About

Larry M. Silverberg is a professor in the Department of Mechanical and Aerospace Engineering at NC State University. His research areas include dynamics and modern physics. Silverberg has authored several books, including 'The Fragment: The Primitive Stuff from which Everything Originates' (2025), 'Fundamentals in Analog Circuits' (2022), 'Unified Field Theory for the Engineer and the Applied Scientist' (2008), and 'Mark's Mechanics: Problem-Solving Companion' (2001). His recent publications focus on topics such as the proof of the GM-GR parity theorem for the two-body problem, reframing spacetime with an emphasis on proper time, quantum-deterministic descriptions at the speed of light, nonlinear dynamics of basketball, and trajectories of spacecraft during interstellar travel. Silverberg's work spans theoretical physics, space science, and applied mechanics, contributing to the understanding of fundamental physical principles and their applications.

Research topics

• Geography
• Mathematics
• Computer Science
• Theoretical physics
• Biology
• Aerospace engineering
• Simulation
• Aeronautics
• Zoology
• Geometry
• Classical mechanics
• Ecology
• Quantum mechanics
• Engineering
• Forestry
• Meteorology
• Physics

Selected publications

• Proof of the GM‐GR parity theorem for the two-body problem

  Physics Essays · 2025-06-10 · 2 citations

  article1st authorCorresponding

  One loosely defines Mechanics as a physical theory that rests on the concepts of mass and force and a law of inertia. In contrast, one loosely defines General Relativity as a physical theory that describes how mass and energy curve spacetime, causing objects to move along the straightest possible paths within that curved geometry. For a long time, scientists viewed Mechanics and General Relativity as fundamentally irreconcilable theories, with neither being a mere modification of the other, but rather grounded in distinct and incompatible physical principles. This theorem reshapes that understanding by proving that a modified Mechanics, called General Mechanics, fully aligns with General Relativity in the two-body problem. The trajectories in both theories are the same, and it follows that both adopt the same physical principles. NOTE FROM THE EDITOR-IN-CHIEF: In a blinded assessment, I asked five scientists to verify the mathematics of the parity theorem presented in this article before the article would undergo a review. All of them verified the mathematics. I took this additional step because of the theorem’s potentially significant impact on the fields of Mechanics and Relativity.

  PublisherDOI

• Reframing spacetime: the emphasis on proper time

  Physics Education · 2025-12-03

  articleOpen access1st authorCorresponding

  Abstract The concept of spacetime often conflates mathematical form with physical meaning, obscuring the central role of proper time. This article argues that such ambiguity contributes to persistent difficulties in teaching relativity. Without grounding in proper time, students frequently misinterpret time itself and struggle with the relativity of simultaneity. To address this, the article reframes spacetime by placing proper time at the center—as the primary expression of physical change. Guided by the principle of light, the article reformulates the Minkowski metric equation in temporal units, which exposes its meaning as reflecting the intuitive observation that one experiences distant objects not as they are now, but as they were when their light departed. The article also interprets the metric equation by a metric triangle, a geometric construct that interprets coordinate time as the orthogonal sum of proper time (internal rhythm) and time latency (from spatial separation). This framework clarifies key conceptual distinctions—between proper and coordinate time, simultaneity, and the metric itself—offering a more coherent and physically grounded understanding of spacetime.

  PublisherDOI

• The parity hypothesis. Comment on “On the parity of general mechanics and general relativity, and misconceptions of Einstein’s theory” by Lane R. Miller

  Physics Essays · 2025-12-14

  article1st authorCorresponding

  The parity hypothesis states that parity is possible between generalized mechanics (GM) and the theory of general relativity (GR). In a recent article, we proved a parity theorem for Schwarzschild two-body problems, referring to it as the GM-GR parity theorem. This article responds to a critique of the correctness of the proof, demonstrating where the critique’s reasoning fails. Additionally, the critique rejects the parity hypothesis in problems that are beyond the scope of the theorem. While the parity hypothesis has only been proven for Schwarzschild two-body problems, we find the critique’s additional objection to be both subjective and unsubstantiated.

  PublisherDOI

• The Minkowski metric equation with a metric triangle applied to the twin paradox

  Physics Education · 2025-08-19 · 2 citations

  articleOpen access1st authorCorresponding

  Abstract Among the popular paradoxes in relativity, the twin paradox stands out as one of the most famous and the most frequently taught in secondary school and higher education. This article suggests that instructors present the twin paradox to their students based on the Minkowski metric equation with a metric triangle instead of the Lorentz transformation. We show that explaining the twin paradox using the Minkowski metric equation with its Euclidean geometric interpretation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>τ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> plane should lead to a deeper understanding of such concepts as coordinate time, proper time, and universal simultaneity and experiential simultaneity.

  PublisherOA PDFDOI

• At the speed of light: Toward a quantum-deterministic description?

