Re: Coherent states of a superposition

[agrayson2000]

On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>>
>> On Mon, Jan 7, 2019 at 9:42 AM  wrote:
>>
>>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
>>> wrote:

 On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
 wrote:
>
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>>
 On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
 agrays...@gmail.com wrote:
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context of 
>>> interference and coherence, without introducing your theory of 
>>> consciousness. Mainstream thinking today is that decoherence does 
>>> occur, 
>>> but this seems to imply preexisting coherence, and therefore 
>>> interference 
>>> among the component states of a superposition. If the superposition 
>>> is 
>>> expressed using eigenfunctions, which are mutually orthogonal -- 
>>> implying 
>>> no mutual interference -- how is decoherence possible, insofar as 
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it is 
>> used off an expansion in terms of a set of mutually orthogonal 
>> eigenvectors. The expansion in some eigenvector basis is written as
>>
>>|psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the dimension 
>> of the Hilbert space. The expansion coefficients are the complex 
>> numbers 
>> a_i. Since these are complex coefficients, they contain inherent 
>> phases. It 
>> is the preservation of these phases of the expansion coefficients 
>> that is 
>> meant by "maintaining coherence". So it is the coherence of the 
>> particular 
>> expansion that is implied, and this has noting to do with the mutual 
>> orthogonality or otherwise of the basis vectors themselves. In 
>> decoherence, 
>> the phase relationships between the terms in the original expansion 
>> are 
>> lost.
>>
>> Bruce 
>>
>
> I appreciate your reply. I was sure you could ascertain my error 
> -- confusing orthogonality with interference and coherence. Let me 
> have 
> your indulgence on a related issue. AG
>

 Suppose the original wf is expressed in terms of p, and its 
 superposition expansion is also expressed in eigenfunctions with 
 variable 
 p. Does the phase of the original wf carry over into the 
 eigenfunctions as 
 identical for each, or can each component in the superposition have 
 different phases? I ask this because the probability determined by any 
 complex amplitude is independent of its phase. TIA, AG 

>>>
>>> The phases of the coefficients are independent of each other.
>>>
>>
>> When I formally studied QM, no mention was made of calculating the 
>> phases since, presumably, they don't effect probability calculations. Do 
>> you have a link which explains how they're calculated? TIA, AG 
>>
>
> I found some links on physics.stackexchange.com which show that 
> relative phases can effect probabilities, but none so far about how to 
> calculate any phase angle. AG 
>

 Here's the answer if anyone's interested. But what's the question? How 
 are wf phase angles calculated? Clearly, if you solve for the 
 eigenfunctions of some QM operator such as the p operator, any phase angle 
 is possible; its value is completely arbitrary and doesn't effect a 
 probability calculation. In fact, IIUC, there is not sufficient 
 information 
 to solve for a unique phase. So, I conclude,that the additional 
 information 
 required to uniquely determine a phase angle for a wf, lies in boundary 
 conditions. If the problem of specifying a wf is defined as a boundary 
 value problem, then, I believe, a unique phase angle can be calculated. 
 CMIIAW. AG 

>
>>> Bruce
>>>
>>
>>> I could use a handshake on this one. Roughly speaking, if one wants to 
>>> express the state of a system as a superposition of eigenstates, how does 
>>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>>>
>>
>> One doesn't. The phases are arbitrary unl

Re: Planck Length

[John Clark]

On Mon, Jan 7, 2019 at 8:03 AM  wrote:

*> How does one calculate Planck length using the fundamental constants G,
> h, and c, and having calculated it, how does one show that measuring a
> length that small with photons of the same approximate wave length, would
> result in a black hole? TIA, AG*


In any wave the speed of the wave is wavelength times frequency and
according to
Planck E= h*frequency  so E= C*h/wavelength.  Thus the smaller the
wavelength the greater the energy. According to Einstein energy is just
another form of mass (E = MC^2) so at some point the wavelength is so small
and the light photon is so energetic (aka massive) that the escape velocity
is greater than the speed of light and the object becomes a Black Hole.

Or you can look at it another way, we know from Heisenberg that to
determine the position of a particle more precisely with light you have to
use a smaller wavelength, and there is something called the  "Compton
wavelength" (Lc) ; to pin down the position of a particle of mass m to
within one Compton wavelength would require light of enough energy to
create another particle of that mass. The formula for the Compton
Wavelength is Lc= h/(2PI*M*c).

