Follow up on Plank Units?

Question

So... plank units are the units we use when setting c=G=h bar=1. Got Ya! Is it just coincidence then that we can't resolve space beyond the plank length and can't resolve time beyond the plank time do to quantum affects? How does it happen to be that the plank mass is the mass needed to meet the criteria of the Schwarzschild black hole with a de Broglie wavelength equal to plank length?

How are these related to arbitrarily choosing c=G= h bar =1?

To better phrase my question: Are these units simply a consequence of setting g=h bar = c = 1 or are they defined by limitations to the resolvability of space-time.

Oh yeah...I have taken GR and QM but only at the undergrad level so far.

I guess i did mean radius not dB wavelength.

But What about the resolution of space-time?

Answer 1

What is the schwarzchild radius of a black hole with mass m?

r = 2Gm/c^2

in planck units, r = 2m (isn't that cleaner?)

So the radius (measured in planck distances) is twice the mass (measured in planck masses).

I'm not sure what you mean by the deBroglie wavelength of the black hole. Is the black hole going somewhere? You need momentum to define a deBroglie wavelength.

I wouldn't read too much into the whole "can't resolve space and time shorter than Planck scale" thing. The fact of the matter is that physics as we now know it (GR and quantum field theory) is broken somehow at the Planck scale. We really don't understand what happens at such high energy scales. Our particle accelerators are many orders of magnitude below that energy, so we may never be able to experimentally probe it, so we are going to have a very hard time understanding the very very very early universe when those sorts of energies were around.

Answer 2

The main thing about the Planck scale is that both General Relativity and Quantum Mechanics are important for its description. Why this is interesting is that GR and QM in their present form have *irreconcilable* differences. This means the QM is valid only in the limit that spacetime curvature, as described by GR, is negligible, and GR is only valid in the limit that the deBroglie wavelength, as described by QM, is negligee. Since Neither assumption is valid at the Planck Scale, we have *no idea* what happens their. Only a "theory of everything", therefore, that reduces to both QM and GR in their respective limits could describe it. When one says that one cannot "resolve" space and time at this scale, one means that spacetime is so distorted that it becomes a mish-mash of something that cannot even be described at the moment.

Answer 3

I think you have just confused the Planck units with the Planck scale. If you're working in quantum mechanics, the Planck length is simply a more convenient unit to work with than meters, centimeters, or feet. Planck units are arguably more fundamental than any other set of units. But its rather inconvenient to do astronomy in Planck units.

The Planck scale refers to the range of dimensions where quantum mechanics applies. The Planck length is more than just a limit to resolution or measurability, it's a limit to granularity. It's not just that you can't measure something smaller than that, it's that there IS nothing smaller than that.

The Planck mass isn't a coincidence. See the third reference for how it is calculated.

Answer 4

Gravitation (c=c, G=G, *h=0*) and quantum field theory (c=c, *G=0*, h=h) become equally important at the Planck scale. Since they are 100% incompatible, physical theory fails.

It is much deeper than number twiddling. General Relativity models continuous spacetime, going beyond conformal symmetry (scale independence) to symmetry under all smooth coordinate transformations - general covariance (the stress-energy tensor embodying local energy and momentum) - resisting quantization. General Relativity is invariant under transformations of the diffeomorphism group. General Relativity predicts evolution of an initial system state with arbitrary certainty. Quantum mechanics' observables display discrete states. Heisenberg's Uncertainty Principle limits knowledge about conjugate variables in a system state, disallowing exact prediction of its evolution. Where GR and QFT overlap there is disaster.

String theory has c=c, G=G, and h=h. String theory has 10^1000 acceptable vacua (the landscape) and makes no empirical predictions. String theory is a disaster.

Can all of physics be wrong? Metric gravitation theory can be trivially demonstrated wrong (empirically falsified). GR postulates the Equivalence Princple, string theory demands it through BRST invariance. Find two lumps that locally vacuum free fall along divergent trajectories and both GR and string theory are dead.

ALL chemical compositions obey the EP. A neutron star core might be strange matter, pion condensate, lambda hyperon, delta isobar, or free quark matter. Gravitationally hyper-bound (~30% of dissiociated rest mass), hyper-spinning (~20% of lightspeed at equator), hyper-magnetic (10^8 tesla), hyper-dense (4-9x10^14 g/cm^3), superconducting neutronium falls consistent with the Equivalence Principle

http://arxiv.org/abs/astro-ph/0609417
Deeply relativistic binary pulsar PSR J0737-3039A/B

Affine, teleparallel, and noncommutative gravitation theories - that wholly contain GR - allow (metaphoric) left and right shoes to measurably violate the EP. Somebody should look.

http://www.mazepath.com/uncleal/qz4.pdf
technicalities
http://www.mazepath.com/uncleal/lajos.htm#a2
fast easy experiment

After all... Chirality (handeness) is NOT a symmetry of smooth coordinate transformations. It is a discrete reflection that cannot be approximated by a sum of infinitesimals (e.g., a Taylor series).

Answer 5

Planck