QUANTUM NON-LOCALITY versus RELATIVISTIC CAUSALITY

 

Scale Relativity proposes that the very nature of spacetime and the laws governing motion are dependent on the scale of observation, or "resolution." It starts from the premise that spacetime is fundamentally fractal, meaning its structure looks complex and non-smooth, possessing intricate details at arbitrarily small levels as you zoom in. General Relativity, in this view, describes the large-scale, smoothed-out behaviour of this fractal spacetime, where it approximates a continuous, differentiable manifold. Quantum mechanics, conversely, is seen as the mechanics governing motion within this complex fractal structure at microscopic scales.

Scale-Dependent Spacetime: From the fractal quantum core to the smooth classical realm, illustrating Scale Relativity's vision of interconnectedness at microscopic levels giving rise to emergent smoothness at macroscopic scales.

The resolution to the apparent conflict between quantum non-locality and relativistic causality hinges on this scale dependence. At the large scales described by General Relativity, spacetime is effectively smooth, and the standard notions of causality apply. Information and physical influences cannot propagate faster than the speed of light, c, ensuring the causal ordering necessary for macroscopic physics and cosmology. This c is the limiting speed for interactions mediated across the smoothed-out spacetime geometry.

However, at the microscopic scales relevant to quantum mechanics, Scale Relativity posits that spacetime is non-differentiable and fractal. In this regime, the concept of a well-defined velocity breaks down, and the usual understanding of distance and time intervals becomes more complex because the length of a path depends intrinsically on the resolution scale. Crucially, this fractal geometry isn't just about paths becoming longer or more tortuous; it inherently possesses an incredibly rich and intricate web of connections that are not apparent at large scales. Nottale argues that quantum non-locality and instantaneous correlations (like those seen in entanglement) are a natural consequence of this underlying fractal structure. Increased fractality implies a denser network of potential pathways and linkages, meaning that two particles, even separated by a significant distance in our large-scale, smoothed-out view, might remain "topologically close" or directly connected within the fine-grained fractal network. The macroscopic metric distance becomes less relevant than the connectivity provided by the fractal fabric.

Therefore, changes in the state of one particle (like a measurement) can instantaneously affect the guiding conditions for the other via these inherent fractal connections, reflecting the interconnectedness of the structure itself, much like perturbing one point in a complex web transmits influence instantly through tension along its strands. This influence doesn't involve a signal propagating faster than c through the large-scale, smoothed-out spacetime but rather operates through the internal "wiring" provided by the fractal geometry at the quantum scale. It's crucial here to distinguish this mechanism for instantaneous quantum correlation from the physical propagation of energy, momentum, or causal influence across spacetime. While the underlying fractal network provides the substrate for these correlations between suitably prepared, coherent quantum states like entangled pairs, it does not necessarily offer a viable pathway for classical propagation. Photons or other particles carrying energy interact primarily with the emergent, large-scale spacetime geometry and are thus bound by its rules, including the speed limit c. Furthermore, the ability to effectively "utilize" or be sensitive to these deep fractal connections might be restricted to these specific, highly coherent quantum states. Attempting to propagate a more complex signal or even a single photon across macroscopic distances via these intricate structures would likely lead to rapid decoherence due to interactions with the complex environment at that scale, effectively forcing the interaction back onto the smoothed-out, relativistic stage where c governs the maximum speed of causal influence.

Essentially, Scale Relativity suggests that the "rules" change with scale. The instantaneous correlations required for quantum mechanics are permissible and operate within the fractal microstructure of spacetime, reflecting its inherent, scale-dependent interconnectedness. The finite speed limit c is an emergent property governing the propagation of energy and causal signals across large scales, where the fractal details are averaged out, and spacetime behaves according to General Relativity. It's not that one theory contradicts the other; rather, they describe different physical regimes and different types of physical phenomena (correlation vs. propagation) arising from the same underlying, scale-dependent fractal reality. The apparent conflict dissolves because the instantaneous quantum effects are seen as features of the fractal geometry's connectivity itself, potentially accessible only by coherent quantum states, while the relativistic speed limit governs how causal influences travel across the large-scale, averaged structure.

is QUANTUM PHYSICS really WEIRD? HOM effect

 

