On 5/12/2017 11:38 am, [email protected] wrote:
On Tuesday, December 5, 2017 at 12:26:58 AM UTC, Bruce wrote:
On 5/12/2017 3:15 am, Bruno Marchal wrote:
> On 01 Dec 2017, at 01:49, Bruce Kellett wrote:
>> On 1/12/2017 8:57 am, Bruce Kellett wrote:
>>> On 1/12/2017 4:21 am, Bruno Marchal wrote:
>>>> On 29 Nov 2017, at 23:16, Bruce Kellett wrote:
>>>> On 30/11/2017 2:24 am, Bruno Marchal wrote:
>>>>>> On 29 Nov 2017, at 04:59, Bruce Kellett wrote:
>>>>>>
>>>>>>> I would suggest that there is no such world. Whether a coin
>>>>>>> comes up head or tails on a simple toss is not a quantum
event;
>>>>>>> it is determined by quite classical laws of physics governing
>>>>>>> initial conditions, air currents and the like.
>>>>>>
>>>>>> It depends. If you shake the coin long enough, the quantum
>>>>>> uncertainties can add up to the point that the toss is a
quantum
>>>>>> event. With some student we have evaluate this quantitavely (a
>>>>>> long time ago) and get that if was enough to shake the coin
less
>>>>>> than a minute, but more than few seconds ... (Nothing
rigorous).
>>>>>
>>>>> That is a misunderstanding of quantum randomness. For the
outcome
>>>>> of a coin toss to be determined by quantum randomness, we would
>>>>> have to have a single quantum event where the outcome was
>>>>> amplified by decoherence so that it was directly entangled with
>>>>> the way the coin landed. Schematically:
>>>>>
>>>>> |quantum event>|coin> = (|outcome A> + |outcome B>)|coin>
>>>>> = (|outcome A>|coin heads> + |outcome B>|coin tails>)
>>>>
>>>> The coin is quantum.
>>>
>>> The coin is classical, consisting of something of the order of
10^22
>>> atoms. Indeterminacy in position as given by the Heisenberg
>>> Uncertainty Principle, is undetectably small.
>>
>> I think it is worth while to put some (approximate) numbers around
>> this. The reduced Planck constant, h-bar, is approximately
10^{-27}
>> g.cm <http://g.cm>^2/s. The Uncertainty Principle is
>>
>> delta(x)*delta(p) >= h-bar/2.
>>
>> For a coin weighing approximately 10 g and moving at 1 cm/s, the
>> momentum is mv = 10 g.cm/s <http://g.cm/s>. Taking the momentum
uncertainty to be of
>> this order, the uncertainty in position, delta(x) is of the
order of
>> 10^{-28} cm. A typical atom has a diameter of about 10^{-8} cm, so
>> the uncertainty in position is approximately 20 orders of
magnitude
>> less than the atomic diameter.
>
> I think that is enough to get the macroscopic superposition, as,
like
> I explained, you have to take into account not just the quantum
> indeterminacy, + the classical chaos. You might need to shake
for some
> minutes.
You could shake for longer than the age of the universe and you will
still not convert quantum uncertainties and classical thermal motions
into a macroscopic superposition. Do you know nothing about
coherence?
And the fact that coherent phases between the components are what
separates a superposition from a mixture?
Are the phase angles of components of a superposition identical? If
so, is this the definition of coherence? TIA, AG
No, why should they be equal. You really do have to learn some basic
quantum mechanics, Alan, and stop bothering the list with such questions.
Bruce
Random quantum uncertainties
and thermal motions are not coherent, so cannot form superpositions.
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