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I have been curious to find what could be the significance of Planck force? It is calculated by the formula $c^4/G = 1.21031359\times 10^{44} \, \mathrm{N}$, where $c$ is the speed of light and $G$ is the gravitational constant.

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The maximal possible force in universe is something that scientists missed to consider, and if they would consider it, then everything what they have done so far would not be worth a dime, ranging from "point-like particles" and up to the "Big Bang". Point-like particle (i.e. photon), or any other imaginary (invented) structure (i.e. strings (line-like sub-Planck-entities), branes (surface-like sub-Planck entities), ..., would be totally invalid structures, because if there is the constraint Fmax, then only and exclusively 3D-particles would be possible. Any particle is, essentially, energy. Force is dE/ds. If we would have, i.e., a particle which has less then 3 dimensions, then the derivative dE/ds along the missing dimension ds would be infinite. In other words, the existence of some 2D (x,y) particle, would require infinite forces all over the x-y-plane along the z-axis, in order to maintain such particle, the 2D particle. In the case of a photon, which is considered to be 0D particle (point-like particle), it could be formed only by infinite forces along each of the lines which go through the point. And, while exchanging its energy with some other particle, a photon would be able to release infinite force upon that other particle. And, that is something what never happens in reality. Simply because all these concepts are wrong. Impossible. There exist the constraint Fmax. And that constraint has nothing to do with Planck (that is another misguidance, present throughout books and internet - these books are the books from which students on each renowned university in the world learn. That is what the most renowned physicists teach their students. That Fmax "is the Planck's force", and that "a photon is point-like particle", and that "Fmax is not the real constraint, but just/only something that is useful for normalization of units").

The Coulomb's law is: $$ F = \frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r^2} $$ And, we know that $\epsilon_0 $ is an important physical property. Which is detected, which is measured. Which is important property of - let us say it in the most general way - existence.

The Newton's law of gravitation is $$ F=G\frac{m_1 m_2}{r^2} $$ where G is also an important physical quantity, detected, measured. Important property of existence. But, we can write Newton's law in a more fundamental way: mass is the package of energy, and the relation among mass and energy is $ m=\frac{E}{c^2} $. c is the maximal possible velocity with which some energy amount can move through the space. So, c is constraint, the upper limit. $$ F = G\frac{\frac{E_1}{c^2} \frac{E_2}{c^2}}{r^2} $$ $$ F = \frac{G}{c^4} \frac{E_1}{r} \frac{E_2}{r} $$ $$ \frac{c^4}{G} F = \frac{E_1}{r} \frac{E_2}{r} $$ $$ F_{max} F = \frac{E_1}{r} \frac{E_2}{r} $$ So, it is completely scientifically legitimate to consider Fmax to be the real constraint. Because, it explicitly appears when we write the Newton's law in the more essential form. If we do not accept that Fmax is really the maximal possible force, then we do not accept that the c is the maximal possible velocity, and/or that G is the constant. And, when we consider Fmax to be the real constraint, then we can easily explain many "inexplicable" things in current/actual physicses, and also the unification of physics becomes an easy thing to do.

There are only two official papers (published papers) which consider the Fmax as the real constraint: 1) http://arxiv.org/abs/physics/0607090 and 2) Зборник радова I (Scientific Proceedings I), ISSN 2217-4362, page 255, title: "Увод у фотонску фундаменталну физику" ("Introduction to the photonic fundamental physics")]

Both are totally ignored by the scientific community.

The 2) is more fundamental, requires only secondary-school math (which is normal, because, fundamental things are simple), and unifies physics.

The extended versions of 2), and written in English, you can find on internet here: http://www.science20.com/the_gem_10-169631

"The noblest pleasure is the joy of understanding" - Leonardo da Vinci So, enjoy! And also: "Observe and think in order to discover the truth. Do not believe what is contrary to reason, and never deceive yourself or others."


@Asher

(and to those 3 persons who think that his comment "adds something useful to the post")

https://en.wikipedia.org/wiki/Electron%E2%80%93positron_annihilation https://en.wikipedia.org/wiki/Annihilation#Proton-antiproton_annihilation https://en.wikipedia.org/wiki/Two-photon_physics

1) each and every real particle is, essentially, the energy package

2) photon is the energy packet. In reality, it has to be the 3D entity. It has to have some energy distribution along each and every direction which goes through it. Since the essential equation of a photon is $E_{ph}\cdot t_{ph} = h$ (where $t_{ph}$ is the time during which the whole energy of the photon passes through some imaginary plane which is perpendicular to the photon’s path), and since it has all derivatives, and since there exist the constraint $F_{max}$, and the constraint $v_{max}$ (or $c$, as it is usually denoted), the distribution of photon’s energy has to be smoothly continual http://mathworld.wolfram.com/SmoothFunction.html https://en.wikipedia.org/wiki/Smoothness So, the photon’s energy distribution has to be some smoothly continual energy bump (i.e. Gaussian-like), along each direction $s$ which goes through it. Draw it. Force is $F = dE/ds$. What is the direction of $F$? It is always towards the center of the bumpy energy distribution. In other words, the bumpy energy distribution maintains its own shape. The forces which maintain it are the result of the very existence of localized energy.

3) see 1), and the links above. Also, consider the energy balances of each and every nuclear reaction/interaction. Any mass $m$ contains the amount of energy $E = m\cdot c^2$. There is nothing which „does not allow us to simply replace mass with energy divided by velocity.“

„We can't solve problems by using the same kind of thinking we used when we created them.“ – A. Einstein Please, follow the link http://www.science20.com/the_gem_10-169631 , to see on your own that is possible to really understand the essentials of the world we live in.


