The Existence Boundary: A Foundational Principle in Cosmology and Quantum Physics ?

[ovidiu t]

 

In modern physics, the question of what constitutes the fabric of reality has been deeply intertwined with the understanding of singularities, the Big Bang, and vacuum energy. However, one fundamental question has remained underexplored: What guarantees the existence of something in the universe, and why is the concept of "nothingness" ultimately unachievable? This texte attempts to propose a new foundational principle, which we call the Existence Boundary (E). The principle posits that something must always exist, and that this concept holds across quantum mechanics, general relativity, and cosmology.

The Existence Boundary (E) operates as a constraint on the physical universe, implying that absolute nothingness — a state where no energy, matter, or structure exists — is an impossibility. This is not only a philosophical statement but also a speculative yet mathematically grounded principle with potential implications for cosmology, quantum field theory (QFT), and the nature of space and time. In this work, we propose a formalization of the Existence Boundary and explore its potential impact on both our understanding of black holes, virtual particles, and the Big Bang.

Key Concepts of the Existence Boundary

1. The Impossibility of Absolute Nothingness: The Existence Boundary asserts that the universe cannot reach a state of absolute void. Even in regions that appear "empty" — such as the vacuum of space — quantum fluctuations, vacuum energy, or dark energy ensure that something always exists. This principle is analogous to the cosmological constant Λ\LambdaΛ, which represents a form of energy intrinsic to spacetime itself.

2. General Relativity and the Existence Boundary: In General Relativity, spacetime is curved by the presence of matter and energy. The Existence Boundary can be viewed as an extension of this principle, ensuring that even in the absence of visible matter, spacetime cannot collapse into "nothingness." Instead, the universe will always maintain some energy density, manifesting as vacuum energy or dark energy. This prevents spacetime from becoming truly empty or reaching a singularity where physics breaks down.

3. Quantum Field Theory and the Existence Boundary: In Quantum Field Theory, the vacuum is not truly empty but is filled with quantum fluctuations that give rise to virtual particles. These particles can briefly appear and disappear, but they represent a continuous, underlying "something" that maintains the fabric of reality. The Existence Boundary is consistent with this framework, suggesting that even the "empty" vacuum is full of potential energy and activity, preventing a true vacuum (or absence of energy).

4. Wave Function and the Existence Boundary: In Quantum Mechanics, the wavefunction Ψ(x,t)\Psi(x,t)Ψ(x,t) describes the probability distribution of a particle's location and state. It is a fundamental tool in understanding quantum systems, but it is never zero — implying that there is always some nonzero probability of finding a particle at any given point in space-time.

   The Existence Boundary can be viewed as an extension of the wavefunction concept, ensuring that the total probability of existence across the entire universe sums to 1:

   

   This equation guarantees that there is always a nonzero probability of something existing, regardless of whether it is observable in a given moment or region. This directly connects the probabilistic nature of quantum mechanics to the foundational constraint of Existence — ensuring that no region of space-time is completely devoid of something.

   Furthermore, this formulation suggests that the Existence Boundary ensures the wavefunction never fully collapses into zero — a principle aligned with quantum mechanics, where even the absence of particles doesn't imply absolute nothingness. The continuous presence of vacuum fluctuations and quantum fields means that something always "exists," even if we cannot always observe it directly.

5. Cosmological Implications: The Existence Boundary offers a solution to the problem of singularities in the Big Bang and the interiors of black holes. By ensuring that something always exists, it implies that the universe’s early state was not a singularity (a point of infinite density and curvature) but rather a bounce or a transition into the current observable universe. Similarly, the interiors of black holes may not collapse into a singularity but instead follow a process consistent with the Existence Boundary, preventing the breakdown of physical laws.

Mathematical Formulation of the Existence Boundary

The Existence Boundary can be expressed in a form consistent with General Relativity and Quantum Field Theory. The simplest approach is to add a term EμνE_{\mu\nu}Eμν to the Einstein Field Equations that represents the vacuum energy and quantum fluctuations inherent in spacetime. This term prevents the collapse of spacetime into a singularity and ensures the continuity of energy and structure.

Where:

For the Existence Boundary, we propose that could be modeled by a combination of vacuum energy (quantum fluctuations) and dark energy:

Where:

This equation ensures that spacetime cannot be empty and that some form of energy exists at all times, whether it manifests as vacuum fluctuations, dark energy, or quantum fields.

Predictions and Observable Phenomena

1. Virtual Particles: The Existence Boundary predicts that virtual particles will exist in the quantum vacuum, even in the absence of matter. These particles momentarily appear and interact, leaving observable effects such as the Casimir effect. They provide indirect evidence of the Existence Boundary.

2. Hawking Radiation: Near the event horizon of black holes, virtual particles are created due to quantum fluctuations. This process, known as Hawking radiation, could be seen as a manifestation of the Existence Boundary, where energy is still present near the black hole even in what seems like a "nothing" region. This supports the idea that something always exists, even in extreme conditions.

3. Accelerating Expansion: The Existence Boundary offers a natural explanation for the accelerating expansion of the universe. Dark energy, which is believed to be driving the expansion, could be a manifestation of the underlying energy described by the Existence Boundary. The continuous presence of this energy ensures that the universe's expansion never decelerates and that spacetime is never empty.

4. Big Bang and Big Bounce: The Existence Boundary offers a framework for understanding the Big Bang not as a singularity but as a bounce from a quantum state, where spacetime itself prevents collapse into nothingness. This aligns with models such as Loop Quantum Gravity, which propose that the universe has undergone a bounce rather than originating from a singularity.

Conclusion

The Existence Boundary is a proposed foundational principle that ensures the continuous presence of something in the universe, preventing the possibility of absolute nothingness. It operates across general relativity, quantum field theory, and cosmology, offering new insights into phenomena such as dark energy, vacuum fluctuations, Hawking radiation, and the Big Bang. By ensuring that spacetime cannot collapse into nothingness, the Existence Boundary provides a possible solution to the problem of singularities and the origin of the universe, suggesting that the Big Bang was not a point of infinite density, but rather a transition or bounce driven by quantum effects.

Further research and observations may allow us to refine this idea, potentially linking it to observable phenomena like gravitational waves, vacuum fluctuations, and the acceleration of the universe. The Existence Boundary could serve as a fundamental concept in understanding the nature of space, time, and the universe itself.

[studiot]

I'm sure we have had something like this before it all sounds very familiar.

[ovidiu t]

20 minutes ago, studiot said:

I'm sure we have had something like this before it all sounds very familiar.

I would be really greatful if you could connect me to the person who had a similar thought. 

[swansont]

Is there any of this that isn’t already part of existing physics? And is it testable?

[exchemist]

4 hours ago, ovidiu t said:

 

In modern physics, the question of what constitutes the fabric of reality has been deeply intertwined with the understanding of singularities, the Big Bang, and vacuum energy. However, one fundamental question has remained underexplored: What guarantees the existence of something in the universe, and why is the concept of "nothingness" ultimately unachievable? This texte attempts to propose a new foundational principle, which we call the Existence Boundary (E). The principle posits that something must always exist, and that this concept holds across quantum mechanics, general relativity, and cosmology.

The Existence Boundary (E) operates as a constraint on the physical universe, implying that absolute nothingness — a state where no energy, matter, or structure exists — is an impossibility. This is not only a philosophical statement but also a speculative yet mathematically grounded principle with potential implications for cosmology, quantum field theory (QFT), and the nature of space and time. In this work, we propose a formalization of the Existence Boundary and explore its potential impact on both our understanding of black holes, virtual particles, and the Big Bang.

Key Concepts of the Existence Boundary

1. The Impossibility of Absolute Nothingness: The Existence Boundary asserts that the universe cannot reach a state of absolute void. Even in regions that appear "empty" — such as the vacuum of space — quantum fluctuations, vacuum energy, or dark energy ensure that something always exists. This principle is analogous to the cosmological constant Λ\LambdaΛ, which represents a form of energy intrinsic to spacetime itself.

