 

(1.67262158*10^(-27)*1.15*10^(11)*2)/(sqrt(1-(299792455.00207542^2)/(299792458^2)))

 

we get .000000000002720261 or .000000000005440521kg for two bunches which is closer, but is still far too low for a miniature black hole, though that will not deter me here, now for some mass energy calculations :doh:

 

i corrected my energy value above, too, had a correct value, it now states collision total energy (if it happens to be an inelastic one)... say mmmmm black hole thermodynamics

 

Very good. You and I are within an order of magnitude now and I certainly agree that's not energetic enough for a black hole, so we're very much on the same page. I will once again quietly follow along.

 

~modest

[alexander]

Ok, checklist for black hole thermodynamics calculations:

 

Home - *looks around - thats a check

Boredom - not too much, but i kind of want to get this done, so check

Some fairly high powered computers - hehe 3 64 bit x86 cores at over 2GHz, 2 64 bit spark cores at 733 MHz, one 32 bit core at 3GHz, one 32 bit core at 400MHz or so... check... i think ... oh wait, overclocked 11MHz processor in my calculator.... most important, thus definitely check :)

 

Brain - that's the hardest one on this list... i'm feeling a maybe there :)

 

ok lets run some numbers, but first let me discuss how many more assumptions are in effect now. We now make an assumption, that if we smash all the particles together into one, we will convert the total kinetic energy of the collision into heat energy. Upon collision we will form a momentary hole, which will consume all of the heat energy, which Schwarzschild predicts will increase the total mass of the black hole.

 

First we need to find entropy of a black hole of the size that can be created by pure mass(we are using mass at near c, though in reality we should be using mass at rest, because at the moment of the creation, all our particles will stop in one place.

 

i also dont have any physics books on me, so i have to assume that when wiki states [math]dS=8\pi MdM=d(4\pi M^2)[/math]

 

the change in entropy depends on the quantity of heat added dQ

[math]dS=\frac{dQ}{T}=8\pi MdQ[/math]

 

this is where my comfort zone for math ends... and i don't like not remembering integration rules that i tried so hard not to learn

 

ok first of all solving for the change in mass:

[math]\int{dS}=\int{d(4\pi M^2)}[/math]

 

my calculator solves it to (positive value only for our needs)

[math]M=\frac{\sqrt{S}}{2\sqrt{\pi}}[/math]

 

so then using the first eq to solve for s with respect to heat energy so we solve it from 0 to heat energy (or so it seems that from looking at the wiki pressure-volume work eq):

[math]S=\int^{244449.423402}_0{8\pi MdQ}[/math]

 

S in this case is 0.000033424842

 

change in mass is therefore

[math]M=\frac{\sqrt{0.000033424842}}{2\sqrt{\pi}}[/math]

 

that comes out to an immensive 0.001630909076 kg ...:shrug: ... dont laugh but that puts us well above minimum weight requirements...

 

can someone check my math, please... theory mainly, equations and differentiation and stuff... i am worried about that part and would not like to have it wrong

[Jay-qu]

The question I have is: When an object collides with a black hole, what becomes of its momentum? Does the black hole gain the momentum?

[Qfwfq]

i am tired of assuring people that this is a safe apparatus, and that black holes are not going to consume the planet, assuming we will even be able to create them. Can someone run some numbers showing this plz :confused:

 

The safety of the LHC

 

And of course, Jay, momentum is conserved! :)

[modest]

Ok, checklist for black hole thermodynamics calculations:

 

Black hole thermodynamics! :eek: Computer scientists with your crazy 4D Rubik's cubes making us all look bad... It’s masochistic I tell ya

 

First we need to find entropy of a black hole of the size that can be created by pure mass(we are using mass at near c, though in reality we should be using mass at rest, because at the moment of the creation, all our particles will stop in one place.

 

Setting aside our quest for entropy for a sec, I couldn’t agree more with the rest of this statement... and I think it’s going to be key in a moment, so let me use my method to calculate it once again.

 

In our frame, each collision has,

[math]14 \ TeV[/math]

Converting to joules,

[math]14 \ TeV \left( \frac{10^{12} \ eV}{1 \ TeV} \right) \left( \frac{1 \ Joule}{6.2415 \times 10^{18} \ eV} \right) = 2.243 \times 10^{-6} \ Joules[/math]

This is energy in our rest frame per proton / proton collision. Considering the energy of 2 colliding bunches:

[math]2.243 \times 10^{-6} \ J \times 1.15 \times 10^{11} = 257950 \ Joules[/math]

This is the total energy of 2 colliding bunches. We can also consider this energy in terms of kilograms without any ambiguity, which will be most useful:

[math]m \ (kg) = \frac{e \ (J)}{c^2 \ (m/s)}[/math]

[math]m = \frac{257950}{299792458^2} = 2.87 \times 10^{-12} \ kg[/math]

This is remarkably close to the value you give in post 35, and we used different methods to get it - so, I’m very happy with it.