  Physics Essays · 2024-12-04

  article1st authorCorresponding

  We examine the quantum-deterministic hypothesis that subatomic bodies consist of an immense number of primitives (particles or fragments of energy) traveling at or near the speed of light. Drawing on the well-proven principle of light and principle of impetus for the deterministic theories, we setup corresponding principles that govern interactions between primitives. Then, we studied the stability of a variety of structures formed from the primitives. One of the primitives for which we present preliminary results has similarities to the photon. These findings suggest a possible relationship between quantum-deterministic and quantum-statistical models and likenesses noticed across realms that we now see as different.

  PublisherDOI

• How Schwarzschild could have discovered and fixed the problem with his metric

  Physics Essays · 2024-03-15 · 1 citations

  article

  Karl Schwarzschild's landmark paper revealed the first ever exact solution to Einstein's gravitational field equation. This was a major scientific achievement. However, his solution for the metric of a spherically symmetric spacetime is different than the one found in textbooks today—because Schwarzschild assumed, like in Newtonian gravity, that only one singularity could exist. Given the newness of Einstein's general theory of relativity and the existing paradigm of Newtonian gravity, his assumption was natural. While other authors have previously pointed out this shortcoming and corrected it, the contribution of this paper is to show how Schwarzschild might have discovered it himself. A simple geometric proof indicates how Schwarzschild, with a different assignment of a single constant of integration, would have arrived at the metric found in textbooks today.

  PublisherDOI

• High performance computing of the nonlinear dynamics of a basketball

  Nonlinear Dynamics · 2024-06-13 · 1 citations

  articleOpen access1st authorCorresponding
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• Bringing classical physics into the modern world with Galileo’s Leaning Tower of Pisa experiment

  2023-12-01

  article1st authorCorresponding
  PublisherDOI

• Ungulate responses and habituation to unmanned aerial vehicles in Africa’s savanna

  PLoS ONE · 2023 · 12 citations

  • Biology
  • Ecology
  • Zoology

  This article tests the hypothesis that “the likelihood that the species will react and level at which they do to the unmanned aerial vehicle (UAV) is related to the altitude, number of passes, sound intensity, type of UAV, takeoff distance, and species.” This paper examined the behavioral responses of a group of free ranging ungulate species (Oryx, Kudu, Springbok, Giraffe, Eland, Hartebeest, and Impala) found in an animal reserve in Namibia to the presence of different in-flight UAV models. The study included 397 passes (trials) over 99 flights at altitudes ranging from 15 to 55 meters in three categories of response level: No response, Alert, and Movement. The ungulates were unhabituated to the UAVs and the study was conducted in the presence of stress-inducing events that occur naturally in the environment. Certain species were found to be more reactive than others, in addition to several displaying different response levels in single or mixed herd environments. Zebras were found to be less responsive in mixed herd environments while Oryx were present, as compared to when the Oryx were not; suggesting that some species may respond based on other species perception of threat or their relative fitness levels. The UAVs also produced inconsistent response rates between movement and alert behavior. The reference vehicle, Phantom 3 was much more likely than the Mavic to induce an alert response, while both having similar probabilities of inducing a movement response. Furthermore, the Custom X8 showed significantly more alert and movement responses than the other UAVs. This shows there may be several aspects to the UAVs that affect the responses of the ungulates. For instance, the sound intensity may alert the species more often, but close proximity may induce a movement response. More generally, the data shows that when the UAV is flying above 50 meters and has a measured sound intensity below 50 dB, the likelihood of inducing a movement response on an ungulate species is below 6% regardless of the vehicle on the first pass over the animals. Additionally, with each subsequent pass the likelihood of response dropped by approximately 20 percent. The results suggest a stronger correlation between flight altitude and response across the different ungulates, and the evidence suggests rapid habituation to the UAVs.

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• Trajectory of a Spacecraft When It Passes by a Gravitational Body During Interstellar Travel

  Journal of Spacecraft and Rockets · 2023-09-08 · 3 citations

  article1st authorCorresponding

  Interstellar space missions will require spacecraft that travel at relativistic speeds. Furthermore, their trajectories will be influenced by gravitational sources. Accordingly, this paper applies to interstellar missions a recently developed formulation of relativistic mechanics that predicts a spacecraft’s trajectory when it passes by a gravitational source at a relativistic speed. The formulation, called spacetime impetus, is unique in that it employs a relativistic universal law of gravitation that does not explicitly require general relativity while producing precisely the same results. Based on these developments, an analyst can now update nonrelativistic mission planning codes to give them general relativistic capabilities. It requires augmenting the code with relativistic velocities and relativistic accelerations, the replacement of the universal law of gravitation with a relativistic universal law of gravitation, and setting up Lorentz transformations between frames.

  PublisherDOI

Frequent coauthors

• Chau Tran

  North Carolina State University

  9 shared

• L. Meirovitch

  9 shared

• Jeffrey W. Eischen

  North Carolina State University

  7 shared

• H. Baruh

  Rutgers, The State University of New Jersey

  5 shared

• Chad Bieber

  Institute For Defense Analyses

  5 shared

• Mark A. Norris

  University of Central Lancashire

  5 shared

• Gregory Washington

  University of California, Irvine

  5 shared

• Jim Redmond

  4 shared