Paradoxes Are Errors in Thinking

I wrote a previous article (Kirsten Hacker : Thought Experiments) about Kirsten Hacker’s video by the same title. In this article I want to focus on her insight that paradoxes are a sign of errors in thinking.

Kirsten is an extremely talented individual who is very knowledgeable about the fields of physics and cosmology, due to her earning a Ph.D. in the field. Her twenty years in the field of particle physics gives her an insider’s perspective. Be sure to check out Kirsten’s intriguing books on Amazon.

There is an amazing section of dialogue in the video, which I have quoted below.

“You have to understand the difference between literal and figurative concepts to talk about relativity. By the end of this talk, I hope you understand how much nonsense is being taught on the internet about these issues.

The first thing to understand about paradoxes, the ancient Greek ones or Einstein’s paradoxes, is that they arise when you do not think outside of the box which defines the problem. That is the sole heuristic purpose of a paradox.

As you can see from bad teaching, they are frequently misused. When the paradoxes of relativity are taught as facts, students are given a feeling that they have learned something when they haven’t actually learned anything. They’ve actually missed the lesson. They are given a false confidence in their understanding of a counterintuitive logic puzzle composed of imaginary situations while gaining no understanding of the subtleties required for the application of the theory to real data.

All the student has learned from these paradoxes is how to feel clever while being gullible, how to throw his common sense in the trash, how to abandon himself to faith in a model, and in a fit of doublespeak, teachers will even tell their students that, ‘despite the fact that the paradoxes demonstrate a contradiction to common sense, they are not really paradoxes.’

When this sort of teaching spreads, even the teachers don’t understand what they’re teaching. This is really frustrating to see, when you understand what the lesson is meant to teach. That the paradoxes are results of errors in thinking, not that they are hoops you have to jump through to detach yourself from your intuition.

Relativity is not the only lesson of physics in which this subversion of basic sense is encouraged.”

Kirsten Hacker, Thought Experiments, 2019

Kirsten then dives into a number of differences between literal and figurative language when it comes to describing concepts and mathematical models. Her points are excellent. I will add that it’s not just paradoxes that indicate errors in thinking. The very large list of major open questions in physics and cosmology are also a signal of errors and gaps in thinking.

To see what is in front of one’s nose needs a constant struggle.

George Orwell

She then turns to special and general relativity, length contraction, and time dilation. I have a new way to think about length contraction and time dilation. In NPQG these concepts are entirely based upon the energy and the gradient of energy of the spacetime æther that any particle finds themselves in at any moment. Here is how it goes:

  • Spacetime æther gains energy in the presence of matter-energy.
  • The strength of gravity is proportional to the gradient of spacetime æther energy.
  • The strength of gravity is a vector at every point in space and in the spacetime æther.
  • You do need multiple coordinate systems – because you have the 3D Euclidean position in absolute space, and you have a position relative to local spacetime æther, and you also have the movement of the spacetime æther particles themselves and the overall flow of spacetime æther in any location.
  • Any matter-energy exchanges energy with adjacent spacetime according to the particle’s relativistic mass, which is a function of the inertial mass energy and the velocity (which along with the momentum) encode an additional mass energy.
  • Acceleration means that a particle is experiencing a gradient in spacetime æther energy. The spacetime æther in front must be less energetic and the æther behind must be more energetic. And isn’t this exactly what we see in everyday processes, such as rocket propulsion?
  • The more energetic the local spacetime æther
    • the smaller the radius of particle shells in the vicinity,
    • the slower the local c in absolute space,
    • and the slower the electrinos and positrinos in absolute space.
  • This is all determined by local permittivity and permeability of the spacetime æther.
  • Regarding the equivalence principle of a still elevator in earth’s gravity and an accelerating elevator in free space
    • they are only equivalent in the micro view of particles and their nearby spacetime æther.
    • The two situations are not equivalent in the macro view when you consider the larger volume in and around the elevator.
  • Regarding constant velocity magnitude in a circular orbit, this has an acceleration vector from gravity that causes the orbit and this is entirely caused by the spacetime æther energy gradient.
  • The direction of your velocity is not relevant to the length contraction or time dilation, i.e., they are symmetric around any rotation in space.
  • If something is accelerating it is also experiencing a spacetime energy gradient. The energy in front is lower than the energy behind. That æther must be near-instantaneously energized to create a temperature differential that matches the acceleration.
  • It is not true that separated twins with one experiencing accelerations and the other not, will be the same age upon meeting up again. Whenever a particle is in higher energy spacetime æther it’s clock runs slow and its length is contracted. Imagine one twin making one or many orbits around a denser object than earth and yet if they make multiple orbits they spend a longer absolute time with a slow clock. So 1 orbit, 5 minutes behind, two orbits 10 minutes behind. The trip there and back don’t cancel out either. It is not the acceleration that causes the length contraction and time dilation, it is the energy of the spacetime æther.