2. General Relativity and the Existence Boundary: In General Relativity, spacetime is curved by the presence of matter and energy. The Existence Boundary can be viewed as an extension of this principle, ensuring that even in the absence of visible matter, spacetime cannot collapse into "nothingness." Instead, the universe will always maintain some energy density, manifesting as vacuum energy or dark energy. This prevents spacetime from becoming truly empty or reaching a singularity where physics breaks down.

3. Quantum Field Theory and the Existence Boundary: In Quantum Field Theory, the vacuum is not truly empty but is filled with quantum fluctuations that give rise to virtual particles. These particles can briefly appear and disappear, but they represent a continuous, underlying "something" that maintains the fabric of reality. The Existence Boundary is consistent with this framework, suggesting that even the "empty" vacuum is full of potential energy and activity, preventing a true vacuum (or absence of energy).

4. Wave Function and the Existence Boundary: In Quantum Mechanics, the wavefunction Ψ(x,t)\Psi(x,t)Ψ(x,t) describes the probability distribution of a particle's location and state. It is a fundamental tool in understanding quantum systems, but it is never zero — implying that there is always some nonzero probability of finding a particle at any given point in space-time.

   The Existence Boundary can be viewed as an extension of the wavefunction concept, ensuring that the total probability of existence across the entire universe sums to 1:

   

   This equation guarantees that there is always a nonzero probability of something existing, regardless of whether it is observable in a given moment or region. This directly connects the probabilistic nature of quantum mechanics to the foundational constraint of Existence — ensuring that no region of space-time is completely devoid of something.

   Furthermore, this formulation suggests that the Existence Boundary ensures the wavefunction never fully collapses into zero — a principle aligned with quantum mechanics, where even the absence of particles doesn't imply absolute nothingness. The continuous presence of vacuum fluctuations and quantum fields means that something always "exists," even if we cannot always observe it directly.

5. Cosmological Implications: The Existence Boundary offers a solution to the problem of singularities in the Big Bang and the interiors of black holes. By ensuring that something always exists, it implies that the universe’s early state was not a singularity (a point of infinite density and curvature) but rather a bounce or a transition into the current observable universe. Similarly, the interiors of black holes may not collapse into a singularity but instead follow a process consistent with the Existence Boundary, preventing the breakdown of physical laws.

Mathematical Formulation of the Existence Boundary

The Existence Boundary can be expressed in a form consistent with General Relativity and Quantum Field Theory. The simplest approach is to add a term EμνE_{\mu\nu}Eμν to the Einstein Field Equations that represents the vacuum energy and quantum fluctuations inherent in spacetime. This term prevents the collapse of spacetime into a singularity and ensures the continuity of energy and structure.

Where:

For the Existence Boundary, we propose that could be modeled by a combination of vacuum energy (quantum fluctuations) and dark energy:

Where:

This equation ensures that spacetime cannot be empty and that some form of energy exists at all times, whether it manifests as vacuum fluctuations, dark energy, or quantum fields.

Predictions and Observable Phenomena

1. Virtual Particles: The Existence Boundary predicts that virtual particles will exist in the quantum vacuum, even in the absence of matter. These particles momentarily appear and interact, leaving observable effects such as the Casimir effect. They provide indirect evidence of the Existence Boundary.

2. Hawking Radiation: Near the event horizon of black holes, virtual particles are created due to quantum fluctuations. This process, known as Hawking radiation, could be seen as a manifestation of the Existence Boundary, where energy is still present near the black hole even in what seems like a "nothing" region. This supports the idea that something always exists, even in extreme conditions.

3. Accelerating Expansion: The Existence Boundary offers a natural explanation for the accelerating expansion of the universe. Dark energy, which is believed to be driving the expansion, could be a manifestation of the underlying energy described by the Existence Boundary. The continuous presence of this energy ensures that the universe's expansion never decelerates and that spacetime is never empty.

4. Big Bang and Big Bounce: The Existence Boundary offers a framework for understanding the Big Bang not as a singularity but as a bounce from a quantum state, where spacetime itself prevents collapse into nothingness. This aligns with models such as Loop Quantum Gravity, which propose that the universe has undergone a bounce rather than originating from a singularity.

Conclusion

The Existence Boundary is a proposed foundational principle that ensures the continuous presence of something in the universe, preventing the possibility of absolute nothingness. It operates across general relativity, quantum field theory, and cosmology, offering new insights into phenomena such as dark energy, vacuum fluctuations, Hawking radiation, and the Big Bang. By ensuring that spacetime cannot collapse into nothingness, the Existence Boundary provides a possible solution to the problem of singularities and the origin of the universe, suggesting that the Big Bang was not a point of infinite density, but rather a transition or bounce driven by quantum effects.

Further research and observations may allow us to refine this idea, potentially linking it to observable phenomena like gravitational waves, vacuum fluctuations, and the acceleration of the universe. The Existence Boundary could serve as a fundamental concept in understanding the nature of space, time, and the universe itself.

Surely if no region of space can be said to be truly void, that is saying there is NO boundary to existence, other than the limits of the cosmos itself?

If so, where is this boundary?

[ovidiu t]

3 hours ago, exchemist said:

Surely if no region of space can be said to be truly void, that is saying there is NO boundary to existence, other than the limits of the cosmos itself?

If so, where is this boundary?

 

4 hours ago, swansont said:

Is there any of this that isn’t already part of existing physics? And is it testable?

Is it new?

Yes, E is new because it formalizes the idea that something must always exist and prevents the possibility of absolute nothingness. While similar concepts are present in quantum theory (like vacuum fluctuations and virtual particles) and cosmology (such as energy persistence in black holes), E offers a unified framework that ties together quantum, cosmological, and relativistic scales. This new perspective gives a fresh outlook on old ideas, showing how they might be connected.

Is it testable?

The direct testability of E is still a challenge, but we can look for indirect signs that support it:

Virtual Particles: These quantum fluctuations in the vacuum are a good example of something always existing, even in "empty" space. If E holds, we’d expect these fluctuations to be an ongoing phenomenon, reinforcing the idea that nothingness isn't possible.

Cosmic Microwave Background (CMB): We might find subtle fluctuations or anomalies in the CMB that suggest the universe didn't start from a true state of nothingness. This would support the concept that something always existed, even in the very early universe.

Gravitational Waves: Observing black hole mergers could reveal small differences in the expected gravitational wave signals, suggesting a non-singular collapse, which supports the Existence Boundary.

Hawking Radiation: If Hawking radiation can be detected from small or primordial black holes, the spectrum could show deviations from the standard model, which may align with the idea of energy-preserving behaviors in line with E.

So while E itself might not be directly observable, we can test its effects through phenomena like virtual particles, the CMB, gravitational waves, and Hawking radiation. If these observations show patterns that align with E, it could provide indirect evidence of this fundamental principle.

3 hours ago, exchemist said:

Surely if no region of space can be said to be truly void, that is saying there is NO boundary to existence, other than the limits of the cosmos itself?

If so, where is this boundary?

The Existence Boundary (E) operates in a slightly different way. Instead of placing a boundary on space itself, E asserts that absolute nothingness—a state where no matter, energy, or structure exists—is impossible.

So, rather than a physical boundary in space, the Existence Boundary is more of a principle that applies across all scales (quantum, relativistic, cosmological). It's not a boundary in the traditional sense, but a constraint on what can exist. This means that, in any point in the universe, something must always exist. It doesn't necessarily define the location of that existence, but rather the principle that existence can't be entirely absent, no matter where you are in the cosmos.

In essence, E prevents "nothing" from ever being truly realized, ensuring that something must always exist, no matter where you look.

[swansont]

1 hour ago, ovidiu t said:

Is it new?

Yes, E is new because it formalizes the idea that something must always exist and prevents the possibility of absolute nothingness. While similar concepts are present in quantum theory (like vacuum fluctuations and virtual particles) and cosmology (such as energy persistence in black holes), E offers a unified framework that ties together quantum, cosmological, and relativistic scales. This new perspective gives a fresh outlook on old ideas, showing how they might be connected.

