Quantum Mechanics, Bohmian Mechanics, and a New Experiment That Challenges Old Ideas

Quantum mechanics, the fundamental theory describing the behavior of particles at the smallest scales, has fascinated and puzzled physicists for over a century. One of the longstanding debates revolves around how to interpret the strange mathematics and probabilistic outcomes that quantum mechanics predicts. Among the many interpretations, one particularly beloved by some physicists is Bohmian mechanics, also known as the pilot-wave theory, proposed by David Bohm about 70 years ago.

What is Bohmian Mechanics?

In standard quantum mechanics, the state of a system is described by a wave function—a mathematical object that encodes the probabilities of different measurement outcomes. Crucially, the wave function itself is not directly observable. Instead, it serves as a tool to calculate the likelihood of finding a particle with a certain property upon measurement. The theory is inherently probabilistic and non-deterministic; it cannot predict exact outcomes but only probabilities.

Bohmian mechanics offers a different perspective. It breaks down the wave function into two parts: a guiding wave and pointlike particles that move according to this wave. The randomness in outcomes, in this view, arises not from fundamental indeterminism but from our ignorance about the precise initial positions of these particles. In other words, if we knew exactly where the particles started, we could in principle predict their trajectories and outcomes deterministically. This interpretation is appealing for those who prefer a particle-centric view of quantum phenomena.

However, Bohmian mechanics differs from standard quantum mechanics in important ways. Notably, it asserts that particle positions are the only true observables, whereas standard quantum mechanics allows measurements of various properties such as energy, spin, and momentum. This mismatch forces proponents of Bohmian mechanics to reinterpret measurements like spin in terms of particle positions, which can be conceptually challenging.

The New Experiment and Its Findings

Recently, an experimental breakthrough has put Bohmian mechanics to the test—and the results are striking. The experiment involved photons (particles of light) traveling through a narrow gap between two mirrors, forming a one-dimensional waveguide. One mirror had tiny carved valleys, shaping the waveguide's depth. The waveguide first widened, then suddenly narrowed, creating a barrier that photons could tunnel through quantum mechanically—a phenomenon where particles pass through barriers they classically shouldn't be able to cross.

Crucially, just before the barrier, a second waveguide was placed close enough for photons to tunnel into it. The experimenters measured how photons spread into this second waveguide after tunneling. According to Bohmian mechanics, the particles should have essentially zero velocity immediately after tunneling, meaning they would remain localized. Instead, the photons were observed to spread out, indicating they did have velocity and moved away from their initial position.

This observation directly contradicts the predictions of Bohmian mechanics but aligns perfectly with the standard quantum mechanical description, which treats the wave function's evolution as fundamental and probabilistic.

What Does This Mean?

Does this experiment mean Bohmian mechanics is completely wrong? The answer is nuanced. While the experiment rules out the idea that Bohmian particles correspond to the particles we observe in nature (like electrons or photons in the standard model), it doesn't necessarily discard all possible variants of hidden-variable theories. It highlights a fundamental mismatch: Bohmian particles are pointlike and deterministic, but the particles we measure have spatial extent, interactions, and complex quantum properties.

From a philosophical standpoint, this challenges the appeal of theories relying on point particles with deterministic trajectories. After all, the infinite precision required for such point particles is physically questionable.

Final Thoughts

This new experimental result marks a significant step forward in our understanding of quantum foundations. It narrows down the viable interpretations and pushes physicists to refine or rethink their models of reality at the quantum level. While Bohmian mechanics offered an intuitive particle picture, nature seems to resist such a simplistic view.

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Thanks for reading! Stay curious, and see you in the next post.

10 Mindblowing Math Facts That Will Change How You See Numbers

Mathematics often reveals truths that are both surprising and profound—truths that challenge our intuition and expand our understanding of the universe. Here, we explore ten fascinating mathematical facts that showcase the beauty, complexity, and mystery of math. Whether you’re a math enthusiast or just curious, these mindblowing insights will surely intrigue and inspire you.

10. P-adic Numbers: Infinite Nines to the Left

Most of us are familiar with real numbers, where digits extend infinitely to the right of the decimal point. For example, 0.999... (with infinite 9s) equals 1. But did you know there’s a completely different number system called p-adic numbers that extends infinitely to the left?

