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In physics, the Planck time (t_P), is the unit of time in the system of natural units known as Planck units. It is the time it would take a photon travelling at the speed of light to cross a distance equal to the Planck length.^[1] The unit is named after Max Planck.

It is defined^[1] as

where:

is the reduced Planck constant

G is the gravitational constant

c is the speed of light in a vacuum

t_P is in seconds.

The two digits between the parentheses denote the uncertainty in the last two digits of the value.

Contents 1 Significance 2 Derivation 3 See also 4 References

According to the Big Bang theory nothing is known about the universe at time=0, though it is presumed that all fundamental forces coexisted and that all matter, energy, and spacetime expanded outward from an extremely hot and dense singularity. One planck time after the event is the closest that theoretical physics can get us to it, and at that time it appears that gravity separated from the other fundamental forces.

The estimated age of the Universe in the Big Bang theory () would be roughly Planck times. The average life expectancy of a human is approximately Planck times.

As of 2006, the smallest unit of time that has been measured is on the order of the attosecond (10 ^{− 18}) timescale - or around 10²⁶ Planck times. ^[2][3]

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Ignoring a factor of π, the Planck mass is roughly the mass of a black hole with a Schwarzschild radius equal to its Compton wavelength. The radius of such a black hole would be, roughly, the Planck length.

The following thought experiment illuminates this fact. The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in principle, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision greater than one Planck length.

This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision greater than the Planck length, or duration to a precision greater than the time a photon moving at c would take to travel a Planck length. Hence in any theory of quantum gravity combining general relativity and quantum mechanics, traditional notions of space and time will break down at distances shorter than the Planck length or times shorter than the Planck time.

• 1 E-44 s
• Planck epoch

1. ^ ^{a b} Big Bang models back to Planck time. Georgia State University (19 June 2005).
2. ^ Shortest time interval measured. BBC News (25 February 2004).
3. ^ Fastest view of molecular motion. BBC News (4 March 2006).

Planck's natural units

Base Planck units: Planck time  | Planck length  | Planck mass  | Planck charge  | Planck temperature

Derived Planck units: Planck energy  | Planck force  | Planck power  | Planck density  | Planck angular frequency  | Planck pressure  | Planck current  | Planck voltage  | Planck impedance  | Planck momentum