The Hong-Ou-Mandel effect, first demonstrated experimentally by Chung Ki Hong, Zheyu Ou, and Leonard Mandel in 1987, stands as a fundamental illustration of quantum interference involving two photons. It elegantly reveals the particle and wave nature of light in a way that starkly contrasts with classical expectations. The experiment typically begins with a source that generates pairs of photons, often through spontaneous parametric down-conversion (SPDC) in a nonlinear crystal. In this process, a single higher-energy pump photon splits into two lower-energy photons, conventionally called the signal and idler. Critically, these photons are generated simultaneously and are often correlated in properties like polarization or momentum.

The setup then directs these two photons along separate paths towards a simple, yet crucial, optical component: a 50/50 beam splitter. This device classically transmits half the light incident upon it and reflects the other half. Detectors are placed at each of the two output ports of the beam splitter, set up to register coincidence counts – instances where both detectors fire simultaneously, indicating one photon exited each port. One of the input paths usually incorporates a mechanism to introduce a variable delay, allowing precise control over the relative arrival time of the two photons at the beam splitter.
The truly remarkable observation occurs when the path lengths are adjusted so that the two photons arrive at the beam splitter at precisely the same moment and are made indistinguishable in all other respects (like polarization, frequency, and spatial mode). Under these conditions, coincidence counts between the two detectors plummet to zero. The photons never exit through different ports; instead, they always leave the beam splitter together, exiting from the same output port, either both being transmitted or both being reflected. Which specific port they exit is random, but they always exit as a pair. As the delay is slightly adjusted away from zero, making the photons distinguishable by their arrival time, the coincidence counts reappear, tracing out a characteristic V-shaped curve known as the "HOM dip" when plotted against the delay.

From the perspective of standard quantum mechanics, this phenomenon is explained through the interference of probability amplitudes, a calculation technique powerfully formalized by Richard Feynman's path integral approach. There are two indistinguishable ways for the two detectors to register a coincidence: both photons could be reflected by the beam splitter, or both photons could be transmitted. Quantum mechanics dictates that we must add the probability amplitudes for these two possibilities. Due to the specific phase shifts associated with reflection and transmission at a beam splitter, these two amplitudes turn out to be equal in magnitude but opposite in sign. They destructively interfere, leading to a zero probability amplitude, and hence zero probability, for detecting one photon at each output port simultaneously when the input photons are identical and arrive together. This explanation, while mathematically precise and predictive, often strikes beginners as profoundly weird. How do the photons, arriving from separate paths, "know" about each other to conspire to always exit together? Why does the outcome depend on summing abstract possibilities rather than a direct interaction? Where are the photons before they hit the beam splitter? The standard interpretation relies on superposition and the collapse of the wave function upon measurement, leaving the underlying mechanism feeling somewhat opaque and magical, lacking a continuous, intuitive physical picture.

The pilot-wave theory, or de Broglie-Bohm theory, offers a different conceptual framework that aims to dissolve this weirdness by positing a more direct physical reality. In this view, photons are always actual particles, possessing definite positions and trajectories at all times, even when not observed. These particles, however, are not moving independently; they are guided or "piloted" by an associated physical wave field. This pilot wave, mathematically related to the standard quantum wave function, permeates space and evolves according to the deterministic Schrödinger equation. For the two-photon HOM experiment, the crucial entity is the pilot wave associated with the entire two-photon system. This wave exists in a higher-dimensional configuration space that describes the possible positions of both particles.  Crucially, the mathematical machinery used to calculate the structure and evolution of this pilot wave is identical to that of standard quantum mechanics; it inherently involves summing the amplitudes for different configurations, just as described by Feynman's approach.

