The Planck scale is, simply, the result of dimensional analysis. From G, h and c (Newton's constant, Planck's constant and the speed of light in vacuum) it is possible to define quantities that have dimensions of mass, length and time. The reason this is useful is in order to employ tthem as units for the case where gravitational, relativistic and quantum effects are comparable. However they don't, for the moment, imply any kind of limit on length, mass or time, that must be shown. But we don't know what the dimensionless prefactors are. Just like in wave phenomena, the wavelength of a wave defines the scale at which diffraction phenomena become relevant, but it doesn't imply that they become relevant sharply below it and are totally absent above it.

Another example: From the dielectric constant of the vacuum and the magnetic permeability of vacuum it is possible to show, using their definition in Coulomb's law and in the Biot-Savart law, that their product has the dimensions of 1/velocity^2; and the value of that velocity is that of light; however from that alone it's not possible to deduce that that velocity has any particular status. It's the properties of Maxwell's equations, discovered much later, that imply their invariance under Lorentz transformations and, even then, whether this property is special to electromagnetism or a general property of all natural phenomena had to be discovered and understood. Same here.

Planck scale effects are early Universe effects, those that occurred before the inflationary epoch. So to test for them, it's necessary to be able to measure signals from that epoch. As the BICEP2 experiments showed, a major background to extracting such signals is our ignorance of the composition of interstellar dust. To extract a signal, it's necessary to control the background to the signal.

The meaning, if any, of the Planck scale can only be understood within a theory of quantum gravity, which remains to be formulated.

Thank you, Stam Nicolis, for such a thoughtful and precise elaboration.

Indeed, dimensional analysis by itself does not imply fundamental limits and I appreciate your analogy with wave phenomena: the presence of a scale (like wavelength) doesn’t instantly impose a boundary, but rather marks where new effects become significant.

Still, I wonder if there’s a deeper epistemic implication lurking here.

You rightly point out that the Planck units arise from combining GGG, ℏ\hbarℏ, and ccc and without a theory of quantum gravity, these remain just formal constructions. But doesn't the fact that these constants represent the pillars of the three major physical regimes (gravity, quantum mechanics, and relativity) suggest that their confluence may carry conceptual, not just dimensional, weight?

Just as the value of ccc emerged as meaningful after Maxwell's equations and only through empirical confirmation, could the Planck scale hold a similar status a kind of placeholder for a principle we haven’t yet formulated?

You also mention early universe signals, like those probed by BICEP2. That's fascinating and it supports the view that Planck-scale physics may leave statistical or fossil-like imprints, rather than be directly observable. But then we’re almost back to my original metaphor: are we trying to photograph shadows cast by something we can’t yet see?

Lastly, while I agree that a theory of quantum gravity is essential for understanding the Planck regime meaningfully, I’m also curious whether quantum information theory or entanglement structure might point to emergent spacetime features that give us indirect handles as explored in holographic duality or tensor network models.

Do you think these approaches can offer anything beyond formal cleverness something testable, even if only at the level of correlations in the CMB or gravitational wave background?

Any conceptual meaning these constants, taken together, may have, can only be understood a posteriori, once a theoretical framework is set up (whatever it may be).

Indeed, we can only infer what might exist more generally, from certain experiments that can be done at all-and lead to certain implications that, in turn, can be tested.

Quantum information theory doesn't rely on quantum fluctuations of spacetime; nor does the phenomenon of entanglement, which is a generic feature of quantum phenomena. That spacetime, as described by general relativity, is an emergent notion is, of course clear; from what it emerges is, for the moment, unknown. The only real hint we have, for the moment, is what can be the degrees of freedom that can account for the finite entropy of black holes, when probed by quantum matter-we, still, don't know how these interact. That knowledge, indeed, is a consequence of holographic duality. Tensor networks are just one way of representing quantum degrees of freedom, in general; how they can describe the properties of black hole microstates remains to be worked out.

