Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 3/19/2019 9:32 AM, John Clark wrote:
On Tue, Mar 19, 2019 at 4:50 AM > wrote:


**

*> I suppose Einstein started with the motivation of finding a
general transformation from one accelerating frame to another, and
later gave up on this project and settled for a theory of gravity.
Is this true? TIA, AG*


Einstein's breakthrough, what he called "the happiest thought of my 
life" was when he realized a man in a falling elevator will not feel 
gravity but a man in a accelerating elevator will. In other words an 
accelerating frame and gravity are the same thing, that's why it's 
called the Equivalence Principle.


I wonder if Einstein ever considered whether a charged particle in the 
falling radiate would radiate?


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 19, 2019 at 10:33:35 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 19, 2019 at 4:50 AM > wrote:
>
> * > I suppose Einstein started with the motivation of finding a general 
>> transformation from one accelerating frame to another, and later gave up on 
>> this project and settled for a theory of gravity. Is this true? TIA, AG*
>
>
> Einstein's breakthrough, what he called "the happiest thought of my life" 
> was when he realized a man in a falling elevator will not feel gravity but 
> a man in a accelerating elevator will. In other words an accelerating frame 
> and gravity are the same thing, that's why it's called the Equivalence 
> Principle.
>
> John K Clark
>
> I think your claim, in response to my question, is that if you have a 
theory of gravity, then via the EP you *also* have a general theory of how 
to transform from one accelerating frame to another which obeys the 
Principle of Relativity. I tend *not* to believe this since gravity is only* 
locally* equivalent to acceleration. AG 

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Re: Connection between Provability Logic (GL) and geometry?

[Philip Thrift]

On Tuesday, March 19, 2019 at 9:16:57 AM UTC-5, Bruno Marchal wrote:
>
>
> On 18 Mar 2019, at 20:33, Philip Thrift > 
> wrote:
>
>
> Might have something of interest ...
>
>
> https://mathoverflow.net/questions/325702/connection-between-provability-logic-gl-and-geometry
>  
> 
>
> ...
>
> There seems to be an existing literature on topological semantics and 
> provability logics. Thomas Icard has slides on this 
> , and the Stanford 
> Encyclopedia of Philosophy has a bit on the topic 
> . 
> I'm not sure how related this is to the specific topological/geometric 
> intuitions you give here, but it might be of interest more broadly. – Noah 
> Schweber  31 mins ago 
> 
>
>
>
>
> I know the work of Leo Esakia, (and of Blok) notably his Russian paper (*) 
> and it is indeed quite interesting. It provides interesting topological 
> semantics for variants of K4 and GL (called G here). Icard has extended 
> such semantics for the logic GLP, which is a polymodal logic axiomatising 
> the provability logic on sequence of stronger and stronger theories. At 
> each level n we have a box [n] obeying to G, and with the two axioms:
>
> [n]p -> [n+1]p
> p -> [n+1]p
>
> for all n, Beklemishev has shown that this is complete for the 
> arithmetical interpretation extended on this succession of theories. I use 
> this in some more detailed exposition. 
> In the work of Esakia, the consistency <>p becomes a special sort of 
> abstract derivative. The idea of using topological model cale from the work 
> of McKinsey and Tarski, in the spirit of the algebraic semantics of Helena 
> Rasiowa and Roman Sikorski “The mathematics of Metamathematics” (an 
> excellent work on algebraic semantics). 
>
> The topological space, in the semantics of Esakia, are not Hausdorff 
> spaces, and are rather peculiar from a topologist standpoint, but 
> nevertheless, that work is quite interesting. It is a good complement of 
> the more traditional Kripke or Krpke-inspired semantics (which I use much 
> more).
>
> Unfortunately, although this will have interesting application for the 
> general theology of “growing machine”, the topology is not related directly 
> to the quantum “geometry” of the “material” variant of G (the Z and X 
> logics I have shown to exist here). 
>
> But thanks for this link. I missed those slides by Icard, and some 
> references therein.
>
> Esakia died in 2010, and was responsible for the great interest in 
> provability logic in Georgia (Europa).
>
> Bruno
>
>
>
> (*) Esakia, L. (1981). Diagonal constructions, Löb’s formula and Cantor’s 
> scattered space (Russian). In Studies in logic and semantics, pages 
> 128–143. Metsniereba, Tbilisi.
>
>
> - pt
>
>
There are now three links supplied in the MathOverflow post:

(SEP article)  
https://plato.stanford.edu/entries/logic-provability/#TopoSemaForProvLogi

*Topological Semantics for Provability Logics*
http://logic.berkeley.edu/colloquium/IcardSlides.pdf

*The Topological Structure of Asynchronous Computability*
http://cs.brown.edu/people/mph/HerlihyS99/p858-herlihy.pdf

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

[John Clark]

On Tue, Mar 19, 2019 at 4:50 AM  wrote:

* > I suppose Einstein started with the motivation of finding a general
> transformation from one accelerating frame to another, and later gave up on
> this project and settled for a theory of gravity. Is this true? TIA, AG*


Einstein's breakthrough, what he called "the happiest thought of my life"
was when he realized a man in a falling elevator will not feel gravity but
a man in a accelerating elevator will. In other words an accelerating frame
and gravity are the same thing, that's why it's called the Equivalence
Principle.

John K Clark



>
>

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Re: Connection between Provability Logic (GL) and geometry?

[Bruno Marchal]

> On 18 Mar 2019, at 20:33, Philip Thrift  wrote:
> 
> 
> Might have something of interest ...
> 
> https://mathoverflow.net/questions/325702/connection-between-provability-logic-gl-and-geometry
> 
> ...
> 
> There seems to be an existing literature on topological semantics and 
> provability logics. Thomas Icard has slides on this 
> , and the Stanford 
> Encyclopedia of Philosophy has a bit on the topic 
> . 
> I'm not sure how related this is to the specific topological/geometric 
> intuitions you give here, but it might be of interest more broadly. – Noah 
> Schweber  31 mins ago 
> 
> 
> 


I know the work of Leo Esakia, (and of Blok) notably his Russian paper (*) and 
it is indeed quite interesting. It provides interesting topological semantics 
for variants of K4 and GL (called G here). Icard has extended such semantics 
for the logic GLP, which is a polymodal logic axiomatising the provability 
logic on sequence of stronger and stronger theories. At each level n we have a 
box [n] obeying to G, and with the two axioms:

[n]p -> [n+1]p
p -> [n+1]p

for all n, Beklemishev has shown that this is complete for the arithmetical 
interpretation extended on this succession of theories. I use this in some more 
detailed exposition. 
In the work of Esakia, the consistency <>p becomes a special sort of abstract 
derivative. The idea of using topological model cale from the work of McKinsey 
and Tarski, in the spirit of the algebraic semantics of Helena Rasiowa and 
Roman Sikorski “The mathematics of Metamathematics” (an excellent work on 
algebraic semantics). 

The topological space, in the semantics of Esakia, are not Hausdorff spaces, 
and are rather peculiar from a topologist standpoint, but nevertheless, that 
work is quite interesting. It is a good complement of the more traditional 
Kripke or Krpke-inspired semantics (which I use much more).

Unfortunately, although this will have interesting application for the general 
theology of “growing machine”, the topology is not related directly to the 
quantum “geometry” of the “material” variant of G (the Z and X logics I have 
shown to exist here). 

But thanks for this link. I missed those slides by Icard, and some references 
therein.

Esakia died in 2010, and was responsible for the great interest in provability 
logic in Georgia (Europa).

Bruno



(*) Esakia, L. (1981). Diagonal constructions, Löb’s formula and Cantor’s 
scattered space (Russian). In Studies in logic and semantics, pages 128–143. 
Metsniereba, Tbilisi.


> - pt
> 
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Re: Towards Conscious AI Systems

[Bruno Marchal]

Hi,

Grayson, Bruce, or anyone,  it is a bit for you that I answer to John Clark. If 
you agree with John, and can better explain its point, let me no. 

I recall the problem. With digital mechanism we can be be “read and cut” in 
Helsinki, and reconstituted in two cities, Washington and Moscow, 
simultaneously, where he get, in both places a cup of coffee. 
I claim that, in Helsinki the guy, who believes in Digital Mechanism  can 
predict this: 

I will with certainty drink a cup of coffee, but I am not sure if it will be 
Russian or American coffee.