In the 10-adic system (where p=10), numbers have infinite digits extending to larger values on the left rather than smaller ones on the right. Here’s a stunning fact: an infinite string of 9s to the left actually equals -1. For example, adding 1 to 999... (infinitely many to the left) yields zero. This counterintuitive arithmetic is not a trick—it’s a fundamental property of p-adic numbers!

9. Gabriel’s Horn: Infinite Surface Area, Finite Volume

Gabriel’s horn is a shape formed by rotating the curve ( y = \frac{1}{x} ) (for ( x \geq 1 )) around the x-axis. This shape has a paradoxical property: it encloses a finite volume but has an infinite surface area. In other words, you could fill it with a finite amount of paint, but you could never coat its entire surface!

8. Optimal Packing of 17 Squares

Imagine you have 17 square tiles. What is the smallest larger square they can all fit into without overlapping? While this might sound straightforward, the optimal packing arrangement for 17 squares is surprisingly difficult to prove. The best known arrangement exists, but mathematicians still haven’t proven it’s truly the smallest possible. This highlights how even simple-looking problems can remain unsolved.

7. Meta-logical Contradictions: The Limits of Self-Reference

Logical paradoxes arise when languages or systems refer to themselves. Classic examples include:

• The Liar Paradox: "This sentence is false." If true, it’s false; if false, it’s true.
• The Barber Paradox: A barber who shaves all those who do not shave themselves—does he shave himself?
• Barry’s Paradox: The smallest positive integer not definable in under 60 letters cannot exist because defining it contradicts its own definition.

These paradoxes reveal deep insights into logic, language, and the foundations of mathematics.

6. The Monster Group: The Largest Sporadic Simple Group

Groups are mathematical objects that capture symmetry and transformations. Beyond infinite families of groups, there are 26 exceptional sporadic simple groups. The largest of these is the monster group, which has approximately ( 10^{54} ) elements—a number so vast it defies easy comprehension.

Amazingly, it has been proven that the monster group is the largest possible sporadic simple group, a fundamental truth in abstract algebra.

5. The Logistic Map: Simple Rules, Complex Chaos

The logistic map is defined by the recurrence:

[
x_{n+1} = r \cdot x_n \cdot (1 - x_n)
]

where (r) is a parameter and (x_0) is between 0 and 1. For certain values of (r), the sequence settles to a fixed point or oscillates between a few values. But past a critical point (~3.57), the system exhibits chaos—unpredictable, highly sensitive behavior.

This simple formula beautifully illustrates how complexity and chaos can arise from straightforward rules.

4. Wild Singular Limits: Sudden and Unpredictable Changes

Singular limits occur when the behavior of a sequence or function changes abruptly and unexpectedly. For example, certain integrals involving products of sign functions remain constant for small cases but suddenly change behavior at higher dimensions. These wild singular limits challenge our understanding of continuity and convergence.

3. The Birthday Problem: Surprising Probabilities

At a party of just 23 people, there’s a greater than 50% chance that two people share the same birthday—a counterintuitive but mathematically proven fact. With 60 people, this probability exceeds 99%. The birthday problem is a classic example of how human intuition often misjudges probabilities in large sets.

2. Most Numbers Are Unknowable: The Mystery of Transcendentals

While many numbers are algebraic (solutions to polynomial equations with rational coefficients), most real numbers are transcendental—they cannot be expressed this way. Famous transcendental numbers include (\pi) and (e).

Interestingly, although transcendental numbers are abundant, we can’t explicitly describe most of them. The set of definable numbers is countable, while transcendental numbers are uncountably infinite. Moreover, it remains an open question whether every possible finite sequence of digits appears in the digits of (\pi).

1. The Banach–Tarski Paradox: Duplicating a Sphere

Using the Axiom of Choice, the Banach–Tarski paradox states that a solid sphere can be decomposed into a finite number of disjoint pieces and reassembled (using only rotations and translations) into two spheres identical to the original.

This paradox defies our intuitive notions of volume and space and raises deep questions about the nature of mathematical infinity and geometry.

Final Thoughts

Mathematics is full of wonders—some that challenge our intuition and others that reveal hidden structures underlying reality. Which of these facts surprised you the most? Let me know in the comments!

