Sampling at 1/n Planck Time: Synchronizing Samplers and Analyzing Data Values

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Discussion Overview

The discussion revolves around the feasibility of synchronizing multiple samplers to sample a system at 1/n Planck time. Participants explore the implications of such sampling on the data values between adjacent samples, considering theoretical and practical limitations.

Discussion Character

  • Debate/contested, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants question the theoretical possibility of synchronizing n samplers at 1/n Planck time, suggesting it may not be feasible.
  • One participant argues that the conclusions drawn from sampling are limited by the Heisenberg Uncertainty Principle (HUP), referencing Hardy's Paradox to illustrate logical contradictions that arise from attempting to sample beyond these limits.
  • Another participant points out that achieving such sampling would require rates of 10^44 times per second, which exceeds the capabilities of current analog-to-digital converters by approximately 33 orders of magnitude.
  • A further inquiry is made regarding the relevance of the Nyquist–Shannon sampling theorem, with a suggestion that quantum mechanical wave functions may have limited bandwidth, affecting the sampling discussion.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of the proposed sampling method, with some asserting it is not theoretically possible while others explore related concepts without reaching a consensus.

Contextual Notes

The discussion highlights limitations related to theoretical assumptions, the implications of the Heisenberg Uncertainty Principle, and the practical constraints of current technology in sampling rates.

Hippasos
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Can we synchronize n samplers so that the system is being sampled at 1/n Planck time?

What could we tell about the data values between two adjacent samples?
 
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Hippasos said:
Can we synchronize n samplers so that the system is being sampled at 1/n Planck time?

What could we tell about the data values between two adjacent samples?

1. Not theoretically possible.

2. Nothing, there are theorems about making assumptions between any 2 sample points. The conclusions are limited by the HUP and attempts to go past that lead to logical contradictions (and results are as predicted by QM). See Hardy's Paradox for example.
 
No, because tat would require us to sample 10^44 times/s.
Which is about 33 orders of magnitude faster than the fastest A/D converter we can currently build.
 
Is this thread referring to the Nyquist–Shannon sampling theorem of band-limited functions? I believe that most QM wave functions have a limited bandwidth (if they spatially limited then they are usually limited in momentum-space also).
 

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