Re: Are Real Numbers Really Real?

[Lawrence Crowell]

Overcomplete coherent states, such as laser states of light have a symplectic 
and Riemannian structure. This makes these states "classical-like " These are 
states in a huge quantum correlation, or a form of entanglement. This is the 
classical spacetime that has no quantum fluctuations. Quantum states that 
deviate are in a relative mixed or separable configuration.

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

The sp

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Re: Are Real Numbers Really Real?

[Bruno Marchal]

> On 5 Dec 2019, at 13:00, Philip Thrift  wrote:
> 
> 
> 
> On Thursday, December 5, 2019 at 5:36:56 AM UTC-6, Lawrence Crowell wrote:
> On Thursday, December 5, 2019 at 3:43:50 AM UTC-6, Philip Thrift wrote:
> 
> 
> On Wednesday, December 4, 2019 at 6:11:25 PM UTC-6, Lawrence Crowell wrote:
> On Wednesday, December 4, 2019 at 4:29:03 PM UTC-6, Philip Thrift wrote:
> 
> 
> On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell wrote:
> On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:
> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell  <>> wrote:
> 
> >>> The entire notion of quantum states and events as localized in regions of 
> >>> space is not entirely applicable. What symmetries exist with these 
> >>> quantum states or field are then not tied to local geometry.
> 
> >> OK, but if quantum states are to explain local geometry, and that is the 
> >> entire point because that is all that experimenters can see, then the 
> >> reverse can not be true, local geometry must be tied to quantum states. 
> 
> > I guess this is not quite clear to me. Largely the quantum states that form 
> > spacetime are quantum gravitation states.
> 
> It seems to me if quantum gravitational states form spacetime, and if 
> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to 
> show, then 2 distinct points that are less than a Planck Length apart must 
> correspond to 2 distinct quantum gravitational states.  Am I wrong?
> 
> No it is not possible to know. If you localize a quantum bit to a Planck 
> length it is in a black hole. If you try to localize two qubits arbitrarily 
> closely they caon only be within 2 Planck areas, if on a horizon,or in two 
> Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So if you 
> try to localize a field is less than two Planck volumes, or within a length 
> 1.26ℓ_p there is a loss of any information about them.
>  
> 
> >> So if the Gamma Ray Burst results hold up and spacetime really is smooth 
> >> and continuous then, would it be correct to say there are a infinite (not 
> >> just astronomically large) number of quantum symmetries and the Planck 
> >> Length and the Planck Time have no physical significance, they are just 
> >> numbers in units of time and space that for no particular reason happen to 
> >> pop out when you mathematically play around with the constants of nature 
> >> in certain ways?
> 
> > The number of quantum states are Virasoro, which is in principle infinite. 
> > However, because the cosmological horizon can only bound a finite number of 
> > such states, as is the case with a black hole with entropy S = A/4ℓ_p^2, 
> > the number of physical states is bounded above. As a result the Virasoro 
> > algebra has high frequency modes that are mathematically possible, but not 
> > physically accessed.
> 
> Then although mathematically infinite as far as physics is concerned there 
> are only a finite number of quantum gravitational states, but if quantum 
> states produces spacetime then why does the Gamma Ray Burst results say 
> spacetime is smooth and continuous? Can 2 points that are arbitrarily close 
> to each other have any physical meaning, does physics need Real Numbers or 
> not?  
> 
> The gamma ray burst data just tells us that different wavelengths of photons 
> have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) predicts different 
> dispersons for different wavelengths of light. Over distances of billions of 
> light years this would be significant. Nothing of this sort was observed. 
> This means there is no "foaminess" or discreteness to spacetime. This is down 
> to a scale of ℓ_p/50, the last I checked.
>  
>  
> > A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. Any 
> > unitary transformation between H_a and H_b defines a boundary if we trace 
> > over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for S_b. 
> > We have removed the off-diagonal terms. We then can define this as a 
> > boundary, aka holographic screen or horizon, between sets of entangled 
> > states. This then defines a form of geometry. The transformation between 
> > H_a and H_b can just as well be time evolution with a boundary that 
> > separates two temporal regions. The Taub-NUT spacetime has this 
> > characteristic as does the region between the spacelike region outside the 
> > inner horizon of a black hole and the mysterious region inside.
> 
> You seem to be saying space may not be fundamental but time is. Would that be 
> a fair representation of your views?
> 
> I tried to indicate that both space and time are emergent.
> 
> LC
>  
> 
> 
> But everything you wrote is in the vocabulary of space+time.
> 
> Even "wavelength".
> 
> @philipthrift 
> 
> This is in reference to the propagation of photons. It illustrates that 
> spacetime is not made of chunks or finite elements. Spacetime is smooth. 
> However, it is an epiphenomenology of quantum entanglement.
> 

Re: Are Real Numbers Really Real?

[Lawrence Crowell]

No that is not the point. Quantum states on the entropy surface deviate from 
horizon states by the measure to which they are separable. There are no quantum 
 metric fluctuations of a virtual nature.

LC

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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Thursday, December 5, 2019 at 5:36:56 AM UTC-6, Lawrence Crowell wrote:
>
> On Thursday, December 5, 2019 at 3:43:50 AM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Wednesday, December 4, 2019 at 6:11:25 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Wednesday, December 4, 2019 at 4:29:03 PM UTC-6, Philip Thrift wrote:



 On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:
>>
>> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>> *>>> The entire notion of quantum states and events as localized in 
> regions of space is not entirely applicable. What symmetries exist 
> with 
> these quantum states or field are then not tied to local geometry.*
>

 >> OK, but if quantum states are to explain local geometry, and 
 that is the entire point because that is all that experimenters can 
 see, 
 then the reverse can not be true, local geometry must be tied to 
 quantum 
 states. 

>>>
>>> *> I guess this is not quite clear to me. Largely the quantum states 
>>> that form spacetime are quantum gravitation states.*
>>>
>>
>> It seems to me if quantum gravitational states form spacetime, and if 
>> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems 
>> to 
>> show, then 2 distinct points that are less than a Planck Length apart 
>> must 
>> correspond to 2 distinct quantum gravitational states.  Am I wrong?
>>
>
> No it is not possible to know. If you localize a quantum bit to a 
> Planck length it is in a black hole. If you try to localize two qubits 
> arbitrarily closely they caon only be within 2 Planck areas, if on a 
> horizon,or in two Planck volumes if in the bulk. A Planck volume is V_p = 
> (4π/3)ℓ_p^3.So if you try to localize a field is less than two Planck 
> volumes, or within a length 1.26ℓ_p there is a loss of any 
> information about them.
>  
>
>>
>> >> So if the Gamma Ray Burst results hold up and spacetime really is 
 smooth and continuous then, would it be correct to say there are a 
 infinite 
 (not just astronomically large) number of quantum symmetries and the 
 Planck 
 Length and the Planck Time have no physical significance, they are 
 just 
 numbers in units of time and space that for no particular reason 
 happen to pop out when you mathematically play around with the 
 constants of 
 nature in certain ways?

>>>
>>> *> The number of quantum states are Virasoro, which is in principle 
>>> infinite. However, because the cosmological horizon can only bound a 
>>> finite 
>>> number of such states, as is the case with a black hole with entropy S 
>>> = 
>>> A/4ℓ_p^2, the number of physical states is bounded above. As a result 
>>> the 
>>> Virasoro algebra has high frequency modes that are mathematically 
>>> possible, 
>>> but not physically accessed.*
>>>
>>
>> Then although mathematically infinite as far as physics is concerned 
>> there are only a finite number of quantum gravitational states, but if 
>> quantum states produces spacetime then why does the Gamma Ray Burst 
>> results 
>> say spacetime is smooth and continuous? Can 2 points that are 
>> arbitrarily 
>> close to each other have any physical meaning, does physics need Real 
>> Numbers or not?  
>>
>
> The gamma ray burst data just tells us that different wavelengths of 
> photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) 
> predicts 
> different dispersons for different wavelengths of light. Over distances 
> of 
> billions of light years this would be significant. Nothing of this sort 
> was 
> observed. This means there is no "foaminess" or discreteness to 
> spacetime. 
> This is down to a scale of ℓ_p/50, the last I checked.
>  
>
>>  
>>
>>> *> A Hilbert space H that contains H_a and H_b is not equal to 
>>> H_a×H_b. Any unitary transformation between H_a and H_b defines a 
>>> boundary 
>>> if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and 
>>> similarly for S_b. We have removed the off-diagonal terms. We then can 
>>> define this as a boundary, aka holographic screen or horizon, between 
>>> sets 
>>> of entangled states. This then defines a form of geometry. The 
>>> transformation between H_a and H_b can just as well be time evolution 
>>> with 
>>> a boundary that separates two temporal regions. The Taub-NUT spacetime 
>>> has 
>>> this characteristic as does the region between the spacelike region 

Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Thursday, December 5, 2019 at 3:43:50 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Wednesday, December 4, 2019 at 6:11:25 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Wednesday, December 4, 2019 at 4:29:03 PM UTC-6, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:
>
> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <
> goldenfield...@gmail.com> wrote:
>
> *>>> The entire notion of quantum states and events as localized in 
 regions of space is not entirely applicable. What symmetries exist 
 with 
 these quantum states or field are then not tied to local geometry.*

>>>
>>> >> OK, but if quantum states are to explain local geometry, and 
>>> that is the entire point because that is all that experimenters can 
>>> see, 
>>> then the reverse can not be true, local geometry must be tied to 
>>> quantum 
>>> states. 
>>>
>>
>> *> I guess this is not quite clear to me. Largely the quantum states 
>> that form spacetime are quantum gravitation states.*
>>
>
> It seems to me if quantum gravitational states form spacetime, and if 
> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems 
> to 
> show, then 2 distinct points that are less than a Planck Length apart 
> must 
> correspond to 2 distinct quantum gravitational states.  Am I wrong?
>

 No it is not possible to know. If you localize a quantum bit to a 
 Planck length it is in a black hole. If you try to localize two qubits 
 arbitrarily closely they caon only be within 2 Planck areas, if on a 
 horizon,or in two Planck volumes if in the bulk. A Planck volume is V_p = 
 (4π/3)ℓ_p^3.So if you try to localize a field is less than two Planck 
 volumes, or within a length 1.26ℓ_p there is a loss of any information 
 about them.
  

