Re: Planck Length

2019-01-24 Thread Philip Thrift


On Thursday, January 24, 2019 at 12:57:00 PM UTC-6, Lawrence Crowell wrote:
>
> On Thursday, January 24, 2019 at 8:59:42 AM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Thursday, January 24, 2019 at 5:54:46 AM UTC-6, Lawrence Crowell wrote:
>>>
>>>
>>>
>>>  
>>>
>>> My point is that in physics what might be called a halting condition is 
>>> an attractor point or limit cycle. Equilibrium is the terminal point in the 
>>> evolution of some system, say thinking according to Landauer's original 
>>> paper on thermodynamics and information. The quantum field theory of black 
>>> holes has no equilibrium condition. Now if the black hole runs away with 
>>> Hawking radiation it will “explode” in a burst of gamma rays and other 
>>> quanta. A Turing machine that does not halt can also be said to burn itself 
>>> out, and if anyone has programmed assembler there were loops you could put 
>>> a machine into that might do damage. 
>>>
>>> Sorry for being slow on this. I forgot to get flu shots this year and I 
>>> have been hit with a real doozy of a flu. Since Sunday night until 
>>> yesterday I was horribly ill, and only now am beginning to feel normal. Get 
>>> the shots, you really do not want this flu!
>>>
>>> LC
>>>
>>
>> I used to think that there *could be* true hypercomputation (what is 
>> called super-Turing machines) in nature, but now I think that there is no 
>> such thing (but anything remains possible, of course).
>>
>> *But the idea of substrate-independent Turing machines is incomplete.*
>>
>> I shouldn't say (if will jinx me!) but I've never gotten a flu shot and I 
>> haven't gotten the flu in over 40 years.
>>
>> But I hope the flu program doesn't start running in / affect my substrate!
>>
>> - pt
>>
>
> I hate to pop your bubble here, but a few years ago at a New Year's party 
> a person who had cancer go into remission made this statement that she 
> never got colds or flus. A doctor I know was there and responded with how 
> not getting these sicknesses is a risk factor for cancer! The woman died a 
> last summer with the return of her non-Hodgkins lymphoma. 
>
> Hyper-Turing computations or results are not accessible to local observers.
>
> LC
>



What about the interviews of people over 100 who say they've never had a 
cold or the flu? 

And where are these hyper-Turing processes occurring?

- pt

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Re: Planck Length

2019-01-24 Thread Lawrence Crowell
On Thursday, January 24, 2019 at 8:59:42 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Thursday, January 24, 2019 at 5:54:46 AM UTC-6, Lawrence Crowell wrote:
>>
>>
>>
>>  
>>
>> My point is that in physics what might be called a halting condition is 
>> an attractor point or limit cycle. Equilibrium is the terminal point in the 
>> evolution of some system, say thinking according to Landauer's original 
>> paper on thermodynamics and information. The quantum field theory of black 
>> holes has no equilibrium condition. Now if the black hole runs away with 
>> Hawking radiation it will “explode” in a burst of gamma rays and other 
>> quanta. A Turing machine that does not halt can also be said to burn itself 
>> out, and if anyone has programmed assembler there were loops you could put 
>> a machine into that might do damage. 
>>
>> Sorry for being slow on this. I forgot to get flu shots this year and I 
>> have been hit with a real doozy of a flu. Since Sunday night until 
>> yesterday I was horribly ill, and only now am beginning to feel normal. Get 
>> the shots, you really do not want this flu!
>>
>> LC
>>
>
> I used to think that there *could be* true hypercomputation (what is 
> called super-Turing machines) in nature, but now I think that there is no 
> such thing (but anything remains possible, of course).
>
> *But the idea of substrate-independent Turing machines is incomplete.*
>
> I shouldn't say (if will jinx me!) but I've never gotten a flu shot and I 
> haven't gotten the flu in over 40 years.
>
> But I hope the flu program doesn't start running in / affect my substrate!
>
> - pt
>

I hate to pop your bubble here, but a few years ago at a New Year's party a 
person who had cancer go into remission made this statement that she never 
got colds or flus. A doctor I know was there and responded with how not 
getting these sicknesses is a risk factor for cancer! The woman died a last 
summer with the return of her non-Hodgkins lymphoma. 

