#planck units

[leapingmonkeys]

Physicists May Have Found a Hard Limit on The Performance of Large Quantum Computers

[blindmen6]

Planck length

In physics, the Planck length, denoted ℓP, is a unit of length, equal to 1.616199(97)×10−35  metres. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.

Value

The Planck length ℓP is defined as

where is the speed of light in a vacuum, G is the gravitational constant, and ħ is the reduced Planck constant. The two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value.

The Planck length is about 10−20 times the diameter of a proton, and thus is exceedingly small.

Theoretical significance

There is currently no proven physical significance of the Planck length; it is, however, a topic of theoretical research. Since the Planck length is so many orders of magnitude smaller than any current instrument could possibly measure, there is no way of examining it directly. According to the generalized uncertainty principle (a concept from speculative models of quantum gravity), the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that.

In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart. The precise effects of quantum gravity are unknown; it is often guessed that spacetime might have a discrete or foamy structure at a Planck length scale.

Visualization

The size of the Planck length can be visualized as follows: if a particle or dot about 0.1 mm in size (which is approximately the smallest the unaided human eye can see) were magnified in size to be as large as the observable universe, then inside that universe-sized "dot", the Planck length would be roughly the size of an actual 0.1 mm dot. In other words, a 0.1 mm dot is halfway between the Planck length and the size of the observable universe on a logarithmic scale.

For an interactive visualization of scale throughout the universe see here.

[prettyphysicsformulae]

By Maita.

[ordinalitis]

Are we in a simulated universe? Well it'd be pretty easy to tell the signs of a computer program. Like if there were a maximum speed, or minimum temperature. Maybe fundamental quantities, like mass, momentum, energy, and time could have minimum error bounds. Things would probably be discrete, like minimum distances and time intervals.

[sciencesoup]

The Quantum of Time

If I ask you for the smallest unit of time you can possibly think of, you might suggest a second, or a millisecond, or a nanosecond if you’re clever. But while these units are small enough to measure everyday events, physicists have to deal with cosmological forces and events on incredibly tiny scales, so they need to use appropriately tiny units to measure them. In 1899, German physicist Max Planck (who was also, incidentally, the founder of quantum theory) proposed a system of natural units of measurement called Planck units, stated in terms of five universal physical constants: the Gravitational constant, the Reduced Planck constant, the speed of light in a vacuum, the Coulomb constant, and Boltzmann’s constant. The system is based on the idea that space and time aren’t continuous—they’re quantised, which means that there’s a shortest possible measurable length (called Planck length) and a shortest possible measurable time (called, surprise, Planck time). Planck length is roughly 1.616 × 10-35 metres, and Planck time is the amount of time it takes for a photon to travel a single Planck length, i.e. 5.391 × 10−44 seconds. This is an unimaginably small quantity, but it helps to define the unimaginable small scale at which current physical theories break down—and helps physicists to study the beginning of the Universe, where the sequence of events in its early evolution was crammed into minute fractions of time.