@ Ilja

I do not know why do you use the word "understand". You study physics. That what you learn on physics faculty has nothing to do with understanding - it is mysticism, the magic:

"There are two kinds of geniuses: the 'ordinary' and the 'magicians'. An ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they've done, we feel certain that we, too, could have done it. It is different with the magicians. Even after we understand what they have done, it is completely dark. Richard Feynman is a magician of the highest calibre." Mark Kac (https://en.wikipedia.org/wiki/Mark_Kac)

“Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd.” (Richard Feynman)

"I think I can safely say that nobody understands quantum mechanics." (Richard Feynman)

So, do you want to say that you understand that what Feynman (and other 20- and 21- century gurus/magicians) did?

And you see, now, you are incapable to understand perfectly simple reasonable things.

Starting from "uncertainty", "spontainety", "relativity", absurdity, it is not possible to make anything sensful/reasonable. You can, though, make a mathematical construction which describes the reality, but that is only the description, like a painting.

Starting from "uncertainty", "spontainety", "relativity", absurdity, there are unlimited options. Which one to choose? Those which some great authority, great visionary, proposes. There are other, equally valid (actually: invalid) options, but these are not accepted.

Authorities do not allow that. Because, they would not be authority anymore.

The fundamentals of reality cannot be invented, they can only be discovered.

There is no "an IDEA, so beautiful, so simple, ..." (Achibald Wheeler), but there are the basic, fundamental FACTS (concrete, fundamental physical phenomena, i.e. photon, electric permittivity and magnetic permeability of SPACE (of SPACE: el.permit. and magn.permeab. are the properties of SPACE)), which just have to be recognized, together with a few basic, fundamental equations, and everything becomes simple, clear, completely comprehensible.

I am trying to explain things to people who are still reasonable, those who still did not pass "the point of no return".

There is no other way to derive (actually: to discover) Fmax than the one presented here. And that, obviously, has nothing, absolutely nothing to do with Planck.

And, only after one has discovered Fmax, in this, here presented way, one can then continue to "play" with it, applying that constraint on length, energy, mass, charge, etc.

And not only that the here presented discovering/revealing of Fmax has nothing to do with Planck, but it also has nothing to do with Einstein (his relativity theories):

Let us imagine the following scenario: We are in a small spaceship, far away in space, in the middle of some huge intergalactic void (that is, there where there are no general-relativity-effects (no "space-curving")). Our spaceship has the lab equipped to accurately measure the mass of electron, positron, as well as the energies of gamma-photons. We have measured the masses of electron and positron. And then, we setup the collision of one slow electron and one slow positron (hence, there are no special-relativity-effects), and we measure the energies of two gamma-photons, which are the result of that collision. If we then divide the total measured energy of gamma-photons E with the sum of masses of electron and positron m, we will get that E/m = c^2. Hence, this result is neither the consequence of special relativity, nor of general relativity – the equation E = mc^2 is the elementary, fundamental-level equation. (By the way, you could also see: Why is it called "annihilation"?)

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IMO, you do not really address the question. And besides, the arguments are somehow strange... I don't understand it at least; and anyways, why should the concept of "force" make sense at all outside Newtonian Mechanics, so what has this to do with $E=mc^2$, and so on...? – Ilja Apr 4 at 18:44
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1) particles have energy, but are not just energy. 2) particles are not formed by forces acting in various directions. 3) E=mc^2 does not allow us to simply replace mass with energy divided by velocity. Among other flaws in this derivation. – Asher Apr 7 at 21:42
    
The $E$ in the expression for force is potential energy, not the nonsense you posted after that claim. – HDE 226868 Apr 8 at 0:03

There is no particular physical significance; it's just a unit. Of course, in any system where such a large force is exerted, out current theories should not be accurate, and a quantum theory of gravity or some as-yet-unknown theory would be needed to accurately describe its behavior.

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When describing the formation of a black hole (or the merger of two equally-sized black holes) in a Newtonian gravity framework, Planck-scale gravitational forces of the order $c^4/G$ enter into the description. This is independent of the mass of the black hole. Such can easily be seen by modeling an infalling spherical shell of dust with mass $M$ under the influence of a Newtonian gravitational force.

Of course, we know that black hole formation and black hole mergers require a general relativistic description, and studying these phenomena in a Newtonian framework means stretching Newtonian gravity beyond its range of applicability. So treat the statement "Planck-scale forces are the forces that occur in the formation of black holes" as nothing more than a rough intuitive scaling argument.

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Planck's constant is a force associated with each cycle of a photon. For instance a photon with the 500 nm wavelength actually oscillates at a frequency more than 600 trillion times per second. Each time it oscillates, Planck's Constant is applied.

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What do you mean when you say "Planck's constant is applied?" How do you "apply" a constant? – Asher Apr 7 at 21:33

I think, the physical signifcance of the Planck force comes fromthe formula: looks like it's the force needed to accelerate the Planck mass to the speed of light in the Planck time right?

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That is the definition of plank force, not the significance thereof. – gonenc Jul 9 '15 at 11:36
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There does not exist a force capable of accelerating the Planck mass to the speed of light in any finite amount of time – Jim Jul 9 '15 at 13:14
    
You might be interested in the help center page on merging multiple accounts: physics.stackexchange.com/help/merging-accounts. – dmckee Jul 9 '15 at 14:59

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