9 Planck masses come pretty close to 268 times the standard atomic mass unit.
Planck's Units
Given the universal constants G (Newton's gravitational constant), h (Planck's constant) and c (the speed of light), we can infer- a mass = √(c.h/G) = 54.565e−9 kg
- a length = √(G.h/c)/c = h/c/mass = 40.507e−36 m
- and a time = length/c = 0.13512e−42 s
On the other hand, c does indeed simply describe the relationship between the units we used for measuring length and time, which the space-time manifold sees as being
of the same kind, so choosing units in which c is 1 does seem reasonable. Ideally, we'd express things in some way that doesn't involve c even if it isn't 1: it's an artifact of our model, just like the change-of-units constant we'd have had to introduce if Newton had distinguished between inertial mass and gravitational mass; or the one we'd have needed to introduce if we measured vertical distance in fathoms and horizontal distance in furlongs, with one furlong equal to 110 fathoms. The naturality of c as unit binds units into families among which ratios are powers of c; thus time and length are members of one family, along with area/time and the inverse of accellerations; while mass, momentum and energy are members of another family.
Whether h should be construed as merely a conversion factor (between wave vector – of dimension inverse length – and momentum) or as carrying information (about the fuzziness of reality) is not so immediately clear; but a careful analysis (see below) of de Broglie's and Planck's results does encourage the former. Taken together with the speed of light, this declares length, time and the inverse of mass to all be quantities
of the same kind: our habit of measuring them in different units is no more meaningful than archaic usage's habit of measuring vertical and horizontal distances in different units, or the weights of grain and gold in different units. In contrast, I construe G as encoding the physics of the system: even if we chose to use units which make its value a unit, it's still a real quantity.
Charge and Current
How about a unit of charge ? Quite a good unit of charge is the charge on the electron, or a third of it, give or take sign: this is clearly a genuine irreducible quantity of charge, making it ideal as a unit, hence widely used. However, the form of Planck's units thus far is based on the constants in the field equations themselves, rather than on the bodies controlled by these: though good (by virtue of its real irreducibility), it is defined in the same spirit as the atomic mass unit, rather than in terms of the field equations.On the other hand, electrodynamics furnishes us with the impedence of free space, Z0 = √(μ0/ε0) = 376.730 Ohm, and √(h/Z0) is a charge: 1.33e−18 Coulombs or 8.278 positrons-worth of charge. Indeed, squaring 8.237 and doubling, we get the inverse of the fine structure constant: α = e.e/(4.π.ε0.c.ℏ); c is 1/√(ε0.μ0) so ε0 is 1/(Z0.c); and 2.π.ℏ is h; yielding α = Z0.e.e/(2.h) or 1/α = 2.(h/Z0)/e/e. (That μ0 = √(Z0/c) also seems worth mentioning.)
For currents, we thus obtain a Planck unit as charge/time: this is about 9.81e24 Amps; that's a pretty big current. Multiplying that by Z0, the unit of impedence (which is of the same kind as resistance), we get a unit of potential (i.e.
Voltage) equal to 3.6978e27 Volts.
Relating the units to the real world
A droplet of water (e.g. in mist) between a third and a half of a millimetre across has volume of order a few dozen nanolitres, making its mass a few dozen nano-kg, i.e. roughly the Planck mass. Such a droplet of water is large enough to contain a lively diversity of life-forms: for example, water bears, a phylum of animals officially called tardigrades, have masses typically less than the Planck mass. The periot and blanc, two archaic units of mass supposedly used by jewelers, are smaller than the Planck mass; as are the masses of many life-forms. How many atoms of hydrogen are there in a Planck mass ? Sort of a Planck's version of Avogadro's number: 32.575 milliards of milliards (I think ten to the eighteen has some better name). As it happens, 9 Planck masses come pretty close to 268 times the standard atomic mass unit.Notice that the Planck momentum is c.√(c.h/G) which (if I've done my sums right) comes to 16.356 kg.m/s, an entirely sensible quantity on the scale of macroscopic creatures such as you and I – a fat cat running vigorously has roughly the Planck momentum, 5.76 stone mile per hour: is this the uncertainty of momentum of a cat shut in a box with a randomly dangerous device ?
