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

Hmm… It contradicts only a digital or discrete version of space. Once we agree 
to assume a continuum, we accept the traditional notion of limits (Cauchy, 
Dedekind) and that solves, bu the usual method, the Zeno paradox. Even the 
antic greeks got this already. It was a paradox because it was thought that an 
infinite sum of non null quantity has to be infinite, but that is not the case.
With mechanism, the structure of space-time is an open problem, but if it is 
discrete, then something else need to be continuous  (it could be “only” the 
amplitude of the wave, usually treated with real/complex numbers).

Bruno




> 
> - pt 
> 
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