 

i also dont have any physics books on me, so i have to assume that when wiki states [math]dS=8\pi MdM=d(4\pi M^2)[/math]

 

This just confuses me. You seem to be trying to solve for mass and I don’t think wiki’s rearranged first law above is helping you. Ignoring all but the first term, the first law would be:

[math]dM = \frac{\kappa}{8 \pi}dA[/math]

and subbing,

[math]S = \frac{A}{4}[/math]

we get,

[math]dM = \frac{\kappa}{2 \pi}dS[/math]

this is equation 7 here. But, then I don’t think you can do this:

 

the change in entropy depends on the quantity of heat added dQ

[math]dS=\frac{dQ}{T}=8\pi MdQ[/math]

 

I wouldn’t swear to this, but it feels like you’re mixing and matching your black hole and classical thermodynamics in an unnatural way. It confuses me, but I think I have a solution you've overlooked.

 

You're solving for mass (more particularly, the mass change of the black hole) and I think you mean to get there from heat added to the black hole. But, we don't need to solve entropy to get this. The change in mass is equal to the energy we put in the hole. We've already solved this above in Joules and Kilograms. That's it... that's the left side of this equation:

[math]dM = \frac{\kappa}{2 \pi}dS[/math]

If you add two accelerated bunches of protons to a black hole then you add 257950 Joules or [imath]2.87 \times 10^{-12} \ kg[/imath] to the hole. That is the change in mass. I don't expect you to take my word on this, so I found a source:

In the corresponding laws, the role of energy, E, is played by the mass, M, of the black hole; the role of temperature, T, is played by a constant times the surface gravity, K, of the black hole; and the role of entropy, S, is played by a constant times the area, A, of the black hole. The fact that E and M represent the same physical quantity provides a strong hint that the mathematical analogy between the laws of black hole mechanics and the laws of thermodynamics might be of physical significance.

 

-Top of page 11, The Thermodynamics of Black Holes

 

I know I said I'd quietly follow along, but this is all so interesting that I can't seem to help myself. Besides, I'm a bit curious myself if we should all be expecting the ground to give way beneath us at any moment :hihi:

 

:phones: Some say the end is near. Some say we'll see armageddon soon. I certainly hope we will cus... I wanna watch it all go down. Watch you flush it all away. :phones:

 

~modest

[Southtown]

The question I have is: When an object collides with a black hole, what becomes of its momentum? Does the black hole gain the momentum?

Turn into heat maybe?

[alexander]

The question I have is: When an object collides with a black hole, what becomes of its momentum? Does the black hole gain the momentum?

Entropy is always conserved, it has to follow the laws of physics, like anything else... In which form it is conserved, however, is a subject of some debate, perhaps :shrug:

 

I wouldn’t swear to this, but it feels like you’re mixing and matching your black hole and classical thermodynamics in an unnatural way.

equation is taken right off the hawking radiation wiki page

 

From the black hole temperature, it is straightforward to calculate the black hole entropy. The change in entropy when a quantity of heat dQ is added is:

[math]dS=\frac{dQ}{T}=8\pi MdQ[/math]

the heat energy that enters serves increases the total mass:

[math]dS=8\pi MdM=d(4\pi M^2)[/math]

[modest]

equation is taken right off the hawking radiation wiki page

 

I see (objection withdrawn), but I think what wiki is saying when they do this:

 

[math]8 \pi MdQ = 8 \pi M dM[/math]

 

is that heat energy added to the hole equals energy added to the hole equals mass change of the hole. Energy is a conserved quantity. I'm still confused why you're going from mass to entropy to mass. I honestly think you could leave out the middle man and just say dQ = dM.

 

~modest

[alexander]

that makes sense somewhat, most of the thermodynamics i have read so far have refered to the change in mass/energy, and we know that mass is energy, so yeah it makes sense, my question still is how i can use it to determine the amount of mass a black hole might gain by absorbing that thermal energy...

 

we need some theoretical physicists here, or people that know what they are talking about... where's Dr.C, he seems to have good grasp of physics, might be able to help... ?

[7DSUSYstrings]

Okay...

 

First of all, we have no absolute proof that black holes are the result of collapsing stars. Theoretically the null geodesics emerge from such compaction, still string theory can show that gravitational intersections in a specific geometrical symmetry could generate one if it was in runaway mode.

 

I find it difficult to believe that probability would generate a black hole so easily through a mere collision. It requires the "clockwork" to be intact. The LHC's mission is to smash the hadrons to the "gears and springs" and the fragments from which they are made. The probability of the clock reassembling itself after such a trauma are about the same as a frog trying to reassemble itself after two experimental juvies tied it to a big, big rock, held another not quite as big rock in their curious hand and said "Hey, frog! You want to meet God?" (giggle, giggle... (these are girls (this is also a true story))) "Okay! Go meet God!" Smoosh!... end of story.

 

The question and perhaps the moral of this story? Does the frog have a soul? Did its soul go directly to God or did it traverse a black hole first?

 

Geometric symmetry as in black holes, worm holes, etc... We're back to engineering the time machine again, thus back to the other thread...

 

 

See you folks in a day or two...

 

Dr. C.

[modest]

my question still is how i can use it to determine the amount of mass a black hole might gain by absorbing that thermal energy...

