What Keeps Discrete Spacetime Together at GR Scales?

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Discussion Overview

The discussion revolves around the nature of spacetime at quantum and general relativity (GR) scales, particularly focusing on the concept of discrete spacetime and what mechanisms might connect or separate spacetime at these different scales. The conversation touches on theoretical implications, philosophical questions, and the relationship between quantum mechanics and general relativity.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that a coarse-grained surface can appear smooth from a distance, suggesting a mechanism that connects discrete spacetime at larger scales.
  • Others argue that in a discrete spacetime, distances and times are fixed and irreducible, which raises philosophical questions about the nature of separation at quantum scales.
  • One participant mentions that discrete spacetime theories like causal set theory, CDT, and LQG approach quantum gravity by viewing gravity as a curvature issue rather than introducing gravitons.
  • A question is raised about the possibility of movement between discrete spacetime points, with a later reply challenging the definition of a straight line in this context.
  • Another participant suggests that movement might be described by a matrix of transition probabilities, where transitions between adjacent sites are more probable for macroscopic objects.
  • There is a discussion about the implications of size on quantum interactions, with one participant noting that larger macroscopic entities may face limitations in interacting with smaller quantum targets.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and remains unresolved regarding the mechanisms that connect or separate spacetime at different scales. Participants express differing opinions on the nature of movement in discrete spacetime and the implications of size on quantum interactions.

Contextual Notes

Participants express uncertainty about the definitions and implications of discrete spacetime, particularly regarding the physical status of distances between adjacent sites and the nature of movement in this framework.

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If spacetime is discrete at the Quantum/Sub-quantum scale, what "joins" and keeps spacetime together at GR scales?

P.S. What "Separates" spacetime at Quantum scales?
 
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The first question is easy. A coarse grained surface looks smooth from a distance.

The second question is more philosophical. In a discrete space-time it is assumed that distances and times come in fixed irreducible chunks.

One attraction of a discrete space time flows from how renormalization is done. Without renormalization, QM equations "blow up" into infinitities, while renormalization sets an arbitrary and consistent cutoff to prevent that from happening and this provides real answers. A discrete space time elevates renormalization from being a mere mathematical trick to an actual feature of space time, and since there is a naturally plausible set of discrete spaces and times (the Planck scale) it is plausible to look to that as the cutoff.

Discrete space-time theories like causal set theory, CDT and LQG all approach quantum gravity from the point of view of time space following GR which views gravity as a time-space curvature issue, rather than from the QM approach of creating a graviton.
 
Since spacetime is discrete at the Quantum/Sub-quantum scale, is it possible that something that occupied a discrete spacetime move to the other discrete through straight line?
 
the definition of straight line does not make sense when alluding to sites which are just neighbors, since the space between two adjacent sites don't have, in principle, a physical status.

Best Regards

DaTario
 
I agree with your opinion. So how do they travel? Do a matter, in Quantum/Subquantum scale, actually travel through higher dimension?
 
I would suggest something which is typical in the quantum formalism. I would suppose the existence of some system of coordinates in which, using this smallest scale, the triples would be always integer numbers. Then I would suggest that movement is in fact the consequence of existing a matrix of transition probability. Transitions from one triple to the other. Due the correspondence principle, adjacent site transitions generally are given higher probabilities when coming to macroscopic objects.
 
DaTario said:
I would suggest something which is typical in the quantum formalism. I would suppose the existence of some system of coordinates in which, using this smallest scale, the triples would be always integer numbers. Then I would suggest that movement is in fact the consequence of existing a matrix of transition probability. Transitions from one triple to the other. Due the correspondence principle, adjacent site transitions generally are given higher probabilities when coming to macroscopic objects.

Logically a Macro entity by virtue of size, will always have this as a limit to "hitting-quantum-targets", for instance if you have two marble's, one the size of Earth and one 'normal' size, then the Earth size will have a problem colliding with a small 'normal' size marble. Conversely, a normal size marble will have no problem at all in being directed to a marble the size of Earth.

Quantum entities have no HUP factors when being directed at Macro Targets, they are sure-fire probable certainties in hitting their targets.

HUP has a 'two-size' dependent principle factoring
 

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