The question is about the first person experience, and my justification is 
that, if we write anything else, in its prediction diary, different from “I 
will feel to be drinking a cup of coffee in W, or I will feel to be drinking a 
cup of coffee in W”. Then the prediction will be wrong, for at least one copy. 
By definition, a correct prediction on the first person experience possible, 
has to be true for all copies, so that they can all confirm it in the 
prediction diary, which has been taken in the read and cut box in Helsinki.

This later is used to say that a universal machine is unable to know which 
computations she is supported by, in the infinitely many computations executed, 
in the mathematical Church-Turing sense, in arithmetic, and that plays a key 
rôle to understand that physics will have to be reduced to a relative 
statistics on computation (a concept definable in any enough rich theory of 
arithmetic, like the theory of combinators + induction, or in Peano arithmetic.

It shows that if Everett used Mechanism, as he claims in some of its paper, and 
in his long text, then the wave itself, not just the collapse, has to be 
explained from the statistics on computations in arithmetic. 

I got this in my childhood, never met anyone taking more than 2 years to grasp. 
Usually, people grasp this in ten minutes. The only exception I know is John 
Clark. Then it took me 30 years to get the quantum logic for the logic of 
“probability one” in that mechanist and arithmetical context, so that QM 
confirms mechanism, up to now. 
You can skip the first comment, to get at this thought experience. It is the 
“step 3” of the reasoning given in the sane04 paper 
(http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html ).



> On 19 Mar 2019, at 00:35, John Clark  wrote:
> 
> On Mon, Mar 18, 2019 at 11:49 AM Bruno Marchal  > wrote:
> 
> >>> the academy of Plato   
> >>  ... knew less science than one bright third grader today.
> 
> >You told me you did not have study it.
> 
> You only need to look at Plato's academy for about 25 seconds to know that 
> they didn't know where the sun went at night but a bright modern third grader 
> does. 


>From Plato came neoplatonism. From this came mathematics and physics. For a 
>scientist, it is not a problem to be wrong, on the contrary, it is a honour to 
>be refuted, and he/she is open to improvement, dialog and research.



>  
> > You invoke your god.
> 
> Apparently your a fan of transcendental meditation and  believe if you just 
> keep chanting your mantra long enough you can make it come true. You've been 
> doing it for a decade now but I guess that's not quite long enough.


Then why do you keep saying that a computation is real only when implemented in 
a primary physical reality?

You can call the objet of your ontological commitment a “physical universe”, 
this does not change that it is non valid to refute a claim by invoking a 
personal ontological commitment.

Mathematician like to homogenise concept, like making 0 and 1 into number, 
which meant numerous, at the start.

God is defined by whatever is at the origin of everything.

The god of the believer in primary Matter is a primary physical universe.
The god of the abrahamic religion is “God” (say).
Note that the statement “there is no god” is still a theological statement, but 
with no value if the notion of God is not made more precise. 

You do seem like a “strong (non agnostic) atheist”, which share the definition 
of God of the Christians, and share the belief in the “material creation”.







> 
> 
> >> A valid proof shows that a statement is grammatically correct in the 
> >> language of mathematics but it does not prove that it exists. If you prove 
> >> that every sentence in a Harry Potter book is grammatically correct in the 
> >> language of English you have not proven that dragons exist.  Dragons don't 
> >> exist but the English word "dragons" does.
> 
> 
> > 2+2 = 5 is grammatically correct in arithmetic, but that has nothing to do 
> > with ^provability or with truth.
> 
> Exactly. All true statements about things that exist made in the language of 
> mathematics are grammatically correct, but there is no reason to think all 
> grammatically correct statements made in the language of mathematics are 
> about things that exist. You can write both fiction and nonfiction in the 
> English language a

Classical geometries emerging from quantum spacetime

[Philip Thrift]

This line of research is that of Daniele Pranzetti [  
https://www.perimeterinstitute.ca/people/daniele-pranzetti ].

"The idea at the basis of our study is that *homogenous classical 
geometries emerge from a condensate of quanta of space introduced in LQG in 
order to describe quantum geometries*," explains [Daniele] Pranzetti. 
"Thus, we obtained a description of black hole quantum states, suitable 
also to describe 'continuum' physics—that is, the physics of space-time as 
we know it."

