DialectAn extraordinary misunderstanding lies at the heart of relativity, born in the overlooked distinction between the empirical verifiability of the two-way speed of light and the presumed isotropy of one-way light speed. What is this distinction exactly, and how might making it explicit shake the foundations of our entire paradigm of modern physics?

Anderson, R., Vetharaniam, I., & Stedman, G.E. (1998). "Conventionality of synchronisation, gauge dependence and test theories of relativity." Physics Reports, 295, 93-180. http://www.terra32.it/trusso/varie/AndVetStedPhRep(1998).pdf

Contents: 00:00 - Intro 01:06 - The Caveat to Einstein's Postulate 03:33 - The One-Way Speed of Light Problem 08:33 - The Epsilon Value 11:23 - The Loophole 14:07 - Invariance of Laws of Physics 16:17 - Absolute Simultaneity/Anisotropic Light 18:16 - New Directions

Einsteins Relativity contains a HUGE Loophole. Its Implications Cant Be Ignored.Dialect2023-11-18 | An extraordinary misunderstanding lies at the heart of relativity, born in the overlooked distinction between the empirical verifiability of the two-way speed of light and the presumed isotropy of one-way light speed. What is this distinction exactly, and how might making it explicit shake the foundations of our entire paradigm of modern physics?

Anderson, R., Vetharaniam, I., & Stedman, G.E. (1998). "Conventionality of synchronisation, gauge dependence and test theories of relativity." Physics Reports, 295, 93-180. http://www.terra32.it/trusso/varie/AndVetStedPhRep(1998).pdf

Contents: 00:00 - Intro 01:06 - The Caveat to Einstein's Postulate 03:33 - The One-Way Speed of Light Problem 08:33 - The Epsilon Value 11:23 - The Loophole 14:07 - Invariance of Laws of Physics 16:17 - Absolute Simultaneity/Anisotropic Light 18:16 - New DirectionsAn Introduction to Curvilinear Coordinates in Differential GeometryDialect2024-04-13 | The equations of General Relativity are written in the language of curvilinear coordinates, where mathematical objects like Basis Vectors, Metric Tensors, and Christoffel Symbols dominate the landscape. But where do these concepts come from and how can we connect them to our physical intuition? Join us to find out. Plus -- hotwheels! (Note: some familiarity with vector calculus is highly recommended.)

Contents: 00:00 - Intro 00:50 - What are Curvilinear Coordinates? 03:28 - Basis Vectors & Parametric Basis 08:00 - Coordinate Acceleration & Levi-Civita Condition 11:47 - The Christoffel Symbols 12:53 - Characterization of Arbitrary Coordinates 14:42 - Characterization of Polar Coordinates 19:12 - Geodesics 20:31 - Curved SurfacesMatrix Theory: Relativity Without Relative Space or TimeDialect2024-02-03 | It's the question that brought you here: what is the physical meaning of Relativity? For well over a century the answer to this question has eluded physicists, thinkers and scientists alike, including even Einstein himself -- but at long last, from out of the canonical labyrinth of confusion, dogma, and mathematical abstraction, some real, tangible answers are finally emerging. But to understand them, you are going to have to first make a choice... math, or physics?

Anderson, R., Vetharaniam, I., & Stedman, G.E. (1998). "Conventionality of synchronisation, gauge dependence and test theories of relativity." Physics Reports, 295, 93-180. http://www.terra32.it/trusso/varie/AndVetStedPhRep(1998).pdf

Contents: 00:00 - Intro 02:15 - The Construct 05:52 - The Real World 10:23 - The Matrix 17:50 - The SourceConceptualizing the Christoffel Symbols: An Adventure in Curvilinear CoordinatesDialect2023-10-07 | What are the Christoffel Symbols, and why do we need them? Our exploration into the world of differential geometry continues, as we strive to lay bare the complex mathematical machinery behind General Relativity. Here we calculate the Christoffel symbols for the most common of curvilinear coordinates system — polar coordinates — in order to build a preliminary intuition for what these symbols represent and how they relate to the metric tensor. As a bonus, we unearth the meaning of concepts like the Levi-Civita connection and parallel transport along the way. Plus: bears!

Contents: 00:00 - Intro 00:54 - Cartesian vs. Polar Land 03:31 - The Metric Tensor 10:16 - The Levi-Civita Connection 14:15 - The Christoffel Symbols 21:14 - A Polar Geodesic 22:27 - Future AgendaWhat Time Dilation ACTUALLY Is In Relativity (Hint: It has nothing to do with time)Dialect2023-08-05 | What causes Time Dilation? In the context of special relativity, where different observers disagree on basic facts about space and time, there has never been a clear consensus on this question, even among the experts. But an alternative interpretation known as Dynamical Relativity offers an entirely mechanistic explanation of the phenomenon, devoid of any mind-bending, space-and-time-altering pseudo-mysticism. What is this explanation exactly, and can it lead us to a deeper, more logically coherent understanding of the theory? Join us to find out. Plus, introducing the affordably-priced SoundBot-2000 -- watch out for its adorable critical-thinking alerts!

