Dear Abbas,

According to modern physics, especially Einstein's theories and quantum mechanics, the smallest meaningful size in the universe is the Planck length, approx. 1.6 x 10^-35 meters. At this scale, space and time themselves are expected to lose their classical meaning. Nothing known in physics can be smaller in a measurable or meaningful way because quantum gravitational effects dominate. Particles such as electrons or quarks are usually considered "point-like' with no internal structure or size, but they exist as excitations or "vibrations" of quantum fields that fill the entire universe.

The vacuum is not truly empty; it is filled with fluctuating energy due to the quantum fields that exist everywhere. These fluctuations can briefly create particle-antiparticle pairs, known as "virtual particles" that appear and vanish very quickly due to the uncertainty principle. In this sense, the quantum vacuum and its vibrations are more fundamental than atoms because they give rise to all particles and forces in nature.

Matter and energy are deeply connected in the quantum world, following Einstein's famous relation E=mc^2. This means matter can turn into energy and vice versa, as happens in particle creation and annihilation processes. Even in "empty" space, energy is present in the form of vacuum energy. This is believed to drive phenomena such as cosmic inflation and the accelerated expansion of the universe; linked to dark energy.

In the cosmological theory you provided, the universe is divided into "massless" and "massive" phases. The "massless" universe, existing at or below the Planck scale, contains pure energy in the form of photons and vacuum energy. As the universe expands and cools, matter particles form from this energy, leading to the "massive" universe described by the standard cosmological models like the Friedmann-Lemaitre equations and inflation theory. The text also proposes an "anti-universe" that evolves in the opposite time direction, with antimatter mirroring matter-potentially explaining why the observable universe contains mostly matter. This idea connects quantum vacuum energy, inflation, and dark energy into a unified, cyclic model of the cosmos.

Hope, it helps :)

Dear Abbas Kashani

In particle physics and physical cosmology, the Planck unit is a system of units of measurement defined in terms of only four universal physical constants: c, G, ħ, and kB. Expressing any of these physical constants in terms of Planck units.

At the Planck length, the theories of relativity break down:

The Planck length is a fundamental unit of length in physics, equal to approximately 1.616255(18) × 10⁻³⁵ meters. It is derived from the speed of light (c) (not determined by Einstein then), Planck's constant (h), and the gravitational constant (G). Although this is not a fundamental limit, it is significant because it marks the scale at which quantum gravitational effects dominate, where our current theories of gravity and spacetime break down.

The Planck frequency, denoted fᴘ, represents the highest possible frequency in the universe. It is calculated by dividing the speed of light by the Planck length and has a value of approximately 1.226 × 10⁴³ Hertz. This frequency is related to the smallest possible time interval, the Planck time, and is considered the theoretical upper limit on the frequency of electromagnetic radiation or any other repeating phenomenon.

Therefore, the answer to your question, "According to Einstein's theory, what is the smallest particle in the universe?" is: Einstein's theories could not predict the smallest particle in the universe, which Max Planck showed in 1899, long before the existence of relativity. Max Planck also gave us the equation for the energy-frequency relationship:

Energy and frequency are directly proportional, meaning that as one increases, the other also increases. This relationship is described by Planck's equation: E = hf, where E is energy, h is Planck's constant, and f is frequency. In other words, the energy of a photon (or electromagnetic wave) is directly proportional to its frequency, where Planck's constant is the proportionality constant.

Dear Soumendra Nath Thakur What is the reason that those theories break down?

Dear Carmen Wrede

I quoted from my previous response, "...the scale at which quantum gravitational effects dominate, where our current theories of gravity and spacetime break down.

The Planck frequency, denoted fᴘ, represents the highest possible frequency in the universe."

Thank you,

Soumendra

Dear Soumendra Nath Thakur

sorry to bother you again, but I have another question:

Since the Planck constant is involved in the relation W = F * s ... it seems to me that it ultimately sets the boundary for the material, visible universe, by defining the smallest meaningful action and therefore the smallest observable frequency.

If the interpretation is correct, wouldn’t it follow that frequencies beyond the Planck frequency might still exist... as structures beyond the limits of classical space-time?

What is your opinion on that possibility?

Best regards,

Carmen Wrede

June 13, 2025

Dear Carmen Wrede,

Thank you sincerely for your thoughtful follow-up and for engaging further with my previous response—not as a bother, but as a meaningful continuation of an essential and profound discussion.

You raised a very pertinent question: whether Planck’s constant h, involved in quantum formulations of action such as E = hf and h∼E⋅t or h∼p⋅x, sets a fundamental boundary for all meaningful interactions—implying that frequencies beyond the Planck frequency may potentially exist but lie outside the observable structure of classical spacetime.

