SUMMARY: On the Holographic Spectral Effects of Time-Interval Subdivisions
New Physics Paper: On the Holographic Spectral Effects of Time-Interval Subdivisions
Time is one of the most fundamental concepts in physics, yet its exact nature remains elusive. While we typically think of time as a continuous flow, like the ticking of a clock, quantum mechanics presents a different picture—one in which time is more closely tied to measurement, energy, and the wave-like behavior of particles. To be specific, time is tightly related to energy, and measurements in time affect what's called the energy spectrum (e.g., colors) of a particle.
My recent paper, On the Holographic Spectral Effects of Time-Interval Subdivisions, proposes that time behaves holographically, meaning that when we attempt to divide it into smaller and smaller intervals, the process itself alters the spectrum, or colors, of the system, indicating that the whole is not simply the sum of its parts.
This idea is built on a mathematical parallel between quantum wavefunction evolution and the diffraction of light, which describes how light waves spread and interfere when passing through an aperture, e.g., a camera or a digital image filter. In the study of diffractive optics, breaking up a wavefront into sections introduces changes in the diffraction pattern, altering the spectrum of the light. In my work, I show that something very similar happens when we attempt to subdivide time intervals in quantum mechanics: the energy spectrum is modified in a predictable way.
How Time Subdivision Changes the Spectrum
In quantum mechanics, measurable time intervals are associated with frequency spectra, or colors, through the Fourier transform—a mathematical tool that connects time and frequency domains. The standard assumption in physics is that dividing a time interval should always be possible, but we have not taken into consideration its spectral characteristics before. My work shows that subdividing the path of a particle (like a photon of light) and its time interval into smaller segments introduces oscillations and broadening in the associated spectrum when it's detected, changing the physical properties of the system.
The key prediction is that when we attempt to measure an event occurring over a given time interval T, the energy spectrum of the system is governed by a well-defined function, typically what's known as a sinc function (a short wavy pulse). However, if we insert an intermediate measurement or try to analyze the interval as two separate parts—say, breaking it into segments of T/3 and 2T/3—the spectrum changes. Instead of a single sinc-like distribution, we get two different sinc patterns, corresponding to the two sub-intervals of time that we created with our measurement. In a way, the specific way the spectrum changes is unimportant, but the very fact that you can distinguish between an event that was treated as a whole versus one that was treated as a sequence of steps is a profound point!
Experimental and Observational Consequences
This prediction has direct consequences in several areas of physics. There are two novel applications laid out in the paper.
1. Stellar Light and a New Method for Distance Measurement
One of the most intriguing applications of this theory is in astrophysics. Light from distant stars travels for years before reaching us, meaning the propagation time itself acts as a well-defined interval. If the holographic time model is correct, then the finite duration of travel should imprint oscillatory features onto the star’s spectrum, creating a predictable pattern of spectral sidebands.
For a star at a distance D, the expected frequency shift due to this effect is approximately:
Δf≈1/T=1/(D/c)
Where T = D/c is the light travel time from the star to Earth.
For Proxima Centauri, which is about 4.24 light-years away, this would correspond to sidebands spaced at nanohertz (nHz) frequencies, a small but detectable shift with modern precision spectrographs. If confirmed, this would provide an entirely new method for measuring astronomical distances, independent of traditional redshift or parallax methods.
2. Detecting Quantum Eavesdropping
Since dividing a time interval in any way alters the Spectrum associated with the travel of a particle, tampering with a quantum signal should leave a trace in its spectrum unique to the time of travel at which eavesdropping took place. My model suggests that an eavesdropper intercepting and re-sending quantum information could introduce spectral artifacts related to their moment of interference, offering a novel way to detect quantum hacking attempts in continuous-variable quantum key distribution (QKD) protocols.
There are also several existing experiments that this model explains well.
3. Ultra-fast Laser Pulses and Spectral Broadening
Research in ultra-short laser pulses, such as femtosecond or attosecond pulses, won the Nobel Prize last year. This process involves very short time scales at which pulses of light are generated. However, it's clear that these pulses are not really individual distinct laser pulses, like bullets, but rather a single coordinated ripple, like the surface of a river passing over rocks. The holographic model of time describes well how these seemingly separate pulses in time are part of a single moment that has structure. Time is usually thought of as a continuous flow of individual points, but thinking of time as a whole interval—not just single points passing you—matches the data well and provides an interesting alternative way of viewing the universe.
4. Time-bin Entanglement and Quantum Computing
Experiments in quantum optics and Quantum computing often rely on time-bin encoding, where single photons travel through interferometers and are measured based on the time of arrival. (A time bin is a fancy way of saying you have detectors that measure the time of arrival of a photon rather than its position on the lab bench.) My paper suggests that the changes to the spectrum between two photons traveling for slightly different times are measurable and could have implications for quantum cryptography and quantum computing, where precise control over when a photon arrives at a detector is crucial.
Implications for the Foundations of Quantum Mechanics
Beyond specific applications, this work raises deeper questions about the nature of time in quantum mechanics. The fact that intermediate measurements modify the spectrum suggests that measurable time is not just a passive background parameter but an active participant in the physics of a system. This aligns with interpretations of quantum mechanics that emphasize measurement-dependent reality, such as relational quantum mechanics and certain approaches to quantum gravity.
Moreover, the results indicate that time intervals are more fundamental than individual time points. In other words, instead of thinking about "now" as a single moment, it may be more accurate to describe time as a holistic entity defined by its entire measurement interval. This resonates with ideas from holographic and emergent space-time theories, where space and time arise from observation or interaction rather than being fundamental themselves.
Summary: A Holographic Perspective on Time
Time behaves holographically—measurable time intervals are encoded in the frequency domain as whole entities.
Attempting to subdivide time into segments introduces new spectral components, altering energy measurements.
This effect could be observed in quantum optics, ultra-fast lasers, and even astronomical light measurements.
If verified, this model could lead to new measurement techniques in physics, quantum technology, and cosmology.
At its core, this work challenges the assumption that time can always be divided into arbitrarily small parts without consequence. Instead, it suggests that time intervals, like holograms, encode information as a whole, and any attempt to break them apart alters the structure of reality itself. If this perspective is correct, it may lead to a deeper understanding of time’s role in quantum mechanics and the universe at large.
The paper can be downloaded open access here: On the Holographic Spectral Effects of Time-Interval Subdivisions