Stevens’ team harnesses both the “wave-ness” and “particle-ness” of quantum objects to develop a groundbreaking imaging technique.
Over the past century, quantum mechanics has dramatically reshaped our view of the universe, uncovering a strange and counterintuitive realm where particles can also behave like waves, and where observation itself can influence outcomes.
More recently, scientists studying this phenomenon, known as wave-particle duality, have developed methods to gauge how much a quantum object leans toward wave-like or particle-like behavior. These measurements have offered insight into the conditions that cause quantum systems to shift between acting like particles and acting like waves.
Now, in a study published in Physical Review Research, a team from Stevens Institute of Technology has introduced a major advancement. They have derived a straightforward yet highly precise formula that captures the exact mathematical connection between a quantum object’s “wave-ness” and its “particle-ness.”
“Wave-particle duality is the cornerstone of quantum mechanics,” says Xiaofeng Qian, the paper’s lead author and an Assistant Professor of Physics at Stevens. “Researchers have been working to quantify wave-particle duality for half a century, but this is the first complete framework to fully quantify wave-like and particle-like behaviors with optimum quantitative measures that are relevant at the quantum level.”
Overcoming the Limits of Previous Models
Previous research showed that wave-ness and particle-ness could be expressed as an inequality, with the sum of an object’s wave-like behaviors (such as visible interference patterns) and particle-like behaviors (such as the predictability of its path or location) being equal to or less than one. “That’s important, because it means that if an object is fully wave-like, then it shows no particle-like behaviors, and vice versa,” Qian explains.
Such models were incomplete, however, because they can describe situations in which an object’s wave-like and particle-like behaviors increase simultaneously—the opposite of the actual exclusive relationship between the two behaviors. To remedy that, the authors introduced a new variable: the coherence of the quantum object.
“Coherence is a tricky concept, but it’s essentially a hidden description of the potential for wave-like interference,” Qian explains. “And the conventional measure visibility represents the amount of wave-ness can be extracted. When we quantify and compensate for coherence, alongside the standard metrics for wave-ness and particle-ness, we find they add up to exactly one.”
From Inequality to Exact Calculation
That enables the calculation of both wave-ness and particle-ness with far more precision. By measuring the coherence in a system, in fact, it becomes possible to calculate a quantum object’s level of wave-ness and particle-ness—not simply as “less than one,” but as an exact value.
The relationship between wave-ness and particle-ness can then be plotted as an elegant curve on a graph—a perfect quarter-circle for a perfectly coherent system, and a flatter ellipse as the level of coherence declines.
Besides expanding our understanding of foundational physics, the team’s breakthrough has significant potential applications in fields such as quantum information and quantum computing.
To demonstrate that, Qian’s team applied their theory to a technique called quantum imaging with undetected photons (QIUP), in which an object aperture is scanned with one of a pair of entangled photons. If the photon passes through unimpeded, coherence remains high; if it collides with the walls of the aperture, coherence falls sharply.
By then, measuring the wave-ness and particle-ness of the entangled partner-photon, Qian’s team could deduce its coherence—and thus map the shape of the aperture. “This shows that the wave-ness and particle-ness of a quantum object can be used as a resource in quantum imaging, and potentially many other quantum information or computational tasks,” Qian says.
Resilience to Environmental Noise
Remarkably, imaging remained possible even as external factors, such as temperature or vibrations, degraded the overall coherence in the quantum system. Such factors equally affect both high coherence situations (where the photon passes through the aperture) and low coherence situations (where the photon impacts the scanned object), so it remains possible to detect the difference in coherence between the two scenarios. “The ellipse gets squeezed, but we’re still able to extract the information of the object we need,” Qian explains.
Further research is needed, most notably to determine how wave-particle duality plays out in more complex multipath quantum scenarios. “The mathematics make it look simple, but we’re a long way from exhausting the weirdness of quantum mechanics,” Qian says. “There are still plenty of frontiers left for us to explore.”
Reference: “Wave-particle duality ellipse and application in quantum imaging with undetected photons” by Pawan Khatiwada and Xiao-Feng Qian, 8 July 2025, Physical Review Research.
DOI: 10.1103/dyg6-l19j
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10 Comments
Wave or Particle? Physicists Crack a 50-Year-Old Quantum Puzzle。
good.
Please ask researchers to think deeply:
What do you think the physical reality of quantum physics should be like?
Many people do not believe that so-called peer-reviewed publications (such as the Nature, Science, Physical Review series, etc) have been systematically disseminating pseudoscience. If researchers are willing to believe in science rather than so-called peer-reviewed publications, please visit https://zhuanlan.zhihu.com/p/1927657274920383767, https://zhuanlan.zhihu.com/p/1925124100134790589 and https://zhuanlan.zhihu.com/p/1928738508329169149 (If the link is not blocked).
We accept the science since that is what it is, and reject your attempts to tar it as pseudoscience.
Thank you for your browsing and comments.
You accept the science since that is what it is, and can continue to delete my reply. However, unfortunately, we live in different worlds. In your world, there are particles bestowed by God, demons, and angels. In your world, two sets of cobalt-60 rotating in opposite directions are mirror images of each other, regardless of symmetry. In your world, a cat both dead and alive is a beloved gentleman, always eloquently lecturing from podiums in major universities. The world you see from your perspective has no filth, ugliness, or shame — you are far too fortunate.