When the two photons approach the beam splitter, their guiding pilot wave interacts with it. The structure of the pilot wave itself is altered by the presence of the beam splitter. The wave function contains components representing both possibilities: both photons reflecting, and both photons transmitting. Because the photons are identical and arrive simultaneously, the symmetry of the situation dictates how these wave components combine. Specifically, the pilot wave develops regions of zero amplitude – nodes – in the configuration space corresponding to the outcome where one photon exits one port and the second photon exits the other. The particles, following the deterministic guidance of the pilot wave, are steered by the wave's gradient. Since the wave amplitude is zero for the separated-exit outcome, the particles are simply never guided into that configuration. They are inevitably directed along trajectories that lead them to exit the same output port. The inherent randomness of quantum mechanics, in this picture, arises not from measurement collapse but from our ignorance of the precise initial positions of the particles within their initial wave packets; depending on these exact starting points, the deterministic wave dynamics will guide them to one shared exit port or the other, but never separate ports.

Introducing a time delay between the photons breaks the symmetry of their arrival at the beam splitter. This changes the structure of the two-photon pilot wave as it interacts with the beam splitter. The nodes corresponding to the anti-coincidence outcome (photons exiting separate ports) are no longer present or are significantly altered. Consequently, the pilot wave can now guide the particles along trajectories that lead them to different output ports, and coincidence counts are registered. The HOM dip is thus explained as a direct consequence of the physical wave dynamics guiding the particles through the beam splitter, with the dip occurring when the wave structure physically prevents the particles from taking separate paths.

This pilot-wave interpretation removes much of the perceived mystery. The photons don't need to "know" about each other in some spooky way; their behaviour is coordinated by the shared physical wave field that carries information about both particles and the entire experimental setup. Interference is not an abstract mathematical cancellation but a real physical effect where the wave guides particles away from certain regions. Particles always have trajectories, and the "measurement problem" is less problematic as the wave evolves smoothly and deterministically guides the particles to the detectors. This perspective, emphasizing the reality of both particles and guiding waves, and grounding interference in the dynamics of these waves influencing particle paths, resonates strongly with modern experimental techniques in quantum optics that increasingly rely on manipulating and understanding the paths and modes of photons to achieve complex quantum effects like entanglement generation via path identity, providing a potentially more intuitive, less "magical" foundation.

is QUANTUM PHYSICS really WEIRD? QUANTUM ERASER

Understanding quantum phenomena often involves grappling with concepts that challenge our everyday intuition. The quantum eraser experiment is a prime example, frequently presented as showcasing the inherent "weirdness" of the quantum world. However, by adopting a different perspective, specifically the pilot-wave interpretation pioneered by Louis de Broglie and later developed by David Bohm, much of this apparent strangeness dissolves, revealing a more coherent, albeit still deeply non-classical, underlying reality.

First, let's outline a typical quantum eraser experiment, variations of which were developed and explored significantly from the 1980s onwards by researchers like Marlan Scully, Herbert Walther, and their colleagues, building on foundational concepts of quantum complementarity. Imagine the classic double-slit experiment: particles, like photons, are sent towards a barrier with two narrow slits. If we simply detect where the photons land on a screen behind the barrier, we observe an interference pattern – alternating bright and dark fringes. This pattern is characteristic of waves interfering, suggesting each photon somehow passes through both slits simultaneously.

Now, to introduce the "which-path" information, we modify the setup. Let's place a device, say a circular polarizer, in front of each slit. One polarizer imparts clockwise circular polarization to photons passing through slit A, and the other imparts counter-clockwise polarization to photons passing through slit B. If we now detect the photons on the screen and measure their polarization, we can tell which slit each photon came through. Crucially, when we do this, the interference pattern completely disappears. We just see two overlapping bands corresponding to photons coming from each slit individually. This demonstrates a core quantum principle: if you acquire information about which path a particle took, the wave-like interference behaviour vanishes. The paths become distinguishable.

The "eraser" stage adds the most counter-intuitive element from the standard viewpoint. After the photons have passed the slits (and received their polarization tag) but before they hit the final detection screen, we insert another optical element – the eraser. A simple example is a linear polarizer oriented at 45 degrees. This polarizer will allow photons with either clockwise or counter-clockwise polarization to pass through, but it projects them onto a single linear polarization state. Effectively, it "erases" the original circular polarization information. Now, if we look only at the sub-set of photons that successfully passed through this linear polarizer (the eraser), the interference pattern miraculously reappears on the final screen. If we look at the photons blocked by the eraser, or the combined pattern of all photons, there is no interference.