Then, of course, we have the Planck energy which, at 4.9 giga Joules, is pretty big: converting to the standard nuclear unit of energy, the electron.Volt, we get 30 milliards of milliards of milliards of electron volts – the energy transfered to a mole of electrons as they pass through a potential difference of 50.82 kilo-volt; in the standard units of nuclear bomb yield, that's the energy released by the detonation of a little over one US ton of TNT.
Thus the …, mass, momentum, energy, … chain straddles real-world sized units in its familiar units. For contrast, note that the item on the …, time, length, … chain which is nearest to order 1 in SI units is .327 metre5 / second4: the Planck length and time are tiny even on the scale of nuclei (after all, a photon with wavelength the Planck length has the Planck mass – which is pretty huge by nuclear standards).
Just as c is a conversion between units of length and time, Boltzmann's thermodynamic constant, k, converts between those of energy and temperature; the consequent Planck temperature, energy / k, is about a third of 1033 Kelvin: (a.k.a. 1e33 K) which is very hot indeed !
Exploiting de Broglie
De Broglie's relationship between 3-momentum and wavelength (spacelike period) for matter combines with Plancks' relationship between energy and frequency (of light's quanta) to say, in Einstein's world, that the structure of (a particle of) matter is periodic along its own world-lines; and a mass m has period h/m/c.Now, when m is Planck's mass, as discussed above, h/m/c is the Planck length. That means a Planck-mass mist drop's proper period is the Planck length (or time, as you wish); this is a factor of 1030 smaller than the physical dimensions of the mist drop, which has much to do with why one doesn't much notice quantum effects on raindrop-sized things. Smaller objects have longer periods; bigger objects have shorter periods. The Earth's period is of order 1e−66 metres, much shorter than the Planck length, and the Sun's is shorter yet: 1e−72 seconds. An electron's period, for comparison, is 2.4263 pico metre.
Back to our water-droplet: the smaller we make it, the larger its period will grow, and it's presently bigger than its period, so let's shrink it until they're equal. The volume of a sphere is cube of diameter times π/6; multiplying by density we get mass; solving for diameter and period both equal to d, we obtain 6.h/π/c/density equal to the fourth power of d, making the diameter 8 pico metres – which is rather smaller than a single water molecule (but bigger than an atomic nucleus). Doing the same sum for liquid hydrogen at 20 Kelvin, with a density of 70.99 gram per litre, I get 15.6 pico metre, which is a little under a sixth of a hydrogen atom's diameter. For gaseous hydrogen at zero Celsius, the matching calculation gives about 83 pm, which is smaller than the diameter of a lone hydrogen atom but larger than the separation of two hydrogen atoms in the H2 molecule; however, it's much smaller than the separation of hydrogen molecules in the gas at zero Celsius. A hydrogen atom's radius is about 40 thousand times its wavelength.
Hiding c
Scaling by c turns mass into momentum into energy; time into length; and each of these sequences is but the familiar portion of a chain stretching off at either end, as length.c = area/time, time/c = 1/acceleration, … and similarly for the momentum chain. On each chain it would be nice to chose a position to think of as themiddle: the rest of the chain will then be the middle times successive powers of c, with the middle at zero power.
For the mass chain, on which we have 3 familiar quantities, the middle one of these looks a good place to chose as mid-point: and anyway I prefer to describe things in terms of momentum. Choosing the middle of the other chain is harder: I can argue for √(length.time) or possibly the fourth root of volume.time, and they could sound more reasonable than either of the two obvious candidates.