Hyper-Turing computations or results are not accessible to local observers.

LC

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Re: Planck Length

2019-01-24 Thread Philip Thrift


On Thursday, January 24, 2019 at 5:54:46 AM UTC-6, Lawrence Crowell wrote:
>
> On Monday, January 21, 2019 at 6:49:12 PM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Monday, January 21, 2019 at 6:19:07 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Monday, January 21, 2019 at 5:09:50 AM UTC-6, Bruno Marchal wrote:


 On 21 Jan 2019, at 00:17, Lawrence Crowell  
 wrote:

 On Sunday, January 20, 2019 at 9:16:01 AM UTC-6, Bruno Marchal wrote:
>
>
> On 19 Jan 2019, at 01:42, Lawrence Crowell  
> wrote:
>
> On Thursday, January 17, 2019 at 6:31:06 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 17 Jan 2019, at 09:22, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 9:25:16 PM UTC, John Clark wrote:
>>>
>>> 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 

Re: Planck Length

2019-01-24 Thread Philip Thrift


On Thursday, January 24, 2019 at 7:14:15 AM UTC-6, Bruno Marchal wrote:
>
>
> On 23 Jan 2019, at 19:01, Philip Thrift > 
> wrote:
>
>
>
> On Wednesday, January 23, 2019 at 5:52:01 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 22 Jan 2019, at 01:49, Philip Thrift  wrote:
>>
>> One of the oddest of things is when physicists use the language of 
>> (various) theories of physics to express what can or cannot be the case. 
>> It's just a language, which is probably wrong.
>>
>> There is a sense in which the Church/Turing thesis is true: All out 
>> languages are Turing in their syntax and grammar. What they refer to is 
>> another matter (pun intended).
>>
>>
>> They refer to the set of computable functions, or to the universal 
>> machine which understand that language. But not all language are Turing 
>> universal. Only the context sensitive automata (in Chomski hierarchy) are 
>> Turing universal. Simple languages, like the “regular” one are typically 
>> not Turing universal. Bounded loops formalism cannot be either.
>>
>> But the notion of language is ambiguous with respect to computability, 
>> and that is why I prefer to avoid that expression and always talk about 
>> theories (set of beliefs) or machine (recursively enumerable set of 
>> beliefs), which avoids ambiguity. 
>> For example, is “predicate calculus” Turing universal? We can say yes, 
>> given that the programming language PROLOG (obviously Turing universal) is 
>> a tiny subset of predicate logic. But we can say know, if we look at 
>> predicate logic as a theory. A prolog program is then an extension of that 
>> theory, not something proved in predicate calculus.
>> Thus, I can make sense of your remark. Even the language with only one 
>> symbol {I}, and the rules that “I” is a wff, and if x is wwf, then Ix is 
>> too, can be said Turing universal, as each program can be coded by a 
>> number, which can be coded by a finite sequence of I. But of course, that 
>> makes the notion of “universality” empty, as far as language are concerned. 
>> Seen as a theory, predicate calculus is notoriously not universal. Even 
>> predicate calculus + the natural numbers, and the law of addition, 
>> (Pressburger arithmetic) is not universal. Or take RA with its seven 
>> axioms. Taking any axiom out of it, and you get a complete-able theory, and 
>> thus it cannot be Turing complete.
>>
>> Bruno
>>
>>
>>
> Here's an example of a kind of "non-digital" language:
>
> *More Analog Computing Is on the Way*
> https://dzone.com/articles/more-analog-computing-is-on-the-way
>
>
>
> *The door on this new generation of analog computer programming is 
> definitely open. Last month, at the Association for Computing Machinery’s 
> (ACM) conference on Programming Language Design and Implementation, 
> a paper  was 
> presented that described a compiler that uses a text based, high-level, 
> abstraction language to generate the necessary low-level circuit wiring 
> that defines the physical analog computing implementation. This research 
> was done at MIT’s Computer Science and Artificial Intelligence Laboratory 
> (CSAIL) and Dartmouth College. The main focus of their investigation was to 
> improve the simulation of biological systems. *
>
>
> *Configuration Synthesis for ProgrammableAnalog Devices with Arco*
> https://people.csail.mit.edu/sachour/res/pldi16_arco.pdf
>
> *Programmable analog devices have emerged as a powerful*
> *computing substrate for performing complex neuromorphic*
> *and cytomorphic computations. We present Arco, a new*
> *solver that, given a dynamical system specification in the*
> *form of a set of differential equations, generates physically*
> *realizable configurations for programmable analog devices*
> *that are algebraically equivalent to the specified system.*
> *On a set of benchmarks from the biological domain, Arco*
> *generates configurations with 35 to 534 connections and 28*
> *to 326 components in 1 to 54 minutes.*
>
>
> - pt
>
>
> Intersting.
>
> Yet, that does not violate the Church-Thesis, even if very useful FAPP. 
> But such computations arise in arithmetic, either directly, or through a 
> infinite sequence of approximations. If all decimals of the analog 
> phenomenon needs to be taken into account, then we are out of my working 
> hypothesis, and even evolution theory becomes wrong, as evolution and life 
> becomes sequences of miracles. But the goal of the authors here is not 
> learning anything in metaphysics, just doing efficacious machine. In that 
> case mechanism explains the plausible necessity of such moves, including 
> quantum computations (which also do not violate Church’s thesis).
>
> Bruno
>
>
>
>


