The Princess and the Pea

When I began my journey, I treated the physical theories of science that already exist as "Innocent, until proven Guilty". Whenever I had a difference of opinion with a physical theory, it was significantly more likely that my opinion was based on too limited information than it was that the physical theory was incorrect. (Actually, it is more accurate to say that I made my own foray into understanding these theories, but treated physical theory as "the answer book" to show me where I was missing information or making mistakes in my assumptions.)

However, I have come to point where I'm confident that I know all there is to know about Special Relativity - what issues evoked a need for it, how it resolves those issues, the mathematical mechanics of how it works, and how the engine core of Special Relativity (both in theoretical terms and in mathematical mechanics) has spread out to General Relativity and by extension, all of Cosmology.

In learning it so thoroughly, I have also come to identify what my instincts have been forcing me to seek out. A tiny (literally point-sized) gap in the mechanics, where Special Relativity doesn't quite solve the problem as it is supposed to. Though tiny, the point-sized problem explodes into a major issue in General Relativity, defeating it as a proper theory of gravity. I also strongly expect that a correction to the theory will show dark matter, and possibly also dark energy, to be artefacts of General Relativity, an incorrect model of the universe.

This is why I'm now adopting a more offensive approach. Given that I can identify the location of the problem, I can then trace it through physics, and I can confidently say which physical theories can be left alone and which need to be recalculated.

 My goals now consist of the following -
  • Create a conceptual model of the corrected Special Relativity
  • Build the mathematics corresponding to the conceptual model
  • Rebuild the equations of relevant physical theories to match; i.e. mechanics and electrodynamics
  • Extend the mathematics of the corrected Special Relativity into a general equation of gravity

Special Relativity is a touch incomplete.

The incompleteness is difficult to spot, and it will be easier to demonstrate if I first compare the Galilean transformation (where the velocity of a baseball relative to Earth is u+v, if the velocity of the train carrying the thrower is u) and the Lorentz transformation, used by Einstein to maintain the speed of light relative to all observers in different inertial reference frames.

Two notable effects of the Lorentz transformation are length contraction and time dilation. Lengths of the observed object (like a baseball thrown from a train) are shortened along the direction of motion and it experiences time ticking away at a longer relative rate than a person watching it standing on the Earth. That way, both the baseball and the person standing on Earth see the light leaving the train headlight at the same velocity.

For straight line movement at constant velocity, it is a single transformation but for non-inertial movement (i.e. accelerations, rotations, or revolutions), the situation is more complicated.

Rotations, as mentioned, do not appear to maintain inertia. Let us confirm by finding out what happens when a Galilean Laboratory is rotated about the center, and we'll fire a beam of light towards the center.

The pre-Einstein Galilean Laboratory reacts in a way that is congruous with what we expect in day-to-day life. Figure 1a is similar to what we might see if we throw a baseball at a randomly spinning person. The baseball travels in a straight line towards the person while they spin.

The perspective of the spinning person is also natural. As the ball comes towards them, the baseball veers left and right in their field of vision. Humans are equipped with biology so that we still generally understand we're spinning and ball is moving in a straight line, but if we're watching a video of that person's perspective, it's not necessarily obvious. Is the object onscreen moving left and right, or is the camera operator rotating around?

Keep in mind, this commonsense perspective does not necessarily keep the speed of light intact, and if not, it doesn't correspond with reality.

Einstein knew that an application of the Lorentz transformation was required here. He reasoned that the outer edges of the spinning Laboratory are moving at a greater velocity than the center, and therefore are subject to Special Relativity to a greater degree than the stationary center, and that the effects of Special Relativity are increasing from the center to the edges. The circumference of the Laboratory shrinks by length contraction, an effect of Special Relativity, and experiences time at a dilated rate compared with the center. By this, he reasoned that the spacetime of the laboratory "bubbles up". You might have seen videos online of how matter affects the fabric of spacetime by creating a dimple in the fabric.

If the Laboratory is rotating wildly back and forth, clockwise and counterclockwise, then it dimples and undimples spacetime with its movement.  The Laboratory shrinks and expands again to its stationary size, and the edges of the Laboratory move slightly ahead in time before equalizing with the center again as a clockwise rotation turns into counterclockwise, and visa versa.  In short, an observer on Earth sees the Laboratory undergoing some pretty spectacular effects in terms of length contraction and time dilation.  However, an observer on Earth sees the beam of light head straight towards the center of the laboratory at the speed of light, exactly as required.

From the perspective of an observer inside the Laboratory, many experiments do not perform as expected, and some might even throw themselves against the outer edge of the Lab. An observer looking outside the Laboratory would see the universe itself shrinking and growing to normal size, and time dilating, as required by the Lorentz transformation to keep the speed of light constant for all observers. The path of the beam of light itself becomes difficult to calculate, with all the length contractions and time dilations going on around it, but it is a warped version of the path from Figure 1b.

Notice that in all of the previous examples, we used the Galilean Laboratory. It is large and spacious, and sensitive to rotations. When a beam of light approaches the Laboratory from the outside, the scientist in the lab can determine what part of the lab detected it. I'm now going to attempt these experiments with the Blain Laboratory, which is a single point rather than a large, spacious laboratory.

When the photon begins it's journey from the emitter (stationary on Earth) towards the Blain Laboratory, we are also stationary with respect to Earth, and so the photon travels at the speed of light as we expect. It hits the Blain Laboratory on-time and at the proper velocity.

However, something strange happens when we observe from the perspective of the Blain Laboratory. The Laboratory is zero-dimensional and therefore has no implicit orientation. With no implicit orientation, we cannot determine how Lorentz transformation applies. If the Blain Laboratory is stationary (i.e. not rotating), then the Lorentz transformation reduces to the regular Galilean transformation and light is travelling at the speed of light toward us, but we can't guarantee that. If the Blain Laboratory is rotating wildly (as in previous examples), then we need to know its precise pattern of rotation or else we cannot properly account for it to correct the speed of light, and we risk losing the correct speed of light. The physics inside the Blain Laboratory would be thrown into utter chaos.

We seem to be stuck in a sea of confusion.   Fortunately, Einstein left us a lifeboat.

When I began my journey, I treated the physical theories of science that already exist as "Innocent, until proven Guilty". Whenever I had a difference of opinion with a physical theory, it was significantly m

No comments:

Post a Comment