>
> >> So if the Gamma Ray Burst results hold up and spacetime really is 
>>> smooth and continuous then, would it be correct to say there are a 
>>> infinite 
>>> (not just astronomically large) number of quantum symmetries and the 
>>> Planck 
>>> Length and the Planck Time have no physical significance, they are just 
>>> numbers in units of time and space that for no particular reason 
>>> happen to pop out when you mathematically play around with the 
>>> constants of 
>>> nature in certain ways?
>>>
>>
>> *> The number of quantum states are Virasoro, which is in principle 
>> infinite. However, because the cosmological horizon can only bound a 
>> finite 
>> number of such states, as is the case with a black hole with entropy S = 
>> A/4ℓ_p^2, the number of physical states is bounded above. As a result 
>> the 
>> Virasoro algebra has high frequency modes that are mathematically 
>> possible, 
>> but not physically accessed.*
>>
>
> Then although mathematically infinite as far as physics is concerned 
> there are only a finite number of quantum gravitational states, but if 
> quantum states produces spacetime then why does the Gamma Ray Burst 
> results 
> say spacetime is smooth and continuous? Can 2 points that are arbitrarily 
> close to each other have any physical meaning, does physics need Real 
> Numbers or not?  
>

 The gamma ray burst data just tells us that different wavelengths of 
 photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) 
 predicts 
 different dispersons for different wavelengths of light. Over distances of 
 billions of light years this would be significant. Nothing of this sort 
 was 
 observed. This means there is no "foaminess" or discreteness to spacetime. 
 This is down to a scale of ℓ_p/50, the last I checked.
  

>  
>
>> *> A Hilbert space H that contains H_a and H_b is not equal to 
>> H_a×H_b. Any unitary transformation between H_a and H_b defines a 
>> boundary 
>> if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and 
>> similarly for S_b. We have removed the off-diagonal terms. We then can 
>> define this as a boundary, aka holographic screen or horizon, between 
>> sets 
>> of entangled states. This then defines a form of geometry. The 
>> transformation between H_a and H_b can just as well be time evolution 
>> with 
>> a boundary that separates two temporal regions. The Taub-NUT spacetime 
>> has 
>> this characteristic as does the region between the spacelike region 
>> outside 
>> the inner horizon of a black hole and the mysterious region inside.*
>>
>
> You seem to be saying space may not be fundamental but time is. Would 
> that be a fair representation of your views?

Re: Are Real Numbers Really Real?

[Philip Thrift]

On Wednesday, December 4, 2019 at 6:11:25 PM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, December 4, 2019 at 4:29:03 PM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:

 On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <
 goldenfield...@gmail.com> wrote:

 *>>> The entire notion of quantum states and events as localized in 
>>> regions of space is not entirely applicable. What symmetries exist with 
>>> these quantum states or field are then not tied to local geometry.*
>>>
>>
>> >> OK, but if quantum states are to explain local geometry, and that 
>> is the entire point because that is all that experimenters can see, then 
>> the reverse can not be true, local geometry must be tied to quantum 
>> states. 
>>
>
> *> I guess this is not quite clear to me. Largely the quantum states 
> that form spacetime are quantum gravitation states.*
>

 It seems to me if quantum gravitational states form spacetime, and if 
 spacetime is smooth and continuous as the Gamma Ray Burst evidence seems 
 to 
 show, then 2 distinct points that are less than a Planck Length apart must 
 correspond to 2 distinct quantum gravitational states.  Am I wrong?

>>>
>>> No it is not possible to know. If you localize a quantum bit to a Planck 
>>> length it is in a black hole. If you try to localize two qubits arbitrarily 
>>> closely they caon only be within 2 Planck areas, if on a horizon,or in two 
>>> Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So 
>>> if you try to localize a field is less than two Planck volumes, or within a 
>>> length 1.26ℓ_p there is a loss of any information about them.
>>>  
>>>

 >> So if the Gamma Ray Burst results hold up and spacetime really is 
>> smooth and continuous then, would it be correct to say there are a 
>> infinite 
>> (not just astronomically large) number of quantum symmetries and the 
>> Planck 
>> Length and the Planck Time have no physical significance, they are just 
>> numbers in units of time and space that for no particular reason 
>> happen to pop out when you mathematically play around with the constants 
>> of 
>> nature in certain ways?
>>
>
> *> The number of quantum states are Virasoro, which is in principle 
> infinite. However, because the cosmological horizon can only bound a 
> finite 
> number of such states, as is the case with a black hole with entropy S = 
> A/4ℓ_p^2, the number of physical states is bounded above. As a result the 
> Virasoro algebra has high frequency modes that are mathematically 
> possible, 
> but not physically accessed.*
>

 Then although mathematically infinite as far as physics is concerned 
 there are only a finite number of quantum gravitational states, but if 
 quantum states produces spacetime then why does the Gamma Ray Burst 
 results 
 say spacetime is smooth and continuous? Can 2 points that are arbitrarily 
 close to each other have any physical meaning, does physics need Real 
 Numbers or not?  

>>>
>>> The gamma ray burst data just tells us that different wavelengths of 
>>> photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) predicts 
>>> different dispersons for different wavelengths of light. Over distances of 
>>> billions of light years this would be significant. Nothing of this sort was 
>>> observed. This means there is no "foaminess" or discreteness to spacetime. 
>>> This is down to a scale of ℓ_p/50, the last I checked.
>>>  
>>>
  

> *> A Hilbert space H that contains H_a and H_b is not equal to 
> H_a×H_b. Any unitary transformation between H_a and H_b defines a 
> boundary 
> if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and 
> similarly for S_b. We have removed the off-diagonal terms. We then can 
> define this as a boundary, aka holographic screen or horizon, between 
> sets 
> of entangled states. This then defines a form of geometry. The 
> transformation between H_a and H_b can just as well be time evolution 
> with 
> a boundary that separates two temporal regions. The Taub-NUT spacetime 
> has 
> this characteristic as does the region between the spacelike region 
> outside 
> the inner horizon of a black hole and the mysterious region inside.*
>

 You seem to be saying space may not be fundamental but time is. Would 
 that be a fair representation of your views?

>>>
>>> I tried to indicate that both space and time are emergent.
>>>
>>> LC
>>>  
>>>
>>
>>
>> But everything you wrote is in the vocabulary of space+time.
>>
>> Even "wave*length"*.
>>
>> @philipthrift 
>>
>
> This is in reference to 

Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 4:29:03 PM UTC-6, Philip Thrift wrote:
>
>
>
> On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:
>>>
>>> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <
>>> goldenfield...@gmail.com> wrote:
>>>
>>> *>>> The entire notion of quantum states and events as localized in 
>> regions of space is not entirely applicable. What symmetries exist with 
>> these quantum states or field are then not tied to local geometry.*
>>
>
> >> OK, but if quantum states are to explain local geometry, and that 
> is the entire point because that is all that experimenters can see, then 
> the reverse can not be true, local geometry must be tied to quantum 
> states. 
>

 *> I guess this is not quite clear to me. Largely the quantum states 
 that form spacetime are quantum gravitation states.*

>>>
>>> It seems to me if quantum gravitational states form spacetime, and if 
>>> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to 
>>> show, then 2 distinct points that are less than a Planck Length apart must 
>>> correspond to 2 distinct quantum gravitational states.  Am I wrong?
>>>
>>
>> No it is not possible to know. If you localize a quantum bit to a Planck 
>> length it is in a black hole. If you try to localize two qubits arbitrarily 
>> closely they caon only be within 2 Planck areas, if on a horizon,or in two 
>> Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So 
>> if you try to localize a field is less than two Planck volumes, or within a 
>> length 1.26ℓ_p there is a loss of any information about them.
>>  
>>
>>>
>>> >> So if the Gamma Ray Burst results hold up and spacetime really is 
> smooth and continuous then, would it be correct to say there are a 
> infinite 
> (not just astronomically large) number of quantum symmetries and the 
> Planck 
> Length and the Planck Time have no physical significance, they are just 
> numbers in units of time and space that for no particular reason 
> happen to pop out when you mathematically play around with the constants 
> of 
> nature in certain ways?
>

