There are no gravitons

There are no gravitons. There is no “need” for gravitons. There is only the potential energy field (spacetime), and the curves (waves) in that field created by and acting upon particles.

The field deforms as e/x^2 - the inverse square law of most forces. The cumulative effect upon another particle is as e/x - hyperbolic motion. Relativistic effects come from projecting the curved reality of the 4D field upon flat 3D space.

Feynman diagrams use an infinite regression of ever more complex arrangements of “virtual” particles to explain interactions. These diagrams have shown themselves to be useful shorthand for preparing the mathematics of quantum interactions. But what scientists continually forget is that the map is not the territory. “Virtual” means “not real”. There are no virtual particles. What exists is the entire rest of the universe, a vast array of particles creating and reacting to waves over unimaginable time periods. This results in a wide variety of waves interacting with each other, the particles under observation, and everything else they encounter, creating yet more waves through these interactions. It’s a chaotic (not just in the mathematical sense) mess.

A particle, if traveling quickly enough, does not necessarily follow the path of the waves it makes. (There are exceptions, like electron orbitals.) It can’t, as these waves propagate at finite speed, barely preceding the particle itself. It instead predominately follows the paths created by the waves generated from every other particle in existence - which we cannot with any real accuracy know. A slowly moving particle follows the path of these other waves, plus those created by its own waves propagating at the speed of causality and interacting with every other wave and particle they encounter. This looks an awful lot like a random assortment of chaos, with less and less predictable results for the particle under examination the longer it goes between observations. And thus, the semi-mystical randomness of traditional quantum physics.

The fundamental error of particle physics is to focus on just a few particles in an interaction and ignore the entire rest of the universe. They do this because it simplifies the math. This then produces nonsensical results like the measurement problem, the insistence that particles travel every infinite path on their way from here to there (violating every other known law of physics on the way), the observer effect and wave function collapse, and so forth. If the theory is not mathematically consistent (and quantum dynamics is not), if the calculations regularly result in infinities and singularities, if the calculations require renormalization (periodically throwing out your results and replacing them with experimentally determined values), then the theory is wrong.

The quantum wave equation is a measure of our necessary ignorance of conditions, not of some bizarre, inherent “unknowableness” of the laws of nature themselves. It would be laughable were it not so sad that those entrusted to study the most base layers of the laws of reality are taught to believe that reality has no inherent laws.

Copenhagen interpretation delenda est!

The stress-energy tensor and you

No, this is not a cheesy filmstrip.  Although there is an element of nostalgia about those sorts of things.  This is an updated version of the previous post, which got borked by Blogger.

The stress-energy tensor.  It sounds scary, and it looks intimidating.  It's a mathematical tool to represent geometry with numbers, and that seldom is easy or clean.

By Maschen, based on File:StressEnergyTensor.svg created by Bamse - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=24940142

The stress-energy tensor is a measure of the potential energy field (AKA spacetime) and how it moves matter. It pushes, it rotates, it stretches and contracts. It’s really all about these red “force” curves.  And it's not all that hard to understand once you have a picture to guide you.

The stress-energy tensor applies to every point in spacetime, here simplified to a single horizontal space axis and vertical time/potential energy axis. Read the indices as “a in the direction of b”. The coordinate scheme is as follows:
0 = time
1 = x axis
2 = y axis
3 = z axis

Energy density (value) is the depth of the red “force” curves. It’s how far the “force” curve (red, inverse square) is below the horizontal axis at any given point. This only requires a single number. (For the particle itself, it’s the green energy line.) Remember, this is the potential energy field. A lack of energy here is the existence of energy in some other form in some other field. Yes, this component is time in the direction of time. Time is, after all, the source and measure of potential energy.

Momentum density (gradient) is the slope of the red “force” curve. This takes three numbers, one for each direction through space, as modified by time. That’s how you show velocity through spacetime (four-momentum) and the Lorentz factor of relativity. (For the particle itself, it’s the slope of the internal green energy line. In this case, a stationary particle has a slope of 0.)

