What is Planck mass: Definition and 19 Discussions

In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants, in such a manner that these physical constants take on the numerical value of 1 when expressed in terms of these units.
Originally proposed in 1899 by German physicist Max Planck, these units are a system of natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one of several systems of natural units, but Planck units are not based on properties of any prototype object or particle (the choice of which is inherently arbitrary), but rather on only the properties of free space. They are relevant in research on unified theories such as quantum gravity.
The term Planck scale refers to quantities of space, time, energy and other units that are similar in magnitude to corresponding Planck units. This region may be characterized by energies of around 1019 GeV, time intervals of around 10−43 s and lengths of around 10−35 m (approximately respectively the energy-equivalent of the Planck mass, the Planck time and the Planck length). At the Planck scale, the predictions of the Standard Model, quantum field theory and general relativity are not expected to apply, and quantum effects of gravity are expected to dominate. The best-known example is represented by the conditions in the first 10−43 seconds of our universe after the Big Bang, approximately 13.8 billion years ago.
The four universal constants that, by definition, have a numeric value 1 when expressed in these units are:

the speed of light in a vacuum, c,
the gravitational constant, G,
the reduced Planck constant, ħ,
the Boltzmann constant, kB.Planck units do not incorporate an electromagnetic dimension. Some authors choose to extend the system to electromagnetism by, for example, adding either the electric constant ε0 or 4πε0 to this list. Similarly, authors choose to use variants of the system that give other numeric values to one or more of the four constants above.

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  1. Alpha2021

    A Is M_{Pl} the Planck mass or the reduced Planck mass?

    What is the value of M_{Pl} used in the Planck (CMB) collaboration's observation papers, such as the one referenced in this link: https://arxiv.org/pdf/1807.06211.pdf. Specifically, I am wondering if it refers to the Planck mass or the reduced Planck mass?
  2. G

    I Why does nothing happen at the Planck mass?

    It appears as clear to me that the Planck mass has a fundamental role, since for it the deBroglie wavelength and the Schwarzschild radius are equal. So it is some borderline between elementary particles and black holes. What intrigues me, however, is that the universe is mostly made up of...
  3. George Keeling

    I Comparing Planck's Mass, Length, Time and Energy

    Sean Carroll gives the Planck's set of four dimensioned quantities: Planck's mass, length, time and energy. I wanted to compare them with actual things.\begin{align} m_p=\sqrt{\frac{\hbar c}{G}}&=2.18\times{10}^{-8}\rm{kg}&\rm{{10}^{7}\ E. coli}\phantom {100000000000000000000}&\phantom...
  4. J

    I Why don't strings have a Planck mass?

    I understand that strings have a size of roughly the Planck length ##l_P## of ##10^{-35}## m. If that is the case then one would expect that their mass would be roughly the Planck mass which is an enormous ##10^{19}## GeV. (Strings that have small spins, like standard model particles, are...
  5. J

    B Direct detection of Planck mass WIMPs?

    Are the current dark matter detection experiments sensitive to Planck mass WIMPs? I've just looked at the Wikipedia WIMP article. It shows the excluded parameter space for the CDMS experiment with WIMP-nucleon cross section vs WIMP mass curves but they only go up to a WIMP mass of 1000 GeV.
  6. Auto-Didact

    A Erebons: Planck mass Dark Matter particles

    Erebon theory is a novel explanation of dark matter recently invented by Roger Penrose. Erebons are scalar particles of the order of a Planck mass which can only interact gravitationally. When erebons decay, they release their energy as oscillating classical gravitational waves on the order of...
  7. C

    B Understanding Planck Mass and Gravity Formula for the Hierarchy Problem

    from the formula M_p=\sqrt{\frac{\hbar c}{G} If gravity is weak.. Planck mass is huge. Does the formula assumes whether general relativity is classical limit of some quantum theory or whether general relativity needs quantization? Because the problem with the Hierarchy problem in the...
  8. sevenperforce

    Stellar-mass black hole formation sequence

    I feel like this could go in quite a few of the Physics subforums (Quantum Physics, Beyond the Standard Model, Special and General Relativity, or High Energy, Nuclear, Particle Physics) instead of Astronomy and Cosmology, but hopefully this will work. This is my first question I've posed here...
  9. K

    Confusion Related to Planck Mass

    Hi all, According to quantum mechanics, the graviton is the measure of the smallest amount of curvature possible in space-time. I read that the mass which would be required to create this curvature is Planck Mass which is close to the value 10^-5g. But the elementary particles, like electrons...
  10. F

    Age of Universe in Planck normalized units

    Hello, I've a problem. I need to find the age of universe in normalized Planck units. In my case, I'm using Planck mass = 1 and: ##H = 1.18 × 10^{-61} \times t_P^{- 1}## With these values, how can I find the age of the universe? Thanks!
  11. newjerseyrunner

    Are Primordial Black Holes Still a Viable Candidate for Dark Matter?

    I've been reading about black holes and dark matter and came across this theory: http://www.nature.com/nature/journal/v329/n6137/abs/329308a0.html where black holes don't completely evaporate, but evaporate until it hits an equilibrium where it's both unable to evaporate anymore (making it...
  12. V

    Upper Energy Limit in Field Theory: Exploring Quantum Gravity

    I see that we use dimensional analysis involving constants of nature to obtain the Planck length and then apply the uncertainty principle to find the corresponding Planck mass-energy. But the energy and length scales were found by invoking a "particle" interpretation of fundamental entities of...
  13. jbunch

    Gravitational Forces on Mass < Planck Mass: Evidence?

    Is there any experimental or observational evidence that conclusively shows gravitational forces acting on mass that is less than the Planck mass? thx
  14. J

    Why don't strings have a huge Planck mass?

    If a string has a Planck length then why doesn't it have a huge Planck mass? Perhaps it does but its negative gravitational self-energy counteracts this huge positive mass/energy. Maybe a closed string can be thought of as a Planck energy electromagnetic wave trapped by its own...
  15. F

    The W boson mass is exp(-4pi^2) of a Planck mass

    Almost: the result is 85 GeV, the measured mass is 80.4 GeV. Is there anybody who has ever looked at this coincidence? François
  16. R

    Large Extra Dims and a derived Planck Mass

    Hey folks, I just had a thought I wanted to share with you guys. Just to review first the idea of Large extra dims before I make the comment: The higher dimensional Einstein-Hilbert action is given by S_{bulk}=-\frac{1}{2}\int d^{4+n}x\sqrt{g^{4+n}}\tilde{M}^{n+2}\tilde{R} where...
  17. C

    Planck mass; time; length derived out of air?

    Greetings, Anyone know how the Planck mass, Planck time, and Planck length were derived in the first place? Please cite experiments or mathematics to support your comment as I'd like to intimately understand this, not just from a metaphorical standpoint. Thanks a bunch, Chaos' lil bro.
  18. G

    Exploring the Mystery of the Planck Mass: Why is it So Big?

    If I understand well, Planck units are fundamental in the sense that they don't depend on any arbitrary choice of measurement scale, but they emerge directly from the laws of physics. For Planck length and Planck time, this seems to fit with the widespread belief that they may well also be...