 *> The number of quantum states are Virasoro, which is in principle 
 infinite. However, because the cosmological horizon can only bound a 
 finite 
 number of such states, as is the case with a black hole with entropy S = 
 A/4ℓ_p^2, the number of physical states is bounded above. As a result the 
 Virasoro algebra has high frequency modes that are mathematically 
 possible, 
 but not physically accessed.*

>>>
>>> Then although mathematically infinite as far as physics is concerned 
>>> there are only a finite number of quantum gravitational states, but if 
>>> quantum states produces spacetime then why does the Gamma Ray Burst results 
>>> say spacetime is smooth and continuous? Can 2 points that are arbitrarily 
>>> close to each other have any physical meaning, does physics need Real 
>>> Numbers or not?  
>>>
>>
>> The gamma ray burst data just tells us that different wavelengths of 
>> photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) predicts 
>> different dispersons for different wavelengths of light. Over distances of 
>> billions of light years this would be significant. Nothing of this sort was 
>> observed. This means there is no "foaminess" or discreteness to spacetime. 
>> This is down to a scale of ℓ_p/50, the last I checked.
>>  
>>
>>>  
>>>
 *> A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. 
 Any unitary transformation between H_a and H_b defines a boundary if we 
 trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for 
 S_b. We have removed the off-diagonal terms. We then can define this as a 
 boundary, aka holographic screen or horizon, between sets of entangled 
 states. This then defines a form of geometry. The transformation between 
 H_a and H_b can just as well be time evolution with a boundary that 
 separates two temporal regions. The Taub-NUT spacetime has this 
 characteristic as does the region between the spacelike region outside the 
 inner horizon of a black hole and the mysterious region inside.*

>>>
>>> You seem to be saying space may not be fundamental but time is. Would 
>>> that be a fair representation of your views?
>>>
>>
>> I tried to indicate that both space and time are emergent.
>>
>> LC
>>  
>>
>
>
> But everything you wrote is in the vocabulary of space+time.
>
> Even "wave*length"*.
>
> @philipthrift 
>

This is in reference to the propagation of photons. It illustrates that 
spacetime is not made of chunks or finite elements. Spacetime is smooth. 
However, it is an epiphenomenology of quantum entanglement.

LC 

-- 
You received this message because you are subscribed 

Re: Are Real Numbers Really Real?

[Philip Thrift]

On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:
>>
>> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>> *>>> The entire notion of quantum states and events as localized in 
> regions of space is not entirely applicable. What symmetries exist with 
> these quantum states or field are then not tied to local geometry.*
>

 >> OK, but if quantum states are to explain local geometry, and that 
 is the entire point because that is all that experimenters can see, then 
 the reverse can not be true, local geometry must be tied to quantum 
 states. 

>>>
>>> *> I guess this is not quite clear to me. Largely the quantum states 
>>> that form spacetime are quantum gravitation states.*
>>>
>>
>> It seems to me if quantum gravitational states form spacetime, and if 
>> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to 
>> show, then 2 distinct points that are less than a Planck Length apart must 
>> correspond to 2 distinct quantum gravitational states.  Am I wrong?
>>
>
> No it is not possible to know. If you localize a quantum bit to a Planck 
> length it is in a black hole. If you try to localize two qubits arbitrarily 
> closely they caon only be within 2 Planck areas, if on a horizon,or in two 
> Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So if 
> you try to localize a field is less than two Planck volumes, or within a 
> length 1.26ℓ_p there is a loss of any information about them.
>  
>
>>
>> >> So if the Gamma Ray Burst results hold up and spacetime really is 
 smooth and continuous then, would it be correct to say there are a 
 infinite 
 (not just astronomically large) number of quantum symmetries and the 
 Planck 
 Length and the Planck Time have no physical significance, they are just 
 numbers in units of time and space that for no particular reason 
 happen to pop out when you mathematically play around with the constants 
 of 
 nature in certain ways?

>>>
>>> *> The number of quantum states are Virasoro, which is in principle 
>>> infinite. However, because the cosmological horizon can only bound a finite 
>>> number of such states, as is the case with a black hole with entropy S = 
>>> A/4ℓ_p^2, the number of physical states is bounded above. As a result the 
>>> Virasoro algebra has high frequency modes that are mathematically possible, 
>>> but not physically accessed.*
>>>
>>
>> Then although mathematically infinite as far as physics is concerned 
>> there are only a finite number of quantum gravitational states, but if 
>> quantum states produces spacetime then why does the Gamma Ray Burst results 
>> say spacetime is smooth and continuous? Can 2 points that are arbitrarily 
>> close to each other have any physical meaning, does physics need Real 
>> Numbers or not?  
>>
>
> The gamma ray burst data just tells us that different wavelengths of 
> photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) predicts 
> different dispersons for different wavelengths of light. Over distances of 
> billions of light years this would be significant. Nothing of this sort was 
> observed. This means there is no "foaminess" or discreteness to spacetime. 
> This is down to a scale of ℓ_p/50, the last I checked.
>  
>
>>  
>>
>>> *> A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. 
>>> Any unitary transformation between H_a and H_b defines a boundary if we 
>>> trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for 
>>> S_b. We have removed the off-diagonal terms. We then can define this as a 
>>> boundary, aka holographic screen or horizon, between sets of entangled 
>>> states. This then defines a form of geometry. The transformation between 
>>> H_a and H_b can just as well be time evolution with a boundary that 
>>> separates two temporal regions. The Taub-NUT spacetime has this 
>>> characteristic as does the region between the spacelike region outside the 
>>> inner horizon of a black hole and the mysterious region inside.*
>>>
>>
>> You seem to be saying space may not be fundamental but time is. Would 
>> that be a fair representation of your views?
>>
>
> I tried to indicate that both space and time are emergent.
>
> LC
>  
>


But everything you wrote is in the vocabulary of space+time.

Even "wave*length"*.

@philipthrift 

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:
>
> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell  > wrote:
>
> *>>> The entire notion of quantum states and events as localized in 
 regions of space is not entirely applicable. What symmetries exist with 
 these quantum states or field are then not tied to local geometry.*

>>>
>>> >> OK, but if quantum states are to explain local geometry, and that is 
>>> the entire point because that is all that experimenters can see, then the 
>>> reverse can not be true, local geometry must be tied to quantum states. 
>>>
>>
>> *> I guess this is not quite clear to me. Largely the quantum states that 
>> form spacetime are quantum gravitation states.*
>>
>
> It seems to me if quantum gravitational states form spacetime, and if 
> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to 
> show, then 2 distinct points that are less than a Planck Length apart must 
> correspond to 2 distinct quantum gravitational states.  Am I wrong?
>

No it is not possible to know. If you localize a quantum bit to a Planck 
length it is in a black hole. If you try to localize two qubits arbitrarily 
closely they caon only be within 2 Planck areas, if on a horizon,or in two 
Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So if 
you try to localize a field is less than two Planck volumes, or within a 
length 1.26ℓ_p there is a loss of any information about them.
 

>
> >> So if the Gamma Ray Burst results hold up and spacetime really is 
>>> smooth and continuous then, would it be correct to say there are a infinite 
>>> (not just astronomically large) number of quantum symmetries and the Planck 
>>> Length and the Planck Time have no physical significance, they are just 
>>> numbers in units of time and space that for no particular reason happen 
>>> to pop out when you mathematically play around with the constants of nature 
>>> in certain ways?
>>>
>>
>> *> The number of quantum states are Virasoro, which is in principle 
>> infinite. However, because the cosmological horizon can only bound a finite 
>> number of such states, as is the case with a black hole with entropy S = 
>> A/4ℓ_p^2, the number of physical states is bounded above. As a result the 
>> Virasoro algebra has high frequency modes that are mathematically possible, 
>> but not physically accessed.*
>>
>
> Then although mathematically infinite as far as physics is concerned there 
> are only a finite number of quantum gravitational states, but if quantum 
> states produces spacetime then why does the Gamma Ray Burst results say 
> spacetime is smooth and continuous? Can 2 points that are arbitrarily close 
> to each other have any physical meaning, does physics need Real Numbers or 
> not?  
>

The gamma ray burst data just tells us that different wavelengths of 
photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) predicts 
different dispersons for different wavelengths of light. Over distances of 
billions of light years this would be significant. Nothing of this sort was 
observed. This means there is no "foaminess" or discreteness to spacetime. 
This is down to a scale of ℓ_p/50, the last I checked.
 

>  
>
>> *> A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. 
>> Any unitary transformation between H_a and H_b defines a boundary if we 
>> trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for 
>> S_b. We have removed the off-diagonal terms. We then can define this as a 
>> boundary, aka holographic screen or horizon, between sets of entangled 
>> states. This then defines a form of geometry. The transformation between 
>> H_a and H_b can just as well be time evolution with a boundary that 
>> separates two temporal regions. The Taub-NUT spacetime has this 
>> characteristic as does the region between the spacelike region outside the 
>> inner horizon of a black hole and the mysterious region inside.*
>>
>
> You seem to be saying space may not be fundamental but time is. Would that 
> be a fair representation of your views?
>

I tried to indicate that both space and time are emergent.

