Can the acceleration of the Universe be analogous to apparent acceleration in a airplane?
When decelerating, during flight, from a fast cruise speed toward a slow approach speed, I notice that as the rate of decrease in speed constantly increases, the sensation is one of deceleration. But once the rate of deceleration is stabilized, constant, and unchanging, the sensation becomes one of hanging there presumably at a steady speed - there is no perception of deceleration (or even of speed for that matter) even though still decelerating. Even more deceptive, if slight control changes are made which cause a constantly decreasing rate of deceleration, the sensation becomes one of acceleration even though the aircraft is still decelerating (but at a decreasing change in the rate of the decreasing change of speed).
The sensations you describe fit perfectly into Einstein's general theory of relativity; in fact, you have experienced the so-called "equivalence principle" first-hand! The equivalence principle states that it is impossible to distinguish a frame which is in constant acceleration (or deceleration) due to an external force from one which is in free-fall. Your plane circling the Earth is what a physicist would call a "frame"; it is a box, or vantage point from which you make observations. A "freely-falling" frame is one which behaves as though there are no external forces acting on it. Thus, if you jump out of a plane you are in "free fall", and astronauts are weightless when they go into space, even though both frames have the force of gravity acting upon them; this is because on the scale of a sky-diver or an astronaut, the force of gravity produces a roughly constant acceleration, and hence the illusion of weightlessness. From the equivalence principle, your plane must mimic a freely falling frame when its acceleration is constant - this is why you couldn't feel that you were moving when this occurred. As soon as the acceleration is not constant, you are no longer in a freely falling frame, and you feel an acceleration or deceleration. The sensation you will feel depends not on your acceleration relative to Earth, but that relative to the plane itself. So, if your deceleration decreases, then you will feel an acceleration (and not a deceleration; the numbers on your console are relative to Earth and not to the plane's past acceleration).
Could this misinterpretation of sensations possibly be analogous to a misinterpretations of measurements regarding the expanding universe. For example, is it in the realm of possibility that as density of the universe decreases with expansion, diluting the influence of gravity, the rate of expansion continues to be slowed by gravity but at an ever decreasing rate of deceleration thus giving the relative illusion of expansion. In other words, is it possible that all this recent talk about the rate of expansion of the universe accelerating, is, (in truth), an illusion caused by a constantly decreasing rate in the rate of deceleration of the expansion?
Unfortunately, the expanding Universe cannot be understood in such simple terms. The equivalence principle only works for frames in which the external forces cause a constant acceleration in the frame. This requirement actually sets the size of a freely falling frame in a force field. We know that different parts of the Universe do not experience the same forces, and so are generally not in the same freely falling frame. Also, the equivalence principle applies the frames which experience acceleration due to external forces, that is, forces which stem from outside the frame. But there is no "outside" when one speaks of the Universe; the expansion must therefore be governed by the geometry of the Universe itself and it contents.
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