Conservation of Metric

First, a disclaimer: This may sound correct or obvious, but if so, it is because that is the way I write.  Nothing should be taken as either factual or as representing the opinions of educated physicists.

The whole of the set of ideas here have started to take a particular shape to me: Metric is conserved.  Mostly this just results in "gravity is sinuisodal", as described previously, but a recent discussion has led to an interesting concept.

First, I start with an idea I have been toying around with, that Lorentz Contraction is caused by a spacial "compression wave", although it isn't really a wave and is spherically distributed around moving mass in its own reference frame.

The “compression wave” almost certainly exists, although it, paradoxically to my original expectations, extends both in front of and behind the traveling object. (To see this must be true, the gravitational field must also be Lorentz Contracted, and that from the perspective of the traveling object, its gravitational field must necessarily fill flat space.)

The compression wave probably accounts for the speed of light limitation, in that any acceleration from the traveling object’s perspective must be within the reference frame of the compression wave – that is, it’s observed flat space – and is, from an outside perspective, likewise Lorentz Contracted. (The vector of acceleration is Lorentz Contracted, basically.)

It is not responsible for time dilation, as I initially posited, or at least not directly. There are two “types” of type dilation; synchronized and unsychronized, for lack of better vocabulary to describe them. Synchronized time dilation is when an object is moving fast relative to another object; because both are standing still in their own reference frame, they experience no time dilation, but because the other for each is moving fast, the other experiences observed time dilation. However, when they are brought to the same speed and location, assuming each is accelerated equally (so suppose they originally accelerate apart, then both accelerate back together and stop), observed time compression precisely offsets the time dilation; they have experienced the same subjective time.  This is, as far as I can grok, standard physics.

Unsynchronized time dilation happens in a gravitational field, and is correlated with the strength of the gravitational field. Gravity bends time, and motion relative to a gravitational field causes unsynchronized time dilation. This matters when we consider our spaceships outside a gravitational field – as we accelerate a ship, we also accelerate its gravitational field. However, the acceleration of the gravitational field happens at light speed, meaning it isn’t instantaneous – meaning that as we accelerate an object, it experiences motion relative to its own gravitational field, but only so long as it is accelerating. This creates unsychronized time dilation.  That is, the accelerating object experienced less subjective time after we bring reference frames together.

The compression bubble might contribute to unsychronized time dilation indirectly, by creating a reference frame in which an internally flat acceleration (from the outside perspective, a given thrust will result in decreasing acceleration, but from the inside perspective, the acceleration for a given thrust remains constant) can provoke the same unsynchronized time dilation – that is, because from your own reference frame your acceleration remains constant, the unsynchronized time dilation you experience likewise remains constant, instead of falling off as your externally observed acceleration decreases as you approach C.

All good so far I think.

But what happens if you reverse causality here?  What if we suppose motion is -caused- by Lorentz Contraction?

Let's think about gravity for a moment.  Imagine two particles falling into one another.  From the perspective of either of the particles, it's own gravitational field remains flat.  It will observe the gravitational field of the other distorting, however.  To see this, remember that gravity is a distortion of space-time, and that changes in gravity propagate at lightspeed - meaning gravity itself propagates through the medium it is distorting.  This means that as our observed particle falls into our reference particle, its gravitational field, which has to pass through denser coordinate space, shrinks somewhat in the direction of the fall.  This looks a little bit like a lopsided Lorentz Contraction.  The sum gravity of two particles should end up very slightly less than twice the gravity of one, because it drops off with distance and the distance is measured across denser coordinate space.

This lopsided Lorentz Contraction compression bubble persists, moreover - momentum is conserved.  In a sense, some of the metric of the observed particle, some of its gravity/space, got converted into the derivative of metric.  And internally to its own reference frame, its own metric was completely conserved, and it is the other particle which lost some metric.  From an "objective" perspective, some of its metric converted from an external field to an internal field, and its reference frame became slightly more subjective.  (Which makes sense, since it interacted with another particle).

Kinetic energy then becomes a scrap of space-time that has been bent in a particular way, and is conserved as part of the general conservation of metric.  It is all relative, of course - every particle's own reference frame is flat, it is everything else that is bent.  The speed of light ceases to be a constant from within this perspective, and is instead just a description of a scrap of bent spacetime that has been bent completely in half.

Now the question I am left with from this line of inquiry: Why would a scrap of bent metric look like motion?  I have an intuition that this might be the result of the interaction of gravity and this bend, and in particular the phase of gravity that we call the cosmological constant, which I suspect dominates our scale of observation, and which I suspect bends time in the direction we think of as forward.  This intuition is based on the fact that the attractive phase of gravity we are familiar with bends time in the opposite direction - that is, time passes more slowly in a gravity well.

But that is a thought that needs more thinking.  In the meantime, I feel slightly closer to a theory of everything, as things are looking increasingly like everything - including possibly the arrow of time - is just various distortions of space-time itself.

Another thought bearing more thinking: I have tended to think of spacetime as a contiguous fabric with various snarls and bends and tears in it.  The Lorentz Contraction compression bubble suggests this view may be wrong, because it is viewing spacetime as if it exists on a privileged reference frame, upon which various weird distortions exist.  This is a large chunk of weirdness I will need a long time to process.