Schwarzschild told us that the radius of a Black Hole (Rs), that is to say
where the escape velocity is the speed of light  is:  Rs= GM/c^2. At some
mass Lc will equal Rs and that mass is the Planck mass, and that Black Hole
will have the radius of the Planck Length, 1.6*10^-35 meters.

Then if you do a little algebra:
GM/c^2 = h/(2PI*M*c)
GM= hc/2PI*M
GM^2 = hc/2*PI
M^2 = hc/2*PI*G
M = (hc/2*PI*G)^1/2and that is the formula for the Planck Mass , it's .02
milligrams.

And the Planck Length turns out to be (G*h/2*PI*c^3)^1/2 and the Planck time
is the time it takes light to travel the Planck length.

The Planck Temperature Tp is sort of the counterpoint to Absolute Zero, Tp
is as hot as things can get because the black-body radiation given off by
things when they are at temperature Tp have a wavelength equal to the
Planck Length, the distance light can move in the Planck Time of 10^-44
seconds. The formula for the Planck temperature is Tp = Mp*c^2/k where Mp
is the Planck Mass and K is Boltzmann's constant and it works out to be
1.4*10^32 degrees Kelvin.  Beyond that point both Quantum Mechanics and
General Relativity break down and nobody understands what if anything is
going on.

The surface temperature of the sun is at 5.7 *10^3  degrees Kelvin so if it
were 2.46*10^28 times hotter it would be at the Planck Temperature, and
because radiant energy is proportional to T^4 the sun would be 3.67*10^113
times brighter. At that temperature to equal the sun's brightness the
surface area would have to be reduced by a factor of 3.67*10^113, the
surface area of a sphere is proportional to the radius squared, so you'd
have to reduce the sun's radius by (3.67*10^113)^1/2, and that is  6.05*10^56.
The sun's radius is 6.95*10^8   meters and  6.95*10^8/ 6.05*10^56  is
1.15^10^-48 meters.

That means a sphere at the Planck Temperature with a radius 10 thousand
billion times SMALLER than the Planck Length would be as bright as the sun,
but as far as we know nothing can be that small. If the radius was 10^13
times longer it would be as small as things can get and the object would be
(10^13)^2 = 10^26 times as bright as the sun. I'm just speculating but
perhaps that's the luminosity of the Big Bang; I say that because that's
how bright things would be if the smallest thing we think can exist was as
hot as we think things can get.

John K Clark

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Re: Materialism and Mechanism

[Bruno Marchal]