LC
 

>
> John K Clark
>

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 12:08:01 PM UTC-6, Brent wrote:
>
>
>
> On 12/4/2019 2:50 AM, Lawrence Crowell wrote:
>
> On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote: 
>>
>>
>>
>> On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote: 
>>>
>>> For symmetry protected quantum states, which are local entanglements, 
>>> they are local because the symmetry or group action is generally covariant. 
>>> This covariant property enforces what we think of as space and time. 
>>>
>>> LC
>>>
>>>
>
>> It's reasonable that space and time precedes symmetry. We get symmetries 
>> from spacial measurements.
>>
>> @philipthrift
>>
>
> An observer witnessing a black hole emit Hawking radiation discovers that 
> while quantum states are approaching the event horizon they also appear as 
> hawking radiation removed from the black hole. The entire notion of quantum 
> states and events as localized in regions of space is not entirely 
> applicable. 
>
>
> Right.  So how can they "approach the event horizon"?  How can they move 
> through space when they are not even localized? 
>
> Brent
>
>
The fields approaching the horizon are in a nonlocal superposition with 
itself far removed. The catch though is this persists even after a 
measurement meant to localize the particle-field. In a funny way the field 
is both in a superposition of two configurations and equivalently the 
entanglement of two field amplitudes.

LC
 

> What symmetries exist with these quantum states or field are then not tied 
> to local geometry. Local geometry is something that emerges instead from 
> the symmetries of quantum fields. This is because they are quantum 
> gravitational. The quantum fields approaching the event horizon, or on the 
> stretched horizon are pure Planck oscillator modes.
>
> Two gravitons that scatter either do so as a 4 point interaction, similar 
> to a φ^4 field theory, or they merge to form a black hole in a 3-point 
> interaction so the quantum BH decays via a 3-point interaction into 
> gravitons. There is no procedure for determining which of these amplitudes 
> occurs, and in fact they both do. QM is odd that way. As a result there is 
> no fundamental meaning to their being some point where a gauge action 
> occurs.
>
> As Arkani Hamed puts it, "Space must die."
>
> LC
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>  
> 
> .
>
>
>

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Re: Are Real Numbers Really Real?

[John Clark]

On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

*>>> The entire notion of quantum states and events as localized in regions
>>> of space is not entirely applicable. What symmetries exist with these
>>> quantum states or field are then not tied to local geometry.*
>>>
>>
>> >> OK, but if quantum states are to explain local geometry, and that is
>> the entire point because that is all that experimenters can see, then the
>> reverse can not be true, local geometry must be tied to quantum states.
>>
>
> *> I guess this is not quite clear to me. Largely the quantum states that
> form spacetime are quantum gravitation states.*
>

It seems to me if quantum gravitational states form spacetime, and if
spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to
show, then 2 distinct points that are less than a Planck Length apart must
correspond to 2 distinct quantum gravitational states.  Am I wrong?

>> So if the Gamma Ray Burst results hold up and spacetime really is smooth
>> and continuous then, would it be correct to say there are a infinite (not
>> just astronomically large) number of quantum symmetries and the Planck
>> Length and the Planck Time have no physical significance, they are just
>> numbers in units of time and space that for no particular reason happen
>> to pop out when you mathematically play around with the constants of nature
>> in certain ways?
>>
>
> *> The number of quantum states are Virasoro, which is in principle
> infinite. However, because the cosmological horizon can only bound a finite
> number of such states, as is the case with a black hole with entropy S =
> A/4ℓ_p^2, the number of physical states is bounded above. As a result the
> Virasoro algebra has high frequency modes that are mathematically possible,
> but not physically accessed.*
>

Then although mathematically infinite as far as physics is concerned there
are only a finite number of quantum gravitational states, but if quantum
states produces spacetime then why does the Gamma Ray Burst results say
spacetime is smooth and continuous? Can 2 points that are arbitrarily close
to each other have any physical meaning, does physics need Real Numbers or
not?


> *> A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b.
> Any unitary transformation between H_a and H_b defines a boundary if we
> trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for
> S_b. We have removed the off-diagonal terms. We then can define this as a
> boundary, aka holographic screen or horizon, between sets of entangled
> states. This then defines a form of geometry. The transformation between
> H_a and H_b can just as well be time evolution with a boundary that
> separates two temporal regions. The Taub-NUT spacetime has this
> characteristic as does the region between the spacelike region outside the
> inner horizon of a black hole and the mysterious region inside.*
>

You seem to be saying space may not be fundamental but time is. Would that
be a fair representation of your views?

John K Clark

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Re: Are Real Numbers Really Real?

['Brent Meeker' via Everything List]

On 12/4/2019 8:14 AM, Lawrence Crowell wrote:
But this can be nonlocally correlated in both space and time as an 
observer finds quantum modes on the BH and outside as Hawking radiation.


What can "nonlocal" in time mean?...at two different times, but the same 
place?  That's what "local" means.


Brent

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Re: Are Real Numbers Really Real?

['Brent Meeker' via Everything List]

On 12/4/2019 2:50 AM, Lawrence Crowell wrote:

On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote:



On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell
wrote:

For symmetry protected quantum states, which are local
entanglements, they are local because the symmetry or group
action is generally covariant. This covariant property
enforces what we think of as space and time.

LC



It's reasonable that space and time precedes symmetry. We get
symmetries from spacial measurements.

@philipthrift


An observer witnessing a black hole emit Hawking radiation discovers 
that while quantum states are approaching the event horizon they also 
appear as hawking radiation removed from the black hole. The entire 
notion of quantum states and events as localized in regions of space 
is not entirely applicable.


Right.  So how can they "approach the event horizon"?  How can they move 
through space when they are not even localized?


Brent

What symmetries exist with these quantum states or field are then not 
tied to local geometry. Local geometry is something that emerges 
instead from the symmetries of quantum fields. This is because they 
are quantum gravitational. The quantum fields approaching the event 
horizon, or on the stretched horizon are pure Planck oscillator modes.


Two gravitons that scatter either do so as a 4 point interaction, 
similar to a φ^4 field theory, or they merge to form a black hole in a 
3-point interaction so the quantum BH decays via a 3-point interaction 
into gravitons. There is no procedure for determining which of these 
amplitudes occurs, and in fact they both do. QM is odd that way. As a 
result there is no fundamental meaning to their being some point where 
a gauge action occurs.


As Arkani Hamed puts it, "Space must die."

LC
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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 7:44:06 AM UTC-6, John Clark wrote:
>
> On Wed, Dec 4, 2019 at 5:50 AM Lawrence Crowell  > wrote:
>  
>
>> *> The entire notion of quantum states and events as localized in regions 
>> of space is not entirely applicable. What symmetries exist with these 
>> quantum states or field are then not tied to local geometry.*
>>
>
> OK, but if quantum states are to explain local geometry, and that is the 
> entire point because that is all that experimenters can see, then the 
> reverse can not be true, local geometry must be tied to quantum states. 
>

I guess this is not quite clear to me. Largely the quantum states that form 
spacetime are quantum gravitation states.
 

>
> > Local geometry is something that emerges instead from the symmetries of 
>> quantum fields. This is because they are quantum gravitational.
>>
>
> So if the Gamma Ray Burst results hold up and spacetime really is smooth 
> and continuous then, would it be correct to say there are a infinite (not 
> just astronomically large) number of quantum symmetries and the Planck 
> Length and the Planck Time have no physical significance, they are just 
> numbers in units of time and space that for no particular reason happen 
> to pop out when you mathematically play around with the constants of nature 
> in certain ways?
>

The number of quantum states are Virasoro, which is in principle infinite. 
However, because the cosmological horizon can only bound a finite number of 
such states, as is the case with a black hole with entropy S = A/4ℓ_p^2, 
the number of physical states is bounded above. As a result the Virasoro 
algebra has high frequency modes that are mathematically possible, but not 
physically accessed. Virasoro states are those of the bosonic string and we 
may think of a black hole as a very large high mode string that wraps 
around the Planck region above the horizon. The largest a black hole could 
become is equal to all the mass in the observable universe. That in turn is 
finite because beyond the cosmological horizon mass can't be accessed. 
 

>
> *> As Arkani Hamed puts it, "Space must die."*
>>
>
> What about time, can space really be separated from it despite what 
> Minkowski said? Time features prominently in Schrödinger's Equation, 
> Dirac's Equation and even Feynman diagrams; you're going to have to go back 
> to square one and rewrite the entirety of Quantum Mechanics without any 
> reference to space or time, and that would be a massive job that I'm not 
> certain could be done, I'm not even certain there would be any point in 
> doing so, it would certainly make Quantum Mechanics far harder to use and 
> its not exactly easy now.
>

A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. Any 
unitary transformation between H_a and H_b defines a boundary if we trace 
over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for S_b. 
We have removed the off-diagonal terms. We then can define this as a 
boundary, aka holographic screen or horizon, between sets of entangled 
states. This then defines a form of geometry. The transformation between 
H_a and H_b can just as well be time evolution with a boundary that 
separates two temporal regions. The Taub-NUT spacetime has this 
characteristic as does the region between the spacelike region outside the 
inner horizon of a black hole and the mysterious region inside.
 

