Uncertainty principle from the noise of gravitons
Abstract The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023) . There the authors have calculated the quantum gravity modified Newton’s law of free fall where t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-02-01
|
| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-12481-7 |
| _version_ | 1797209177250070528 |
|---|---|
| author | Soham Sen Sunandan Gangopadhyay |
| author_facet | Soham Sen Sunandan Gangopadhyay |
| author_sort | Soham Sen |
| collection | DOAJ |
| description | Abstract The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023) . There the authors have calculated the quantum gravity modified Newton’s law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum. |
| first_indexed | 2024-03-07T14:45:17Z |
| format | Article |
| id | doaj.art-fd601aa7268b41ce9263f1a0ea14832b |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T09:50:33Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-fd601aa7268b41ce9263f1a0ea14832b2024-04-14T11:26:48ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-02-0184211110.1140/epjc/s10052-024-12481-7Uncertainty principle from the noise of gravitonsSoham Sen0Sunandan Gangopadhyay1Department of Astrophysics and High Energy Physics, S. N. Bose National Centre for Basic SciencesDepartment of Astrophysics and High Energy Physics, S. N. Bose National Centre for Basic SciencesAbstract The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023) . There the authors have calculated the quantum gravity modified Newton’s law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum.https://doi.org/10.1140/epjc/s10052-024-12481-7 |
| spellingShingle | Soham Sen Sunandan Gangopadhyay Uncertainty principle from the noise of gravitons European Physical Journal C: Particles and Fields |
| title | Uncertainty principle from the noise of gravitons |
| title_full | Uncertainty principle from the noise of gravitons |
| title_fullStr | Uncertainty principle from the noise of gravitons |
| title_full_unstemmed | Uncertainty principle from the noise of gravitons |
| title_short | Uncertainty principle from the noise of gravitons |
| title_sort | uncertainty principle from the noise of gravitons |
| url | https://doi.org/10.1140/epjc/s10052-024-12481-7 |
| work_keys_str_mv | AT sohamsen uncertaintyprinciplefromthenoiseofgravitons AT sunandangangopadhyay uncertaintyprinciplefromthenoiseofgravitons |