> On 6 Jan 2019, at 15:20, Philip Thrift  wrote:
> 
> 
> 
> On Sunday, January 6, 2019 at 8:04:20 AM UTC-6, Jason wrote:
> 
> 
> On Sun, Jan 6, 2019 at 4:47 AM Philip Thrift  > wrote:
> 
> 
> On Saturday, January 5, 2019 at 6:02:39 PM UTC-6, Jason wrote:
> 
> 
> On Sat, Jan 5, 2019 at 2:05 PM Philip Thrift > wrote:
> 
> 
> On Saturday, January 5, 2019 at 12:52:19 PM UTC-6, Jason wrote:
> 
> 
> On Saturday, January 5, 2019, Philip Thrift > wrote:
> 
> 
> On Saturday, January 5, 2019 at 12:02:53 PM UTC-6, Jason wrote:
> 
> 
> On Sat, Jan 5, 2019 at 6:13 AM Philip Thrift > wrote:
> 
> On Saturday, January 5, 2019 at 4:26:11 AM UTC-6, Bruno Marchal wrote:
> 
>> On 4 Jan 2019, at 17:25, Philip Thrift > wrote:
>> 
>> Physicists today (as I've observed) are not (for the most part) real 
>> materialists.
> 
> 
> That is true, and physicists have rarely problem with the consequence of 
> Mechanism. Now, some physicist can be immaterialist, but still physicalist 
> (like Tegmark was at some moment at least). The physical reality would be a 
> mathematical reality among others, but with computationalism, the physical 
> reality comes from a more global mathematical phenomenon based on the 
> behaviour/semantics of the material mode of self-rereyence (involving 
> probabilities, i.e., for those who have studied the self-referential modes 
> available, the []p & X modes, with X being either p, or <>t, or p & <>t).
> 
> This makes mechanism testable, and if quantum mechanics did not exist, I 
> would have thought that Mechanism is already refuted.
> 
> Bruno
> 
> 
> 
> 
> "Physicalism"/"Physical" are words that needs deprecating, as they can mean 
> (to some philosophers of science) "can be reduced to physics", and physics is 
> what is currently-accepted in the physics scientific community.
> 
> (When I use "physical", I mean it in the sense of being "explainable" by 
> physics.)
> 
> It gets worse: "In this entry, I will adopt the policy of using both terms 
> ['materialism' and 'physicalism'] interchangeably, though I will typically 
> refer to the thesis we will discuss as ‘physicalism’."
> https://plato.stanford.edu/entries/physicalism/ 
> 
> 
> Better to just use "materialism" and reject the use of "physicalism" (unless 
> it refers to a the particular meaning of "can be reduced to physics"), though 
> materialism has a "weak" and "strong" definition.
> 
> Galen Strawson defines what "hard-nosed materialism" is:
> 
> https://www.youtube.com/watch?v=HvHVo6TslV4 
> 
> 
> 
> The important distinction, which may be lost in your definitions, is whether 
> "primariness" is assumed or not.  These diagrams I made highlight the 
> difference:
> 
> 
> Primary Physicalism (Physics is at the bottom, and cannot be explained or 
> derived from anything else):
> 
> 
> Non-Primary Physicalism (Physics is not at the bottom, and can be explained 
> or derived from something more fundamental):
> 
> 
> You could also be agnostic on the question, let's call someone with that 
> belief a "Primary Physicalism Agnostic".
> 
> Currently, scientists have collected zero evidence in favor of Primary 
> Physicalism. So if you strongly believe it, you might want to consider why it 
> is you believe in something so strongly despite there being no evidence for 
> it.
> 
>  
> 
> 
> But what exactly would be a "test for Mechanism"?
> 
> 
> If you replace one or more of your neurons with a mechanical yet functionally 
> equivalent replacement and experience no change in consciousness.
> 
> The existence and utility of cochlear implants can be seen as a loose 
> confirmation of digital mechanism.
> 
> Jason
> 
> 
> 
> A question remains though: Can chemistry (or biology for that matter) be 
> reduced to physics? By that it is typically meant "Can problems of 
> theoretical chemistry be reduced to The Standard Model?"  
> 
> See  List of unsolved problems in chemistry
> -  https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_chemistry 
> 
> 
> Except for a leap of faith ("The Standard Model can explain all of these open 
> problems in chemistry"), there could be chemical properties not reducible to 
> physical properties.
> 
> Doesn't that require chemical reactions that violate physical laws?
>  
> 
> If that is the case, what is physical (as I have defined physical) does not 
> cover what is chemical (much less biological).
> 
> Matter includes all levels of "stuff": physical, chemical, biological, 
> psychical. So materialism is the agnostic position: It doesn't matter whether 
> everything can be reduced to the physical or not.
> 
> 
> 
> In "replace one or more of your neurons with a mechanical yet functionally 
> equivalent replacement", mechanical could of course include biomechanical (as 
> defined in synthetic biology), as there was no restriction of "mechanical".
> 
>

Re: Coherent states of a superposition

[agrayson2000]

On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
>
> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
>
>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>>> wrote:

 On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
 wrote:
>
> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>
>>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>>> agrays...@gmail.com wrote:

 On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>
>>
>> *Thanks, but I'm looking for a solution within the context of 
>> interference and coherence, without introducing your theory of 
>> consciousness. Mainstream thinking today is that decoherence does 
>> occur, 
>> but this seems to imply preexisting coherence, and therefore 
>> interference 
>> among the component states of a superposition. If the superposition 
>> is 
>> expressed using eigenfunctions, which are mutually orthogonal -- 
>> implying 
>> no mutual interference -- how is decoherence possible, insofar as 
>> coherence, IIUC, doesn't exist using this basis? AG*
>>
>
> I think you misunderstand the meaning of "coherence" when it is 
> used off an expansion in terms of a set of mutually orthogonal 
> eigenvectors. The expansion in some eigenvector basis is written as
>
>|psi> = Sum_i (a_i |v_i>)
>
> where |v_i> are the eigenvectors, and i ranges over the dimension 
> of the Hilbert space. The expansion coefficients are the complex 
> numbers 
> a_i. Since these are complex coefficients, they contain inherent 
> phases. It 
> is the preservation of these phases of the expansion coefficients 
> that is 
> meant by "maintaining coherence". So it is the coherence of the 
> particular 
> expansion that is implied, and this has noting to do with the mutual 
> orthogonality or otherwise of the basis vectors themselves. In 
> decoherence, 
> the phase relationships between the terms in the original expansion 
> are 
> lost.
>
> Bruce 
>

 I appreciate your reply. I was sure you could ascertain my error -- 
 confusing orthogonality with interference and coherence. Let me have 
 your 
 indulgence on a related issue. AG

>>>
>>> Suppose the original wf is expressed in terms of p, and its 
>>> superposition expansion is also expressed in eigenfunctions with 
>>> variable 
>>> p. Does the phase of the original wf carry over into the eigenfunctions 
>>> as 
>>> identical for each, or can each component in the superposition have 
>>> different phases? I ask this because the probability determined by any 
>>> complex amplitude is independent of its phase. TIA, AG 
>>>
>>
>> The phases of the coefficients are independent of each other.
>>
>
> When I formally studied QM, no mention was made of calculating the 
> phases since, presumably, they don't effect probability calculations. Do 
> you have a link which explains how they're calculated? TIA, AG 
>

 I found some links on physics.stackexchange.com which show that 
 relative phases can effect probabilities, but none so far about how to 
 calculate any phase angle. AG 

>>>
>>> Here's the answer if anyone's interested. But what's the question? How 
>>> are wf phase angles calculated? Clearly, if you solve for the 
>>> eigenfunctions of some QM operator such as the p operator, any phase angle 
>>> is possible; its value is completely arbitrary and doesn't effect a 
>>> probability calculation. In fact, IIUC, there is not sufficient information 
>>> to solve for a unique phase. So, I conclude,that the additional information 
>>> required to uniquely determine a phase angle for a wf, lies in boundary 
>>> conditions. If the problem of specifying a wf is defined as a boundary 
>>> value problem, then, I believe, a unique phase angle can be calculated. 
>>> CMIIAW. AG 
>>>

>> Bruce
>>
>
>> I could use a handshake on this one. Roughly speaking, if one wants to 
>> express the state of a system as a superposition of eigenstates, how does 
>> one calculate the phase angles of the amplitudes for each eigenstate? AG
>>
>
> One doesn't. The phases are arbitrary unless one interferes the system 
> with some other system.
>
> Bruce 
>

If the phases are arbitrary and the system interacts with some other 
system, the new phases presumably are also arbitrary. So there d

Re: Planck Length

[agrayson2000]

On Sunday, January 6, 2019 at 11:39:03 PM UTC, Brent wrote:
>
>
>
> On 1/6/2019 1:56 PM, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, January 6, 2019 at 7:53:52 AM UTC, Brent wrote: 
>>
>> To measure small things you need comparably short wavelengths.  If you 
>> make a photon with a wavelength so short it can measure the Planck 
>> length it will have so much mass-energy that it will fold spacetime 
>> around it and become a black hole...so you won't be able to use it to 
>> measure anything. 
>>
>> Brent 
>>
>
> TY. That's clear enough. But there's a related question I was unable to 
> explain to a friend recently. Suppose we have a small spherical cork 
> floating on a lake, and we introduce a wave disturbance. If the wave length 
> is much larger than the diameter of the sphere, it will just bob up and 
> down as the wave passes. But if the wave length is comparable to the 
> diameter, the wave will be partially reflected. What is a good *physical* 
> argument for the existence of the reflected wave, tantamount to a detection 
> of the cork? I am at loss to offer a physical explanation. TIA, AG
>
>
> When the wavelength is on the order of the cork dimension or smaller the 
> cork can't react to the wave as if it were just part of the water. Because 
> of its extent it cannot move with the water at all points, so there are 
> pressure gradients around the cork which become the source of scattered 
> ripples.
>
> Brent
>