Contents: 00:00 - Intro 01:03 - "Hearing" Time 03:11 - Deriving Gamma 05:36 - The Clock Paradox 09:54 - The Twin Paradox 10:56 - Dynamical Relativity 13:40 - It's About Uncertainty, SillyWhy The Theory of Relativity Doesnt Add Up (In Einsteins Own Words)Dialect2023-06-24 | Relativity is as successful a theory as it is mind-bending - yet Einstein himself did not believe it was complete, and in a 1914 paper he critiqued its internal consistency at some length. Indeed, at one time or another we have all found ourselves in a state of healthy skepticism about the tenets of relativity, seemingly confronted by a mysticism of warping space and time that is nigh impossible to wrap one's head around -- and so here we find ourselves compelled to ask the same question Einstein did over a century ago: is the theory of relativity truly consistent, and if not, what does this mean for its future?

Contents: 00:00 - Intro 01:04 - Of Axioms & Absolutes 04:22 - Einstein Calls Out His Own Theory 05:54 - Defining "Absolute" Acceleration 07:35 - What are We Accelerating Relative to? 10:00 - Einstein's Mistake 11:57 - Where Do We Go From Here? 16:14 - AcknowledgmentsThe REAL Reason You Dont Understand RelativityDialect2023-04-29 | Think Relativity is confusing? Well, it's not just you -- even the experts can't seem to agree on its meaning, and often get basic facts about the formalism completely wrong. Here, we critique one such renowned professional who, in claiming to be clarifying the standardized theory of relativity, turns out to actually be promoting a misguided personal interpretation. What is this expert's confusion exactly, and why are such misconceptions so prevalent amongst the physics community?

Indeed, be cautious of posturers, gaslighters, stigmatizers, and Giordano-Bruno-burners who want to convince you that your inability to understand Relativity stems from your own deficient reasoning -- because when even the experts can't agree, you know there is something up...

A link to minutephysics twin paradox video: https://www.youtube.com/watch?v=0iJZ_QGMLD0&t=101s (Note that where minutephysics says that there are "gaps" in the accelerated observer's accounting for time, this is the phenomenon of accelerative time-contraction, i.e. where observers perceive gravitational fields/time speeding up.)

Some of Einstein's Relevant Papers:

His 1905 Special Relativity Paper: https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf His 1914 (not 1913) Paper "On the Relativity Problem": https://einsteinpapers.press.princeton.edu/vol4-trans/318 His 1918 discussion of the Twin Paradox and the Gravity-based solution: https://einsteinpapers.press.princeton.edu/vol7-trans/82 His 1920 lecture at the University of Leiden on the ether: https://einsteinpapers.press.princeton.edu/vol7-trans/176

Contents: 00:00 - Intro 01:11 - The Many Interpretations of Relativity 04:55 - Examining Sabine's Interpretation, Pt. 1 08:30 - Examining Sabine's Interpretation, Pt. 2 10:58 - The Source of Confusion 12:12 - Are There Better Interpretations?The Strengthened Liar and Paradoxes of IncompletenessDialect2023-04-08 | The Liar's Statement is one the most infamous problems in logic, but less well-understood is this paradox's connection to the concept of formal incompleteness. Indeed a close examination of this relationship produces an unexpected connection, leading us to ask — are some of the most famous theorems that have come out of mathematics, logic, and computability over the last century nothing more than a trivial application of reasoning known as the Strengthened Liar?

Content: 00:00 - Intro 00:57 - The Liar's Paradox and Incompleteness 05:53 - The Meaning of Incompleteness 09:45 - The Strengthened LiarThe River Model of General RelativityDialect2023-03-11 | Does space "flow" like a river? There's an analogy in General Relativity positing exactly that, and which, astonishingly enough, conveys the sophistication of Einstein's theory via a few simple intuitions. But how truthful is such a view, and what would it imply about the most infamous of massive objects to inhabit our universe -- that of the black hole? Climb aboard our river-boat and find out! Plus -- Curious Edgar finds himself in more than one vertiginous predicament.