Your Interpretation of W=F⋅s and h

As you correctly observed, W = F⋅s is a classical expression representing the mechanical work done by a force over a displacement. While this equation does not directly involve Planck’s constant, your intuition to connect it with h—which defines the smallest unit of quantized action—is insightful.

Indeed, Planck’s constant does set a lower bound to physically meaningful action, as understood from:

• The Heisenberg uncertainty principle, Δx⋅Δp ≳ ℏ and ΔE⋅Δt ≳ ℏ,
• And the quantum of action, originally proposed by Max Planck and forming the foundation of quantum theory.

Thus, while W = F⋅s is not quantized in itself, when we approach the limit where action becomes quantized, classical descriptions lose fidelity, and quantum mechanical formulations governed by h take over.

On Planck Frequency and "beyond": Things that lies above the limit.

You insightfully ask:

Could frequencies beyond the Planck frequency exist as structures beyond the limits of classical space-time?

The answer, from the perspective of Extended Classical Mechanics (ECM), is Yes—with qualifications.

In ECM, the Planck scale is not simply a quantized boundary—it is a domain of extreme energetic and gravitational conditions, where:

• Gravitational interactions become nearly infinite in strength.
• Known forces unify under an effective gravitational influence.
• Rest mass ceases to exist, and only kinetic (energetic) oscillation remains.
• No conventional spacetime exists in the familiar sense—space itself is under vibrational strain.

At such a threshold:

• Classical physics fails.
• Even quantum mechanics becomes inadequate.
• And Planck’s constant h may no longer apply to describe energy transitions.

Instead, another constant k—not yet fully formalized but referenced in ECM—may govern the energetic exchanges involving super-Planckian oscillations, i.e., when:

Δf = f₀−fᴘₗₐₙₖ during t₀ − tᴘₗₐₙₖ,

suggesting that a new proportionality could replace E=hf in this domain.

Observable Frequencies vs. Theoretical Extremes

While Planck frequency fᴘ = c³/Gh ≈ 1.855×10⁴³Hz or in angular form ωp = 2πfᴘ ≈ 2.952 × 1044  rad/s, is often cited as the upper bound of meaningful oscillations, it is important to note:

• Our current technological and observational reach ends far below this threshold.
• For example, the highest observed gamma-ray frequencies are on the order of 10²⁸ Hz.
• Thus, Planck frequency is not an observable boundary, but a mathematical limit associated with energy density, time interval, and gravitational curvature.

The ECM Perspective: Planck Limit as Energetic Domain

In ECM, the Planck domain is not a limit of our mathematics, but a zone of energetic transformation where:

• The origin of space and time emerges from pure energetic displacement.
• Only vibration exists, not matter.
• Potential energy converts directly into kinetic energy, with no rest mass carriers.
• Energetic waveforms may propagate at or beyond luminal speeds, though not in the form of conventional radiation.
• And crucially, energy conservation remains valid, though mediated by different constants and mechanisms.

The environment here is not simply the "smallest meaningful action," but an ultra dense, vibrational field domain, where ECM proposes alternative mathematical expressions f or behaviour and interactions.

For Further Reading: ECM-Derived Documents and References

Your question aligns closely with several ECM research efforts. You may find deeper insights in the following documents, which address precisely the transitions and extensions beyond the Planck limit:

Your question opens the gateway to a much-needed philosophical and mathematical expansion of what constitutes "physics" at its foundational limit. I appreciate your openness and speculative rigor. I hope this perspective from ECM offers both a physical insight and a conceptual direction for such questions.

Warm regards, Soumendra Nath Thakur

Dear Soumendra Nath Thakur ,

sorry to bother you again. You wrote:

"In ECM, the Planck scale is not simply a quantized boundary—it is a domain of extreme energetic and gravitational conditions, where:

• Gravitational interactions become nearly infinite in strength.
• Known forces unify under an effective gravitational influence.
• Rest mass ceases to exist, and only kinetic (energetic) oscillation remains.
• No conventional spacetime exists in the familiar sense—space itself is under vibrational strain."

But does the Planck scale not also exist in regions without extreme gravitational influence as the smallest meaningful unit of space throughout the universe? Would it not be more than a boundary condition, more like a universal resolution limit, even in regions of minimal curvature?

Dear Carmen Wrede,

Thank you once again for your continued interest and your perceptive question, which strikes at the heart of how we interpret the Planck scale—not just as a mathematical construct, but as a physically meaningful threshold in various energetic and gravitational regimes.

You asked whether the Planck scale might still exist as a universal resolution limit, even in regions without extreme gravitational influence or spacetime curvature.

This is a very important consideration, and I’d be pleased to clarify how Extended Classical Mechanics (ECM) approaches this concept.

