Re: Planck Length

[Philip Thrift]

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
 

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Re: Discrete theories of space

[Bruno Marchal]

> On 23 Jan 2019, at 11:28, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, January 23, 2019 at 3:04:38 AM UTC-6, agrays...@gmail.com wrote:
> 
> 
> On Wednesday, January 23, 2019 at 12:17:11 AM UTC, agrays...@gmail.com <> 
> wrote:
> 
> 
> On Tuesday, January 22, 2019 at 11:31:06 PM UTC, Philip Thrift wrote:
> 
> 
> On Tuesday, January 22, 2019 at 5:04:15 PM UTC-6, agrays...@gmail.com <> 
> wrote:
> 
> 
> On Tuesday, January 22, 2019 at 10:47:57 PM UTC, Philip Thrift wrote:
> 
> 
> On Tuesday, January 22, 2019 at 3:23:02 PM UTC-6, agrays...@gmail.com <> 
> wrote:
> 
> 
> On Sunday, January 20, 2019 at 3:14:39 PM UTC, Lawrence Crowell wrote:
> On Saturday, January 19, 2019 at 5:42:12 AM UTC-6, agrays...@gmail.com <> 
> wrote:
> Since it seems conceptually impossible to model a theory with DISJOINT 
> discrete spatial units, thus requiring the units to be juxtaposed, do such 
> theories acknowledge difficulty of motion between the units, which might or 
> might not have boundaries? TIA, AG
> 
> I am not sure how to impress people with how bad this thinking is. 
> 
> In retrospect, I don't think you were being rude. You were just reinforcing 
> my conclusion, offering additional technical reasons, why the idea of 
> discrete space is an unintelligible concept. AG
> 
> These slice and diced chunks of spacetime, whether voxels, plaquettes and so 
> forth have violations of Lorentz symmetry of spacetime. This means that 
> curiously the symmetry of gravitation would be violated at higher energy, and 
> in fact where it is quantized. These ideas have further been falsified by the 
> lack of dispersion from distant sources. These ideas are bad interpretations 
> of the Planck length. The Planck length is just the smallest length beyond 
> which you can isolate a quantum bit. Remember, it is the length at which the 
> Compton wavelength of a black hole equals its Schwarzschild radius. It is a 
> bit similar to the Nyquist frequency in engineering. In order to measure the 
> frequency of a rotating system you must take pictures that are at least 
> double that frequency. Similarly to measure the frequency of an EM wave you 
> need to have a wave with Fourier modes that are 2 or more times the frequency 
> you want to measure. The black hole is in a sense a fundamental cut-off in 
> the time scale, or in a reciprocal manner the energy, one can sample space to 
> find qubits. 
> 
> The levels of confusion over this are enormous. It does not tell us that 
> spacetime is somehow sliced and diced into briquets or pieces. It does not 
> tell us that quantum energy of some fields can't be far larger than the 
> Planck energy, or equivalently the wavelength much smaller. This would be 
> analogous to a resonance state, and there is no reason there can't be such a 
> thing in quantum gravity. The Planck scale would suggest this sort of state 
> may decay into a sub-Planckian energy.  Further, it is plausible that quantum 
> gravity beyond what appears as a linearized weak field approximation similar 
> to the QED of photon bunched pairs may only exist at most an order of 
> magnitude larger than the Planck scale anyway. A holographic screen is then a 
> sort of beam splitter at the quantum-classical divide.
> 
> LC
> 
> 
> 
> 
> But you have to admit that a truly continuous space in reality is more 
> unintelligible than a discrete space.
> 
> Where do you observe a true (spacetime) continuum in nature?
> 
> A true continuum in reality is more problematic in many ways than a "quantum" 
> spacetime.
> 
> - pt
> 
> Calculus is essentially based on continuity and seems to model the real 
> world. But for me discrete space seems to make motion problematic, so my 
> inclination is to reject it. AG
> 
> 
> What about Zeno's paradox?
>  
> I brought this issue up myself a few months ago. Seems to show space is not 
> infinitely divisible. OTOH, GR is hugely successful and assumes space-time 
> continuity. AG
> 
> What version of Zeno's paradox do you subscribe to which suggests space is 
> not infinitely divisible? TIA, AG 
> 
> 
> And don't let that brainwashing from calculus math teachers fool you. :)
> 
> - pt
> 
> 
> All three paradoxes of motion [ listed in Wikipedia - 
> https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Paradoxes_of_motion ]
> 
> 1 Paradoxes of motion 
> 1.1   
> Achilles and the tortoise 
> 
> 1.2   Dichotomy paradox 
> 
> 1.3   Arrow paradox 
> 
>  "contradict" continuous spacetime (space in 1, 2 and time in 3).