>  
>
>> * > The quantum fields approaching the event horizon, or on the stretched 
>> horizon are pure Planck oscillator modes.*
>>
>
> But a Planck oscillator is something that absorbs or emits energy only in 
> amounts which are integer multiples of Planck's constant times the 
> frequency of the oscillator, however frequency is the number of repeating 
> events per unit of TIME.
>

But this can be nonlocally correlated in both space and time as an observer 
finds quantum modes on the BH and outside as Hawking radiation.

LC 

>
>
>  John K Clark
>

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Re: Are Real Numbers Really Real?

[John Clark]

On Wed, Dec 4, 2019 at 5:50 AM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:


> *> The entire notion of quantum states and events as localized in regions
> of space is not entirely applicable. What symmetries exist with these
> quantum states or field are then not tied to local geometry.*
>

OK, but if quantum states are to explain local geometry, and that is the
entire point because that is all that experimenters can see, then the
reverse can not be true, local geometry must be tied to quantum states.

> Local geometry is something that emerges instead from the symmetries of
> quantum fields. This is because they are quantum gravitational.
>

So if the Gamma Ray Burst results hold up and spacetime really is smooth
and continuous then, would it be correct to say there are a infinite (not
just astronomically large) number of quantum symmetries and the Planck
Length and the Planck Time have no physical significance, they are just
numbers in units of time and space that for no particular reason happen to
pop out when you mathematically play around with the constants of nature in
certain ways?

*> As Arkani Hamed puts it, "Space must die."*
>

What about time, can space really be separated from it despite what
Minkowski said? Time features prominently in Schrödinger's Equation,
Dirac's Equation and even Feynman diagrams; you're going to have to go back
to square one and rewrite the entirety of Quantum Mechanics without any
reference to space or time, and that would be a massive job that I'm not
certain could be done, I'm not even certain there would be any point in
doing so, it would certainly make Quantum Mechanics far harder to use and
its not exactly easy now.


> * > The quantum fields approaching the event horizon, or on the stretched
> horizon are pure Planck oscillator modes.*
>

But a Planck oscillator is something that absorbs or emits energy only in
amounts which are integer multiples of Planck's constant times the
frequency of the oscillator, however frequency is the number of repeating
events per unit of TIME.

 John K Clark

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote:
>>
>> For symmetry protected quantum states, which are local entanglements, 
>> they are local because the symmetry or group action is generally covariant. 
>> This covariant property enforces what we think of as space and time.
>>
>> LC
>>
>>

> It's reasonable that space and time precedes symmetry. We get symmetries 
> from spacial measurements.
>
> @philipthrift
>

An observer witnessing a black hole emit Hawking radiation discovers that 
while quantum states are approaching the event horizon they also appear as 
hawking radiation removed from the black hole. The entire notion of quantum 
states and events as localized in regions of space is not entirely 
applicable. What symmetries exist with these quantum states or field are 
then not tied to local geometry. Local geometry is something that emerges 
instead from the symmetries of quantum fields. This is because they are 
quantum gravitational. The quantum fields approaching the event horizon, or 
on the stretched horizon are pure Planck oscillator modes.

Two gravitons that scatter either do so as a 4 point interaction, similar 
to a φ^4 field theory, or they merge to form a black hole in a 3-point 
interaction so the quantum BH decays via a 3-point interaction into 
gravitons. There is no procedure for determining which of these amplitudes 
occurs, and in fact they both do. QM is odd that way. As a result there is 
no fundamental meaning to their being some point where a gauge action 
occurs.

As Arkani Hamed puts it, "Space must die."

LC

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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote:
>
> For symmetry protected quantum states, which are local entanglements, they 
> are local because the symmetry or group action is generally covariant. This 
> covariant property enforces what we think of as space and time.
>
> LC
>
>
>>>
It's reasonable that space and time precedes symmetry. We get symmetries 
from spacial measurements.

@philipthrift

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

For symmetry protected quantum states, which are local entanglements, they 
are local because the symmetry or group action is generally covariant. This 
covariant property enforces what we think of as space and time.

LC

On Tuesday, December 3, 2019 at 7:29:13 AM UTC-6, John Clark wrote:
>
>
> On Mon, Dec 2, 2019 at 8:30 PM Lawrence Crowell  > wrote:
>
> > *Spacetime is an epiphenomenology of entanglement. There are several 
>> ways entanglement can happen. There is topological order that has no 
>> scaling, or where the entanglement occurs without any reference to space or 
>> distance.*
>>
>
> If there is no reference to space or distance in that sort of 
> entanglement then where does the epistemological phenomenon of distance 
> come from? Do 2 points in space less than a Planck Length apart 
> correspond to 2 different entanglements, and is there any experimental 
> evidence that could help us answer this question? It seems to me the Gamma 
> Ray Burst results must be telling us something. 
>  
> And what about time, is it fundamental; it's right there in the 
> Schrödinger equation and just takes it as a given.
>  
>
>> > *Then there are symmetry protected topological orders, where there is 
>> a locality.*
>>
>
> But we know from experiment that Bell's Inequality is violated, so I don't 
> see how that sort of entanglement could have produced the world we 
> observe. 
>
>  John K Clark
>
>>
>>

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Re: Are Real Numbers Really Real?

[John Clark]

On Mon, Dec 2, 2019 at 8:30 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

> *Spacetime is an epiphenomenology of entanglement. There are several ways
> entanglement can happen. There is topological order that has no scaling, or
> where the entanglement occurs without any reference to space or distance.*
>

If there is no reference to space or distance in that sort of entanglement then
where does the epistemological phenomenon of distance come from? Do 2
points in space less than a Planck Length apart correspond to 2 different
entanglements, and is there any experimental evidence that could help us
answer this question? It seems to me the Gamma Ray Burst results must be
telling us something.

And what about time, is it fundamental; it's right there in the Schrödinger
equation and just takes it as a given.


> > *Then there are symmetry protected topological orders, where there is a
> locality.*
>

But we know from experiment that Bell's Inequality is violated, so I don't
see how that sort of entanglement could have produced the world we observe.

 John K Clark

>
>

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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Tuesday, December 3, 2019 at 4:38:56 AM UTC-6, Lawrence Crowell wrote:
>
>
>>
> I am not thinking of this. In fact this idea seems completely wrong 
> headed. It might have been that people would have tried to capture QM by 
> imposing stochastic Wiener processes and the like. 
>
> LC
>  
>

There is a connection between

"The subject [of path integration in stochastic processes] began with the 
work of *Wiener *during the 1920's, corresponding to a sum over random 
trajectories, *anticipating by two decades Feynman's famous work* on the 
path integral representation of quantum mechanics."
(Path Integrals for Stochastic Processes: An Introduction, Horacio S. Wio) 

and the

"Path integral on the SLM[stochastic Lorentz metric]-space"
(Stochastic metric space and quantum mechanics, Yoshimasa Kurihara).


@philipthrift 

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Tuesday, December 3, 2019 at 2:40:27 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Monday, December 2, 2019 at 7:30:13 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote:
>>>
>>> On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell <
>>> goldenfield...@gmail.com> wrote:
>>>
>>> > Spacetime does not really fundamentally exist. It is just a geometric 
 representation for how qubits interact and are entangled with each other.

>>>
>>> I agree it's possible Spacetime is not fundamental, it might be a 
>>> composite and be constructed out of something else, but if that more 
>>> fundamental "something else" is how Qubits interact and if there is a 
>>> smallest scale at which a quantum bit of information can be localized then 
>>> how can there be a one to one correspondence between the finite number of 
>>> such localized areas and the infinite number of points in smooth continuous 
>>> geometric spacetime that the Gamma Ray Burst results seem to indicate is 
>>> the way things really are?
>>>
>>>  John K Clark
>>>
>>
>> Spacetime is an epiphenomenology of entanglement. There are several ways 
>> entanglement can happen. There is topological order that has no scaling, or 
>> where the entanglement occurs without any reference to space or distance. 
>> Then there are symmetry protected topological orders, where there is a 
>> locality. How these two are related is a matter of research, but it is a 
>> sort of quantum phase transition. 
>>
>> An event horizon is a region where on either side there are entangled 
>> states. Close to the horizon there is are small regions on either side that 
>> are entangled. Further away these regions are larger. This has a sort of 
>> scaling and fractal geometry to it. As with fractals or chaos there are 
>> regions with regular dynamics where things are smooth and these are related 
>> to fractal geometry by the Feigenbaum number 4.669... . Classical spacetime 
>> is the a manifestation of a condensate of symmetry protected states that 
>> construct a surface that is smooth.
>>
>> LC
>>
>
>
I am not thinking of this. In fact this idea seems completely wrong headed. 
It might have been that people would have tried to capture QM by imposing 
stochastic Wiener processes and the like. 