Is it testable?

The direct testability of E is still a challenge, but we can look for indirect signs that support it:

Virtual Particles: These quantum fluctuations in the vacuum are a good example of something always existing, even in "empty" space. If E holds, we’d expect these fluctuations to be an ongoing phenomenon, reinforcing the idea that nothingness isn't possible.

Cosmic Microwave Background (CMB): We might find subtle fluctuations or anomalies in the CMB that suggest the universe didn't start from a true state of nothingness. This would support the concept that something always existed, even in the very early universe.

Gravitational Waves: Observing black hole mergers could reveal small differences in the expected gravitational wave signals, suggesting a non-singular collapse, which supports the Existence Boundary.

Hawking Radiation: If Hawking radiation can be detected from small or primordial black holes, the spectrum could show deviations from the standard model, which may align with the idea of energy-preserving behaviors in line with E.

So while E itself might not be directly observable, we can test its effects through phenomena like virtual particles, the CMB, gravitational waves, and Hawking radiation. If these observations show patterns that align with E, it could provide indirect evidence of this fundamental principle.

You say yes, it’s new, but haven’t listed anything new. These effects are already known, so they don’t test your idea unless you quantify the deviations.

[exchemist]

10 hours ago, ovidiu t said:

 

Is it new?

Yes, E is new because it formalizes the idea that something must always exist and prevents the possibility of absolute nothingness. While similar concepts are present in quantum theory (like vacuum fluctuations and virtual particles) and cosmology (such as energy persistence in black holes), E offers a unified framework that ties together quantum, cosmological, and relativistic scales. This new perspective gives a fresh outlook on old ideas, showing how they might be connected.

Is it testable?

The direct testability of E is still a challenge, but we can look for indirect signs that support it:

Virtual Particles: These quantum fluctuations in the vacuum are a good example of something always existing, even in "empty" space. If E holds, we’d expect these fluctuations to be an ongoing phenomenon, reinforcing the idea that nothingness isn't possible.

Cosmic Microwave Background (CMB): We might find subtle fluctuations or anomalies in the CMB that suggest the universe didn't start from a true state of nothingness. This would support the concept that something always existed, even in the very early universe.

Gravitational Waves: Observing black hole mergers could reveal small differences in the expected gravitational wave signals, suggesting a non-singular collapse, which supports the Existence Boundary.

Hawking Radiation: If Hawking radiation can be detected from small or primordial black holes, the spectrum could show deviations from the standard model, which may align with the idea of energy-preserving behaviors in line with E.

So while E itself might not be directly observable, we can test its effects through phenomena like virtual particles, the CMB, gravitational waves, and Hawking radiation. If these observations show patterns that align with E, it could provide indirect evidence of this fundamental principle.

The Existence Boundary (E) operates in a slightly different way. Instead of placing a boundary on space itself, E asserts that absolute nothingness—a state where no matter, energy, or structure exists—is impossible.

So, rather than a physical boundary in space, the Existence Boundary is more of a principle that applies across all scales (quantum, relativistic, cosmological). It's not a boundary in the traditional sense, but a constraint on what can exist. This means that, in any point in the universe, something must always exist. It doesn't necessarily define the location of that existence, but rather the principle that existence can't be entirely absent, no matter where you are in the cosmos.

In essence, E prevents "nothing" from ever being truly realized, ensuring that something must always exist, no matter where you look.

OK I see.  I think in that case it makes more sense to refer to this idea as an existence "principle" rather than a  "boundary", as the latter implies some sort of edge or limit, in either time or space, beyond which some other regime may apply, whereas what you mean is a universal  feature of the cosmos.

It seems to me what you are doing is restating the old philosophical idea that "nature abhors a vacuum": https://en.wikipedia.org/wiki/Horror_vacui_(physics)

There does seem to be a certain truth to this, in that even the vacuum has quantifiable properties (ε₀, μ₀ and hence c). The vacuum therefore can't be said to be "nothing" in a philosophical sense, since how could mere "nothingness" have measurable physical properties? By the way it seems to me that is a conclusion one can reach without even going into such things as the QFT theory of vacuum fluctuations.

However, like @swansont I struggle at the moment to see how this idea of yours is a scientific idea, as it seems to have no observationally testable consequences. 

 

Edited Thursday at 10:33 AM by exchemist

[studiot]

16 hours ago, ovidiu t said:

but it is never zero — implying that there is always some nonzero probability of finding a particle at any given point in space-time.

Are you sure ?

What about an infinite potential barrier or the node points in an s orbital ?

 

Thus far you have stated you one 'principle' , and stated without derivation of any sort, that your principle is compatible with existing theory, which has its own derivation that does not depend upon your E theory in any way.

You need to show a path or chain of reasoning demonstrating why this E principle is either true or necessary.

 

16 hours ago, ovidiu t said:

Quantum Field Theory and the Existence Boundary: In Quantum Field Theory, the vacuum is not truly empty but is filled with quantum fluctuations that give rise to virtual particles. These particles can briefly appear and disappear, but they represent a continuous, underlying "something" that maintains the fabric of reality. The Existence Boundary is consistent with this framework, suggesting that even the "empty" vacuum is full of potential energy and activity, preventing a true vacuum (or absence of energy).

So stating that empty space must have virtual particles in it is not enough.

Existing theory provides the necessary chain of reasoning starting from the principle of least energy for why it may (but does not have to ) contain virtual particles, rather than being full to the brim with red and green striped unicorns.

Edited Thursday at 01:39 PM by studiot
add data about s orbitals

[MigL]

On 1/1/2025 at 10:30 AM, ovidiu t said:

propose a new foundational principle, which we call the Existence Boundary (E)

As Swansont and others have pointed out, what is the need for such a principle when there are already Physical laws preventing 'nothingness' ?
Might there be places where Physical laws do not apply, necessitating your 'principle' to save the universe from having boundaries of 'nothingness' ?

[ovidiu t]

2 hours ago, MigL said:

As Swansont and others have pointed out, what is the need for such a principle when there are already Physical laws preventing 'nothingness' ?
Might there be places where Physical laws do not apply, necessitating your 'principle' to save the universe from having boundaries of 'nothingness' ?

The Existence Boundary (E) is not designed to replace existing physical laws but rather to formalize an implicit principle: the impossibility of absolute nothingness. While physical laws like quantum mechanics and general relativity address "somethingness" in fragmented ways, the Existence Boundary unifies this observation across scales and theories.

1. Why is this principle necessary?

While existing physics (e.g., quantum field theory's vacuum fluctuations and general relativity’s singularities) implies that nothingness is avoided, these implications are scattered and domain-specific. The Existence Boundary explicitly frames this observation as a universal principle, applicable to all scenarios—before the Big Bang, within black holes, or in the vacuum.

Instead of positing a physical boundary, the Existence Boundary provides a logical boundary to nothingness, showing why "something" must always exist, regardless of the scale or context.

2. Does it "save the universe" or change physics?

No, it doesn’t "save" the universe. Rather, it highlights that physical laws inherently prevent true nothingness. By formalizing this, the Existence Boundary acts as a meta-principle that connects disparate phenomena and ensures coherence across scales. For example:

In quantum mechanics, it aligns with the normalization of the wave function: if something doesn’t exist in one place, it must exist elsewhere.

In general relativity, it reinforces why singularities might lead to phenomena like Hawking radiation rather than absolute collapse.

In cosmology, it suggests why the Big Bang likely emerged from a pre-existing state rather than nothing.

3. What is new here?

The Existence Boundary is new in its framing and scope:

It proposes that absolute nothingness is universally impossible—not just in specific contexts.

It bridges quantum mechanics, cosmology, and general relativity, offering a unifying concept that ties together disparate observations and constraints.

It gives a mathematical foundation to something previously only implied, such as ensuring the universe never crosses into absolute nothingness.

4. Is it testable?

While directly testing E is challenging, its consequences are indirectly testable:

Observations of black hole mergers or Hawking radiation could reveal deviations from singularity models, consistent with E.