Fix, then, on momentum: and examine Newton's equation re-arranged as G = r.r.F/(m.M). We need to re-express the product of masses, m.M, as the inner product of two 4-momenta, p·P/c/c. Now, F is a rate of change of momentum so r.F has the units of speed×momentum. This gives us G/pow(c,3) as a length/momentum quantity: call this D. Combining with h, which is a length.momentum, we obtain √(h/D) as a momentum, √(h.D) as a length. (We can equally use D/c = G/pow(c,4), a time/momentum, and h/c, time.momentum, if we want to use time rather than length.)
Now, the definition of h is as the constant in the law of proportionality, E = h.f, between the energy of a photon and its frequency, f. But I want to work in terms of momenta, so consider p = h.f/c and notice that f/c is a 1/length, which means a gradient (equally p = h/wavelength). This fits well with the view, in quantum mechanics, of momentum as the differential operator in space-time (which has the dimensions of a gradient).
That gives me a hint that it'll be worth working in terms of length and momentum: but, of course, if I use h/c in place of h, I'd equally be working in terms of time and momentum. This is just a choice of whether h or h/c gets to be regarded as the
fundamentalconstant, the other being
derived, and is exactly equivalent to the choice of whether to treat length or time as
middleon their chain.
Perhaps we can clarify the issue by considering what another factor of h (and some factors of c) will get us on the other side of length and time. We have momentum divided by h as a 1/length; dividing by h again we get the inverse of the product of area and momentum. One factor of c turns the product of area and momentum into a product of volume and force; a second turns it into a product of volume and power.
Refinements and variations
Note that taking Z0 and c as units makes ε0 and μ0 units also. Now, ε0 is the constant in the field equation of electrostatics; it's the constant of proportionality between the gradient of the field and the charge density. Contrast this with G, which is the constant of proportionality in Newton's gravitational law, which describes a special case – the two-body problem – whose analogue in electrostatics is the Coulomb law, which uses 1/(4.π.ε0) in place of G. When Newtonian gravitation is described by a field equation, the constant of proportionality between gradient of the field and mass density (analogous to ε0 in electrostatics) is 4.π.G (or its inverse). We might thus argue for replacing G in our system of units with 4.π.G. In Einstein's field equation for gravitation, the constant which shows up is 8.π.G, give or take some factors of c, so we might sensibly use this in place of G. Either way, we perturb the units that result by some factors of two, π and their square roots.Likewise, we could try to justify using Dirac's constant (a.k.a. ℏ = h / 2 / π) in place of Planck's constant; or half of Dirac's constant (the spin of those Fermions with the least non-zero spin of all particles). These choises, likewise, throw in some stray factors of two, π and their square roots. However, these choices are more in the spirit of using a unit based on the actual properties of observed particles (the least-spin Fermions), whereas Planck's constant arises naturally in a field equation. We do get Dirac's constant in field equations – it appears naturally in Schrödinger's equation, and it's the constant of proportionality between the gradient and momentum operators in the field equations of Quantum Mechanics – so this isn't necessarily a fatal objection.
Here, then, are a few of the alternative systems (C = Coulomb, e is the charge on the positron) of Planck-like units we can come up with, using choices I could justify as above:
- c, Z0, G, h
- length: 40.507e−36 m
- time: 135.12e−45 s
- mass: 54.565e−9 kg
- charge: 1.32621118e−18 C = 8.2780 e
- c, Z0/4/π, G, h
- length: 40.507e−36 m
- time: 135.12e−45 s
- mass: 54.565e−9 kg
- charge: 4.7012962e−18 C = 29.3446 e
- c, Z0, 8.π.G, h
- length: 203.07e−36 m
- time: 677.37e−45 s
- mass: 10.884e−9 kg
- charge: 1.32621118e−18 C = 8.2780 e
- c, Z0, 8.π.G, ℏ/2
- length: 57.285e−36 m
- time: 191.08e−45 s
- mass: 3.0703e−9 kg
- charge: 0.37411727e−18 C = 2.33517 e
- c, Z0, 4.π.G, ℏ
- length: 57.285e−36 m
- time: 191.08e−45 s
- mass: 6.1407e−9 kg
- charge: 0.52908171e−18 C = 3.30243 e
Written by Eddy.