Hmm… It contradicts only a digital or discrete version of space. Once we agree 
to assume a continuum, we accept the traditional notion of limits (Cauchy, 
Dedekind) and that solves, bu the usual method, the Zeno paradox.

Re: Planck Length

[Bruno Marchal]

> On 22 Jan 2019, at 01:49, 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 
 Planck length? 
 TIA, AG 
>>> 
>>> That is a very good question. I have 

Re: Discrete theories of space

[Philip Thrift]

On Wednesday, January 23, 2019 at 3:04:38 AM UTC-6, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, January 23, 2019 at 12:17:11 AM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Tuesday, January 22, 2019 at 11:31:06 PM UTC, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Tuesday, January 22, 2019 at 5:04:15 PM UTC-6, agrays...@gmail.com 
>>> wrote:



 On Tuesday, January 22, 2019 at 10:47:57 PM UTC, Philip Thrift wrote:
>
>
>
> On Tuesday, January 22, 2019 at 3:23:02 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Sunday, January 20, 2019 at 3:14:39 PM UTC, Lawrence Crowell wrote:
>>>
>>> On Saturday, January 19, 2019 at 5:42:12 AM UTC-6, 
>>> agrays...@gmail.com wrote:

 Since it seems conceptually impossible to model a theory with 
 DISJOINT discrete spatial units, thus requiring the units to be 
 juxtaposed, 
 do such theories acknowledge difficulty of motion between the units, 
 which 
 might or might not have boundaries? TIA, AG

>>>
>>> I am not sure how to impress people with how bad this thinking is. 
>>>
>>
>> *In retrospect, I don't think you were being rude. You were just 
>> reinforcing my conclusion, offering additional technical reasons, why 
>> the 
>> idea of discrete space is an unintelligible concept. AG*
>>
>> These slice and diced chunks of spacetime, whether voxels, plaquettes 
>>> and so forth have violations of Lorentz symmetry of spacetime. This 
>>> means 
>>> that curiously the symmetry of gravitation would be violated at higher 
>>> energy, and in fact where it is quantized. These ideas have further 
>>> been 
>>> falsified by the lack of dispersion from distant sources. These ideas 
>>> are 
>>> bad interpretations of the Planck length. The Planck length is just the 
>>> smallest length beyond which you can isolate a quantum bit. Remember, 
>>> it is 
>>> the length at which the Compton wavelength of a black hole equals its 
>>> Schwarzschild radius. It is a bit similar to the Nyquist frequency in 
>>> engineering. In order to measure the frequency of a rotating system you 
>>> must take pictures that are at least double that frequency. Similarly 
>>> to 
>>> measure the frequency of an EM wave you need to have a wave with 
>>> Fourier 
>>> modes that are 2 or more times the frequency you want to measure. The 
>>> black 
>>> hole is in a sense a fundamental cut-off in the time scale, or in a 
>>> reciprocal manner the energy, one can sample space to find qubits. 
>>>
>>> The levels of confusion over this are enormous. It does not tell us 
>>> that spacetime is somehow sliced and diced into briquets or pieces. It 
>>> does 
>>> not tell us that quantum energy of some fields can't be far larger than 
>>> the 
>>> Planck energy, or equivalently the wavelength much smaller. This would 
>>> be 
>>> analogous to a resonance state, and there is no reason there can't be 
>>> such 
>>> a thing in quantum gravity. The Planck scale would suggest this sort of 
>>> state may decay into a sub-Planckian energy.  Further, it is plausible 
>>> that 
>>> quantum gravity beyond what appears as a linearized weak field 
>>> approximation similar to the QED of photon bunched pairs may only exist 
>>> at 
>>> most an order of magnitude larger than the Planck scale anyway. A 
>>> holographic screen is then a sort of beam splitter at the 
>>> quantum-classical 
>>> divide.
>>>
>>> LC
>>>
>>
>
>
>
> But you have to admit that a truly continuous space in reality is *more 
> unintelligible* than a discrete space.
>
> Where do you observe a true (spacetime) continuum in nature?
>
> A true continuum in reality is more problematic in many ways than a 
> "quantum" spacetime.
>
> - pt
>

 *Calculus is essentially based on continuity and seems to model the 
 real world. But for me discrete space seems to make motion problematic, so 
 my inclination is to reject it. AG*

>>>
>>>
>>> What about Zeno's paradox?
>>>
>>  
>
>> *I brought this issue up myself a few months ago. Seems to show space is 
>> not infinitely divisible. OTOH, GR is hugely successful and assumes 
>> space-time continuity. AG*
>>
>
>
> *What version of Zeno's paradox do you subscribe to which suggests space 
> is not infinitely divisible? TIA, AG *
>
>
>> And don't let that *brainwashing* from calculus math teachers fool you. 
>>> :)
>>>
>>> - pt
>>>
>>