Anomalies in the cosmic microwave background might hint at pre-Big Bang structures.

The behavior of vacuum fluctuations and virtual particles could further affirm the impossibility of nothingness.

 

The Existence Boundary doesn’t propose new physical laws but identifies a unifying principle embedded within them. It clarifies the impossibility of nothingness as a foundational constraint that prevents the collapse of reality into nonexistence. Far from redundant, it complements and enriches current physics while opening pathways for deeper inquiry into the origins and fate of the universe.

7 hours ago, studiot said:

Are you sure ?

What about an infinite potential barrier or the node points in an s orbital ?

 

Thus far you have stated you one 'principle' , and stated without derivation of any sort, that your principle is compatible with existing theory, which has its own derivation that does not depend upon your E theory in any way.

You need to show a path or chain of reasoning demonstrating why this E principle is either true or necessary.

 

So stating that empty space must have virtual particles in it is not enough.

Existing theory provides the necessary chain of reasoning starting from the principle of least energy for why it may (but does not have to ) contain virtual particles, rather than being full to the brim with red and green striped unicorns.

1. The Observation Across Fields

The Existence Boundary is derived from a simple, universal observation: something must always exist. This is not just a philosophical proposition but a logical extension of what is already observed across quantum mechanics, general relativity, and cosmology.

The reasoning begins with a foundational observation:

The wave function in quantum mechanics shows that if a particle's presence is zero in one region, it must exist elsewhere (wave function normalization ensures this). Thus, absolute absence is impossible.

Vacuum fluctuations in quantum field theory demonstrate that even "empty" space is active, producing temporary particle-antiparticle pairs. This again suggests that nothingness cannot persist.

General relativity shows that energy-matter equivalence (E=mc²) ensures the conservation of energy, even in extreme conditions like black holes, preventing the universe from collapsing into a state of true "nothingness."

2. Addressing Nodes and Barriers

The critique references nodes in an s orbital or infinite potential barriers, asking whether E is necessary. These concepts are entirely compatible with E:

Nodes in quantum mechanics refer to points of zero probability density, but they don’t imply absolute nothingness. Instead, they are part of a broader wave function where probabilities remain nonzero elsewhere. E aligns with this reasoning, stating that if something is absent in one place, it must exist elsewhere.

Infinite potential barriers in quantum mechanics represent localized regions where particles cannot exist. However, particles still exist on either side of the barrier. This again demonstrates that while existence can be locally restricted, absolute nothingness is forbidden.

E is not about removing nodes or barriers; it formalizes the impossibility of a universe-wide void.

3. Chain of Reasoning for E

The reasoning for the Existence Boundary follows these steps:

Quantum Mechanics: Wave function normalization guarantees that the sum of probabilities equals 1. This implies the existence of the particle somewhere in the universe.

Quantum Field Theory: The principle of least energy suggests vacuum fluctuations. These fluctuations prevent any region from being entirely devoid of existence.

General Relativity: Energy conservation prevents the collapse of spacetime into true nothingness. Even singularities maintain some form of energy or information (e.g., Hawking radiation).

By connecting these observations, E emerges as a universal boundary condition that applies across scales, from the quantum to the cosmological.

4. Not Unicorns, but Logical Connections

The Existence Boundary is not an arbitrary principle added to physics. It is not claiming that empty space must contain random phenomena (like "striped unicorns"). Instead, E frames a universal constraint implied by physics:

Virtual particles, dark energy, gravitational waves, and Hawking radiation all point to the impossibility of absolute nothingness.

The Existence Boundary doesn’t invent new elements but rather highlights a shared principle across theories.

5. Why E is Necessary

Existing theories address specific domains but don’t explicitly rule out the possibility of absolute nothingness:

Quantum mechanics deals with probabilities but doesn’t assert that "something must always exist."

General relativity focuses on spacetime and mass-energy equivalence but doesn’t formalize the impossibility of nothingness.

Cosmology describes the universe’s evolution but doesn’t address what preceded the Big Bang.

The Existence Boundary formalizes this shared foundation, creating a unifying principle that spans these domains.

6. Testability

E’s implications can be indirectly tested:

Wave Function: If normalization fails anywhere, it would challenge E. So far, normalization holds universally.

Vacuum Fluctuations: The presence of virtual particles in all "empty" space aligns with E.

Gravitational Waves: Deviations in black hole mergers could suggest non-singular collapses, consistent with E.

Cosmic Microwave Background: Anomalies in the CMB could hint at pre-Big Bang structures or an eternal universe, both aligning with E.

 

E is not an unnecessary addition to physics. It formalizes what existing theories already imply but don’t explicitly state: the impossibility of absolute nothingness. By uniting observations from quantum mechanics, general relativity, and cosmology, the Existence Boundary offers a powerful tool for understanding the universe’s foundational constraints.

[Genady]

I think that the proposed principle is wrong and absolute nothingness is possible.

[studiot]

6 hours ago, ovidiu t said:

The wave function in quantum mechanics shows that if a particle's presence is zero in one region, it must exist elsewhere (wave function normalization ensures this). Thus, absolute absence is impossible

This unsupported calim is as wrong as the previous one that you made about wave functions and I challenged.

6 hours ago, ovidiu t said:

2. Addressing Nodes and Barriers

The critique references nodes in an s orbital or infinite potential barriers, asking whether E is necessary. These concepts are entirely compatible with E:

Nodes in quantum mechanics refer to points of zero probability density, but they don’t imply absolute nothingness. Instead, they are part of a broader wave function where probabilities remain nonzero elsewhere. E aligns with this reasoning, stating that if something is absent in one place, it must exist elsewhere.

Infinite potential barriers in quantum mechanics represent localized regions where particles cannot exist. However, particles still exist on either side of the barrier. This again demonstrates that while existence can be locally restricted, absolute nothingness is forbidden.

This is a different, weaker statement than the absolute one you originally made

once again

On 1/1/2025 at 3:30 PM, ovidiu t said:

but it is never zero

please respond with a proper chain of reasoning rather than a bald unsupported claim

[studiot]

Of course it is in the nature of probability, which is a point function, for the following statement

The probability of finding a particle at this point is 0.6

to imply

That the probability of not finding the particle at this point is 0.4

 

This of course must allow for the possibility and probability that there is / is not something else there.

 

[studiot]

Thank whoever liked my last post.

In point of fact, I think the idea refutes your basic premise as follows.

 

Since probability is always strictly less than 1 it is nowhere = 1.

This must be so for the inergral over all space to equal 1.

This means that every point has a probability that it is empty or contains nothing at all.

 

[Genady]

1 hour ago, studiot said:

Thank whoever liked my last post.

You're welcome 🙂.

[ovidiu t]

On 1/2/2025 at 11:12 AM, exchemist said:

OK I see.  I think in that case it makes more sense to refer to this idea as an existence "principle" rather than a  "boundary", as the latter implies some sort of edge or limit, in either time or space, beyond which some other regime may apply, whereas what you mean is a universal  feature of the cosmos.

It seems to me what you are doing is restating the old philosophical idea that "nature abhors a vacuum": https://en.wikipedia.org/wiki/Horror_vacui_(physics)

There does seem to be a certain truth to this, in that even the vacuum has quantifiable properties (ε₀, μ₀ and hence c). The vacuum therefore can't be said to be "nothing" in a philosophical sense, since how could mere "nothingness" have measurable physical properties? By the way it seems to me that is a conclusion one can reach without even going into such things as the QFT theory of vacuum fluctuations.

However, like @swansont I struggle at the moment to see how this idea of yours is a scientific idea, as it seems to have no observationally testable consequences. 

 

Thank you for your thoughtful engagement! I appreciate the opportunity to clarify and expand on the Existence Boundary (E) concept and address the points raised.

Why "Boundary" and Not Just a Principle?