If you’re inspired to dive deeper into mathematics and science, I highly recommend Brilliant.org. Their interactive courses make complex topics accessible and engaging, with visualizations and problem-solving that help the concepts truly click. Plus, with their free trial and special offers, it’s a great way to expand your mathematical horizons.

Happy math exploring!

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The Controversy Around Eric Weinstein: A Candid Perspective on Theoretical Physics and Its Gatekeepers

The world of theoretical physics is no stranger to controversy and fierce debates. Recently, Eric Weinstein, a mathematician and economist known for his “geometric unity” theory—a proposed theory of everything—has become a lightning rod for criticism and online vitriol. After watching a contentious episode featuring Eric Weinstein and Sean Carroll on Piers Morgan’s show and witnessing the harsh backlash, it’s clear that the conversation around Eric reveals deeper issues within the physics community itself.

Who Is Eric Weinstein?

I’ve known Eric for nearly two decades, and I can say he is a good and fairly normal person—qualities that get lost amid the flood of hate he receives from many who don’t really know him. Eric’s lifelong work centers on his geometric unity theory, an attempt at unification akin to many others in physics aiming to reconcile the fundamental forces of nature. While physicists have long pursued unification theories, none have yet succeeded in producing definitive evidence or predictions.

What Is Geometric Unity?

At its core, geometric unity builds on the mathematical framework of the Standard Model of particle physics, which is based on symmetry groups denoted U(1), SU(2), and SU(3). Physicists often seek larger symmetry groups to encompass these, hoping to find a “unified” group that explains everything. The challenge is that infinite groups exist, many including the Standard Model groups, resulting in countless proposed unified theories—none of which have been conclusively validated.

Eric’s approach involves relating Einstein’s four-dimensional spacetime metric tensor (with 10 independent components) to a particular symmetry group called SO(10). His idea essentially doubles the gravitational part of Einstein’s theory and tries to generate a unification framework from there. While the details are complex and somewhat sketchy, the mathematics align with approaches familiar to physicists working in foundational theory.

The Fallout from the Piers Morgan Interview

The interview between Eric and Sean Carroll highlighted the divide in the physics community’s reception of Eric’s work. Sean Carroll, a prominent physicist, criticized Eric’s paper for lacking concrete predictions, like plots or calculations related to dark matter or dark energy, necessary for gaining serious attention in the field. Eric responded sharply, defending his work and pointing out Sean’s own career struggles.

Despite the sharp exchange, it’s notable that Sean agreed to the interview—something many physicists would have avoided. Yet, the larger issue is the hypocrisy within the field: many working on ambitious theories face similar shortcomings—lack of tangible predictions, incomplete formulations, and unresolved mathematical problems—but these are often overlooked if they come from established insiders.

The Gatekeeping and Groupthink in Physics

The intense backlash against Eric seems less about the merits of his ideas and more about his outsider status and unwillingness to conform to the established norms. Theoretical physics is currently plagued by groupthink, where dissenting voices or unconventional approaches are marginalized. People expect their peers to join in criticizing Eric, and those who might defend him often remain silent out of fear of professional repercussions.

Rumors circulated about Eric’s association with the Perimeter Institute, suggesting he was rejected or had to pay to give a talk—none of which is true. In reality, the science community’s fear of embracing new theories or even entertaining them publicly has created a toxic atmosphere that stifles innovation.

Voices of Support and Courage

Thankfully, some figures have stood by Eric. Brian Keating openly supported him despite facing criticism, and Curt Jaimungal produced an extensive video exploring Eric’s theory and interviewed him, recognizing the remarkable dedication behind it. These acts of courage highlight the need for openness and dialogue, even when ideas are unfinished or controversial.

What This Means for Theoretical Physics

Eric Weinstein’s experience exposes the rot in foundational physics: a field heavily reliant on large grants, entrenched ideas, and a reluctance to truly think outside the box. Many working on big ideas have yet to deliver clear, testable predictions, but only Eric seems to attract harsh public condemnation—likely because he is an outsider challenging the status quo without the backing of big institutional support.

In truth, Eric’s geometric unity theory is no better or worse than many other speculative theories in physics. The difference is he hasn’t spent millions of taxpayer dollars or marshaled a large research team to obscure its flaws. His work is a reminder that innovation sometimes comes from the fringes and that the scientific community needs to embrace genuine curiosity and criticism, rather than gatekeeping and groupthink.

