Distribution Function of the Atoms of Spacetime and the Nature of Gravity
The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-10-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/11/7420 |
| _version_ | 1811278980884463616 |
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| author | Thanu Padmanabhan |
| author_facet | Thanu Padmanabhan |
| author_sort | Thanu Padmanabhan |
| collection | DOAJ |
| description | The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter should appear in the variational principle through the combination Tabnanb where na is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area! |
| first_indexed | 2024-04-13T00:46:45Z |
| format | Article |
| id | doaj.art-81fcf1eebfd54fc0ba8c003bb9d6d457 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T00:46:45Z |
| publishDate | 2015-10-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-81fcf1eebfd54fc0ba8c003bb9d6d4572022-12-22T03:09:59ZengMDPI AGEntropy1099-43002015-10-0117117420745210.3390/e17117420e17117420Distribution Function of the Atoms of Spacetime and the Nature of GravityThanu Padmanabhan0IUCAA, Pune University Campus, Ganeshkhind, Pune 411007, IndiaThe fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter should appear in the variational principle through the combination Tabnanb where na is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area!http://www.mdpi.com/1099-4300/17/11/7420spacetime entropyemergent gravitycosmological constanthorizon entropyquantum gravityzero-point lengthhorizon thermodynamics |
| spellingShingle | Thanu Padmanabhan Distribution Function of the Atoms of Spacetime and the Nature of Gravity Entropy spacetime entropy emergent gravity cosmological constant horizon entropy quantum gravity zero-point length horizon thermodynamics |
| title | Distribution Function of the Atoms of Spacetime and the Nature of Gravity |
| title_full | Distribution Function of the Atoms of Spacetime and the Nature of Gravity |
| title_fullStr | Distribution Function of the Atoms of Spacetime and the Nature of Gravity |
| title_full_unstemmed | Distribution Function of the Atoms of Spacetime and the Nature of Gravity |
| title_short | Distribution Function of the Atoms of Spacetime and the Nature of Gravity |
| title_sort | distribution function of the atoms of spacetime and the nature of gravity |
| topic | spacetime entropy emergent gravity cosmological constant horizon entropy quantum gravity zero-point length horizon thermodynamics |
| url | http://www.mdpi.com/1099-4300/17/11/7420 |
| work_keys_str_mv | AT thanupadmanabhan distributionfunctionoftheatomsofspacetimeandthenatureofgravity |