Now let’s turn our attention to using NPQG to explain time dilation and length contraction. The reader may be acquainted with various explanations of the special and general theories of relativity. According to Kirsten Hacker, and I agree, those are figurative explanations and figurative mathematics. I won’t recap those explanations here, but the careful reader may want to refer to their favourite explanations as they study the discussion below.

Let’s start with the Wikipedia synopsis of time dilation

Time dilation is a difference in the elapsed time measured by two clocks, either due to them having a velocity relative to each other, or by there being a gravitational potential difference between their locations. After compensating for varying signal delays due to the changing distance between an observer and a moving clock (i.e. Doppler effect), the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer’s own reference frame. A clock that is close to a massive body (and which therefore is at lower gravitational potential) will record less elapsed time than a clock situated further from the said massive body (and which is at a higher gravitational potential).


First, the synopsis says time dilation occurs when two clocks have a relative velocity between them. Note that in this particular case there is no acceleration of either clock and there is no gravity difference. This form of time dilation falls under Einstein’s special theory of relativity.

Let’s take a simple case in NPQG. Let’s say there is a spacetime æther wind moving relative to absolute space at velocity Vsp and that the energy density of the spacetime æther is a constant E1 in this scenario. We’ll define the velocities of the clocks relative to Vsp, so we won’t need Vsp again. Now presuming the two clocks are moving along parallel straight lines, then clock 1 has velocity v1 and clock 2 has velocity v2. Unlike Einstein’s special relativity, it actually matters what v1 and v2 are relative to spacetime æther because as we defined above the matter-energy of each particle determines the local elevation in spacetime energy. It is is not correct to simply consider relative velocity. Nature cares about the actual energy of each particle relative to spacetime æther. This should come as some relief to many because it portends a simpler and more logical understanding of nature.

Relativity vs. NPQGSpecial Relativity
(two particle—clocks with a velocity relative to each other)
General Relativity
(two particle—clocks with acceleration relative to each other)
Time dilation

Nature’s implementation of time is local to each particle and we must factor in the local energy of spacetime æther.

At low velocities the local energy increase of spacetime æther is also low and the gradient energy slope is very flat. Therefore it would take extremely precise instrumentation to measure effects on the photon. Only as the relative velocity approached local c would we see the curved path of the photon as it traveled through the declining energy gradient of the spacetime æther.
In general relativity the particle is experiencing a changing differential in the spacetime energy between the front and back of the particle.

As a particle is accelerated to higher velocity, energy is transferred to the shell, the payload, and the energy ante in spacetime æther increases. The payload primarily gains momentum. The shell energy grows as the speed of its electrinos and positrinos approaches local c. Note that in absolute space, the spin rate of the shell is slowing, but this is because local permittivity and permeability have increased and it takes more energy to move.
Length contractionAt high speed, the particle shell and the surrounding spacetime æther have high energy. This causes all particles, including the æther particles to shrink in radius to compensate.This is the same as the special relativity case except that work is being down to increase the energy of the shell and the surrounding æther.

In NPQG the time dilation of a particle-clock is due to the local energy of spacetime and the matter-energy of the particle and in particular the shell. The local energy of spacetime æther depends on the relative velocity to the particle and the proximity to other matter-energy. Also, as particles are accelerated they are gaining shell energy as well as putting more energy on ‘deposit’ in the surrounding æther.

