On Thursday, January 31, 2019 at 7:52:08 AM UTC-6, Lawrence Crowell wrote:
>
>
>
> On Tuesday, January 29, 2019 at 5:03:11 AM UTC-6, Philip Thrift wrote:
>>
>>
>> This replaces space, time, particles, fields with histories.
>>
>> I think this is compatible with universal machines.
>>
>>
>> https://codicalist.wordpress.com/2019/01/28/histories-of-phenomenally-everything-hope/
>>
>>
>> - pt
>>
>
> This illustrates a problem with the epistemology of physics. It stems from 
> Newton's laws, in particular the second law of motion F = ma. On the left 
> hand side we have the dynamics in a force. We have on the right a physical 
> quantity in the mass of a body as a scalar quantity. We then have the 
> acceleration 
>
> a = lim_{Δt → 0}Δ^2x/Δt^2 = d^2x/dt^2.
>
> This then multiplies the physical scalar mass to give a dynamical, which 
> means measurable, force that has a direction. We can then think of this as 
> a strange equation that multiplies a physical quantity by a geometric 
> quantity that then gives a dynamical force that is physical. Issac Newton 
> wrote this according to a construction called fluxions, which in time gave 
> was to the calculus based more on Leibniz and ultimately Weierstrass. Yet 
> the early period was full of roiling controversy over what we meant by 
> these infinitesimals and so forth. The geometric aspect of Newton's second 
> law appeared to have a different meaning from what would be expected of 
> something physical.
>
> This confusion continues into general relativity. We might write the 
> Einstein field equation as 
>
> Geometric curvature = physical dynamics,
>
> where Einstein was most enamored with the left hand side, calling it 
> marble, while the right hand side he cited as wood. There is the mixing of 
> categories in general relativity that is remarkably similar to Newtonian 
> mechanics. The general theory of relativity is based on the equivalence 
> principle, and this tells us that for a sufficiently local frame there is 
> no experiment that can determine if the frame is global in free space or in 
> a gravitational field. This gives the sort of calculus rule, small frames 
> removes geometric information and thus dynamics, and the geometrodynamical 
> theory is built from atlas-chart constructions on such infinitesimal frames.
>
> General relativity gives geometry more of an active role. There may be 
> gravitational waves, undulations of space that evolve in time, that we 
> observe by the physical displacement of interferometer elements. We have in 
> our minds these mental models of space and spacetime, but ultimately we 
> have a category problem; space and spacetime while defined by clocks and 
> rulers, is not in of itself something that has direct physics. 
>
> We might then consider quantum gravitation. I think that spacetime is an 
> emergent property of quantum entanglement. Given a group G for the 
> symmetries of a quantum system or field, then in the Cartan decomposition G 
> = H×K the subgroup H is G modulo the action of K so H = G/K, and for a 
> quantum system this means the wave function is invariant with respect to 
> some description. Such as for entangled spins, the entangled wave function 
> has no description according to the spins. 
>
> In general relativity dynamics can be thought of as what extremizes the 
> action S = ∫d^4x sqrt(g)R, for R the Ricci curvature. Action and entropy 
> share an equivalency under the euclideanized map t/ħ = 1/kT for t time and 
> T temperature. We can also work this within complexity, and with quantum 
> gravitation the importance is with entanglement entropy or complexity. This 
> means that quantum gravitation is built from quantum states, which as we 
> all should be aware are not ontological entities in a standard sense. We 
> still have physics, in particular the aspect of physics that conveys 
> geometric or spatial relationship content, that is not ontologically solid. 
> This appears to be a fundamental aspect of physics, or at least physics as 
> we can understand.
>
> For this reason I think ideas that have spacetime composed of little 
> elements that are physical are not likely correct. This has been a long 
> standing critique I have of quantum gravitation theories outside of string 
> theory. This is not to say I think string theory has everything sewed up. 
> However, these various ideas such as LQG, DT and SD etc seem to have 
> category conflicts.
>
> LC
>
>
I should note that in my histories framework (which is all it is right now) 
I added

*29 Jan 2019*

By “historical paths (curves or walks)”, “Histories have a path 
representation as a sequence”, I mean sequence in terms of having a 
linearly ordered index I, so each element of the history is indexed:

            (στ,φ)ᵢ     i ∈ I



The type of "linearly ordered index" I is not specified, so it could be 
discrete or continuous, in principle.


- pt

 

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