From the perspective of standard quantum mechanics, particularly interpretations influenced by the Copenhagen school, this experiment highlights several points often described as "weird" or "marvelous," which can make the theory seem opaque. The first is the stark wave-particle duality: how can a photon be a wave spreading through both slits (to interfere) and yet a particle whose path can be marked? Standard interpretations often state that which aspect manifests depends on the experimental question asked – the measurement context dictates reality. Second is the measurement problem: the very act of potentially knowing the path (by tagging the polarization) seems to collapse the wave function and destroy the interference. Why should the possibility of information fundamentally alter the physical outcome? Third, and most perplexing, is the delayed-choice aspect. The decision to insert the eraser or not can be made long after the photon has passed the slits. How can a choice made now affect whether the photon behaved like a wave or a particle in the past? This leads to interpretations involving retrocausality or a fundamental denial of particles having definite trajectories before measurement. It suggests reality is not fixed until observed, which feels deeply unsatisfactory and "magical" to many.

The de Broglie-Bohm (dBB) pilot-wave theory offers a radically different, yet fully consistent, explanation that dispels this weirdness. The core idea is simple but profound: quantum entities are both particle and wave, always. There exists a real particle with a definite position at all times, and simultaneously there exists a real physical field, the pilot wave (mathematically described by the quantum wave function), which guides the particle's motion. The particle does not spread out; it follows a precise trajectory. The wave, however, does spread out, passes through both slits, and interferes with itself.

It's crucial to acknowledge here that this pilot wave is inherently non-local. Its configuration across the entire experimental setup, potentially spanning large distances, instantaneously influences the particle's trajectory based on the wave's overall structure. Detractors often seize upon this feature, sometimes termed "action at a distance," as physically implausible or in direct conflict with the spirit of relativity. However, from the dBB perspective, this non-locality isn't an awkward add-on; it is accepted as a fundamental aspect of quantum reality, explicitly built into the guiding mechanism. It's the same underlying non-locality experimentally confirmed in Bell tests involving entangled particles. Rather than emerging mysteriously from measurement postulates, in dBB theory, the pilot wave is the physical carrier of these non-local correlations, whether guiding a single particle through interfering paths or linking the fates of distant entangled particles.

This acceptance of instantaneous influence contrasts sharply with General Relativity. Einstein, troubled by the action-at-a-distance implied by Newtonian gravity, formulated GR such that mass/energy curves spacetime locally, and objects follow geodesics within this curved structure. Crucially, any change in the mass-energy distribution, and therefore any change in the spacetime curvature and the resulting geodesics, propagates outwards at the finite speed of light, c. This finite speed is essential for the causal structure of GR and the stability it describes on cosmological scales, as confirmed by observations of gravitational waves. Einstein explicitly rejected faster-than-light influences in both gravity and quantum mechanics. The dBB pilot wave, therefore, operates fundamentally differently from the spacetime geodesics of GR in terms of how changes are communicated. While both frameworks employ a guiding structure (pilot wave/geodesic) for a guided entity (particle/mass), the instantaneous nature of pilot wave updates seems fundamentally distinct from the c-limited propagation of gravitational changes. One might speculate that this difference reflects distinct requirements for stability or dynamics operating at the micro versus macro scales – instantaneous correlations might be permissible or necessary for quantum phenomena, while the large-scale universe demands the causal ordering imposed by a finite propagation speed for gravitational influence.

Let's re-examine the eraser experiment through this lens. Initially, the pilot wave passes through both slits and creates an interference pattern downstream. The particles, arriving one by one, are guided by this non-local wave, and their trajectories naturally cluster in the high-intensity regions, statistically building up the interference pattern.

When we add the circular polarizers, we modify the pilot wave across its entire extent relevant to the experiment. The wave function now includes polarization components entangled with the spatial components. The particle still goes through only one slit, but its guiding wave is the entire, modified, non-local wave function. This modified wave no longer has the structure that leads to simple spatial interference fringes. The particle trajectories, dictated by this new wave structure (which is instantaneously different everywhere due to the polarizer modification), spread out, and the interference pattern disappears.