Anti-hydrogen Captured, Held For First Time
The electrodes (gold) of the trap used to combine positrons and antiprotons to form antihydrogen.N. MADSEN, ALPHA/SWANSEA
Antimatter is produced in equal quantities with matter when energy is converted into mass. This happens in particle colliders like CERN and is believed to have happened during the Big Bang at the beginning of the universe.
“A good way to think of antimatter is a mirror image of normal matter,” said team spokesman Jeffrey Hangst, a physicist at Aarhus University in Denmark. “For some reason the universe is made of matter, we don’t know why that is, because you could in principle make a universe of antimatter.”
In order to study antimatter, scientists have to make it in a laboratory. The ALPHA collaboration at CERN has been able to make antihydrogen – the simplest antimatter atom – since 2002, producing it by mixing anti- protons and positrons to make a neutral anti-atom. “What is new is that we have managed to hold onto those atoms,” said Hangst, by keeping atoms of antihydrogen away from the walls of their container to prevent them from getting annihilated for nearly a tenth of a second.
The antihydrogen was held in an ion trap, with electromagnetic fields to trap them in a vacuum, and cooled to 9 Kelvin (-443.47 degrees Fahrenheit, -264.15 degrees Celsius). To actually see if they made any antihydrogen, they release a small amount and see if there is any annihilation between matter and antimatter.
The next step for the ALPHA collaboration is to conduct experiments on the trapped antimatter atoms, and the team is working on a way to find out what color light the antihydrogen shines when it is hit with microwaves, and seeing how that compares to the colors of hydrogen atoms.
CERN Press release
ALPHA collaboration
Nature article.
Print publication will be in one of the next editions.
*stickler for detail*
C*Y_q(x,t) = Y_{-q}(x,t) charge reversal
P*Y_q(x,t) = Y_q(-x,t) space reversal
T*Y_q(x,t) = Y_q(x,-t) time reversal
The CPT operation (composition) CPT*Y_q(x,t) = Y_{-q}(-x,-t) and the symmetry is that this is Y_q(x,t). Therefore the composition CPT = 1. This symmetry turns out to be very important for local quantum field theories with Lorentz symmetry — or that transform by relativity.
It turns out that CP can be violated, which corresponds to a T violation as well. Yet CPT = 1 remains. The violation of CP symmetry means the wave function CP*Y_q(x,t) = Y_{-q}(-x,t) can differ from Y_q(x,t) in strange ways.
This unfortunately has nothing to do with war drives, which I suppose comes from the Star Trek reference to anti-matter pods.
LC
Aneutronic fusion doesn’t emit neutrons and release millions of times more energy than chemical reactions.
Production of enough quantities of antimatter is impossible in a short time, but aneutronic fusion can be a reality soon and could power space drives.
http://www.youtube.com/watch?v=9ScAHXN_kAY
I’m all for engaging the public by using analogies most can understand but these type of reports are as good as useless. Look at the report that the LHC was going to destroy us all with a black hole, how the Higgs boson is refered to as The God Particle, how every NEO is classified as ‘an Earth-killer’.
Very annoying.
This will not be some new energy source. The antimatter or antihydrogen has a mass that is given by the energy you input into the system with the accelerator. So this is not an energy source. As for aneutronic fusion, that looks like science fiction more than science.