The term "boundary" is intentionally chosen to signify a universal constraint rather than a spatial or temporal edge. The Existence Boundary doesn’t denote a physical edge to the universe but instead acts as a limit condition that makes absolute nothingness fundamentally impossible. It is a boundary in the conceptual and mathematical sense, preventing "nothing" from being realized, whether in the quantum vacuum, the fabric of spacetime, or the energy density of the cosmos.

This boundary is a necessary condition for existence to manifest across scales, ensuring that the universe cannot reach a state devoid of structure, energy, or potential. Unlike a "principle," which suggests a philosophical or heuristic rule, "boundary" underscores the foundational and universal nature of the idea.

Is It Just Restating "Nature Abhors a Vacuum"?

While it resonates with the philosophical idea that "nature abhors a vacuum," the Existence Boundary goes much further:

• It formalizes this concept mathematically, tying it to quantum mechanics (wavefunction normalization), general relativity (vacuum energy and spacetime curvature), and quantum field theory (vacuum fluctuations and virtual particles).
• It integrates existing physical laws into a unified framework, demonstrating that the impossibility of nothingness is already implicitly enforced across these theories but has not been explicitly articulated as a single foundational boundary.

In short, the Existence Boundary aims to unify disparate observations and principles, transforming a philosophical intuition into a precise scientific proposal.

Observational and Testable Consequences

The idea of the Existence Boundary is not merely philosophical—it has potential observable implications:

1. Quantum Fluctuations and Virtual Particles: Quantum field theory ensures that even the vacuum is "something," filled with fleeting virtual particles. These are observable indirectly through effects like the Casimir effect and the Lamb shift, which align with E’s assertion of the impossibility of a true vacuum.

2. Big Bang and Black Hole Singularities: E proposes that true singularities (e.g., infinite density in black holes or the Big Bang) are mathematically impossible. Instead, the universe undergoes a "bounce" or transition near extreme densities. Observationally, this could appear as deviations in gravitational wave signals or traces of pre-Big Bang phenomena in the cosmic microwave background (CMB).

3. Hawking Radiation: Near black hole horizons, virtual particles arise due to quantum fluctuations. E ensures that these particles and the resulting radiation exist, highlighting that "nothingness" is prevented even under extreme gravitational collapse.

4. Dark Energy and Universe Expansion: E can be linked to the persistence of dark energy, which prevents the universe from collapsing into nothingness and drives its accelerating expansion. Observations of this acceleration provide indirect support for the boundary condition.

5. Wavefunction Collapse: In quantum mechanics, the wavefunction is never zero across all space and time. E ensures that the normalization of the wavefunction (Σ|Ψ|² = 1) is upheld universally, guaranteeing the persistence of existence.

Why Is It Scientific?

The Existence Boundary does not override existing theories—it extends them:

• In Quantum Mechanics: It aligns with wavefunction normalization, showing that the probability of existence is always non-zero.
• In General Relativity: It prevents singularities, aligning with the idea that spacetime must have some minimum structure or curvature.
• In Quantum Field Theory: It explains the necessity of vacuum fluctuations and virtual particles, reinforcing the impossibility of a true vacuum.

While direct testing is challenging, these connections to existing physics suggest ways to indirectly validate the principle through observed phenomena. The Existence Boundary provides a fresh lens to interpret known effects while offering potential predictions for phenomena not yet fully understood.

Final Thoughts

The Existence Boundary is not about redefining existing laws but rather highlighting a unifying constraint that connects them. It provides a deeper understanding of why "something" must always exist, bridging philosophical intuitions and scientific observations. As such, it stands as both a conceptual and a potentially testable addition to our understanding of the universe.

23 hours ago, Genady said:

I think that the proposed principle is wrong and absolute nothingness is possible.

The claim that absolute nothingness is possible contradicts well-established principles in quantum mechanics, quantum field theory, and general relativity. Here's why:

---

1. Quantum Vacuum Fluctuations

The quantum vacuum is not empty but filled with fluctuating fields giving rise to virtual particles. These fluctuations are observable through phenomena like the Casimir effect and Lamb shift, which directly demonstrate that the vacuum has quantifiable, nonzero properties. This provides a strong case against the possibility of absolute nothingness, even in regions considered "empty."

---

2. Wavefunction Normalization

In quantum mechanics, the wavefunction Ψ(x,t) must satisfy the normalization condition:

This ensures that the total probability of finding a particle across all space is always 1. While the probability of presence in one specific region can be zero, there is always a nonzero probability elsewhere. This condition rules out absolute nothingness, as it guarantees the existence of something at all times.

---

3. General Relativity and Spacetime Curvature

In general relativity, spacetime itself is a physical entity shaped by the presence of energy and matter. Even in the absence of visible matter, spacetime cannot collapse into absolute nothingness due to the persistence of vacuum energy or dark energy. The cosmological constant Λ\LambdaΛ, for instance, represents a nonzero energy density intrinsic to spacetime. This ensures:

• The impossibility of a true void in the universe.
• A minimum energy density that prevents spacetime from becoming truly "empty."

Additionally, the Existence Boundary (E) can be seen as an extension of general relativity, ensuring that spacetime itself maintains a baseline structure, even in extreme conditions like black hole interiors or the early universe.

---

The Existence Boundary

The Existence Boundary unifies these principles to assert that something must always exist across scales:

• At quantum scales, wavefunction normalization and vacuum fluctuations ensure nonzero probabilities.
• At macro scales, spacetime curvature and dark energy ensure the persistence of structure.
• Across theoretical scales, E acts as a boundary condition, preventing the universe from collapsing into a singularity or absolute nothingness.

This assertion is supported not only by quantum mechanics but also by cosmological phenomena like the accelerating expansion of the universe.

---

 

[Genady]

44 minutes ago, ovidiu t said:

The claim that absolute nothingness is possible contradicts well-established principles in quantum mechanics, quantum field theory, and general relativity.

No, it does not. All the referred principles show that something exists. They don't show that nothingness does not exist.

[exchemist]

1 hour ago, ovidiu t said:

Thank you for your thoughtful engagement! I appreciate the opportunity to clarify and expand on the Existence Boundary (E) concept and address the points raised.

Why "Boundary" and Not Just a Principle?

The term "boundary" is intentionally chosen to signify a universal constraint rather than a spatial or temporal edge. The Existence Boundary doesn’t denote a physical edge to the universe but instead acts as a limit condition that makes absolute nothingness fundamentally impossible. It is a boundary in the conceptual and mathematical sense, preventing "nothing" from being realized, whether in the quantum vacuum, the fabric of spacetime, or the energy density of the cosmos.

This boundary is a necessary condition for existence to manifest across scales, ensuring that the universe cannot reach a state devoid of structure, energy, or potential. Unlike a "principle," which suggests a philosophical or heuristic rule, "boundary" underscores the foundational and universal nature of the idea.

Is It Just Restating "Nature Abhors a Vacuum"?

While it resonates with the philosophical idea that "nature abhors a vacuum," the Existence Boundary goes much further:

• It formalizes this concept mathematically, tying it to quantum mechanics (wavefunction normalization), general relativity (vacuum energy and spacetime curvature), and quantum field theory (vacuum fluctuations and virtual particles).
• It integrates existing physical laws into a unified framework, demonstrating that the impossibility of nothingness is already implicitly enforced across these theories but has not been explicitly articulated as a single foundational boundary.

In short, the Existence Boundary aims to unify disparate observations and principles, transforming a philosophical intuition into a precise scientific proposal.

Observational and Testable Consequences

The idea of the Existence Boundary is not merely philosophical—it has potential observable implications:

1. Quantum Fluctuations and Virtual Particles: Quantum field theory ensures that even the vacuum is "something," filled with fleeting virtual particles. These are observable indirectly through effects like the Casimir effect and the Lamb shift, which align with E’s assertion of the impossibility of a true vacuum.

2. Big Bang and Black Hole Singularities: E proposes that true singularities (e.g., infinite density in black holes or the Big Bang) are mathematically impossible. Instead, the universe undergoes a "bounce" or transition near extreme densities. Observationally, this could appear as deviations in gravitational wave signals or traces of pre-Big Bang phenomena in the cosmic microwave background (CMB).