Planck Scale in ECM: Not a Built-In Resolution, but an Emergent Threshold

In ECM, the Planck scale is not regarded as a pre-defined "pixel size" of space that operates equally across the entire universe. Instead, it represents a critical energetic threshold—a regime where the known constructs of mass, force, space, and time collapse into pure oscillatory energy.

Unlike certain quantum gravity models (such as loop quantum gravity), which treat the Planck length as the smallest possible unit of spacetime, ECM makes a crucial distinction:

Planck values only become physically meaningful when the conditions of the system—its energy density, frequency, or gravitational force—approach Planck-scale thresholds.

So in the normal universe, where gravitational forces and curvature are modest or even negligible, the Planck scale remains a latent mathematical limit, but it does not impose a dynamic resolution on space.

Why Not a Universal Resolution Limit?

Your question rightly touches on the idea of minimum curvature and whether the Planck length functions as a base resolution even there.

In ECM, the answer is: no—not dynamically.

This is because:

• ECM does not interpret gravity through curvature, but as a classical force acting through energetic systems.
• The Planck length does not structure space like a grid or lattice. Instead, it signals a collapse condition, beyond which space and time are no longer meaningful in the classical sense.
• Therefore, in regions with low energy or flat spacetime, the Planck scale has no operative function—it remains a non-intrusive constant.

Planck Scale as a Transformative, Not Constitutive, Boundary

I deeply appreciate your suggestion that the Planck scale might be more than a boundary. From an ECM viewpoint, it certainly is more—but not in the sense of a static, ever-present resolution.

Rather, it is a transformative boundary, one that emerges only when:

• Rest mass dissolves into kinetic oscillation.
• Gravitational energy becomes extreme or unified.
• Conventional quantum descriptions break down.

So while it exists throughout the universe as a theoretical threshold, it becomes physically activated only under conditions of near-infinite energetic intensity.

Summary of ECM View in Response to Your Question is attached as an image "Summary" below.

Regards

Soumendra Nath Thakur

Dear Soumendra Nath Thakur ,

how can energy decoupled from space couple into space again? How can a high energy oscillating wave generate low energy radio waves?

Now of course one could argue that high-energy particles generate secondary radiation, similar to that in a particle accelerator. However this is extremely inefficient. ​​A black hole would have to radiate for billions of years to get a few radio photons.

So a planck oscillator cannot emit radio waves unless there is a strongly nonlinear medium or quantum processes that massively downmixes frequencies. Direct generation is physically impossible. Indirect generation is possible, but inefficient and not explained in ECM.

Honestly... ECM has a fundamental explanatory gap here. And this gap is not just a little cosmetic or technical problem. I think it is irreparable.

Dear Carmen Wrede,

Thank you for continuing the exchange. However, it seems that the recent direction of the discussion has moved away from engaging with the structure and principles of ECM as they have been presented.

Your assertion—“how can energy decoupled from space couple into space again?”—presupposes that space is the generator or container of energy, which contradicts the ECM framework where energy is primary and space is an emergent or abstract extension, not a causal substrate. This ontological reversal lies outside ECM and cannot serve as a critique of it without misunderstanding its foundation.

Your second claim, implying that high-energy oscillations must directly downmix into low-frequency radio waves, does not reflect anything proposed in the ECM formulation you were responding to. The dynamics of wave transitions, energetic thresholds, and interaction channels (including nonlinear effects and resonance harmonics) are a broader domain not central to the previous discussion on the Planck scale.

While I respect critical inquiry, dismissing ECM as having an “irreparable explanatory gap” without identifying a contradiction or engaging with its postulates in context does not constitute scientific disagreement—it amounts to a declaration of disinterest.

For that reason, I will conclude the exchange here, as further responses would risk serving neither understanding nor respect for intellectual integrity.

Best regards, Soumendra Nath Thakur

Dear Soumendra Nath Thakur ,

"does not reflect anything proposed in the ECM formulation"

Exactly. Since you obviously did not reflect it, I am asking you now how you plan to solve it, now that the problem is on the table. Because not talking about a problem will surely not solve the problem. Also not talking about a gap, in order to not stir a contradiction, does not mean that the contradiction does not exist.

"For that reason, I will conclude the exchange here, as further responses would risk serving neither understanding nor respect for intellectual integrity."

Well... yes, try to run. Maybe that will do the trick.

Carmen Wrede You are officially out from my profile(.)

I am out of your profile. But your theory left science... You don't have to thank me. My pleasure.

In Islam it is said : حبة خردل

this khardal is the smallest particle ever known

Allah almighty defind this by if he put it in mass scale he knows its value and the mass of anything larger or smaller than this seed.