Final Thoughts

The saga of Eric Weinstein is not just about one man or one theory; it’s a reflection of the challenges facing theoretical physics today. If the field hopes to progress, it must foster an environment where unconventional ideas can be discussed openly without fear of personal or professional attack. Otherwise, we risk losing the very essence of scientific discovery.

If you found this discussion insightful, consider supporting independent voices in science by checking out my Patreon. Your support helps keep these important conversations alive.

Is Dark Energy Changing Over Time? New Evidence Challenges a Fundamental Cosmic Constant

One of the most intriguing scientific developments in recent years revolves around a profound question in cosmology: Is the cosmological constant truly constant? This constant, often associated with dark energy, has long been thought to drive the accelerated expansion of our universe at a steady rate. However, recent evidence is challenging this notion, suggesting that dark energy might actually be changing over time—specifically, that it was stronger in the past and is now weakening.

What is Dark Energy and the Cosmological Constant?

Dark energy is the mysterious force propelling the universe's expansion to speed up rather than slow down. The simplest explanation for dark energy is the cosmological constant—a fixed amount of energy inherent to empty space itself. Imagine that even "nothing" has energy, more than enough to push galaxies apart faster and faster as time goes on.

New Data Challenges the Constant Nature of Dark Energy

Over the past year, new results from several cutting-edge experiments have hinted that dark energy is not fixed. The Dark Energy Survey (DES) analyzed light from distant supernovae to study how the universe's expansion has changed over time. Simultaneously, the DESI (Dark Energy Spectroscopic Instrument) project studied the distribution of galaxies and galaxy clusters, focusing on patterns called baryon acoustic oscillations—relics of sound waves from the early universe.

Both DES and DESI found tentative evidence (around a three sigma confidence level) that dark energy is weakening. While this is not definitive proof, it corresponds to roughly a 3 in 1,000 chance that the signal is a fluke.

New Support from the South Pole Telescope

Adding weight to these findings, the South Pole Telescope (SPT) recently released precise measurements of the cosmic microwave background (CMB)—the afterglow radiation from the Big Bang. Unlike telescopes scanning the entire sky, the SPT focuses on a small patch with high precision, measuring temperature and polarization fluctuations.

SPT data confirms the ongoing "Hubble tension"—a discrepancy between local and early universe measurements of the universe's expansion rate—with a striking 6.2 sigma significance. More importantly for dark energy, their data also supports the idea that dark energy was stronger in the past, though their results are slightly closer to the classic cosmological constant model. When combined with DESI data, the evidence for weakening dark energy becomes even stronger.

Why Does This Matter?

If dark energy changes over time, it could help resolve the Hubble tension, an outstanding puzzle in cosmology concerning differing measurements of the universe’s expansion rate. More fundamentally, a time-varying dark energy implies it is not just a constant property of space but a dynamic field permeating the cosmos.

In physics, fields are linked to particles. This means dark energy might be related to a new, undiscovered particle or connected to known particles like the Higgs boson. Various theories have proposed such links, though none have been conclusively validated. These new findings may encourage physicists to revisit these ideas.

Implications for the Fate of the Universe

A constant dark energy predicts that cosmic expansion will accelerate forever, leading to a cold, ever-expanding cosmos. But if dark energy weakens—or even disappears—this could slow or reverse expansion, potentially leading to a cosmic collapse or cyclic universe with recurring big bangs.

Caution and Open Questions

While these results are exciting, they come with caveats. The analyses assume a specific cosmological model, and it’s possible the real solution lies elsewhere—not in dark energy’s constancy, but in our understanding of the universe's overall framework.

Staying Informed with Balanced News

In a world where news often blends facts with opinion, platforms like Ground News offer a valuable way to get a balanced perspective. Ground News aggregates coverage from across the political spectrum, rates factuality, and highlights blind spots in media coverage. This helps readers break out of information bubbles and understand complex issues like these new cosmological findings with context and clarity.

The story of dark energy is still unfolding, and these latest findings invite us to rethink some of our deepest assumptions about the universe. Whether dark energy is truly fading or not, the quest to understand it pushes the boundaries of science—and our imagination.

Stay tuned for more updates on this cosmic mystery, and keep questioning the universe around you.

🎥 10 Physics Myths You Probably Believe!