Orbit in constant temperature æther has a constant magnitude of potential energy in an absolute sense, but the potential vector is constantly shifting, always pointing towards the center which corresponds to the maximally steep gradient of spacetime energy.

To understand NPQG relativity you must realize that everything is about particle shell energy and the local energy density in æther shells. The physics has no idea what is out there, it just knows the energy densities of the spacetime æther and the gradient of that energy. It also senses the electromagnetic fields. It should be possible to calculate the speed and diffraction of the photon as it passes through a variation of spacetime energy.

That was a rather long winded explanation of relativity in NPQG. I hope to make it even simpler to understand in the future.

Electrino and positrino charges are fixed and immutable in NPQG. You could say they are discrete or quantum. However, many aspects of nature are continuous at the fundamental level. By continuous I mean mathematically continuous, not discrete jumps. At the fundamental level of nature — electric fields, magnetic fields, electromagnetic and kinetic energy, velocity, and space are continuous. However, higher level structures and patterns formed by electrinos and positrinos may and do exhibit discrete quantum behaviour. There seems to be a correspondence where analog is to digital as fundamental nature is to emergent natural patterns. That isn’t a perfect duality, but it is illustrative.

Every electrino and positrino in the universe is constantly experiencing the potential field of all other point charges, and sometimes themselves. Fields naturally attenuate with distance so the largest effect on each particle tends to come from nearby electrinos and positrinos.

For example, a photon is hypothetically made from three orbiting electrino/positrino pairs, possibly behaving as dipoles, forming an empty orbital shell in three dimensions of space. The velocity of the electrinos and positrinos in the shell corresponds to the pace of time for that particle. Thus the energy of the photon is related to the velocity of the electrinos and positrinos in the shell. If that photon is involved in a reaction, it may emerge with lesser energy corresponding to lesser electrino/positrino velocity in the shell. But what really happened in that reaction? Electrinos and positrinos did not make a quantum leap from one place to another. No, they followed some path to a different orbital wave equation. What shall we call that transitional path between two wave equations at different energy levels? Perhaps it is related to the uncertainty principle. It is certainly related to the so called collapse of the wave equation.

It’s important to note that shell volume decreases the more energetic the shell. Well, that is up to a point of course, and it depends on whether the shell is empty or has a payload, and of course what is the electrino/positrino composition of the payload, and what is the energy of the payload. So, you can imagine an incredibly fascinating phase diagram of the universe in the sense of phases of matter that we learn in high school chemistry. Each phase is a different pattern of elements and patterns of elements and patterns of patterns and so on. Molecular reactions are patterns, molecules are patterns, atoms are patterns, electrons and neutrons and protons are patterns, electron orbits are patterns, and all of the particles of the standard model are patterns and follow patterns—the key finding of NeoClassical Physics and Quantum Gravity is that everything in the universe emerges as patterns upon patterns of structure based on the basic ingredients of Nature. It is fascinating that the fundamental character of nature is to enable incredible emergence from such simple ingredients:

  • a 3D Euclidean void
  • ample pairs of point charges, equal and opposite, immutable — the electrino and the positrino.
  • energy in kinetic and electromagnetic potential forms that may only be carried by point charges.
  • Maxwell’s equations and neoclassical mechanics.

In the familiar case in the universe, each electrino and positrino finds themselves to varying degrees in proximity with other electrinos and positrinos. Of course each electrino and positrino has their own instantaneous velocity and is generating fields that emanate as well as responding to received fields. Each electrino and positrino in a shell like structure may well be following a wave equation. All of these electrinos and positrinos would form a large variety of patterns of composite particles and characteristics under diverse phase and reaction conditions. We call some of those patterns the particles of the standard model. But there are more patterns – the mathematical patterns which GR and QM have established but with neither a fundamental understanding nor a unification.

Let’s consider what would happen if a free electrino or positrino or particle assembly encountered a truly empty void of time and space, not even much or any spacetime æther. The only place I think we can frequently see such a situation is in jets of Planck plasma. A Planck plasma jet would presumably cause decay spacetime æther assemblies. Thus these jets may be superluminal for some distance, until their energy is no longer sufficient to fully displace the spacetime æther and any other assemblies that have accumulated due to reactions fueled by the jet.

J Mark Morris : San Diego : California