3. Hawking Radiation: Near black hole horizons, virtual particles arise due to quantum fluctuations. E ensures that these particles and the resulting radiation exist, highlighting that "nothingness" is prevented even under extreme gravitational collapse.

4. Dark Energy and Universe Expansion: E can be linked to the persistence of dark energy, which prevents the universe from collapsing into nothingness and drives its accelerating expansion. Observations of this acceleration provide indirect support for the boundary condition.

5. Wavefunction Collapse: In quantum mechanics, the wavefunction is never zero across all space and time. E ensures that the normalization of the wavefunction (Σ|Ψ|² = 1) is upheld universally, guaranteeing the persistence of existence.

Why Is It Scientific?

The Existence Boundary does not override existing theories—it extends them:

• In Quantum Mechanics: It aligns with wavefunction normalization, showing that the probability of existence is always non-zero.
• In General Relativity: It prevents singularities, aligning with the idea that spacetime must have some minimum structure or curvature.
• In Quantum Field Theory: It explains the necessity of vacuum fluctuations and virtual particles, reinforcing the impossibility of a true vacuum.

While direct testing is challenging, these connections to existing physics suggest ways to indirectly validate the principle through observed phenomena. The Existence Boundary provides a fresh lens to interpret known effects while offering potential predictions for phenomena not yet fully understood.

Final Thoughts

The Existence Boundary is not about redefining existing laws but rather highlighting a unifying constraint that connects them. It provides a deeper understanding of why "something" must always exist, bridging philosophical intuitions and scientific observations. As such, it stands as both a conceptual and a potentially testable addition to our understanding of the universe.

The claim that absolute nothingness is possible contradicts well-established principles in quantum mechanics, quantum field theory, and general relativity. Here's why:

---

1. Quantum Vacuum Fluctuations

The quantum vacuum is not empty but filled with fluctuating fields giving rise to virtual particles. These fluctuations are observable through phenomena like the Casimir effect and Lamb shift, which directly demonstrate that the vacuum has quantifiable, nonzero properties. This provides a strong case against the possibility of absolute nothingness, even in regions considered "empty."

---

2. Wavefunction Normalization

In quantum mechanics, the wavefunction Ψ(x,t) must satisfy the normalization condition:

This ensures that the total probability of finding a particle across all space is always 1. While the probability of presence in one specific region can be zero, there is always a nonzero probability elsewhere. This condition rules out absolute nothingness, as it guarantees the existence of something at all times.

---

3. General Relativity and Spacetime Curvature

In general relativity, spacetime itself is a physical entity shaped by the presence of energy and matter. Even in the absence of visible matter, spacetime cannot collapse into absolute nothingness due to the persistence of vacuum energy or dark energy. The cosmological constant Λ\LambdaΛ, for instance, represents a nonzero energy density intrinsic to spacetime. This ensures:

• The impossibility of a true void in the universe.
• A minimum energy density that prevents spacetime from becoming truly "empty."

Additionally, the Existence Boundary (E) can be seen as an extension of general relativity, ensuring that spacetime itself maintains a baseline structure, even in extreme conditions like black hole interiors or the early universe.

---

The Existence Boundary

The Existence Boundary unifies these principles to assert that something must always exist across scales:

• At quantum scales, wavefunction normalization and vacuum fluctuations ensure nonzero probabilities.
• At macro scales, spacetime curvature and dark energy ensure the persistence of structure.
• Across theoretical scales, E acts as a boundary condition, preventing the universe from collapsing into a singularity or absolute nothingness.

This assertion is supported not only by quantum mechanics but also by cosmological phenomena like the accelerating expansion of the universe.

---

 

 

What you describe is not a boundary, though, as there isn’t anything outside it.

I must say also that  the QM wave function stuff seems to be a mere truism. Clearly, if a QM entity exists, i.e. a wave function can in principle be written for it, it must be detectable somewhere. Therefore the integral over all space must be unity. This is trivially obvious and not some great insight on your part.

I’m also intrigued by the point made earlier by @studiot, that wave functions with nodes imply there are points in space at which the probability of detection of the entity is, in fact, zero. How does that square with your idea?

[ovidiu t]

8 hours ago, studiot said:

Of course it is in the nature of probability, which is a point function, for the following statement

The probability of finding a particle at this point is 0.6

to imply

That the probability of not finding the particle at this point is 0.4

 

This of course must allow for the possibility and probability that there is / is not something else there.

 

1. Wavefunction Normalization and Nonzero Total Probability

The wavefunction in quantum mechanics must satisfy the normalization condition:

• Local Probability: represents the probability density at position x. At any single point x, this probability can be zero (e.g., nodes in the wavefunction).
• Global Constraint: The integral over all space ensures that the particle exists somewhere with total probability :

  Implication for E:

• The Existence Boundary extends this principle to the entire universe, ensuring that while there may be local absences  the global probability of existence remains conserved: 

  2. Nodes in Quantum Mechanics

  In quantum systems, nodes represent regions where , but this does not imply nothingness:

• Mathematical Example: Consider the wavefunction for a particle in a 1D box:

• where n is the quantum number, and L is the box length.

• At specific points:  forming nodes. However, the wavefunction is nonzero elsewhere, ensuring global existence. 

  Implication for E:

• Nodes are consistent with E. Local absence does not negate global existence, which is guaranteed by the wavefunction's normalization.

  3. Quantum Field Theory: Vacuum Fluctuations

  In QFT, even the vacuum has nonzero energy and fluctuations:where H is the Hamiltonian and represents the zero-point energy of the quantum harmonic oscillator.

• Casimir Effect: The attractive force between uncharged conducting plates arises from differences in vacuum energy:

  where a is the separation between the plates.

• Lamb Shift: A shift in energy levels of hydrogen due to vacuum fluctuations provides further evidence of nonzero vacuum properties.

  Implication for E:

• Vacuum fluctuations are a direct manifestation of E, showing that the vacuum is not "nothing" but a dynamic state filled with energy and activity.
   

  ---

  4. General Relativity: Spacetime Structure

  The Einstein field equations describe spacetime curvature caused by energy and matter: where  is the Einstein tensor, is the cosmological constant, and is the stress-energy tensor.

  Cosmological Constant Λ\LambdaΛ: Represents vacuum energy density, ensuring spacetime curvature persists even in the absence of matter:

  Implication for E:

  The Existence Boundary can be expressed as an additional termenforcing a minimum curvature or energy density:

  Unified Mathematical Representation of E

  Emergence refers to the phenomenon where higher-order properties (e.g., macroscopic or relativistic effects) arise naturally from the collective behavior of fundamental interactions or principles at smaller scales (e.g., quantum scales). In the context of the Existence Boundary (E), the emergence describes the transition of E from a scalar form at the quantum level to a tensor form at relativistic or macroscopic scales.

  Unified Mathematical Representation of E: Explanation

  The proposed scale-dependent formulation of E captures this emergent behavior mathematically:

  where:

  - is a scale-dependent interpolation function that smoothly transitions between quantum and relativistic regimes.

  - At quantum scales 

  At relativistic/macroscopic scales: a rank-2 tensor.

  The emergent behavior is captured in the mathematical interpolation, where the properties of E evolve naturally as a function of the scale ℓ\ellℓ.

   

   

  ---

  Role of Scale Interpolation Function

  The function λ(ℓ)\lambda(\ell)λ(ℓ) governs the scale-dependent behavior of E. It can be explicitly defined as:

  where:This function ensures a smooth, continuous transition between quantum and relativistic scales, avoiding abrupt discontinuities.

  Emergent Transition from Scalar to Tensor:

  

  

   

  ---

  Relation to the Emergence Phenomenon

  The mathematical interpolation and scale-dependent transition of E reflect a key feature of emergence:

  • At small scales, the Existence Boundary (E) enforces probabilistic constraints, ensuring that something must exist (quantum normalization).
  • As scale increases, the cumulative effects of these constraints manifest as geometric properties, contributing to the curvature and structure of spacetime 

  This emergence mirrors how:

  • Quantum fluctuations give rise to macroscopic phenomena like vacuum energy.
  • The statistical behavior of individual particles transitions into thermodynamic laws at larger scales

    Observable Implications

  • Quantum Regime:

    • Virtual particles and vacuum fluctuations (Casimir effect, Lamb shift) manifest as direct consequences of E at small scales.