Congratulations!
Note 2507181419_Source1.Reinterpretation [*]
Reveal my thoughts that have become scientifically and philosophically very important proof of concept in human history. Huh.
Of course, there are so many people who underestimate and know them as SNS jokes. But the truth is still in magicsum. Hmmm.
Source 1.
https://scitechdaily.com/wave-or-particle-physicists-crack-a-50-year-old-quantum-puzzle/
Wave or Particle? Physicists Solve 50-Year-Old Quantum Puzzle
Stevens College of Engineering, July 17, 2025
1.
Physicists have discovered a new formula that fully quantifies how quantum objects transition the behavior of waves and particles, opening up a deeper understanding of quantum science and new applications. Source: Stock
Stephens’ team has developed groundbreaking imaging techniques by leveraging both the “wave nature” and “particleity” of quantum objects.
Over the past century, quantum mechanics has dramatically changed our view of the universe, revealing strange and counterintuitive areas where particles can also behave like waves and the observation itself can influence the results.
1-1.
Recently, scientists studying the phenomenon, known as wave-particle duality, have developed a method to measure how much a quantum object leans toward an action, such as a wave or particle. These measurements have provided insight into the conditions under which a quantum system moves between behaving like a particle and behaving like a wave.
The research team at Stevenson University of Technology has made significant progress in a study published in Physical Review Research. They have come up with a simple yet very accurate formula that captures the exact mathematical connection between the “wave nature” and “particle nature” of a quantum object.
1-2.
“Wave-particle duality is a cornerstone of quantum mechanics,” says Xpeng Zheng, lead author of the paper and an assistant professor of physics at Stevens. “While researchers have been working to quantify wave-particle duality for half a century, this paper is the first complete framework to fully quantify the behavior of waves and particles using significant optimal quantitative measurements at the quantum level.”
2. Overcoming the limitations of previous models
Previous studies have shown that wave properties and particulate properties can be expressed as inequalities. In other words, the sum of the wave properties (e.g., visible light interference patterns) and the particle properties (e.g., path or position predictability) of the object is less than or equal to 1. “This is important, because if the object is completely wave-like, then the particle properties don’t appear at all, and vice versa,” Chen explains.
_[2] It is not well understood to represent the duality of quantum particles as an inequality, but I am sure that msbase has wave nature (*) and qpeoms has particle nature (*). Huh.
2-1.
However, these models were incomplete because they could explain the situation in which the wave and particle nature of an object increased simultaneously, i.e., the opposite of the exclusive relationship between the two behaviors. To address this, the authors introduced a new variable called quantum object coherence.
_[2-1】
Because the duality of the particles is mismatched?? So the absolute value of the inequality has not changed. The absolute value of the sample 2. qcell is 1. They represent the double overlap of +1, -1 with the 2qvixer. So? We can’t be sure that +1 has particulate properties and -1 has wave properties.
_】이면In that way, do we see the quantum characteristics of double interference, entanglement, and double measurement as the re-interpretation (*) of the duality secondary characteristic? Well!!
Rather, isn’t the duality of the quantum outside the quantum domain? msbase is a galaxy of space-time with masses dominated by electromagnetic fields. But most of that mass is in the qpeoms particle nature, which is a unit set of the quantum domain. Uh-huh.
_【*】
However, there is an intuition that ‘the more…||’ exists. This implies a huge multiverse before the Big Bang and outside our current universe. This is a philosophical problem of msbase.qpeoms, not a science fiction hypothesis. Hmm.
This simply means they are playing with a math that joins wave functions with particles (which are discrete and allow people to add and subtract with thinking too much). There are no particles; – math should try mimicking reality.
Wavefunctions are not “joined” with particle field perturbations, they describe field states such as single or multiple particles.
Everything is a wave. The secret is out we can manipulate spacetime itself and teleport planes.
MY Math is waveform mechanics have already been submitted.13 papers total.
Getting sick and tired of you guys, ignoring what I’ve done and trying to appropriate it into your work.I’ve already solved everything you’re ignoring and I’m going to the courts.I swear to God all of my papers.Have work is block chain backed.
STOP ACTING LIKE YOU CAME UP WITH IT. no I won’t go away.You are never going to be able to beat me at this cause the block chain.The a i’s and everybody else knows that i’ve already had this style out there and done.
? You have done nothing it seems (which is presumably why you don’t provide evidence of references).
Quantum field theory replaced quantum mechanics a century ago, dissolving the notion of “duality”. As a modern particle physicist describes it:
“This quantum field theory viewpoint didn’t really fit with Bohr’s vision. But it’s quantum field theory that agrees with experiment, not the quantum physics of Bohr’s era. Nevertheless, Bohr’s interpretation persisted (and still persists) in many textbooks and philosophy books. I learned about it myself at the age of sixteen in a class on the philosophy of science. That was several years before I learned the mathematics of quantum field theory and began to question Bohr’s thinking.
From the perspective of quantum field theory, as I’ve outlined here, a wavicle does have features of both waves and particles, but it also lacks features of both waves and particles. For this reason, I would personally prefer to say that it is neither one. I don’t think it’s useful to say that it is both wave and particle, or to say that it is sometimes wave and sometimes particle. It’s simply something else.”