Credit for the thumbnail title goes to this webpage: https://jila.colorado.edu/~ajsh/insidebh/waterfall.html

Content: 00:00 - Intro 01:05 - The Set-Up 01:54 - Accelerated Frames & "Flowing" Space 04:24 - Acceleration at the Surface of the Earth 06:10 - Reinterpreting Gravity 07:36 - Riverine Analogies 11:12 - Constructing the River of Space 12:43 - Phenomena on the River 16:05 - A Black Hole is a Waterfall of Space 18:09 - ConclusionLogic at its Limit: The Grelling-Nelson ParadoxDialect2023-01-14 | Whoever said logic was infallible? Certainly not the German logicians who, in 1908, discovered this mind-bending paradox. Learn how they beat reason at its own game, all by asking a single question about two simple words. Don't skimp out or you'll miss the surprise twist at the end! Plus: a very brief, totally not copyright-infringing appearance by The Sorting Hat.

Contents: 00:00 - A Tale of Two Words 02:04 - Semantic Sorting 03:30 - Paradox in a Nutshell 04:41 - Grammatical Formulas 06:53 - Breaking Logic 10:12 - The Naive Objection 11:18 - This was never about words, was it?The Geometry of a Black HoleDialect2022-12-17 | Gravity is said to be the curvature of space and time, but what does such curvature actually look like? In this video we explore the foremost solution to Einstein's equations -- the Schwarzschild solution -- in order to construct a concrete visualization of the spacetime manifold. Will this visualization grant us new insight into our higher-dimensional reality? The secrets of gravity are locked away... in The Geometry of a Black Hole.

Contents: 00:00 - Intro 00:50 - The Schwarzschild Metric 02:03 - The Schwarzschild Coordinates 06:30 - Resizing Space and Time 10:48 - Visualizing the Manifold 12:07 - Motion on the Manifold 14:14 - Reconstructing the Classical Gravitational Field 15:02 - The Geometry of a Black Hole 17:22 - ConclusionWhy General Relativity (and Newtons Laws) tell us The Sky is Falling UpDialect2022-11-05 | Understanding the Equivalence Principle is pretty straightforward -- so long as you're willing to throw out some basic intuitions about your everyday motion. Indeed, there is an astonishing truth about why objects actually "fall" at the surface of the earth that most people are completely oblivious to. Join us as we take to rocket ships, rooftops, cow pens, and other exotic settings in an attempt to expose it. Plus: plenty of monkey business along the way!

Contents: 00:00 - Introduction 01:02 - Intuition, a Fickle Mistress 02:20 - The Operative Definition 03:58 - Motion in a Rocket Ship 07:27 - Motion at the Surface of the Earth 09:48 - The Equivalence Principle 12:37 - The "Switch" 15:11 - Motion Falling off of a Building 17:54 - Tidal Forces 20:48 - The Sky is Falling Up!The Spacetime MetricDialect2022-09-02 | In the (epic?) conclusion to our metric tensor trilogy, we dive a little deeper into the origins of the metric tensor in an attempt to bridge the conceptual gulf that lies between our ordinary, intuitive understanding of geometry and that abstracter comprehension of it required to master General Relativity's four-dimensional spacetime. Can we pave ourselves a path to clearer understanding in twenty minutes? Let us know in the comments.

Contents: 00:00 - Intro / Describing Distance 01:56 - Maps and Metrics 04:28 - Intro to Spacetime Cartography 09:07 - Formulating the Metric 11:57 - Interpreting the Metric 13:57 - An Analogous Explication of Spacetime 16:11 - The Spacetime Metric 20:29 - ConclusionsThe TRUE Cause of Gravity in General RelativityDialect2022-06-18 | Alternatively titled, "Physics Myth-Busters: why time dilation does NOT cause gravity" this video explores an explanation of General Relativity whose monumental erroneousness is commensurate only to its popularity. What is this explanation, why is it so wrong, and how did so many high-profile YouTubers get suckered into promoting it? Prepare for a heavy dose of critical thinking, as we attempt to sift facts from falsehood and approach a deeper, more meaningful understanding of the actual nature of gravity.

Contents: 00:00 - Introduction 01:17 - Interpreting Curvature 01:55 - The "Time Dilation Causes Gravity" Explanation 04:00 - First Confusions 05:30 - Distinctions between Gravity & Gravitational Attraction 07:36 - The Problem of the Uniform Gravitational Field 11:03 - "Gravity" at the Surface of the Earth 13:30 - Spacetime Diagrams vs. Spacetime 16:39 - Testing for Curvature 19:19 - A Hidden Coordinate Transformation 21:11 - The True Cause of Gravity 24:09 - Planes of Simultaneity 24:50 - We Need Your Help!The Meaning of the Metric TensorDialect2022-05-07 | In the follow-up to our prior video, Demystifying the Metric Tensor, we continue to explore the physical and conceptual intuition behind the complex mathematical object known as The Metric Tensor, whose crucial role in the General Relativity, requisite to understanding the theory, tends to be easily obscured by abstract ideas and mathematics.