I don't believe in (or know what are) miracles (although a real 
hypercomputer - one you could give any statement of arithmetic to - e.g. 
*Goldbach's 
conjecture*  -  and it could check through all - infinite number of -  
integers and tell you "true" or 

Re: Planck Length

2019-01-24 Thread Bruno Marchal

> On 24 Jan 2019, at 12:54, Lawrence Crowell  
> wrote:
> 
> On Monday, January 21, 2019 at 6:49:12 PM UTC-6, Philip Thrift wrote:
> 
> 
> On Monday, January 21, 2019 at 6:19:07 PM UTC-6, Lawrence Crowell wrote:
> On Monday, January 21, 2019 at 5:09:50 AM UTC-6, Bruno Marchal wrote:
> 
>> On 21 Jan 2019, at 00:17, Lawrence Crowell > 
>> wrote:
>> 
>> On Sunday, January 20, 2019 at 9:16:01 AM UTC-6, Bruno Marchal wrote:
>> 
>>> On 19 Jan 2019, at 01:42, Lawrence Crowell > 
>>> wrote:
>>> 
>>> On Thursday, January 17, 2019 at 6:31:06 AM UTC-6, Bruno Marchal wrote:
>>> 
 On 17 Jan 2019, at 09:22, agrays...@gmail.com <> wrote:
 
 
 
 On Monday, January 7, 2019 at 9:25:16 PM UTC, John Clark wrote:
 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
 
 Later I'll post some questions I have about your derivation of the Planck 
 length, but for now here's a philosophical question; Is there any 
 difference between the claim that space is discrete, from the claim or 
 conjecture that we cannot in principle measure a length shorter than the 