⏱️ Duration: 11:30
🔗 Watch on YouTube

Overview

This video systematically debunks ten of the most pervasive myths in physics as
perpetuated by popular science media. The presenter clarifies misconceptions,
explains the actual science behind each myth, and encourages viewers to approach
physics with a more nuanced and critical perspective.

Main Topics Covered

• Quantum particles and superposition
• Entropy and the concept of disorder
• Gravitational pull of black holes
• The speed of light and human motion in spacetime
• The cosmological constant misconception
• Time dilation and the behavior of time at relativistic speeds
• Quantum entanglement and information transfer
• Einstein's views on quantum physics
• The nature of dark energy vs. anti-gravity
• Faster-than-light travel in Einstein’s theories
• The pitfalls of popular science communication

Key Takeaways & Insights

• Quantum Superposition: The phrase "particles can be in two places at once" is a misleading simplification of a mathematical concept; no one truly knows what this means physically.
• Entropy ≠ Disorder: Entropy is often described as disorder, but this is not always accurate—especially when considering gravitational effects in the universe.
• Black Holes' Gravity: Black holes don’t have a stronger gravitational pull than stars of the same mass; their danger comes from their compactness, not increased gravity.
• Speed of Light Misconceptions: Statements like "we all move at the speed of light" are either meaningless or misinterpretations of spacetime concepts.
• Cosmological Constant: The claim that its prediction was off by 120 orders of magnitude is a misrepresentation; there was never a proper prediction, just a flawed estimate.
• Time Dilation: Time does slow down under acceleration or strong gravity, and this is a real, measurable effect (e.g., different time progression on Earth vs. the Moon).
• Quantum Entanglement: Entangled particles do not transmit information faster than light; no experiment has shown "spooky action at a distance" to be physically real.
• Einstein and Quantum Mechanics: Einstein’s skepticism about quantum mechanics has not been proven wrong, contrary to popular belief.
• Dark Energy: Dark energy is not anti-gravity; it does not behave as something repelled by normal matter or clump together.
• Faster-than-Light Travel: Einstein’s theories do not strictly forbid faster-than-light travel; rather, they indicate that accelerating from below to above the speed of light requires infinite energy, signaling a breakdown of the theory, not an absolute prohibition.

Actionable Strategies

• Critical Consumption: Don’t take popular science explanations at face value; seek out more rigorous or primary sources for accurate scientific understanding.
• Deepen Understanding: Use interactive educational platforms (like Brilliant) to build a more robust foundation in physics and related sciences.
• Question Simplifications: Recognize when analogies or simplified statements (like “entropy is disorder”) might not fully capture the scientific truth.

Specific Details & Examples

• Quantum Superposition: Mathematically, a wave function can be a sum of two locations ("superposition"), but physically, the meaning is ambiguous.
• Entropy in the Universe: An evenly distributed dye in water has maximum entropy due to likelihood, but the early universe's even matter distribution had low entropy because gravity tends to clump matter.
• Black Hole vs. Star: The gravitational pull at a black hole’s event horizon is stronger only because you can get closer, not because the pull is inherently greater than a star of the same mass.
• Time Dilation Example: Time passes more slowly on Earth’s surface compared to the Moon—a real effect important for things like precise time synchronization (e.g., NASA's proposal for separate "moon time").
• Quantum Information Transfer: Mathematical theorems prove you cannot use quantum effects to send information faster than light; quantum teleportation is not an exception.
• Spin and Force Carriers: For gravity (spin-2 carrier), like masses attract and unlike masses repel, unlike electromagnetism (spin-1 carrier).

Warnings & Common Mistakes

• Misleading Popular Science: Relying on popular science can lead to persistent misunderstandings about fundamental physics concepts.
• Over-Simplified Analogies: Terms like “disorder” for entropy or “spooky action” for entanglement can obscure more than they clarify.
• Assuming Myths Are Facts: Believing repeated statements (like the cosmological constant’s “prediction”) without checking their scientific basis.

Resources & Next Steps

• Brilliant.org: Recommended as a resource for learning physics, mathematics, computer science, and related topics through interactive courses and visualizations.
• Special offer: 30-day free trial and 20% off annual premium via the presenter’s link.
• Deeper Learning: The presenter encourages viewers to seek out more rigorous educational materials and to comment with additional myths for future videos.