Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: FrediFizzx (fredifizzx_at_hotmail.com)
Date: 02/04/05 

Date: Thu, 3 Feb 2005 18:26:18 -0800

"John Baez" <baez@math-cl-n03.math.ucr.edu> wrote in message
news:ctu2uv$pa$1@glue.ucr.edu...
| In article <1107418335.324750.294210@o13g2000cwo.googlegroups.com>,
| Keith Ramsay <kramsay@aol.com> wrote:
|
| >examachine@gmail.com wrote:
|
| >| I think the evidence for a discrete world far outweighs the
evidence
| >| for a continuous world, which is basically non-existent.
|
| >On the contrary, there's essentially no evidence that the
| >world is discrete. Really, there's not much that could
| >reasonably be called evidence in either direction.
|
| Hi, Keith.
|
| Indeed, there's not a shred of experimental evidence that
| "the world is discrete". If you take quantum theory seriously,
| it's natural to guess it applies even to the geometry of spacetime,
| and this would mean that you can't simultaneously measure everything
| about the geometry of spacetime with arbitrary precision. But, that's
| not yet "discreteness". Quantum theory allows for lots of options.
|
| For example, in ordinary quantum mechanics you can't measure the
| position and velocity of a particle both at the same time with
| arbitrarily good precision, but there's nothing "discrete" going
| on here. You can measure either the position or velocity with as
| much precision as you like, and they don't come in discrete steps.
|
| There are other quantum systems, like the energy levels of an atom,
| that show a kind of discreteness - though not the naive discreteness
| of evenly spaced steps.
|
| And while a bunch of people including myself have worked on theories
| where area and volume are "discrete" in about the same way as the
| energy levels of an atom:
|
| Loop Quantum Gravity
| http://math.ucr.edu/home/baez/acm/
|
| these are still theories, not "evidence" of discreteness. And, they
| are highly controversial theories!
|
| >If the world were discrete, one could hope to observe the
| >fact by examining it at a small enough scale. In principle,
| >then, one should be able to model it at that level. But none
| >of our best actually working models of the world is entirely
| >discrete.
|
| Right.
|
| >The approach to quantum gravity known as "spin networks"
| >comes close, but still the state of a system is
| >a superposition of states, where the weights can vary
| >continuously. John Baez has pointed out that it's also
| >consistent to have both a model such as the spin network
| >model and a model in which the states are treated as having
| >continuous space. The model is discrete in some respects
| >and continuous in others.
|
| Right. And, the spin network theory of quantum gravity has not
| received any experimental confirmation thus far.
|
| >| There is also something called Heisenberg's uncertainty principle.
Why
| >| would I believe that something exists beneath the Planck scale,
while
| >| our physics tells us that you cannot physically subdivide the
Planck
| >| scale.
|
| >Where does it say that? The Planck length is simply a length
| >small enough that to model physics on that scale, quantum
| >gravity effects have to be taken into consideration.
|
| Right. And in fact, even this is just a guess. To be very clear,
| we should admit that the Planck length is the simplest quantity
| with units of length that we can cook up from the speed of light (c),
| Newton's gravitational constant (G), and Planck's constant (hbar).
| It's about 1.6 x 10^{-35} meters.
|
| By dimensional analysis, we can *guess* that if quantum gravity
| effects become important at some length scale, it's around the
| Planck length.
|
| But, this guess assumes that no other physical quantities are
| important in determining this length scale! E.g., not the mass
| of the electron, or anything else like that.
|
| So, this guess could easily be wrong. And, it's important to
| remember that we don't have any direct evidence for what happens
| at the Planck scale, or even length scales much bigger than this.
|
| The diameter of a proton is about 10^{-15} meters. We've done
| experiments that probe much shorter distance scales, but they're
| still vastly larger than the Planck length.
|
| I always forget how short are the distance scales we've probed so
| far... let me work it out. Cheating, I'll start by looking in T. D.
| Lee's book on particle physics, in the chapter "Order-of-Magnitude
| Estimates"... let's see... good! He says the electron mass is .51
| MeV, and that this corresponds to (4 x 10^{-11} cm)^{-1}, where
| he's using c and hbar to convert energies to inverse lengths.
| So, doing particle collision experiments at an energy of .51 MeV
| we can probe distance scales of about 4 x 10^{-13} meters. Or,
| roughly, 1 Mev corresponds to 10^{-13} meters. That's what I should
| remember! Anyway, the best accelerator in the world is still LEP
| (until LHC comes online), and that reached energies of about 113 GeV.
| So, roughly 100 GeV, or 10^5 MeV - so distance scales of about
10^{-18}
| meters.
|
| So, unless I made a stupid mistake, we can currently probe distances
| about 1/1000th the size of a proton, and we haven't seen any trace of
| spacetime discreteness...

Is a proton part of spacetime? If so, then we have seen a trace of
spacetime discretness.

FrediFizzx

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