Thank you, but I am unable to intuit the physicality of those pressure 
gradients and their wave length dependencies. I think I need to look up how 
scattering amplitudes are calculated to see the wave length dependencies 
for scattering. I don't recall it being done in my classical or quantum 
physics courses, a long long time ago, in a galaxy far far away. AG 

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Re: Planck Length

[agrayson2000]

On Sunday, January 6, 2019 at 2:59:39 PM UTC, John Clark wrote:
>
> There is a related concept, the Planck Mass that also involves the 3 most 
> fundamental constants in nature, the speed of light the Planck constant and 
> the Gravitational constant. If you take the Planck energy 
> (c^5*h/2*PI*G)^1/2 and confine it in a box one Planck length 
> (G*h/2*PI*c^3)^1/2 on a side it will turn into a Black Hole. To find the 
> Planck Mass we use E=MC^2 and divide the Planck Energy by c^2. The Planck 
> Mass works out to be .02 milligrams, about the mass of a single grain of 
> salt; nothing less massive than the Planck Mass can form a Black Hole 
> regardless of how much you compress it. Some, such as Roger Penrose, 
> think this marks the boundary between the quantum realm and the realm of 
> classical physics but most think that's a oversimplification.
>
>  John K Clark  
>

*How does one calculate Planck length using the fundamental constants G, h, 
and c, and having calculated it, how does one show that measuring a length 
that small with photons of the same approximate wave length, would result 
in a black hole? TIA, AG *

>   
>

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Re: What is comparable and incomparable between casually disconnected universes?

[Philip Thrift]

On Sunday, January 6, 2019 at 10:10:36 AM UTC-6, Jason wrote:
>
> I am trying to make a list of what properties are comparable between two 
> universes and which properties are incomparable. I think this has 
> applications regarding what knowledge can be extracted via simulation of 
> (from one's POV) other abstract realities and worlds (which may be actual 
> from someone else's point of view).
>
> So far this is what I have, but would appreciate other's 
> insights/corrections:
>
> Incomparable properties:
>
>- Sizes (e.g., how big is something in another universe, is a galaxy 
>in that universe bigger or smaller than a planet in our universe?)
>- Distances (what possible meaning could a meter have in that other 
>universe?)
>- Strength of forces (we could say how particles are affected by these 
>forces in their universe, but not how they would translate if applied to 
>our own)
>- Time (how long it takes for anything to happen in that other 
>universe)
>- Age (when it began, how long the universe has existed)
>- Speeds (given neither distance nor time is comparable)
>- Present (what the present time is in the other universe)
>- Position (it has no relative position, or location relative to our 
>own universe)
>
> Comparable properties:
>
>- Information content (how many bits are needed to describe state)
>- Computational complexity (how many operations need to be computed to 
>advance)
>- Dimensionality of its objects (e.g. spacetime, strings, etc.)
>- Entropy
>- Plankian/discrete units (e.g. in terms of smallest physically 
>meaningful units)
>
> Unsure:
>
>- Mass? (given forces are not comparable, but also related to energy)
>- Energy (given its relation to both entropy and mass)
>
>
> So if we simulate some other universe, we can describe and relate it to 
> our own physical universe in similar terms of information content, 
> computational complexity, dimensionality, discrete units, etc. but many 
> things seem to have no meaning at all: time, distance, size.
>
> Do these reflect limits of simulation, or are they limits that apply to 
> our own universe itself?  e.g., if everything in this universe was made 
> 100X larger, and all forces similarly scaled, would we notice?  Perhaps 
> incomparable properties are things that are variant (and illusory) in an 
> objective sense.
>
> A final question, are they truly "causally disconnected" given we can 
> simulate them? E.g. if we can use computers to temporarily compel matter in 
> our universe to behave like things in that simulated universe, then in some 
> sense isn't that a causal interaction?  What things can travel through such 
> portals of simulation beyond information?
>
> Jason
>
> P.S.
>
> It is interesting that when we consider mathematical/platonic objects, we 
> likewise face the same limits in terms of being able to understand them.  
> e.g., we can't point to the Mandlebrot set, nor compare its size in terms 
> of physical units.
>




This is the idea of the *matter compiler,* first in SF, and now in NSF 
research projects.


- pt 

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