  • Macroscopic Regime:

    • contributes to preventing singularities, supporting scenarios like the Big Bounce in cosmology.

  • Intermediate Scales:

    • The smooth transition governed by may influence phenomena like Hawking radiation near black holes or the early universe's inflationary phase.

    • Conclusion: A Unified Perspective on the Existence Boundary (E)

      The Existence Boundary (E) offers a unifying framework that ties together fundamental principles from quantum mechanics, quantum field theory, and general relativity to address the impossibility of absolute nothingness. Here’s how:

    • Wavefunction Normalization and Global Existence:

      • The Existence Boundary formalizes the principle that while local absence (e.g., nodes in quantum mechanics) is possible, global existence is conserved.
      • This is mathematically guaranteed through wavefunction normalization, extending the principle from single particles to the universe as a whole.

    • Nodes and Vacuum Fluctuations:

      • Nodes in quantum systems and vacuum fluctuations in quantum field theory demonstrate that even in regions of local absence or "emptiness," the broader system retains dynamic, nonzero properties.
      • E provides a conceptual and mathematical boundary that ensures these fluctuations and dynamic properties are consistent with the impossibility of absolute void.

    • Emergence Across Scales:

      • E evolves naturally from a scalar at quantum scales (enforcing probabilistic constraints) to a tensor at macroscopic scales (manifesting as spacetime curvature). This reflects the phenomenon of emergence, where small-scale principles give rise to large-scale behaviors.
      • The smooth interpolation function ensures a seamless transition, avoiding discontinuities and ensuring the continuity of physical laws across scales.

    • Observable Implications:

      • Quantum Regime: E is consistent with observable phenomena like virtual particles, the Casimir effect, and the Lamb shift.
      • Relativistic Regime: At larger scales, E contributes to the structure and curvature of spacetime, influencing phenomena like the prevention of singularities in black holes and the Big Bounce in cosmology.
      • Intermediate Scales: E offers potential explanations for transitions observed in phenomena like Hawking radiation and early universe inflation.

    • A Foundational Principle:

      • E is not an arbitrary imposition but emerges from established principles, providing a boundary condition that ensures the persistence of existence across all scales.
      • It offers a new perspective on the unification of quantum mechanics and general relativity, addressing fundamental questions about the nature of existence and the structure of reality.

    • Broader Significance:

      The Existence Boundary reaffirms the interconnectedness of quantum and relativistic phenomena. By emphasizing the impossibility of absolute nothingness, it provides a foundation for understanding the universe's continuity and resilience, even under extreme conditions like black holes or the early moments of the Big Bang.

      While speculative, E offers a mathematically grounded and physically plausible framework that could inspire further research and exploration. Its observable consequences and alignment with established physics make it a valuable concept in bridging the gaps between different domains of physics.

5 minutes ago, exchemist said:

What you describe is not a boundary, though, as there isn’t anything outside it.

I must say also that  the QM wave function stuff seems to be a mere truism. Clearly, if a QM entity exists, i.e. a wave function can in principle be written for it, it must be detectable somewhere. Therefore the integral over all space must be unity. This is trivially obvious and not some great insight on your part.

I’m also intrigued by the point made earlier by @studiot, that wave functions with nodes imply there are points in space at which the probability of detection of the entity is, in fact, zero. How does that square with your idea?

[exchemist]

25 minutes ago, ovidiu t said:

1. Wavefunction Normalization and Nonzero Total Probability

The wavefunction in quantum mechanics must satisfy the normalization condition:

• Local Probability: represents the probability density at position x. At any single point x, this probability can be zero (e.g., nodes in the wavefunction).
• Global Constraint: The integral over all space ensures that the particle exists somewhere with total probability :

  Implication for E:

• The Existence Boundary extends this principle to the entire universe, ensuring that while there may be local absences  the global probability of existence remains conserved: 

  2. Nodes in Quantum Mechanics

  In quantum systems, nodes represent regions where , but this does not imply nothingness:

• Mathematical Example: Consider the wavefunction for a particle in a 1D box:

• where n is the quantum number, and L is the box length.

• At specific points:  forming nodes. However, the wavefunction is nonzero elsewhere, ensuring global existence. 

  Implication for E:

• Nodes are consistent with E. Local absence does not negate global existence, which is guaranteed by the wavefunction's normalization.

  3. Quantum Field Theory: Vacuum Fluctuations

  In QFT, even the vacuum has nonzero energy and fluctuations:where H is the Hamiltonian and represents the zero-point energy of the quantum harmonic oscillator.

• Casimir Effect: The attractive force between uncharged conducting plates arises from differences in vacuum energy:

  where a is the separation between the plates.

• Lamb Shift: A shift in energy levels of hydrogen due to vacuum fluctuations provides further evidence of nonzero vacuum properties.

  Implication for E:

• Vacuum fluctuations are a direct manifestation of E, showing that the vacuum is not "nothing" but a dynamic state filled with energy and activity.
   

  ---

  4. General Relativity: Spacetime Structure

  The Einstein field equations describe spacetime curvature caused by energy and matter: where  is the Einstein tensor, is the cosmological constant, and is the stress-energy tensor.

  Cosmological Constant Λ\LambdaΛ: Represents vacuum energy density, ensuring spacetime curvature persists even in the absence of matter:

  Implication for E:

  The Existence Boundary can be expressed as an additional termenforcing a minimum curvature or energy density:

  Unified Mathematical Representation of E

  Emergence refers to the phenomenon where higher-order properties (e.g., macroscopic or relativistic effects) arise naturally from the collective behavior of fundamental interactions or principles at smaller scales (e.g., quantum scales). In the context of the Existence Boundary (E), the emergence describes the transition of E from a scalar form at the quantum level to a tensor form at relativistic or macroscopic scales.

  Unified Mathematical Representation of E: Explanation

  The proposed scale-dependent formulation of E captures this emergent behavior mathematically:

  where:

  - is a scale-dependent interpolation function that smoothly transitions between quantum and relativistic regimes.

  - At quantum scales 

  At relativistic/macroscopic scales: a rank-2 tensor.

  The emergent behavior is captured in the mathematical interpolation, where the properties of E evolve naturally as a function of the scale ℓ\ellℓ.

   

   

  ---

  Role of Scale Interpolation Function

  The function λ(ℓ)\lambda(\ell)λ(ℓ) governs the scale-dependent behavior of E. It can be explicitly defined as:

  where:This function ensures a smooth, continuous transition between quantum and relativistic scales, avoiding abrupt discontinuities.

  Emergent Transition from Scalar to Tensor:

  

  

   

  ---

  Relation to the Emergence Phenomenon

  The mathematical interpolation and scale-dependent transition of E reflect a key feature of emergence:

  • At small scales, the Existence Boundary (E) enforces probabilistic constraints, ensuring that something must exist (quantum normalization).
  • As scale increases, the cumulative effects of these constraints manifest as geometric properties, contributing to the curvature and structure of spacetime 

  This emergence mirrors how:

  • Quantum fluctuations give rise to macroscopic phenomena like vacuum energy.
  • The statistical behavior of individual particles transitions into thermodynamic laws at larger scales

    Observable Implications

  • Quantum Regime:

    • Virtual particles and vacuum fluctuations (Casimir effect, Lamb shift) manifest as direct consequences of E at small scales.

  • Macroscopic Regime:

    • contributes to preventing singularities, supporting scenarios like the Big Bounce in cosmology.

  • Intermediate Scales:

    • The smooth transition governed by may influence phenomena like Hawking radiation near black holes or the early universe's inflationary phase.