LC
 

>
> I don't see how this relates to stochastic metric spaces:
>
>
> https://iopscience.iop.org/article/10.1088/2399-6528/aaa851
>
> Stochastic Metric Quantization (SMQ)
>
> In this work, a new quantization method based on the mathematical theory 
> of probability is proposed. The concept is developed as follows: We 
> consider the decay process of a given radioisotope. Because the probability 
> of observing a decay during a unit of time is constant, the number of 
> decays observed during a given time interval follows a Poisson 
> distribution. Using this phenomenon, a clock in which the second hand 
> advances each time a decay observed can be constructed; hereafter, this 
> will be referred to as a Poisson-clock. We assume for simplicity that the 
> Poisson-clock is designed to advance one tick per second on average. We 
> then compare this clock to an ordinary mechanical clock, in which the time 
> interval per tick of the second hand is constant. From the point of view of 
> an observer using the mechanical clock, the second hand of the 
> Poisson-clock seems to move randomly; however, this is of course a relative 
> observation tied to the reference frame of the mechanical clock. If instead 
> the time measured by the Poisson-clock is defined as the regular interval, 
> the running of the mechanical clock becomes random. A distribution of 'one 
> second' of the Poisson-clock, as measured by the mechanical clock, becomes 
> an exponential distribution with an average value of unity. Following the 
> central limit theorem, the deviation between the Poisson and the mechanical 
> clock after n seconds will have a Gaussian distribution around zero with a 
> variance of n. Using the mechanical clock to measure the time-of-flight of 
> a free particle following a classical inertial path will result in a 
> constant measured velocity. On the other hand, if the Poisson-clock is 
> used, measurement becomes a stochastic-process based on the Wiener measure 
> and can be expressed using a stochastic differentiation equation. It has 
> been shown that such as expression agrees with the stochastic equation 
> obtained by Nelson [6] that is used in stochastic quantization. Thus, 
> classical mechanics with a Poisson-time measure results in QM, which 
> suggests a new quantization method—Stochastic Metric Quantization(SMQ). 
> This observation can be extended to spatial coordinates as well, and an 
> equal treatment of space and time is necessary to apply this method to 
> relativistic quantum field theories. A quantum field theory can be given on 
> the stochastic metric space, not only for flat spaces such as Minkowski 
> space, but also for 

Re: Are Real Numbers Really Real?

[Bruno Marchal]

> On 2 Dec 2019, at 19:10, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 12/2/2019 12:41 AM, Bruno Marchal wrote:
>> In First Order Logic, Real Numbers are the one which simplifies. The first 
>> order theory of the real is decidable, unlike the first order theory of the 
>> natural numbers. The digital, or discrete, reality is more complex than the 
>> reals, which fits all holes, and provides (in the complex extensions) all 
>> roots for the polynomials.
> 
> Do you know whether Gisin's "random" numbers produce a decidable structure?

It certainly does not. Real numbers are logically much simpler than Natural 
Numbers (think about x^n + y^n = z^n in integer structure and with real numbers 
for example), but Gisin use QM, which adds the trigonometrical functions, or 
complex numbers, and this re-intrdouces the discrete structure and the integers 
in the picture (sin(2pi*x) = 0). Trigonometry, or waves, is what makes the 
continuum able to imitate the digital. Whatever physics can appear from 
arithmetic, it is described by a continuum, and it needs to be able to imitate 
the digital machines (or we would not be there (assuming Mechanism of course).

Bruno



> 
> Brent
> 
>> Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” by 
>> “physical”), which requires a non Mechanist theory of mind.
>> With Mechanism, real number are phenomenological constructs by digital 
>> entities. It is real, but not ontologically real.
>> 
>> Bruno
> 
> 
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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Monday, December 2, 2019 at 7:30:13 PM UTC-6, Lawrence Crowell wrote:
>
> On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote:
>>
>> On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>> > Spacetime does not really fundamentally exist. It is just a geometric 
>>> representation for how qubits interact and are entangled with each other.
>>>
>>
>> I agree it's possible Spacetime is not fundamental, it might be a 
>> composite and be constructed out of something else, but if that more 
>> fundamental "something else" is how Qubits interact and if there is a 
>> smallest scale at which a quantum bit of information can be localized then 
>> how can there be a one to one correspondence between the finite number of 
>> such localized areas and the infinite number of points in smooth continuous 
>> geometric spacetime that the Gamma Ray Burst results seem to indicate is 
>> the way things really are?
>>
>>  John K Clark
>>
>
> Spacetime is an epiphenomenology of entanglement. There are several ways 
> entanglement can happen. There is topological order that has no scaling, or 
> where the entanglement occurs without any reference to space or distance. 
> Then there are symmetry protected topological orders, where there is a 
> locality. How these two are related is a matter of research, but it is a 
> sort of quantum phase transition. 
>
> An event horizon is a region where on either side there are entangled 
> states. Close to the horizon there is are small regions on either side that 
> are entangled. Further away these regions are larger. This has a sort of 
> scaling and fractal geometry to it. As with fractals or chaos there are 
> regions with regular dynamics where things are smooth and these are related 
> to fractal geometry by the Feigenbaum number 4.669... . Classical spacetime 
> is the a manifestation of a condensate of symmetry protected states that 
> construct a surface that is smooth.
>
> LC
>



I don't see how this relates to stochastic metric spaces:


https://iopscience.iop.org/article/10.1088/2399-6528/aaa851

Stochastic Metric Quantization (SMQ)

In this work, a new quantization method based on the mathematical theory of 
probability is proposed. The concept is developed as follows: We consider 
the decay process of a given radioisotope. Because the probability of 
observing a decay during a unit of time is constant, the number of decays 
observed during a given time interval follows a Poisson distribution. Using 
this phenomenon, a clock in which the second hand advances each time a 
decay observed can be constructed; hereafter, this will be referred to as a 
Poisson-clock. We assume for simplicity that the Poisson-clock is designed 
to advance one tick per second on average. We then compare this clock to an 
ordinary mechanical clock, in which the time interval per tick of the 
second hand is constant. From the point of view of an observer using the 
mechanical clock, the second hand of the Poisson-clock seems to move 
randomly; however, this is of course a relative observation tied to the 
reference frame of the mechanical clock. If instead the time measured by 
the Poisson-clock is defined as the regular interval, the running of the 
mechanical clock becomes random. A distribution of 'one second' of the 
Poisson-clock, as measured by the mechanical clock, becomes an exponential 
distribution with an average value of unity. Following the central limit 
theorem, the deviation between the Poisson and the mechanical clock after n 
seconds will have a Gaussian distribution around zero with a variance of n. 
Using the mechanical clock to measure the time-of-flight of a free particle 
following a classical inertial path will result in a constant measured 
velocity. On the other hand, if the Poisson-clock is used, measurement 
becomes a stochastic-process based on the Wiener measure and can be 
expressed using a stochastic differentiation equation. It has been shown 
that such as expression agrees with the stochastic equation obtained by 
Nelson [6] that is used in stochastic quantization. Thus, classical 
mechanics with a Poisson-time measure results in QM, which suggests a new 
quantization method—Stochastic Metric Quantization(SMQ). This observation 
can be extended to spatial coordinates as well, and an equal treatment of 
space and time is necessary to apply this method to relativistic quantum 
field theories. A quantum field theory can be given on the stochastic 
metric space, not only for flat spaces such as Minkowski space, but also 
for highly curved spaces such as the surface of the black hole. As 
applications of this method, quantum effects in the early universe can be 
analyzed.

A main purpose of this work is to give a new framework of a quantum theory 
using mathematical tools of the stochastic metric space. In other words, a 
new stochastic quantization method is proposed in this work. A concept of 
our method is, in 

Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote:
>
> On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell  > wrote:
>
> > Spacetime does not really fundamentally exist. It is just a geometric 
>> representation for how qubits interact and are entangled with each other.
>>
>
> I agree it's possible Spacetime is not fundamental, it might be a 
> composite and be constructed out of something else, but if that more 
> fundamental "something else" is how Qubits interact and if there is a 
> smallest scale at which a quantum bit of information can be localized then 
> how can there be a one to one correspondence between the finite number of 
> such localized areas and the infinite number of points in smooth continuous 
> geometric spacetime that the Gamma Ray Burst results seem to indicate is 
> the way things really are?
>
>  John K Clark
>

Spacetime is an epiphenomenology of entanglement. There are several ways 
entanglement can happen. There is topological order that has no scaling, or 
where the entanglement occurs without any reference to space or distance. 
Then there are symmetry protected topological orders, where there is a 
locality. How these two are related is a matter of research, but it is a 
sort of quantum phase transition. 

An event horizon is a region where on either side there are entangled 
states. Close to the horizon there is are small regions on either side that 
are entangled. Further away these regions are larger. This has a sort of 
scaling and fractal geometry to it. As with fractals or chaos there are 
regions with regular dynamics where things are smooth and these are related 
to fractal geometry by the Feigenbaum number 4.669... . Classical spacetime 
is the a manifestation of a condensate of symmetry protected states that 
construct a surface that is smooth.

LC

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Re: Are Real Numbers Really Real?

[John Clark]

On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

> Spacetime does not really fundamentally exist. It is just a geometric
> representation for how qubits interact and are entangled with each other.
>

I agree it's possible Spacetime is not fundamental, it might be a composite
and be constructed out of something else, but if that more fundamental
"something else" is how Qubits interact and if there is a smallest scale at
which a quantum bit of information can be localized then how can there be a
one to one correspondence between the finite number of such localized areas
and the infinite number of points in smooth continuous geometric spacetime
that the Gamma Ray Burst results seem to indicate is the way things really
are?