The CMB correlations are described by classical, not quantum, gravity, as is any gravitational wave background. These are effects of classical gravity. When they are relevant, quantum gravitational effects are no longer relevant.

They are relevant much before that epoch.

These papers might be useful: Preprint Quantum stress-energy at timelike boundaries: testing a new ...

Preprint The Spectroscopic Stage-5 Experiment

Preprint TF1 Snowmass Report: Quantum gravity, string theory, and black holes

Preprint Snowmass Theory Frontier: Astrophysics and Cosmology

Preprint Snowmass White Paper: Cosmology at the Theory Frontier

“...But perhaps we need to stop treating the Planck scale as a distance or energy level — and start treating it as a category shift in physics itself.....”

- yeah, that is quite correct, including the real physics development must be for sure only as a next step on the way “classical physics” – QM - Planck scale physics.

And in this case there is no any “...Like trying to photograph silence.....” . In the really outstanding utmost fundamental in XX century von Weizsäcker and Fredkin-Toffoli findings they quite rationally showed that Matter is based on a binary [von Weizsäcker, “UR hypothesis” , 1954 ] , for whar is necessary and sufficient for Matter’ space be 3D - as it is 3D, - and [Fredkin-Toffoli, 1970] reversive, logics.

Basing on the outstanding findings above in 2007 - till now the Shevchenko-Tokarevsky’s Planck scale informational physical model, , two main recent papers are https://www.researchgate.net/publication/391209088_The_Informational_Conception_and_Basic_Physics, [ in the paper secton 2.9 “Mediation of the forces in complex systems” can be passed since this is more comprehensively given in section 6.“Mediation of the fundamental forces in complex systems” in other paper below] , and

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics was/is developed.

In the model in accordance with the findings, it is postulated that Matter is based on a binary reversible logics, and so the ultimate and utmost universal base of Matter is [5]4D dense lattice of primary elementary logical structures – binary reversible fundamental logical elements [FLE] that have [5]4 utmost universal – “kinematical” degreases of freedom at changing its state – “FLE binary flips”

The lattice is placed in the corresponding Matter’s utmost universal fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, [5]4D spacetime with metrics (cτ,X,Y,Z,ct), where cτ,X,Y,Z, are 4 space dimensions, ct is the time dimension. FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP,

[von Weizsäcker and Fredkin-Toffoli thought that Matter’s spacetime is 4D with metrics (cτ,X,Y,Z), as that is in whole mainstream physics till now, what is wrong]

However besides the utmost universal “kinematical” space dimensions above, the space contains also at least 4 dimensions that relate to 4 specific FLE degreases of freedom to change its state [to be “charged”] that relate to the at least 4 known now fundamental Nature Gravity, Weak, Electric, and Nuclear/Strong forces [more see the 2-nd link, section 6 “Mediation of the fundamental forces in complex systems”], so FLE has (at least) 4+4+1 degreases of freedom, and so whole Matter’s spacetime fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, spacetime that has metrics (at least) [4+4+1]4D (cτ,X,Y,Z, g,w,e,s,ct).

In the whole model above the initial Planck scale models Forces are developed – see the pointed above section 6. All in whole model is in complete accordance with all really reliable experimental data,

- while the ratio of the Forcers’ strengths is in accordance with experiments only if FLE “size” and “FLE binary flip time” are as pointed above “Planck units”,

- and everything in Matter, i.e. particles and the Forces mediators, is/are only some disturbances in the lattice.

That’s all, here is no any “spacetime itself dissolves into quantum foam, and the classical ideas of cause and effect collapse into something altogether stranger”, so on, including, say, when this

“....That spacetime, as described by general relativity, is an emergent notion is, of course clear; from what it emerges is, for the moment, unknown......”

is quite true, in the mainstream the fundamental phenomena/notions “space/time/spacetime” are fundamentally transcendent, and in the mainstream the problem above so principally cannot be really scientifically clarified, but in the model [more correctly on the 2007 SS&VT “The Information as Absolute” conception] that is rigorously clarified, including why and how the the spacetime absolutely fundamentally necessarily exist.