Shear stress (curl) is the rotation of the “force” curve in the three possible planes - xy, xz, yz. It’s curved motion, and is the reason why the Earth is attracted to where the sun is, not where it was 8 minutes ago. I can’t draw well enough to show that. Use your imagination. You’ve seen water forming a whirlpool as it goes down a drain. (See also frame dragging.)

Pressure (divergence) is deformation, or the sink effect of the particle in the middle.  There are no sources, because the potential energy field is maxed out when their are no other influences.

You may have noticed the diagonal symmetry of the stress-energy tensor. For my purposes, the bottom-left "flux" portion represents the actions of the force curve (red lines), and the upper portion represents the actions of the particle itself.  The usual way of formatting the spacetime stress energy tensor has the two sides symmetric across the diagonal.

Gravity and motion

Here we have two different particles in the potential energy field (AKA spacetime). Blue has ten times the mass of red. The force they exert on each other is the inverse square curvature of the field (mass/distance^2), propagated at the speed of causation. How do they move?

Well, assuming a stationary start, they move towards each other. The velocity path they each follow is the sum of the force (acceleration) acting upon them. That propagates as a hyperbola (mass/distance). Here’s what that looks like before the motion starts.

Of course, as they move towards each other, their velocities will increase, and their curves will be gradually compressed in the direction of motion, and stretched out in the opposite direction.

The velocity of a particle is a localized gradient. This gradient has its center at the particle’s mass (which is, of course, subtracted from the potential energy), and is angled down (less potential, more kinetic) in the direction of motion, up in the opposite. The gradient is entirely localized, and does not exist outside the particle’s boundaries (±1 from its center). The combination of this inner energy gradient and the outer curvature is the cause of blue and red shift.

Note that the force acting upon each particle doesn’t care about its mass. The only thing that matters is the curvature of the potential energy field, which is caused by the other particle. But notice how much more the heavier particle curves the field. This causes the lighter particle to accelerate faster than the heavier, and move further before they meet.

Mass curves spacetime. Curvature accelerates mass.

How much does the curvature accelerate the particle? You simply integrate the curvature along the path, and then divide by the time it takes the particle to follow that path. After all, a slower moving particle has more time to be influenced by the curvature than a fast moving one. How do you find the time? Form the particle’s velocity, of course.

The kinetic energy is altered by the path curvature of the potential energy over time. Or, more simply, the momentum gradient is altered by the potential gradient over time.

This is equivalent to the action, which in units is energy multiplied by time (mass * velocity[kinetic] * velocity[potential] * time). Note that in actual use, the mass can often be factored out, because it is both invariant and irrelevant in most cases. (The mass of a satellite doesn’t much affect the motion of the Earth, just as the sun isn’t noticeably perturbed by the orbit of Mars.)

Why does action have the same units as angular momentum? Because what you’re really doing is rotating the angle of the momentum gradient. The principle of least action applies to particles moving in the potential energy field (AKA spacetime) in exactly the same manner as in quantum physics. It is one of the foundations of the equations of general relativity.

Aside 1 - The Heisenberg uncertainty principle shows that the edges of a particle, where the inner kinetic gradient meets the outer potential gradient, are a smooth curve instead of a sharp discontinuity.

Aside 2 - The same principles hold true for the electromagnetic field, except that like charges (those that distort the field’s zero base line in the same direction) repel and opposites attract.

Aside 3 - A stable orbit is that which holds the angle of the momentum gradient constant after one full orbit (which may be different from one rotation). This is a form of quantization.

Copenhagen interpretation delenda est!

Reposted from my substack.

Follow the science!

 The "Science":

“The case against science is straightforward: much of the scientific literature, perhaps half, may simply be untrue. Afflicted by studies with small sample sizes, tiny effects, invalid exploratory analyses, and flagrant conflicts of interest, together with an obsession for pursuing fashionable trends of dubious importance, science has taken a turn towards darkness.”

 - Richard Horton, editor of The Lancet (the premier British medical journal), upon his resignation in 2015

Things have not improved since then.

This is real, published "research" in a "scientific" journal.