Can you imagine geometry without matter and light?

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Discussion Overview

The discussion centers around the concept of geometry in the absence of matter and light, exploring whether geometry can exist meaningfully without physical entities. Participants examine the implications of an empty universe on geometric principles, considering both theoretical and mathematical perspectives.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that geometry is inherently tied to matter and cannot be conceived meaningfully without it, suggesting that distances and angles require physical entities to measure.
  • Others propose that from a mathematical standpoint, geometry can exist independently of physical reality, with some asserting that various geometries do not necessitate a physical interpretation.
  • A few participants mention specific solutions in general relativity, such as de Sitter and anti-de Sitter spaces, which exhibit curvature without matter, raising questions about the independence of space from matter.
  • There is a suggestion that empty space could have its own energy, potentially allowing for a form of geometry that exists apart from matter.
  • Some participants express skepticism about the meaningfulness of discussing geometric concepts in a universe devoid of matter, questioning the relevance of mathematical results in such a scenario.
  • One participant introduces the idea of thermal behavior in empty space-time metrics, implying a connection between geometry and the collective behavior of particles.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the relationship between geometry, matter, and the physical universe. Some maintain that geometry is meaningless without matter, while others argue for its mathematical independence.

Contextual Notes

Participants highlight the importance of defining "geometry" in the context of the discussion, noting that different interpretations may lead to varying conclusions about its relationship with physical reality.

  • #31
It is not exactly the same situation as with the electrostatic potential. Here we know what all of space and time is and can tell whether there is more space other than the region with no charge.
 
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  • #32
us40 said:
First of all thanks for your reply and to put my question as thread.

What I am try to say about is we are approaching de sitter phase and universe was also in de sitter phase when inflation epoch started.(http://en.wikipedia.org/wiki/De_Sitter_universe).So all matter and energy will be diluted so nothing left but ever expanding space with cosmological constant.So doesn't it mean that space was there before big bang when all matter and radiation created and after there when all will be diluted so space is not property of big bang but only time is.Means time is created with big bang and it may be the reason time has property like arrow but space does not because entities that perceive time creates with big bang.While space doesn't need it.(Here I think an analogy,if you drink coffee you need mug first,and after you drink coffee mug is still there.But when coffee was there it increase temperature the surface of mug,like when universe was in matter dominated era expansion of universe is slower,but after you consume your coffee,mug retain its temperature and like that space retain its energy dominated properties again.)

Please reply...
 
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