    • Conclusion: A Unified Perspective on the Existence Boundary (E)

      The Existence Boundary (E) offers a unifying framework that ties together fundamental principles from quantum mechanics, quantum field theory, and general relativity to address the impossibility of absolute nothingness. Here’s how:

    • Wavefunction Normalization and Global Existence:

      • The Existence Boundary formalizes the principle that while local absence (e.g., nodes in quantum mechanics) is possible, global existence is conserved.
      • This is mathematically guaranteed through wavefunction normalization, extending the principle from single particles to the universe as a whole.

    • Nodes and Vacuum Fluctuations:

      • Nodes in quantum systems and vacuum fluctuations in quantum field theory demonstrate that even in regions of local absence or "emptiness," the broader system retains dynamic, nonzero properties.
      • E provides a conceptual and mathematical boundary that ensures these fluctuations and dynamic properties are consistent with the impossibility of absolute void.

    • Emergence Across Scales:

      • E evolves naturally from a scalar at quantum scales (enforcing probabilistic constraints) to a tensor at macroscopic scales (manifesting as spacetime curvature). This reflects the phenomenon of emergence, where small-scale principles give rise to large-scale behaviors.
      • The smooth interpolation function ensures a seamless transition, avoiding discontinuities and ensuring the continuity of physical laws across scales.

    • Observable Implications:

      • Quantum Regime: E is consistent with observable phenomena like virtual particles, the Casimir effect, and the Lamb shift.
      • Relativistic Regime: At larger scales, E contributes to the structure and curvature of spacetime, influencing phenomena like the prevention of singularities in black holes and the Big Bounce in cosmology.
      • Intermediate Scales: E offers potential explanations for transitions observed in phenomena like Hawking radiation and early universe inflation.

    • A Foundational Principle:

      • E is not an arbitrary imposition but emerges from established principles, providing a boundary condition that ensures the persistence of existence across all scales.
      • It offers a new perspective on the unification of quantum mechanics and general relativity, addressing fundamental questions about the nature of existence and the structure of reality.

    • Broader Significance:

      The Existence Boundary reaffirms the interconnectedness of quantum and relativistic phenomena. By emphasizing the impossibility of absolute nothingness, it provides a foundation for understanding the universe's continuity and resilience, even under extreme conditions like black holes or the early moments of the Big Bang.

      While speculative, E offers a mathematically grounded and physically plausible framework that could inspire further research and exploration. Its observable consequences and alignment with established physics make it a valuable concept in bridging the gaps between different domains of physics.

Yes, yes, no need to copy/paste formulae for the particle in a box. But you are not addressing the point at issue. Your claim, at least as you originally stated it,  is there is nowhere where there is complete nothingness. Yet at the nodes in the wave function of bound systems, the probability density is zero. So surely it must be false to say that there is nowhere where there is complete nothingness, mustn’t it?

Edited 21 hours ago by exchemist

[ovidiu t]

1. Localized Nothingness (Nodes):

   • Nodes, where the probability density is zero in the wave function, represent localized nothingness. However, they are always within a broader wave function where the probability density is nonzero elsewhere.
   • In this sense, nodes do not represent total nothingness; instead, they are surrounded by something. They are part of a system where the normalization condition guarantees that the total probability sums to 1.

2. Distinction Between Local and Total Nothingness:

   • My claim does not deny localized regions of zero probability, such as nodes.
   • I am asserting that total nothingness within a system or framework is impossible. Even if one region or point within a system has no particles, energy, or matter, the system as a whole will have "something" elsewhere to ensure the total probability remains normalized.

3. Implication of the Existence Boundary:

   • The Existence Boundary (E) posits that the universe cannot reach a state of total nothingness. While localized regions of "nothingness" may exist (e.g., nodes), they are always embedded within a system where "something" persists globally.
   • If the probability of "nothingness" approaches 99.999...% in one region, normalization ensures that the remaining probability, no matter how small, must manifest as something elsewhere.

4. Why Absolute Nothingness is Impossible:

   • Total nothingness would imply a global absence of all energy, matter, or structure, violating principles like wave function normalization, vacuum fluctuations (quantum field theory), and spacetime curvature (general relativity).
   • Localized nothingness is always "bounded" by the presence of existence elsewhere, ensuring that "something" must always exist in the broader framework.

---

Conclusion: I am not claiming that "nowhere there is nothingness." Instead, I assert that total nothingness across an entire system or framework is impossible. Localized nothingness, such as nodes in a wave function, is entirely consistent with the Existence Boundary, as they exist within a broader framework where something must always be present.

This refined claim emphasizes the impossibility of global nothingness while acknowledging the reality of localized phenomena like nodes. It aligns with established principles and ensures clarity in addressing your critique.

[studiot]

Just now, ovidiu t said:

Distinction Between Local and Total Nothingness:

• My claim does not deny localized regions of zero probability, such as nodes.
• I am asserting that total nothingness within a system or framework is impossible. Even if one region or point within a system has no particles, energy, or matter, the system as a whole will have "something" elsewhere to ensure the total probability remains normalized.

Whilst this is quite different from your original claim,

where exactly in QM is the requirement for any wave function to exist  at all ?

what is preventing an entire region or universe being totally empty ?

Yes there are formulae such as you have quoted if and only if there is a particle with a wavefuntion and those formulae have been found to be quite accurate.

But what pray is the wavefunction for

Just now, ovidiu t said:

if one region or point within a system has no particles, energy, or matter,

such a region ?

what exactly is the wavefunction for a non particle in that region ?

 

And further i have already asked where exactly in QM are the theorems, formulae etc which require virtual particles ?

Yes QM allows virtual particles and offers a credible mechanism for their operation.

But for this you need to go back to Goldstein,  and Higgs.

 

And this business of suddenly introducing local and global and trying to wriggle out of admitting your original claim went too far.

That claim is rather like two men in a bar.

One has finished his beer the other still has some beer in his glass.

So he claims there is beere somwhere (in my glass) and there are no such things as empty glasses.

[ovidiu t]

At any scale—whether quantum, relativistic, or cosmological—absolute nothingness cannot dominate the entirety of the framework in which physical phenomena occur. Even if we imagine the universe condensed into the size of a room, a grain of sand, or stretched infinitely, the probability that the entirety of the framework is filled with "nothingness" is exactly zero.

This impossibility arises because:

1. Wavefunction Normalization: In quantum mechanics, the total probability across all of space must sum to 1. Even if local regions (nodes) show zero probability, other regions must compensate with nonzero values. This guarantees that "something" must always exist somewhere within the framework.

2. Quantum Fluctuations: In quantum field theory, the vacuum is not empty but filled with fluctuations that generate virtual particles. This activity means "nothingness" is never truly realized, even in the smallest scales or "empty" regions.

3. Spacetime Curvature: In general relativity, spacetime itself is never devoid of energy or structure. Even "empty" space maintains energy density (e.g., the cosmological constant), ensuring the persistence of something—whether vacuum energy, dark energy, or the geometry of spacetime itself.

4. Scaling the Framework: Whether the framework is as small as a particle or as vast as the cosmos, these principles remain valid. The fundamental laws of physics ensure that some form of existence—energy, fluctuations, or curvature—persists, preventing the framework from being completely devoid of all existence.

[Markus Hanke]

8 hours ago, ovidiu t said:

The Existence Boundary can be expressed as an additional termenforcing a minimum curvature or energy density:

But this is functionally identical to the ordinary field equations with cosmological constant, thus \(E_{\mu \nu}=\lambda g_{\mu \nu}\). There is nothing new here.

8 hours ago, ovidiu t said:

The proposed scale-dependent formulation of E captures this emergent behavior mathematically:

This is not a valid tensor equation, and thus quite meaningless. 

The other thing of course is that we know from experiment and observation that the motion of free-fall particles outside local masses (eg Earth) is very well described by vacuum solutions to the ordinary Einstein equations without cosmological constant. This puts very stringent limits on whatever modification to the field equations you propose.

PS. The forum software here supports LaTeX, I’d suggest you use it instead of embedded pictures.