 John K Clark

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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Monday, December 2, 2019 at 11:58:13 AM UTC-6, Lawrence Crowell wrote:
>
>
>
> Spacetime does not really fundamentally exist. It is just a geometric 
> representation for how qubits interact and are entangled with each other.
>
> LC 
>



Or it could be the other way around: qubits come out of (stochastic) 
spacetime.

https://arxiv.org/abs/1612.04228

@philipthrift

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Re: Are Real Numbers Really Real?

['Brent Meeker' via Everything List]

On 12/2/2019 12:41 AM, Bruno Marchal wrote:
In First Order Logic, Real Numbers are the one which simplifies. The 
first order theory of the real is decidable, unlike the first order 
theory of the natural numbers. The digital, or discrete, reality is 
more complex than the reals, which fits all holes, and provides (in 
the complex extensions) all roots for the polynomials.


Do you know whether Gisin's "random" numbers produce a decidable structure?

Brent

Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” 
by “physical”), which requires a non Mechanist theory of mind.
With Mechanism, real number are phenomenological constructs by digital 
entities. It is real, but not ontologically real.


Bruno



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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Monday, December 2, 2019 at 10:48:48 AM UTC-6, John Clark wrote:
>
> On Mon, Dec 2, 2019 at 6:10 AM Lawrence Crowell  > wrote:
>
> >> what does "discrete spacetime" mean?
>>>
>>
>> > It is a form of quotient geometry.
>>
>
> Hawking said the Entropy of a Black Hole is one quarter of it's Event 
> Horizon in areas of Planck Length squared, so Entropy is discrete. And 
> Entropy is proportional to the logarithm of the microstates that made the 
> Black Hole, so there are a discrete number of microstates.  And if there is 
> also a smallest scale that a Qubit of information can be localized at then 
> regardless of what quotient geometry and pure mathematics may say I'm 
> having a hard time attaching physical significance to the statement that 
> spacetime could still not be discreet. And if the recent results from Gamma 
> Ray Bursts do not show that Spacetime lacks graininess then what do they 
> show?
>
> John K Clark
>

Spacetime does not really fundamentally exist. It is just a geometric 
representation for how qubits interact and are entangled with each other.

LC 

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Re: Are Real Numbers Really Real?

[John Clark]

On Mon, Dec 2, 2019 at 6:10 AM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

>> what does "discrete spacetime" mean?
>>
>
> > It is a form of quotient geometry.
>

Hawking said the Entropy of a Black Hole is one quarter of it's Event
Horizon in areas of Planck Length squared, so Entropy is discrete. And
Entropy is proportional to the logarithm of the microstates that made the
Black Hole, so there are a discrete number of microstates.  And if there is
also a smallest scale that a Qubit of information can be localized at then
regardless of what quotient geometry and pure mathematics may say I'm
having a hard time attaching physical significance to the statement that
spacetime could still not be discreet. And if the recent results from Gamma
Ray Bursts do not show that Spacetime lacks graininess then what do they
show?

John K Clark

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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Monday, December 2, 2019 at 5:10:54 AM UTC-6, Lawrence Crowell wrote:
>
>
>
> Quantum physics has complementaries that are both deterministic and 
> nondeterministic. As a system of wave mechanics it is completely 
> deterministic. However, the Fourier components are amplitudes that in polar 
> form define probabilties for outcomes that occur by stochastic means. So 
> how one frames QM, either deterministic or nondeterministic, is up to the 
> choice of the analyst or how one performs an experiment or interprets the 
> outcomes of an experiment.
>
> LC 
>



Q: "So when you say that probability doesn’t exist, you mean that objective 
probability doesn’t exist."

A: "Right, it doesn’t exist as something out in the world without a 
gambling agent."
-- Christopher Fuchs [ 
https://quantamagazine.org/quantum-bayesianism-explained-by-its-founder-20150604/
 
]

So there are those who think probabilities don't exist as 
fundamental, unreducible, objective physical entities out in the world 
having nothing to do with us, and those that do. I think the former is a 
kind of religious pining (as William James said).

@philipthrift

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Sunday, December 1, 2019 at 2:19:44 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Saturday, November 30, 2019 at 6:11:37 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote:
>>>
>>>
>>>
>>> On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell <
>>> goldenfield...@gmail.com> wrote:
>>>
>>> *> The Planck unit of length and time does not mean space or spacetime 
 is discrete. All it means is this is the smallest scale one can localize a 
 quantum bit of information. It does not mean that spacetime is somehow 
 discrete.*

>>>
>>> If discrete spacetime does not mean there is a smallest scale that a 
>>> Qubit of information can be localized then what does "discrete spacetime" 
>>> mean?
>>>
>>
>>> John K Clark
>>>
>>
>> It is a form of quotient geometry. For 
>>
>> 1 →  G → H → K → 1
>>
>> for G = U(1), H = U(N) and K = PSU(N) = SU(N)/Z_N this short exact 
>> sequence defines a discrete  gauge group. The projective Lie group is a 
>> Kleinian and for a manifold associated with SU(N), say AdS_5 = U(2, 
>> 2)/O(4,1) the quotient defines an underlying discretization. Of course to 
>> do this in greater generality we need to have a discrete system with 
>> polytopes that define cells. So G could be the Coxeter group for a 
>> polytope. Say for G the Coxeter group for the 4-dim icosian H the group 
>> O(3,2) ≈ AdS_4×O(3,1) then K would be this spacetime, with the Lorentz 
>> group, in a quotient with a lattice space.
>>
>> LC
>>
>
>
> https://arxiv.org/pdf/1803.06824.pdf :
>
> One may object that this view is arbitrary as there is no natural bit 
> number where the transition from determined to random bits takes place. 
> This is correct, though not important in practice as long as this 
> transition is far away down the bit series. The lack of a natural 
> transition is due to the fact that, in classical physics, there is no 
> equivalent to the Plank constant of quantum theory. But this is quite 
> natural, as the fact is that when one looks for this transition in the 
> physical description of classical systems, one hits quantum physics.
>
> In summary, physics with all its predictive and explanatory powers can 
> well be presented as intrinsically non-deterministic. The dominant view 
> according to which classical physics is deterministic is due, first, to a 
> false impression generated by it’s huge success in astronomy and in the 
> design of clocks and other simple mechanical (integrable) systems, and, 
> second, to a lack of appreciation of its implication for (infinite) 
> information density. Finally, an indeterministic world is hospitable to Res 
> Potentia and to the passage of time.
>
> https://arxiv.org/pdf/1709.03595.pdf
>
> It is argued that quantum theory is best understood as requiring an 
> ontological duality of res extensa and res potentia, where the latter is 
> understood per Heisenberg's original proposal, and the former is roughly 
> equivalent to Descartes' 'extended substance.' However, this is not a 
> dualism of mutually exclusive substances in the classical Cartesian sense, 
> and therefore does not inherit the infamous 'mind-body' problem. Rather, 
> res potentia and res extensa are proposed as mutually implicative 
> ontological extants that serve to explain the key conceptual challenges of 
> quantum theory; in particular, nonlocality, entanglement, null 
> measurements, and wave function collapse. It is shown that a natural 
> account of these quantum perplexities emerges, along with a need to 
> reassess our usual ontological commitments involving the nature of space 
> and time.
>
>
> @philipthrift 
>

Quantum physics has complementaries that are both deterministic and 
nondeterministic. As a system of wave mechanics it is completely 
deterministic. However, the Fourier components are amplitudes that in polar 
form define probabilties for outcomes that occur by stochastic means. So 
how one frames QM, either deterministic or nondeterministic, is up to the 
choice of the analyst or how one performs an experiment or interprets the 
outcomes of an experiment.

LC 

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Re: Are Real Numbers Really Real?

[Bruno Marchal]

In First Order Logic, Real Numbers are the one which simplifies. The first 
order theory of the real is decidable, unlike the first order theory of the 
natural numbers. The digital, or discrete, reality is more complex than the 
reals, which fits all holes, and provides (in the complex extensions) all roots 
for the polynomials.
Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” by 
“physical”), which requires a non Mechanist theory of mind.
With Mechanism, real number are phenomenological constructs by digital 
entities. It is real, but not ontologically real.

Bruno


> On 30 Nov 2019, at 20:15, Philip Thrift  wrote:
> 
> 
> https://arxiv.org/abs/1803.06824 <https://arxiv.org/abs/1803.06824>
> 
> (V2: several mineurs changes ) !
> 
> Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real 
> Numbers Really Real?
> 
> Nicolas Gisin 
> <https://arxiv.org/search/quant-ph?searchtype=author=Gisin%2C+N>
> (Submitted on 19 Mar 2018 (v1 <https://arxiv.org/abs/1803.06824v1>), last 
> revised 31 May 2019 (this version, v3))
> It is usual to identify initial conditions of classical dynamical systems 
> with mathematical real numbers. However, almost all real numbers contain an 
> infinite amount of information. I argue that a finite volume of space can't 
> contain more than a finite amount of information, hence that the mathematical 
> real numbers are not physically relevant. Moreover, a better terminology for 
> the so-called real numbers is ``random numbers'', as their series of bits are 
> truly random. I propose an alternative classical mechanics, which is 
> empirically equivalent to classical mechanics, but uses only 
> finite-information numbers. This alternative classical mechanics is 
> non-deterministic, despite the use of deterministic equations, in a way 
> similar to quantum theory. Interestingly, both alternative classical 
> mechanics and quantum theories can be supplemented by additional variables in 
> such a way that the supplemented theory is deterministic. Most physicists 
> straightforwardly supplement classical theory with real numbers to which they 
> attribute physical existence, while most physicists reject Bohmian mechanics 
> as supplemented quantum theory, arguing that Bohmian positions have no 
> physical reality.
> Comments: 8 pages. Presented at the David Bohm Centennial Symposium, 
> London, Octobre 2017 V2: several mineurs changes and additions
> Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics 
> (physics.hist-ph)
> Cite as:  arXiv:1803.06824 <https://arxiv.org/abs/1803.06824> [quant-ph]
>   (or arXiv:1803.06824v3 <https://arxiv.org/abs/1803.06824v3> [quant-ph] 
> for this version)
> 
> 
> 
> @philipthrift
> 
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Re: Are Real Numbers Really Real?

