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P: 66
 Quote by Willowz On what basis can physicists suppose that there are dimensionless constants if they can only be calculated by physical measurement?
This 'thought experiment' shows one. All of the constants on the 3 ratios below can be regarded as time or distance (based on the distance travelled by light in the time). Mass is not part of any ratio used in this 'thought experiment'.

If I started photographing a light around 6 and a bit feet away, and the light was being spun in a circle 2 feet in diameter and I captured the light from the spinning light in one complete circle the ratio (A) of the time between the rotating source and the observer over the diameter of rotation would be roughly equal to Pi.
In this case the ratio (B) of the actual distance between source and observer over the distance travelled by light in a year would be very small and the ratio (C) of the observation period over the time it takes for the light to be rotated once will equal one. All observations should have a width of field that covers the complete diameter of rotation of the source being observed.

If I halve the exposure period I get half a circle and capture half as much light and when I double the exposure period I get 2 circles over each other and twice as much light in my photograph. If the light is rotated twice as fast I would expect something that looked similar to when I doubled the exposure period but I would also expect to capture the same amount of light from only one rotation despite the doubling of the speed of rotation. If I put two lights together I could halve the exposure time and double the speed of rotation to capture a similar amount of light from 1 light doing 1 complete rotation. If the light moved at an angle to me I would observe an oval instead of a circle but the amount of light captured would remain the same as in a complete circle.

In this simplest base context A = Pi, B = tiny, C = 1 and the observer will capture one complete cycle. On any scale where C >= 1 the observer will capture at least one complete cycle despite the size of B.

On any scale where A = Pi * x, B >= 1 and C < 1 the observer will only capture the light from B * C = x of one rotation during any observation regardless of the speed of rotation of the same object.

On a galactic year scale where A = Pi * x, B = 230 million and C = 1/230 million you would expect to capture the light from B * C = x rotations or roughly one rotation regardless of the speed of rotation.

On a galactic year scale where A = Pi * x, B = 4.2 billion and C = 1/4.2 billion you would expect to capture the light from B * C = x rotations or roughly one rotation.

Only changes in brightness can really make a difference on any scale as the speed of rotation does not change the total amount of light captured from the same source during any similar observation period. I have used figures for convenience, put your own figures in and keep ratio A as Pi * x and you will have a base point to compare observations.

This 'thought experiment' illustrates a common ratio that allows for a perceived mass and size variation from double, as per this threads title, to parity and one half. While it would be impossible to calculate the galactic years of every observed rotating source in the universe it would be logical to say that the difference in the sum of the perceived universal mass calculated from optical observations verses the perceived universal mass calculated from x ray observations is equal to the average of the number of galactic year rotations of each discrete source captured in your visible data sets.