Surface volume of 3-sphere with radius of 2 Planck length?

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Discussion Overview

The discussion revolves around the calculation of the surface area (referred to as "surface volume") of a 3-sphere with a radius of 2 Planck lengths. Participants also explore the relationship between this volume and the product of Planck's constant, Einstein's proportionality constant, and Planck time, questioning the significance of any potential equivalence.

Discussion Character

  • Technical explanation, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant asks for the surface area of a 3-sphere with a radius of 2 Planck lengths and questions if it relates to the product of Planck's constant, Einstein's proportionality constant, and Planck time.
  • Another participant cites a formula from Wikipedia for the cubic hyperarea of a 3-sphere, suggesting it answers the mathematical question posed.
  • Some participants express confusion over the terms being used, particularly regarding the distinction between area and volume, and the meaning of the radius in the context of the discussion.
  • There is a challenge regarding the ability to equate the proposed quantities, with one participant suggesting that proving the equivalence would be trivial.
  • Repeated inquiries about the significance of the proposed equivalence indicate a lack of clarity on the implications of the relationships being discussed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the significance of the relationships discussed, and there is disagreement regarding the clarity of the terms and concepts being used.

Contextual Notes

There are unresolved questions about the definitions of "surface volume," the specific relationships between the constants mentioned, and the mathematical steps required to establish any equivalence.

mitrasoumya
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What is the surface area ("surface volume") of a 3-sphere having a radius of 2 Planck lengths?

Is the product of the Planck's constant, Einstein's proportionality constant and Planck time also equal to this volume?

Does this equivalence signify anything? What does it signify?
 
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According to wikipedia, the 3-dimensional cubic hyperarea of a 3-sphere of radius r is 2 pi^2 r^3, which should answer your math questions.
 
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Gigaz said:
According to wikipedia, the 3-dimensional cubic hyperarea of a 3-sphere of radius r is 2 pi^2 r^3, which should answer your math questions.

Is the product of the Planck's constant, Einstein's proportionality constant and Planck time also equal to this volume (i.e. where r=2 Planck lengths)?

Does this equivalence signify anything?

What does it signify?
 
I see you are still ignoring what people are telling you about the Planck length. There's no magic to it.

mitrasoumya said:
Is the product of the Planck's constant, Einstein's proportionality constant and Planck time also equal to this volume (i.e. where r=2 Planck lengths)?

Well, you need to make up your mind what you are trying to say. Area? Volume? r? 2r?

mitrasoumya said:
Does this equivalence signify anything?

If you're actually able to get things so the things you are purporting to be equal to actually be equal - something you haven't yet done - you will have proven π = π.
 
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Vanadium 50 said:
Well, you need to make up your mind what you are trying to say. Area? Volume? r? 2r? .
I'll try to reword that. What I am saying is - the product of Planck's constant, Einstein's proportionality constant and Planck time is equal to the "surface" volume of a 3-sphere having the radius of 2 Planck lengths.

Vanadium 50 said:
If you're actually able to get things so the things you are purporting to be equal to actually be equal - something you haven't yet done - you will have proven π = π.
I am sorry I could not understand this part.
 

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