00:00 - Introduction 00:54 - Spacetime Cartography 02:30 - Maps / Coordinate Systems 04:00 - Bar Scales / Metrics 06:03 - Spacetime Distance 07:30 - Topological Transformations 08:39 - The 2D Metric 13:58 - The 3D Metric 18:39 - ConclusionNewton vs. Mach: The Bucket ExperimentDialect2022-02-18 | What is the ultimate nature of motion? Two influential physicists famously debated this question, invoking a bucket-and-water thought experiment to do so -- but they arrived at starkly different conclusions. Can we determine which one of them was right? Join us on a journey that spans centuries of metaphysical thought, books worth of controversial literature, and twenty-minutes of bad attempts at animating water spinning in a bucket.

Contents:

00:00 - Intro 01:05 - Newton's Absolutes 04:15 - The Bucket Experiment 07:31 - Round 1: Mach 11:14 - Round 2: Newton 13:06 - Round 3: Sudden DeathDemystifying The Metric Tensor in General RelativityDialect2021-10-22 | The path to understanding General Relativity starts at the Metric Tensor. But this mathematical tool is so deeply entrenched in esoteric symbolism and complex mathematics that its simplistic, intuitive purpose often goes neglected. Here we attempt to expose the basic principles behind the Metric Tensor -- and investigate how they tie into General Relativity -- in as simplistic a manner as possible. Do we succeed? Feel free to let us know in the comments!

00:00 - Intro 00:54 - The Equations of General Relativity 01:33 - The Metric as a Bar Scale 02:45 - Reading Topography on a Map 04:53 - Coordinate Distance vs. Real World Distance 05:35 - Components of the Metric Tensor 08:50 - Mapping the Earth 09:48 - Stretching and Skewing / Law of Cosines 11:37 - Geometrical Interpretation of the Metric Tensor 12:37 - Coordinate Systems vs. Manifolds 13:39 - ConclusionsEven More Paradoxical: The Twin Paradox in Curved SpacetimeDialect2021-06-18 | The Twin Paradox gets a stranger, even more mind-bending upgrade in General Relativity's world of curved spacetime. We explore the surprising and relatively unknown results to these new scenarios, while getting our toes wet in some of GR's conceptual frameworks. And finally, after several twists and turns, we are able to narrow down the only relevant criteria for resolving the Twin Paradox.

Support us on Patreon: https://www.patreon.com/dialect_philosophyEinstein, Gravity, and the Twin Paradox (Einsteins 1918 Solution)Dialect2021-01-09 | Surprisingly few people are aware of Einstein's preferred solution to the Twin Paradox, which he detailed in a 1918 paper. We examine this solution, purported to take place within the framework of General Relativity, in hopes of finally finding an explanation to the twin paradox that can appease our empathic skepticism. Along the way we learn a thing or two about the nature of gravity, the distinctions between special and general relativity, and the philosophy of motion.

Feel free to leave questions or concerns in the comments below!

Link to Einstein's 1918 "Dialogue on Objections to the Theory of Relativity" Paper: https://einsteinpapers.press.princeton.edu/vol7-trans/82

We are indebted to this paper for much of our historical information: https://www.academia.edu/3771200/Einstein_and_twin_paradoxDo Inertial Frames Resolve The Twin Paradox?Dialect2020-10-27 | Or more precisely titled, does "switching" between inertial frames of reference adequately account for the asymmetry of the twin paradox? Our investigation of another highly-touted YouTube solution leads to some surprising conclusions.

Full Twin Paradox Playlist: https://www.youtube.com/playlist?list=PL__fY7tXwodlaZp8pCI-Snv6pad5RuSdQSolutions to the Twin Paradox are STILL WrongDialect2020-05-15 | Are "solutions" to the twin paradox STILL leaving you confused and skeptical? In our follow-up to "Why Solutions to the Twin Paradox are Wrong" we dive deeper into popular YouTube videos, examining spacetime diagrams, the Lorentz Transformations, and other tools that are often incorrectly used to resolve the paradox.

Feel free to leave any questions or thoughts in the comments below!

Support us on Patreon! https://www.patreon.com/dialect_philosophyCan You Feel Force?Dialect2020-04-10 | It's often taught to us in physics that you can "feel a force". But what do statements about feeling force even mean, and are they accurate? The answer will surprise you. A follow-up video to "Why Solutions to the Twin Paradox are Wrong."Why You Cant Travel Backwards in SpaceDialect2019-12-14 | Turns out time isn't the only one with an arrow! Discover why traveling backwards in space is just as impossible as traveling backwards in time.Why Solutions to the Twin Paradox are WRONGDialect2019-05-10 | Do "solutions" to the twin paradox leave you confused or skeptical? You're not alone. An examination of three popular YouTube videos pinpointing where and why they get it wrong. Plus, Albert and Emmy get chatty.