LC
Okay, he talks about symmetry. The big bang or inflation theory seems awfully one sided to me and therefore unsymmetrical. What if it occurred as suggested but included another universe in the other direction made of antimatter? Yes, I realize the inflationary cone does not illustrate actual direction but in that other universe would be all the antimatter and anyone there would be wondering where all the anti-antimatter was. It just stands to reason that the two would not be created in the same universe as then that universe would self annihilate and really never have been at all. Then the net production of matter would be zero and not violate a whole bunch of laws of physics. Just saying is all! (:
(mc^2)^2 = E^2 – (pc)^2
for E = energy and p = momentum. if you set the momentum p = 0 you get the celebrated E = mc^2. This can be easily looked up. In quantum mechanics you replace the variables p and E with their quantum operators
p –> -ih&/&x, E = ih&/&t
for & meaning partial derivative and h = Dirac-Planck unit of action. If you plug this into the above equation and assume it acts on a quantum wave Y you get
&^2Y/&t^2 – &^2Y/&x^2 + (mc^2)^2Y/h.
This is the Klein-Gordon equation for a relativistic wave that has zero spin.
To include spin what Dirac realized is that some spin matrices have properties s^2 = -1 and he constructed more general spin operators so one could take the “square root” of the K-G equation above. Now the square root of something has two roots, and one root is matter, the other anti-matter.
The spacetime cosmology we observe might have an arrow of time that is fixed by certain phase conditions within a larger higher dimensional spacetime. With the mulitiverse concept, or a universe with multiple spacetime cosmologies, others might have opposite time directions or be dominated by what we might call anti-matter.
LC
&^2Y/&t^2 – &^2Y/&x^2 + (mc^2)^2Y/h = 0.
Oh, and if you don’t know about differential equations — pity.
LC
Once I calculated how big the event horizon would be for a LHC proton collision turning into a black hole and came up with a number that is way smaller than the Planck scale, the same for the evaporation time.
I thought something smaller than a Planck scale means = it makes no sense anymore.
How do I have to interpret this:
A: The event horizon will be minimal the Planck length?
B: No black hole can be formed since it has not enough mass
C: Something I have not thought about.
I wrote an essay on this that is semi-mathematical a few weeks ago. I could apply that here, though I am not sure whether that many would read it or understand it. I might wait until there is a topic more relevant to that subject.
LC
I gather it is answer C:
But the event horizon would be basically a plank scale, because of stuff.
The one idea is to arrange for an array of balloons in the upper atmosphere which have various detectors. The Earth’s upper atmosphere is then a sort of particle calorimeter, similar to ALICE or ATLAS at the LHC. Another idea is to put in orbit two spacecrafts. One points a high powered laser at a cosmic ray source. Another spacecraft is a detector system. The cosmic rays scatter with the laser photons and the scatter products are measured by the detector system. That part is a bit tough to arrange. It is not entirely trivial to get an ATLAS sized hadron calorimeter type of device in space. Further, since the scattering is not going to be in the center of mass frame, the detector has to be an array which measures scattering particles coming at it, and not scattering in all directions. It is possible that the high energy laser is placed in Earth orbit and the ground based balloon system then serves as the detector.
The point of schemes like this will be to get signatures of scattering events which have signatures of this conformal quantum field RG flow. This will not focus so much on detecting new particles, such as a search for the Higgs at 115GeV or the tan(beta) parameter for the MSSM Higgs etc. So the stats might be liberalized some.
LC
1) Can control antimatter and contain it.They should have no affect on matter.
2) Why do the magnetic fields of energy(mass) not annihilate the antimatter?
Chris Landau
Anti-matter has the same mass-energy content as matter. An electron and anti-electron annihilate each other to give photons with energy E = 2mc^2, for m the mass of the electron and anti-electron.
LC
Thanks
Chris
The electromagnetic field or photon only carries the quantum number for spin = 1. It carries no charges or quantum numbers assigned to fermions, such as protons, electrons, neutrinos and so forth. So there is no anti-photon. The matter-antimatter structure comes from the Dirac equation with two roots. This pertains to spin = 1/2 particles or fermions, or the quantum numbers they carry. Things get a bit complicated with nonabelian gauge vector bosons which also carry these numbers.
LC