# Planck time

In physics, the Planck time (tP) is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length.1 The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:2

$t_P \equiv \sqrt{\frac{\hbar G}{c^5}}\approx 5.39106 (32) \times 10^{-44} \mbox{ s}$

where:

$\hbar = h / 2 \pi$ is the reduced Planck constant (sometimes $h$ is used instead of $\hbar$ in the definition1)
G = gravitational constant
c = speed of light in a vacuum
s is the SI unit of time, the second.

The two digits between parentheses denote the standard error of the estimated value.

## Physical significance

One Planck time is the time it would take a photon traveling at the speed of light in a vacuum to cross a distance equal to one Planck length. Theoretically, this is the smallest time measurement that will ever be possible,3 roughly 10−43 seconds. Within the framework of the laws of physics as we understand them today, for times less than one Planck time apart, we can neither measure nor detect any change. As of May 2010, the smallest time interval uncertainty in direct measurements is on the order of 12 attoseconds (1.2 × 10−17 seconds), about 3.7 × 1026 Planck times.4

The Planck time comes from a field of mathematical physics known as dimensional analysis, which studies units of measurement and physical constants. The Planck time is the unique combination of the gravitational constant G, the relativity constant c, and the quantum constant h, to produce a constant with units of time. For processes that occur in a time t less than one Planck time, the dimensionless quantity tP / t is greater than one. Dimensional analysis suggests that the effects of both quantum mechanics and gravity will be important under these circumstances, requiring a theory of quantum gravity. All scientific experiments and human experiences happen over billions of billions of Planck times, making any events happening at the Planck scale hard to detect.

Analysis of the Hubble Space Telescope's deep field images in 2003 led to a debate about the physical implications of the Planck time as a physical minimum time interval. According to Lieu and Hillman,5 speculative theories of quantum gravity "foam" where there are space–time fluctuations on the Planck scale predict that images of extremely distant objects should be blurry. However, blurring was not seen in the Hubble images, which was claimed to be problematic for such theories.6 Other authors have disputed this, in particular Ng et al.,7 who stated that the blurring effect was overestimated by Lieu and Hillman by factors of between 1015 and 1030, and thus the observations are very much less effective in constraining theory: "the cumulative effects of spacetime ﬂuctuations on the phase coherence of light [in certain theories of 'foamy' spacetime] are too small to be observable".

## Notes and references

1. ^ a b "Big Bang models back to Planck time". Georgia State University. 19 June 2005.
2. ^ CODATA Value: Planck Time – The NIST Reference on Constants, Units, and Uncertainty.
3. ^ "Planck Time". COSMOS - The SAO Encyclopedia of Astronomy. Swinburne University.
4. ^ "12 attoseconds is the world record for shortest controllable time". 2010-05-12. Retrieved 2012-04-19.
5. ^ Lieu, Richard; Hillman, Lloyd W. (2003-03-10). "The Phase Coherence of Light from Extragalactic Sources: Direct Evidence against First-Order Planck-Scale Fluctuations in Time and Space". The Astrophysical Journal 585 (2): L77–L80. arXiv:astro-ph/0301184. Bibcode:2003ApJ...585L..77L. doi:10.1086/374350.
6. ^ "Hubble Pictures Too Crisp, Challenging Theories of Time and Space". Space.com. 2003-04-02. Retrieved 2008-05-30.
7. ^ Ng, Y. Jack; Christiansen, W. A.; van Dam H. (2003-07-10). "Probing Planck-Scale Physics with Extragalactic Sources?". The Astrophysical Journal Letters (The American Astronomical Society) 591 (2): L87–L89. arXiv:astro-ph/0302372. Bibcode:2003ApJ...591L..87N. doi:10.1086/377121.