Editing Quantum foam (section)

===Constraints on the size of quantum fluctuations===

The fluctuations characteristic of a spacetime foam would be expected to occur on a length scale on the order of the [[Planck length]] (≈&nbsp;10<sup>−35</sup>&nbsp;m),<ref name="Hawking1978">{{cite journal |last1=Hawking |first1=Stephen W. |date=November 1978 |title=Spacetime foam |journal=Nuclear Physics B |volume=144 |issue=2–3 |pages=349–362 |bibcode=1978NuPhB.144..349H |doi=10.1016/0550-3213(78)90375-9}}</ref> but some models of [[quantum gravity]] predict much larger fluctuations.

Photons should be slowed by quantum foam, with the rate depending on the wavelength of the photons. This would violate [[Lorentz invariance]]. But observations of radiation from nearby [[quasar]]s by Floyd Stecker of [[NASA|NASA's]] [[Goddard Space Flight Center]] failed to find evidence of violation of Lorentz invariance.<ref>{{cite web|url=http://www.nasa.gov/centers/goddard/news/topstory/2003/1212einstein.html|title=Einstein makes extra dimensions toe the line|publisher=NASA|access-date=9 February 2012|archive-date=18 July 2019|archive-url=https://web.archive.org/web/20190718093350/https://www.nasa.gov/centers/goddard/news/topstory/2003/1212einstein.html|url-status=dead}}</ref>

A foamy spacetime also sets limits on the accuracy with which distances can be measured because photons should diffuse randomly through a spacetime foam, similar to light diffusing by passing through fog. This should cause the image quality of very distant objects observed through telescopes to degrade. X-ray and gamma-ray observations of quasars using NASA's [[Chandra X-ray Observatory]], the [[Fermi Gamma-ray Space Telescope]] and ground-based gamma-ray observations from the [[VERITAS|Very Energetic Radiation Imaging Telescope Array]] (VERITAS) showed no detectable degradation at the farthest observed distances, implying that spacetime is smooth at least down to distances 1000 times smaller than the nucleus of a hydrogen atom,<ref>{{cite web | url=https://www.nasa.gov/mission_pages/chandra/nasa-telescopes-set-limits-on-spacetime-quantum-foam.html | title=NASA Telescopes Set Limits on Spacetime Quantum "Foam" | date=28 May 2015 }}</ref><ref>{{Cite web|title = Chandra Press Room :: NASA Telescopes Set Limits on Space-time Quantum "Foam":: 28 May 15|url = http://chandra.si.edu/press/15_releases/press_052815.html|website = chandra.si.edu|access-date = 2015-05-29}}</ref><ref>{{Cite web |title=Chandra X-ray Observatory – NASA's flagship X-ray telescope |url=http://chandra.si.edu/ |access-date=2015-05-29 |website=chandra.si.edu}}</ref><ref>{{Cite journal|title =  New Constraints on Quantum Gravity from X-ray and Gamma-Ray Observations|journal = The Astrophysical Journal|volume = 805|pages = 10|arxiv = 1411.7262|last1 =  Perlman|first1 = Eric S.|last2 =  Rappaport|first2 = Saul A.|last3 =  Christensen|first3 = Wayne A.|last4 =  Jack Ng|first4 = Y.|last5 = DeVore|first5 = John|last6 = Pooley|first6 = David|year = 2014| issue=1 |doi = 10.1088/0004-637X/805/1/10|bibcode=2015ApJ...805...10P|s2cid = 56421821}}</ref><ref>{{Cite web|title = Chandra :: Photo Album :: Space-time Foam :: May 28, 2015|url = http://chandra.si.edu/photo/2015/quantum/|website = chandra.si.edu|access-date = 2015-05-29}}</ref> setting a bound on the size of quantum fluctuations of spacetime.