Re: Planck Length

2019-01-24 Thread Bruno Marchal

> On 23 Jan 2019, at 19:01, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, January 23, 2019 at 5:52:01 AM UTC-6, Bruno Marchal wrote:
> 
>> On 22 Jan 2019, at 01:49, Philip Thrift > 
>> wrote:
>> 
>> One of the oddest of things is when physicists use the language of (various) 
>> theories of physics to express what can or cannot be the case. It's just a 
>> language, which is probably wrong.
>> 
>> There is a sense in which the Church/Turing thesis is true: All out 
>> languages are Turing in their syntax and grammar. What they refer to is 
>> another matter (pun intended).
> 
> They refer to the set of computable functions, or to the universal machine 
> which understand that language. But not all language are Turing universal. 
> Only the context sensitive automata (in Chomski hierarchy) are Turing 
> universal. Simple languages, like the “regular” one are typically not Turing 
> universal. Bounded loops formalism cannot be either.
> 
> But the notion of language is ambiguous with respect to computability, and 
> that is why I prefer to avoid that expression and always talk about theories 
> (set of beliefs) or machine (recursively enumerable set of beliefs), which 
> avoids ambiguity. 
> For example, is “predicate calculus” Turing universal? We can say yes, given 
> that the programming language PROLOG (obviously Turing universal) is a tiny 
> subset of predicate logic. But we can say know, if we look at predicate logic 
> as a theory. A prolog program is then an extension of that theory, not 
> something proved in predicate calculus.
> Thus, I can make sense of your remark. Even the language with only one symbol 
> {I}, and the rules that “I” is a wff, and if x is wwf, then Ix is too, can be 
> said Turing universal, as each program can be coded by a number, which can be 
> coded by a finite sequence of I. But of course, that makes the notion of 
> “universality” empty, as far as language are concerned. 
> Seen as a theory, predicate calculus is notoriously not universal. Even 
> predicate calculus + the natural numbers, and the law of addition, 
> (Pressburger arithmetic) is not universal. Or take RA with its seven axioms. 
> Taking any axiom out of it, and you get a complete-able theory, and thus it 
> cannot be Turing complete.
> 
> Bruno
> 
> 
> 
> Here's an example of a kind of "non-digital" language:
> 
> More Analog Computing Is on the Way
> https://dzone.com/articles/more-analog-computing-is-on-the-way
> 
> 
> The door on this new generation of analog computer programming is definitely 
> open. Last month, at the Association for Computing Machinery’s (ACM) 
> conference on Programming Language Design and Implementation, a paper  
> was presented that 
> described a compiler that uses a text based, high-level, abstraction language 
> to generate the necessary low-level circuit wiring that defines the physical 
> analog computing implementation. This research was done at MIT’s Computer 
> Science and Artificial Intelligence Laboratory (CSAIL) and Dartmouth College. 
> The main focus of their investigation was to improve the simulation of 
> biological systems. 
> 
> 
> Configuration Synthesis for ProgrammableAnalog Devices with Arco
> https://people.csail.mit.edu/sachour/res/pldi16_arco.pdf
> 
> Programmable analog devices have emerged as a powerful
> computing substrate for performing complex neuromorphic
> and cytomorphic computations. We present Arco, a new
> solver that, given a dynamical system specification in the
> form of a set of differential equations, generates physically
> realizable configurations for programmable analog devices
> that are algebraically equivalent to the specified system.
> On a set of benchmarks from the biological domain, Arco
> generates configurations with 35 to 534 connections and 28
> to 326 components in 1 to 54 minutes.
> 
> 
> - pt

Intersting.

Yet, that does not violate the Church-Thesis, even if very useful FAPP. But 
such computations arise in arithmetic, either directly, or through a infinite 
sequence of approximations. If all decimals of the analog phenomenon needs to 
be taken into account, then we are out of my working hypothesis, and even 
evolution theory becomes wrong, as evolution and life becomes sequences of 
miracles. But the goal of the authors here is not learning anything in 
metaphysics, just doing efficacious machine. In that case mechanism explains 
the plausible necessity of such moves, including quantum computations (which 
also do not violate Church’s thesis).

Bruno





>  
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
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> 

Re: Planck Length

2019-01-24 Thread Lawrence Crowell
On Monday, January 21, 2019 at 6:49:12 PM UTC-6, Philip Thrift wrote:
>
>
>
> On Monday, January 21, 2019 at 6:19:07 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Monday, January 21, 2019 at 5:09:50 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 21 Jan 2019, at 00:17, Lawrence Crowell  
>>> wrote:
>>>
>>> On Sunday, January 20, 2019 at 9:16:01 AM UTC-6, Bruno Marchal wrote:


 On 19 Jan 2019, at 01:42, Lawrence Crowell  
 wrote:

 On Thursday, January 17, 2019 at 6:31:06 AM UTC-6, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 09:22, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 7, 2019 at 9:25:16 PM UTC, John Clark wrote:
>>
>> 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
>>
>
>
> *Later I'll post some questions I have about your derivation of 