 

The only way a black hole can absorb energy is by swallowing a particle. Each accelerated particle is 7 TeV which is 1.12E-6 Joules or 1.25E-23 kg by e=mc^2.

 

If the black hole were to swallow an unaccelerated proton, it would only gain 1.67E-27 kg, being that's the proton's rest mass.

 

If the black hole were lucky enough to be exactly where two protons collided then it would absorb 14 TeV or 2.5E-23 kg. I would consider this the worst case scenario, because I don't think a micro black hole could be in two places to catch the energy of two collisions - let alone a whole bunch. Even if all the protons of two bunches collided at the same time, a black hole in the area would likely absorb no energy unless it was exactly touched by one of the protons or a quark or some other product of the reaction.

 

But, considering the vast amounts of interatomic space - it's far more likely that a black hole (if made) would pass all the way through the earth and out the other side without touching anything (just like a neutrino). I don't think there's any reason to assume it would be inclined to absorb more thermal energy from a subsequent collision in the LHC. More likely, it would be a hundred thousand kilometers away by then.

 

~modest

[7DSUSYstrings]

The only way a black hole can absorb energy is by swallowing a particle.

 

Then you are saying that energy is a particle?

 

 

It is possible for a naked singularity to exist on the quantum level (See Hawking-Penrose:The Nature of Space and Time). My argument is that timelike curves are closely associated with quantum gravitational geodesics to the extent one cannot exist without the other, or at least not for more than 10^-43 seconds; the initial time of expansion.

 

This returns us to the necessity of temporal frames. Frames of time will need gravity with infinite range (proven at Fermilab) thus potential infinite velocity. Zero point energy will limit the time-gravity velocity to a stable state particle and partner having variable velocity dependent upon the r_{abcd tensor density of the particular geodesic.}

 

_{For a frame to exist that is dependent upon the prior frame, it must have a compact plane from which its origination can expand into a multidimensional spherical volume. From this we can derive a global hyperbolicity and if you run the data to form a curve, you'll see that it splits into to equal and opposite curves assymptotically.}

 

_{We actually see a quantum level representation of this in the path of an electron within it "lobe" of an atomic structure. Put another atom near it and the lobe becomes warped to combine them or perhaps drive them apart. The question arising asks whether the atom is the projection or the projector. I believe it is more likely the atoms we know are the projections...}

 

 

_{Dr. C.}

[maddog]

I vaguely remember where Brookhaven had collided two beams of gold ions together.

They had measure a Quark plasma. They also weren't sure as some evidence implied

some mbh's in the residue explosion (impact). I think this was earlier this year.

 

It was Hawking's early paper proposing Hawking Radiation limiting mbh's of size less than

10 e-15 Kg (asteroid / proton sized).

 

What I speculate about (with the understanding that electrons are assumed to be

point sized) couple Hawking explanation with the Pauli Exclusion Principle to consider

as the radius of curvature of the event horizon of an mbh gets smaller, wouldn't the

PEP prevent this radiation effect from being linear as the radius of curvature goes to 0.

I wonder if radiation would instead be asymptotic as the radius goes to 0. This could

make a few mbh very small indeed with behavior like elementary particles.

 

If possible that Electrons were Not pointwise particles yet had some geometry smaller

than we can currently see, this falloff would be exacerbated.

 

In either case the gravitational effects from mbh's would not become a problem from

running the LHC to full power and beyond. It may even detect any anomalies and

resolve connundrums between the Standard Model and GR.

 

maddog

[maddog]

... we have no absolute proof that black holes are the result of collapsing stars. Dr. C.

 

Maybe not "absolute" yet very strong evidence -- Cygnus X1, Center of our

and many galaxies are thought to house black holes. I remember back when

I took Astrophysics and I asked my professor could Black Holes be Galactic

Centers; his response was "Absolutely NOT!" Times change.

 

maddog

[7DSUSYstrings]

Maddog,

(Have you ever said "maddog" backwards?:D)

 

The PEP would very likely prevent linearity, but the principle itself is governing curved tensors in the orbitals to begin with.

 

Absolute is often a key word to many failable hypotheses. On the other hand it comes into play when determining the validity of a theory based upon the failability principle.

 

Perhaps I should have stated intersections as a curved path tangent to another. I did to some degree in my "intro" thread, suggest hypotrochoidal geometry to the so-called "massless" particles' MFP (mean free path). I also mentioned there, so reitering here, this concept aligns with the physics of chemistry (an oxymoron?). There, however, I didn't specify tangential intersection.

 

Brookhaven, BTW, was not certain whether MHB's were produced; that was a speculation, like so many, based upon abstract balance of equations.

 

Dr. C.

[modest]

The only way a black hole can absorb energy is by swallowing a particle.

Then you are saying that energy is a particle?

 

No, I'm just saying that two things need to touch in order to transfer energy. In classical thermodynamics heat can be from radiation, conduction or convection, and all require physical interaction. This is true (or should be) if you're transferring energy to a black hole too. The difference being that a black hole will eat whatever particle just gave it energy. So, the black hole gets the kinetic energy and the mass. Some people like to call that the "relativistic mass" and some call it total energy - either way, the black hole gets it all.

 

~modest