All three paradoxes of motion [ listed in Wikipedia - 
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Paradoxes_of_motion ]

1Paradoxes of motion 

   
   - 1.1Achilles and the tortoise 
   

Re: Discrete theories of space

[agrayson2000]

On Wednesday, January 23, 2019 at 12:17:11 AM UTC, agrays...@gmail.com 
wrote:
>
>
>
> On Tuesday, January 22, 2019 at 11:31:06 PM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Tuesday, January 22, 2019 at 5:04:15 PM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Tuesday, January 22, 2019 at 10:47:57 PM UTC, Philip Thrift wrote:



 On Tuesday, January 22, 2019 at 3:23:02 PM UTC-6, agrays...@gmail.com 
 wrote:
>
>
>
> On Sunday, January 20, 2019 at 3:14:39 PM UTC, Lawrence Crowell wrote:
>>
>> On Saturday, January 19, 2019 at 5:42:12 AM UTC-6, 
>> agrays...@gmail.com wrote:
>>>
>>> Since it seems conceptually impossible to model a theory with 
>>> DISJOINT discrete spatial units, thus requiring the units to be 
>>> juxtaposed, 
>>> do such theories acknowledge difficulty of motion between the units, 
>>> which 
>>> might or might not have boundaries? TIA, AG
>>>
>>
>> I am not sure how to impress people with how bad this thinking is. 
>>
>
> *In retrospect, I don't think you were being rude. You were just 
> reinforcing my conclusion, offering additional technical reasons, why the 
> idea of discrete space is an unintelligible concept. AG*
>
> These slice and diced chunks of spacetime, whether voxels, plaquettes 
>> and so forth have violations of Lorentz symmetry of spacetime. This 
>> means 
>> that curiously the symmetry of gravitation would be violated at higher 
>> energy, and in fact where it is quantized. These ideas have further been 
>> falsified by the lack of dispersion from distant sources. These ideas 
>> are 
>> bad interpretations of the Planck length. The Planck length is just the 
>> smallest length beyond which you can isolate a quantum bit. Remember, it 
>> is 
>> the length at which the Compton wavelength of a black hole equals its 
>> Schwarzschild radius. It is a bit similar to the Nyquist frequency in 
>> engineering. In order to measure the frequency of a rotating system you 
>> must take pictures that are at least double that frequency. Similarly to 
>> measure the frequency of an EM wave you need to have a wave with Fourier 
>> modes that are 2 or more times the frequency you want to measure. The 
>> black 
>> hole is in a sense a fundamental cut-off in the time scale, or in a 
>> reciprocal manner the energy, one can sample space to find qubits. 
>>
>> The levels of confusion over this are enormous. It does not tell us 
>> that spacetime is somehow sliced and diced into briquets or pieces. It 
>> does 
>> not tell us that quantum energy of some fields can't be far larger than 
>> the 
>> Planck energy, or equivalently the wavelength much smaller. This would 
>> be 
>> analogous to a resonance state, and there is no reason there can't be 
>> such 
>> a thing in quantum gravity. The Planck scale would suggest this sort of 
>> state may decay into a sub-Planckian energy.  Further, it is plausible 
>> that 
>> quantum gravity beyond what appears as a linearized weak field 
>> approximation similar to the QED of photon bunched pairs may only exist 
>> at 
>> most an order of magnitude larger than the Planck scale anyway. A 
>> holographic screen is then a sort of beam splitter at the 
>> quantum-classical 
>> divide.
>>
>> LC
>>
>



 But you have to admit that a truly continuous space in reality is *more 
 unintelligible* than a discrete space.

 Where do you observe a true (spacetime) continuum in nature?

 A true continuum in reality is more problematic in many ways than a 
 "quantum" spacetime.

 - pt

>>>
>>> *Calculus is essentially based on continuity and seems to model the real 
>>> world. But for me discrete space seems to make motion problematic, so my 
>>> inclination is to reject it. AG*
>>>
>>
>>
>> What about Zeno's paradox?
>>
>  

> *I brought this issue up myself a few months ago. Seems to show space is 
> not infinitely divisible. OTOH, GR is hugely successful and assumes 
> space-time continuity. AG*
>


*What version of Zeno's paradox do you subscribe to which suggests space is 
not infinitely divisible? TIA, AG *


> And don't let that *brainwashing* from calculus math teachers fool you. :)
>>
>> - pt
>>
>

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