[Philip Thrift]

On Saturday, November 30, 2019 at 6:11:37 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote:
>>
>>
>>
>> On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>> *> The Planck unit of length and time does not mean space or spacetime is 
>>> discrete. All it means is this is the smallest scale one can localize a 
>>> quantum bit of information. It does not mean that spacetime is somehow 
>>> discrete.*
>>>
>>
>> If discrete spacetime does not mean there is a smallest scale that a 
>> Qubit of information can be localized then what does "discrete spacetime" 
>> mean?
>>
>
>> John K Clark
>>
>
> It is a form of quotient geometry. For 
>
> 1 →  G → H → K → 1
>
> for G = U(1), H = U(N) and K = PSU(N) = SU(N)/Z_N this short exact 
> sequence defines a discrete  gauge group. The projective Lie group is a 
> Kleinian and for a manifold associated with SU(N), say AdS_5 = U(2, 
> 2)/O(4,1) the quotient defines an underlying discretization. Of course to 
> do this in greater generality we need to have a discrete system with 
> polytopes that define cells. So G could be the Coxeter group for a 
> polytope. Say for G the Coxeter group for the 4-dim icosian H the group 
> O(3,2) ≈ AdS_4×O(3,1) then K would be this spacetime, with the Lorentz 
> group, in a quotient with a lattice space.
>
> LC
>


https://arxiv.org/pdf/1803.06824.pdf :

One may object that this view is arbitrary as there is no natural bit 
number where the transition from determined to random bits takes place. 
This is correct, though not important in practice as long as this 
transition is far away down the bit series. The lack of a natural 
transition is due to the fact that, in classical physics, there is no 
equivalent to the Plank constant of quantum theory. But this is quite 
natural, as the fact is that when one looks for this transition in the 
physical description of classical systems, one hits quantum physics.

In summary, physics with all its predictive and explanatory powers can well 
be presented as intrinsically non-deterministic. The dominant view 
according to which classical physics is deterministic is due, first, to a 
false impression generated by it’s huge success in astronomy and in the 
design of clocks and other simple mechanical (integrable) systems, and, 
second, to a lack of appreciation of its implication for (infinite) 
information density. Finally, an indeterministic world is hospitable to Res 
Potentia and to the passage of time.

https://arxiv.org/pdf/1709.03595.pdf

It is argued that quantum theory is best understood as requiring an 
ontological duality of res extensa and res potentia, where the latter is 
understood per Heisenberg's original proposal, and the former is roughly 
equivalent to Descartes' 'extended substance.' However, this is not a 
dualism of mutually exclusive substances in the classical Cartesian sense, 
and therefore does not inherit the infamous 'mind-body' problem. Rather, 
res potentia and res extensa are proposed as mutually implicative 
ontological extants that serve to explain the key conceptual challenges of 
quantum theory; in particular, nonlocality, entanglement, null 
measurements, and wave function collapse. It is shown that a natural 
account of these quantum perplexities emerges, along with a need to 
reassess our usual ontological commitments involving the nature of space 
and time.


@philipthrift 

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote:
>
>
>
> On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell  > wrote:
>
> *> The Planck unit of length and time does not mean space or spacetime is 
>> discrete. All it means is this is the smallest scale one can localize a 
>> quantum bit of information. It does not mean that spacetime is somehow 
>> discrete.*
>>
>
> If discrete spacetime does not mean there is a smallest scale that a Qubit 
> of information can be localized then what does "discrete spacetime" mean?
>

> John K Clark
>

It is a form of quotient geometry. For 

1 →  G → H → K → 1

for G = U(1), H = U(N) and K = PSU(N) = SU(N)/Z_N this short exact sequence 
defines a discrete  gauge group. The projective Lie group is a Kleinian and 
for a manifold associated with SU(N), say AdS_5 = U(2, 2)/O(4,1) the 
quotient defines an underlying discretization. Of course to do this in 
greater generality we need to have a discrete system with polytopes that 
define cells. So G could be the Coxeter group for a polytope. Say for G the 
Coxeter group for the 4-dim icosian H the group O(3,2) ≈ AdS_4×O(3,1) then 
K would be this spacetime, with the Lorentz group, in a quotient with a lattice 
space.

LC

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Re: Are Real Numbers Really Real?

['Brent Meeker' via Everything List]

On 11/30/2019 2:29 PM, John Clark wrote:



On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell 
> wrote:


/> The Planck unit of length and time does not mean space or
spacetime is discrete. All it means is this is the smallest scale
one can localize a quantum bit of information. It does not mean
that spacetime is somehow discrete./


If discrete spacetime does not mean there is a smallest scale that a 
Qubit of information can be localized then what does "discrete 
spacetime" mean?


Discrete spacetime does mean there is a smallest scale at which things 
can be localized.  But that there is a smallest scale at which things 
can be located doesn't mean spacetime is discrete.


Brent

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Re: Are Real Numbers Really Real?

[John Clark]

On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

*> The Planck unit of length and time does not mean space or spacetime is
> discrete. All it means is this is the smallest scale one can localize a
> quantum bit of information. It does not mean that spacetime is somehow
> discrete.*
>

If discrete spacetime does not mean there is a smallest scale that a Qubit
of information can be localized then what does "discrete spacetime" mean?

John K Clark

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Re: Are Real Numbers Really Real?

[Lawrence Crowell]

On Saturday, November 30, 2019 at 3:08:42 PM UTC-6, John Clark wrote:
>
> I think it depends on if the Planck Length and Planck Time have physical 
> significance, it they do then spacetime is not continuous and Real Numbers 
> are not real; but if spacetime is smooth and continuous as the data from 
> Gamma Ray Bursters seems to indicate then Real Numbers are real and there 
> is no hope of ever developing a Quantum Theory Of Gravity. 
>
> John K Clark 
>

The Planck unit of length and time does not mean space or spacetime is 
discrete. All it means is this is the smallest scale one can localize a 
quantum bit of information. It does not mean that spacetime is somehow 
discrete.

LC 

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Re: Are Real Numbers Really Real?

[John Clark]

I think it depends on if the Planck Length and Planck Time have physical
significance, it they do then spacetime is not continuous and Real Numbers
are not real; but if spacetime is smooth and continuous as the data from
Gamma Ray Bursters seems to indicate then Real Numbers are real and there
is no hope of ever developing a Quantum Theory Of Gravity.

John K Clark

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Are Real Numbers Really Real?

[Philip Thrift]

https://arxiv.org/abs/1803.06824

(V2: several *mineurs* changes ) !

Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real 
Numbers Really Real?
Nicolas Gisin 
<https://arxiv.org/search/quant-ph?searchtype=author=Gisin%2C+N>
(Submitted on 19 Mar 2018 (v1 <https://arxiv.org/abs/1803.06824v1>), last 
revised 31 May 2019 (this version, v3))

It is usual to identify initial conditions of classical dynamical systems 
with mathematical real numbers. However, almost all real numbers contain an 
infinite amount of information. I argue that a finite volume of space can't 
contain more than a finite amount of information, hence that the 
mathematical real numbers are not physically relevant. Moreover, a better 
terminology for the so-called real numbers is ``random numbers'', as their 
series of bits are truly random. I propose an alternative classical 
mechanics, which is empirically equivalent to classical mechanics, but uses 
only finite-information numbers. This alternative classical mechanics is 
non-deterministic, despite the use of deterministic equations, in a way 
similar to quantum theory. Interestingly, both alternative classical 
mechanics and quantum theories can be supplemented by additional variables 
in such a way that the supplemented theory is deterministic. Most 
physicists straightforwardly supplement classical theory with real numbers 
to which they attribute physical existence, while most physicists reject 
Bohmian mechanics as supplemented quantum theory, arguing that Bohmian 
positions have no physical reality.

Comments: 8 pages. Presented at the David Bohm Centennial Symposium, 
London, Octobre 2017 V2: several mineurs changes and additions
Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics 
(physics.hist-ph)
Cite as: arXiv:1803.06824 <https://arxiv.org/abs/1803.06824> [quant-ph]
  (or arXiv:1803.06824v3 <https://arxiv.org/abs/1803.06824v3> [quant-ph] for 
this version)



@philipthrift

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