*Loop quantum gravity theory offers glimpse beyond the event horizon*
https://phys.org/news/2016-05-loop-quantum-gravity-theory-glimpse.html

*Horizon entropy from quantum gravity condensates*
Daniele Oriti, Daniele Pranzetti, Lorenzo Sindoni
(Submitted on 23 Oct 2015 (v1), last revised 26 May 2016 (this version, v3))
https://arxiv.org/abs/1510.06991

*Black Holes as Quantum Gravity Condensates*
Daniele Oriti, Daniele Pranzetti, Lorenzo Sindoni
(Submitted on 4 Jan 2018)
https://arxiv.org/abs/1801.01479

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 12, 2019 at 4:05:04 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, March 7, 2019 at 3:19:39 AM UTC-7, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, March 6, 2019 at 11:42:33 AM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 3/6/2019 1:27 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote: 



 On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:



 On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com 
 wrote: 
>
>
>
> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 



 On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

 *Are you assuming uniqueness to tensors; that only tensors can 
 produce covariance in 4-space? Is that established or a mathematical 
 speculation? TIA, AG *


 That's looking at it the wrong way around.  Anything that 
 transforms as an object in space, must be representable by tensors. 
 The 
 informal definition of a tensor is something that transforms like an 
 object, i.e. in three space it's something that has a location and an 
 orientation and three extensions.  Something that doesn't transform as 
 a 
 tensor under coordinate system changes is something that depends on 
 the 
 arbitrary choice of coordinate system and so cannot be a fundamental 
 physical object.

 Brent

>>>
>>> 1) Is it correct to say that tensors in E's field equations can be 
>>> represented as 4x4 matrices which have different representations 
>>> depending 
>>> on the coordinate system being used, but represent the same object? 
>>>
>>>
>>> That's right as far as it goes.   Tensors can be of any order.  The 
>>> curvature tensor is 4x4x4x4.
>>>
>>> 2) In SR we use the LT to transform from one* non-accelerating* 
>>> frame to another. In GR, what is the transformation for going from one 
>>> *accelerating* frame to another? 
>>>
>>>
>>> The Lorentz transform, but only in a local patch.
>>>
>>
>> *That's what I thought you would say. But how does this advance 
>> Einstein's presumed project of finding how the laws of physics are 
>> invariant for accelerating frames? How did it morph into a theory of 
>> gravity? TIA, AG *
>>
>
> *Or suppose, using GR, that two frames are NOT within the same local 
> patch.  If we can't use the LT, how can we transform from one frame to 
> the 
> other? TIA, AG *
>
> *Or suppose we have two arbitrary accelerating frames, again NOT 
> within the same local patch, is it true that Maxwell's Equations are 
> covariant under some transformation, and what is that transformation? 
> TIA, 
> AG*
>


 *I think I can simplify my issue here, if indeed there is an issue: did 
 Einstein, or anyone, ever prove what I will call the General Principle of 
 Relativity, namely that the laws of physics are invariant for accelerating 
 frames? If the answer is affirmative, is there a transformation equation 
 for Maxwell's Equations which leaves them unchanged for arbitrary 
 accelerating frames? TIA, AG *


 Your question isn't clear.  If you're simply asking about the equations 
 describing physics* as expressed* in an accelerating (e.g. rotating) 
 reference frame, that's pretty trivial.  You write the equations in 
 whatever reference frame is convenient (usually an inertial one) and then 
 transform the coordinates to the accelerated frame coordinates.   But if 
 you're asking about what equations describe some physical system while it 
 is being accelerated as compared to it not being accelerated, that's more 
 complicated. 

>>>
>>> *Thanks, but I wasn't referring to either of those cases; rather, the 
>>> case of transforming from one accelerating frame to another accelerating 
>>> frame, and whether the laws of physics are invariant. *
>>>
>>>
>>> For simplicity consider just flat Minkowski space time.  If you know the 
>>> motion of a particle in reference frame, whether the reference frame is 
>>> accelerated or not, you can determine its motion in any other reference 
>>> frame.  As for the particle path through spacetime, that's just some 
>>> geometric path and you're changing from describing it in one coordinate 
>>> system to describing it in another system...no physics is changing, just 
>>> the description.  If the reference frame