On 12/12/2017 9:46 pm, smitra wrote:
On 12-12-2017 02:20, Bruce Kellett wrote:
On 12/12/2017 11:39 am, smitra wrote:
On 11-12-2017 23:11, Bruce Kellett wrote:
On 12/12/2017 1:51 am, smitra wrote:
On 11-12-2017 15:12, Bruno Marchal wrote:
On 10 Dec 2017, at 23:38, Bruce Kellett wrote:
On 11/12/2017 2:19 am, Bruno Marchal wrote:
On 09 Dec 2017, at 00:03, Bruce Kellett wrote:
On 9/12/2017 4:21 am, Bruno Marchal wrote:
Similarly, a shroedinger car, once alive + dead, will never
become a pure alive, or dead cat. It will only seems so for
anyone looking at the cat, in the {alive, dead}
base/apparatus. Superposition never disappear, and a coin
moree or less with a precise position, is always a
superposition of a coin with more or less precise momenta.
The relation is given by the Fourier transforms, which gives
the relative accessible states/worlds.
I pointed out that for a macroscopic object such as a coin,
the uncertainty relations give uncertainties in positions
and/or momentum far below any level of possible detection.
Of possible practical detection. That is good FAPP, but
irrelevant for theoretical consideration.
This is a purely rhetorical objection, Bruno. And when you trot
this out, as you do regularly, I know that your purpose is to
obfuscate, and hide the fact that you have no rational argument
to offer.
You confuse physics and metaphysics. The difference is not
rhetorical,
but fundamental in this thread.
We actually do detect quantum uncertainties for macroscopic
objects routinely when doing typical quantum experiments.
Interference experiments involving photons is a good example.
Suppose we have an interferometer that has mirrors in it, the
photons bounce off the mirrors and at some spot the different
possible paths come together and you can then detect or not detect
photons there.
One can then ask why the momentum absorbed by the mirror when a
photon bounces off it, does not destroy the interference pattern.
One may consider here a thought experiment where the mirrors are
freely floating in a magnetic field. But that's not actually
necessary, if you could in principle detect the momentum from the
recoil of the photons, then you won't get interference and in
general the interference becomes weaker if you can in principle
get partial information.
The answer to this question is that macroscopic objects such as
the mirror in interferometers do not have sharply defined momenta.
In fact, you could argue that unless the mirror surface is not
located to well within the wavelength of light, you obviously
wouldn't get interference, and applying the uncertainty relations
then also gives you an uncertainty in the momentum. But this
doesn't tell you what the uncertainty in the momentum typically is.
The uncertainty in the center of mass position can be estimated
crudely as the thermal De-Broglie wavelength. A displacement well
within this length scale will not lead to the environment
interacting appreciably differently with it. So, the uncertainty
in the position will be of the order of h/sqrt(m k T). The
interpretation is then that a wavefunction spreading beyond this
length will effectively collapse back to within this length scale
due to the environment effectively having located the center of
mass within this scale.
The uncertainty in the momentum is then of the order of sqrt(m k
T), and this can actually be quite large for large objects. This
large uncertainty in the momentum in absolute terms explains why
you can actually do quantum experiments using macroscopic
measurement devices.
There is a fairly serious error in your analysis. You use an
expression for the momentum, p = mv = sqrt(3mkT), which applies to
molecules in an ideal gas. Mirrors in quantum experiments are not
molecules in an ideal gas! What is more, molecules in an ideal gas are
not located within their de Broglie wavelengths. You forget that the
uncertainty principle applies to the uncertainty in measurement
results, and the molecules of the gas are not constrained such that
their position uncertainty is that small.
In other words, you are talking nonsense.
No, your arguments are totally wrong here.
The thermal de Broglie wavelength is a measure for the coherence
length of the molecules in a gas and this then gives the coherence
length in momentum space via the uncertainty relation
No, the de Broglie wavelength is the wavelength, not the coherence
length. The coherence length is given by the size of the wave packet,
so for photons, the coherence length is often orders of magnitude
greater than the wavelength.
(if you want to invoke measurement here, you can say that the
environment consisting of all other molecules effectively "measure"
the position of the center of mass). To a good approximation this
also applies to atoms in a solid, the fact that a solid is not an
ideal gas doesn't actually matter all that much for the coherence
length.
So, the mistake you made here is to assume that the coherence length
is given by the volume a molecule is known to be in, which is
obviously wrong.
I have not assumed this. What I have said is that the uncertainty
relations do not apply to the wavelength, whether of a molecule,
photon, or car. They apply to the uncertainty of the position, which,
for photons for example, is given by the size of the wave packet,
which can be many wavelengths. If you have a well-defined photon
energy (wavelength), the the wave packet is correspondingly extended.
Notwithstanding this, your estimate of the momentum uncertainty,
sqrt(mkT), is not actually very large. Taking k = 10^{-23} J/K and T =
300K, for a mass of 100gm,
sqrt(mkT) = sqrt(10^-1*10^-23*300) ~ 10^{-11} kg m/s, which is
actually quite small.
The velocity, p/m = 10^{-10} m/s, which is about an atomic diameter
per second.
So I still don't know what your calculation is supposed to show.
Yes, it's only an estimation but it yields a good order of magnitude
estimate for the center of mass. What the calculation shows is that
quantum superpositions do exists at the macroscopic level and these
can then be amplified by chaotic dynamics. Of course, it then becomes
incoherent, but in the MWI that's besides the point.
MWI splitting depends on coherence, so it is certainly not beside the
point for the coin toss.
Bruce
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