I’ve been trying to fins some info on the web about the Planck Scale…the ultimate system of measurement in physics. I found the values, bot not their respective significances for one particular measurement.
Planck length =(approx)10^-32 meters;
smallest possible unit of length.
Planck Interval =(approx)10^-44 seconds;
smallest possible unit of time.
Planck Mass =(approx)10^-11 grams (kilograms?);
NOT smallest possible unit of mass. I could not find an explanation to this measurement’s significance. Why is it a big deal?
I think, if you had a Planck mass inside a Planck length, you’d have a tiny black hole.
There seems to be a problem with your definitions of Planck mass and Planck length. I’ve seen this recently too–where is it coming from? The Planck mass is 2 (or 5) x 10^-8 kg, a full million times that value.
Oh, the page I quoted from was just trying to advocate using different units for subatomic physics…I don’t think he was advocating some new theory for physics itself.
After much searching, I couldn’t find a simple clear explanation (I don’t mean definition) for Planck mass.
That’s not the page I read. I think he calls his theory Holistic Quantum Cosmology.
I’m beginning to get a feel for what it is you are asking for. I hope.
If you set G=1 and c=1 (both dimensionless), as is often done (see p.36 of MTW’s Gravitation), then mass can be expresssed in meters! One of MTW’s examples is that the mass of the sum is 1.477 kilometers.
If you do this, then the Planck mass = Planck length. But it is only when the Planck mass is compressed to the Planck length that there is a significant effect.
Or is your question, why can’t we have distances smaller than the Planck length, or times smaller than the Planck time, yet we can obviously have masses smaller than the Planck mass?
From Cosmological Physics, by Peacock, in a section on quantum gravity:
This gives a value for m[sub]P[/sub] of about 10[sup]19[/sup] GeV, or about 2 x 10[sup]-8[/sup] kg, as RM Mentock said.
Also, from what little I know about string theory (just a couple of colloquia’s worth), I seem to recall that the energies of the fundamental modes of oscillations of superstrings are supposed to be integer multiples of the Planck energy (the Planck mass times c[sup]2[/sup]). This leads naturally to the question of why the particles we see have such small energies compared with the Plank energy; I know this has something to do with cancellation effects from quantum uncertainties, but someone with more quantum mechanics knowledge will have to get in here to try to explain that.
Nobody’s ever claimed that you can’t have distances/times smaller than the Planck scale… Presumably, you can. It’s just that we don’t know how things would work at such scales, because at that level, both gravity (G) and quantum mechanics (hbar) are significant, and we don’t have a quantum theory of gravity.
Plank units are derived from re-arranging three fundamental constants in nature: G–the gravitational constant; h-bar–Plank’s constant; and c–the speed of light. The Plank length is the square root of Gh-bar/c^3 = 1.62x10^-33 cm. Plank time is Plank length/c or the square root of Gh-bar/c^5 = 5x10^-44 sec. Plank area is Plank length squared or Gh-bar/c^3 = 2.61x10^-66 cm^2. Plank mass (or energy) is the square root of h-barc/G = 2.18x10^-5 gm = 1.22x10^19 GeV. Although G J Stoney was the first to consider the idea of combining constants for fundamental units (and Plank took his idea and substituted h-bar for the unit of charge,e), it was John Wheeler who led the way to understanding their deeper significance.
When you look down at a Plank length (gedankenly speaking), the extreme quantum fluctuations in the fabric of spacetime overwelm science as currently known to humans. Since Plank time is just the time it takes light to travel a Plank length, time loses meaning at this scale. Therefore, so does space. (Or you can say space loses meaning because of the energy densities involved and therefore so does time. That’s the problem: down there our logic and math do not work.) It is assumed that a quantum theory of gravity would explain what is going on down there.
Plank mass is an interesting boundary point again involving a quantum theory of gravity. A speck of dust weighs a Plank mass but it is not subject to quantum forces because of its size. A proton at rest has a rest mass (or energy) of just under 1 GeV (billion electron volts). Current theory says once you can get energy levels up to 10^16 GeV, the strong, weak, & electromagnetic forces will all be one. Take the energy level on up to the Plank energy and Gravity will join them. (Engineers say you’ll need a particle accelerator as big as the universe.) Because gravity will greatly increase in strength, again the quantum effects of gravity become important.
Or you can look at the Plank mass from the other direction. A black hole radiates energy and very slowly loses mass. When it finally gets down to the mass of a mountain, the radiation rate increases and the mass drops faster. When the black hole mass drops to the Plank mass, quantum gravity dominates because the time scale for further change in mass is smaller than Plank time. It is assumed (for no good reason) that black holes completely evaporate at this point.
The Plank area pops up in black hole thermodynamics. The entropy of a black hole is the number of Plank areas on the sphere of the event horizon. It is a really big number.
Philbuck is correct in how Plank energy shows up in superstring ideas. To put it another way, the positive energy (mass) derived from the string tensions starts at the Plank energy and scales up. This mass (energy) is offset by the negative energy derived from the quantum fluctuations of the string. The residual mass (energy) corresponds to known particles. Ain’t string ideas grand? Too bad no one can prove any of it.
Here’s someone who has. Click on the link, and go to paper 9610066. The author shows that measurements of lengths shorter than the Planck length, and time intervals shorter than the Planck time, are fundamentally impossible. I’ve only read part of the paper, but so far he’s shown that all of physics is invalid. Maybe he’ll fix it by the end of the paper. (It is a serious paper, not just some crackpot.)
(Credit dylan_73 with the link in this thread that led me to the paper, which reminded me of this thread.)
I lost the link (it was probably at Scientific American or New Scientist), but I recall an article where they were speculating that black holes stabillize at about a Planck mass.
(It is a serious paper, not just some crackpot.)