Now, consider the eraser. This element acts on the pilot wave as it passes through. For the component of the wave that is transmitted, the eraser projects the different polarization states onto one, removing the entanglement between the spatial and polarization parts within that transmitted portion of the non-local wave. The pilot wave emerging from the eraser now locally resembles the original interfering wave structure. Consequently, the particles whose trajectories happen to be guided by this "erased" portion of the wave will again be directed into interference fringes. Particles associated with wave components absorbed or reflected by the eraser follow different paths, determined by the guidance of those respective parts of the overall wave.

In the dBB picture, the "weirdness" vanishes:

1. No Wave-Particle Duality Issue: It's always particle and wave.

2. No Measurement Problem: Measuring is an interaction changing the pilot wave globally (non-locally), which then guides the particle differently.

3. No Retrocausality (Delayed Choice): The particle always follows a definite path influenced by the current state of the non-local pilot wave. The eraser changes the wave downstream, affecting the particle's future trajectory after encountering the eraser, not its past. The non-local nature ensures the wave guiding the particle reflects the presence or absence of the eraser instantaneously.

This pilot-wave perspective resonates strongly with experiments, like those involving path interference and interaction-free measurements, where manipulating seemingly "empty" paths influences observed outcomes. In dBB, these paths are regions where the guiding pilot wave exists and exerts its non-local influence. Interference, entanglement, and measurement outcomes all arise from the continuous, deterministic (though potentially chaotic and non-local) evolution of the particle guided by its pilot wave. There is no need for quantum jumps, collapses, or observer-dependent reality. The physics, while explicitly non-local, is objective and provides a clear ontology, removing the layer of "magic" and offering a concrete, causal explanation for quantum phenomena.

Open letter to Prof. Gerard 't Hooft

 Dear Professor 't Hooft,

I hope this email finds you well.

I read with great interest the article outlining your perspective that quantum mechanics, as currently understood, might not be the final word and that a deeper, perhaps deterministic, reality might underlie it. I deeply respect your work and your willingness to question foundational assumptions.

Your thoughts resonate with the idea that perhaps the limitations lie not in nature itself, but in the mathematical tools we currently employ to describe it – specifically, the assumption of differentiability and a smooth spacetime continuum at all levels.

In this context, I wanted to respectfully draw your attention to the work of Dr. Laurent Nottale and his theory of Scale Relativity. Developed since the 1980s/90s, Scale Relativity proposes abandoning the hypothesis of differentiability and posits that spacetime itself is fundamentally fractal. By extending the principle of relativity to include transformations of scale (resolution), Nottale's framework attempts to derive the fundamental laws of quantum mechanics (including the Schrödinger and Klein-Gordon equations, and potentially the origin of quantum properties) as consequences of the resulting fractal geometry and the non-differentiable nature of particle paths (geodesics). It suggests a potentially deterministic geometric origin for quantum behaviour, which seemed to align with the spirit of your search for a deeper underlying theory.

Furthermore, related work by Prof.M.S. El Naschie also explores fractal spacetime concepts, particularly in relation to E-infinity theory, the holographic principle, and attempts to unify quantum mechanics and general relativity, offering another perspective rooted in fractal geometry.

While Scale Relativity may not be considered mainstream, its foundational approach—starting from a modification of the properties of spacetime itself (positing it as fractal and non-differentiable) and deriving quantum laws from first principles—seems potentially relevant to the questions you've raised about the interpretation and completeness of quantum mechanics. SR builds conceptually on the exploration of paths, akin to Richard Feynman's path integral formalism, but grounding these paths in the geometry of fractal spacetime. Furthermore, it appears to embody David Bohm's insightful idea that the reality is perhaps "particle and path" rather than "particle or path," with the particle's observable properties emerging from its dynamic interaction with an infinity of underlying fractal geodesics. This fundamental emphasis on the path itself might even resonate with recent theoretical explorations suggesting that quantum effects like entanglement could be mediated purely through path information, without requiring a classical notion of particles traversing them. This overall geometric approach, deriving quantum behaviour from the structure of spacetime, seems potentially relevant to the search for a deeper, potentially deterministic, foundation for quantum physics.

Thank you very much for considering these perspectives. I understand you are exceptionally busy and greatly appreciate any moment you might spare.

With utmost respect and admiration for your contributions to physics,

Sincerely,