Re: Coherent states of a superposition

2019-01-24 Thread agrayson2000


On Sunday, January 20, 2019 at 11:54:43 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, January 20, 2019 at 9:56:17 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 18 Jan 2019, at 18:50, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, January 18, 2019 at 12:09:58 PM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 17 Jan 2019, at 14:48, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, January 17, 2019 at 12:36:07 PM UTC, Bruno Marchal wrote:


 On 17 Jan 2019, at 09:33, agrays...@gmail.com wrote:



 On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>
>
>
> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
>
>
>
> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: 
>>
>>
>>
>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>
>> This means, to me, that the arbitrary phase angles have absolutely no 
>> effect on the resultant interference pattern which is observed. But 
>> isn't 
>> this what the phase angles are supposed to effect? AG
>>
>>
>> The screen pattern is determined by *relative phase angles for the 
>> different paths that reach the same point on the screen*.  The 
>> relative angles only depend on different path lengths, so the overall 
>> phase 
>> angle is irrelevant.
>>
>> Brent
>>
>
>
> *Sure, except there areTWO forms of phase interference in Wave 
> Mechanics; the one you refer to above, and another discussed in the 
> Stackexchange links I previously posted. In the latter case, the wf is 
> expressed as a superposition, say of two states, where we consider two 
> cases; a multiplicative complex phase shift is included prior to the sum, 
> and different complex phase shifts multiplying each component, all of the 
> form e^i (theta). Easy to show that interference exists in the latter 
> case, 
> but not the former. Now suppose we take the inner product of the wf with 
> the ith eigenstate of the superposition, in order to calculate the 
> probability of measuring the eigenvalue of the ith eigenstate, applying 
> one 
> of the postulates of QM, keeping in mind that each eigenstate is 
> multiplied 
> by a DIFFERENT complex phase shift.  If we further assume the eigenstates 
> are mutually orthogonal, the probability of measuring each eigenvalue 
> does 
> NOT depend on the different phase shifts. What happened to the 
> interference 
> demonstrated by the Stackexchange links? TIA, AG *
>
> Your measurement projected it out. It's like measuring which slit the 
> photon goes through...it eliminates the interference.
>
> Brent
>

 *That's what I suspected; that going to an orthogonal basis, I departed 
 from the examples in Stackexchange where an arbitrary superposition is 
 used 
 in the analysis of interference. Nevertheless, isn't it possible to 
 transform from an arbitrary superposition to one using an orthogonal 
 basis? 
 And aren't all bases equivalent from a linear algebra pov? If all bases 
 are 
 equivalent, why would transforming to an orthogonal basis lose 
 interference, whereas a general superposition does not? TIA, AG*


 I don’t understand this. All the bases we have used all the time are 
 supposed to be orthonormal bases. We suppose that the scalar product (e_i 
 e_j) = delta_i_j, when presenting the Born rule, and the quantum formalism.

 Bruno

>>>
>>> *Generally, bases in a vector space are NOT orthonormal. *
>>>
>>>
>>> Right. But we can always build an orthonormal base with a decent scalar 
>>> product, like in Hilbert space, 
>>>
>>>
>>>
>>> *For example, in the vector space of vectors in the plane, any pair of 
>>> non-parallel vectors form a basis. Same for any general superposition of 
>>> states in QM. HOWEVER, eigenfunctions with distinct eigenvalues ARE 
>>> orthogonal.*
>>>
>>>
>>> Absolutely. And when choosing a non degenerate 
>>> observable/measuring-device, we work in the base of its eigenvectors. A 
>>> superposition is better seen as a sum of some eigenvectors of some 
>>> observable. That is the crazy thing in QM. The same particle can be 
>>> superposed in the state of being here and there. Two different positions of 
>>> one particle can be superposed.
>>>
>>
>> *This is a common misinterpretation. Just because a wf can be expressed 
>> in different ways (as a vector in the plane can be expressed in uncountably 
>> many different bases), doesn't mean a particle can exist in different 
>> positions in space at the same time. AG*
>>
>>
>> It has a non null amplitude of probability of being here and there at the 
>> same time, like having a non null amplitude of probability of going through 
>> each slit in the two slits experience.
>>
>> If not, you can’t explain the inference patterns, especially in the 
>>