More see the links above, recent SS post in https://www.researchgate.net/post/Did_Einstein_ever_question_the_Constancy_of_G is relevant in this case.

Cheers

Dear Saiful Miqdar

The Planck scale is generally understood to represent the scale at which quantum mechanics and general relativity both become significant, often considered the smallest unit to which current physical theories can be applied. However, since the Planck scale is not a minimum length or energy scale restricted by any fundamental physical principle, it has been theoretically accepted that scales smaller than the Planck scale are possible and not inherently limited.

While studying gravitational binding energy and gravitational self-energy, which are entirely unrelated to the Planck scale, I discovered that the Planck scale holds profound physical significance.

The concept of gravitational self-energy(U_gs) is the total of gravitational potential energy possessed by a certain object M itself. Since a certain object M itself is a binding state of infinitesimal mass dMs, it involves the existence of gravitational potential energy among these dMs and is the value of adding up these. M = ΣdM. The gravitational self-energy is equal to the minus sign of the gravitational binding energy. Only the sign is different because it defines the gravitational binding energy as the energy that must be supplied to the system to bring the bound object into a free state.

*To understand the basic principle, we can look at the problem in Newtonian mechanics, and for the actual calculation, we can use the binding energy formula of general relativity to find the value.

U_gs=-(3/5)(GM^2)/R

In gravitationally bound systems, changes in configuration (e.g., orbital reduction) lead to a decrease intotal energy and equivalent mass due to energy radiation, as seen in celestial mechanics. Although potential energy changes to kinetic energy, in order to achieve a stable bonded state, a part of the kinetic energy must be released to the outside of thesystem. As a result, this leads to a decrease in the equivalent mass of the system.

In the case of a spherical uniform distribution, the total energy of the system, including gravitational potential energy (binding energy), is

E_T = Σm_ic^2 + Σ-(Gm_im_j/r_ij) = Mc^2 - (3/5)(GM^2/R)

In the general case, the value of total gravitational potential energy (gravitational self-energy) is small enough to be negligible, compared to mass energy Mc^2.

However, as R gets smaller, the absolute value of U_gs increases. For this reason, we can see that U_gs is likely to offset the mass energy at a certain radius. The mass defect effect due to binding energy has already been demonstrated in particle physics.

Thus, looking for the size in which (negative) gravitational self-energy becomes equal to (positive) rest mass energy,

|U_gs|=Mc^2

(3/5)(GM^2)/R=Mc^2

R_gs=(3/5)GM/c^2

At the critical radius R_gs, the negative gravitational self-energy cancels out the positive mass energy, so the total energy becomes zero, and therefore the gravity becomes zero.

R_gs = (3/5)GM/c^2

(*For the detailed calculation based on general relativity, please refer to the paper.)

https://preview.redd.it/sphere-theory-beyond-string-theory-completing-quantum-v0-533irrdk2aaf1.jpg?width=320&crop=smart&auto=webp&s=ed9be1db8cc97f67ad074c23c3773482630df1f0

The integration of the gravitational binding function is not analytical. Using the first-term approximation, we obtain the value R_{gs-GR-1st} ~ 1.16G_NM_fr/c^2 ~ 0.58R_S. If we calculate the integral itself numerically and apply the virial theorem to it, we obtain the value R_{gp-GR-vir} ~ 1.02G_NM_fr ~ 0.51R_S. Since the process in which actual celestial bodies contract gravitationally to become black holes is very complex, these values may be slightly different.

The important thing here is not the exact value, but the fact that there exists a actual critical radius R_gs where the negative gravitational self-energy offsets the positive mass energy.

R_gs ~ GM/c^2

What this critical radius R_gs means is that,

If the object were to shrink further (R