A variable speed of light model, kind of.

This discussion is an offshoot from the “ask the expert” forum.

The following example describes a version of a variable speed of light model. It is based upon an expanding metric previously posted in this forum.
The Expanding Metric


First a few terms and concepts or assumptions need to be described.

The Light Clock
A light clock is used to define an interval of time. It is simply two parallel mirrors separated by a distance with a photon burst traveling back and forth between the two mirrors. For example, two mirrors separated 3 x 10^8 meters would describe an interval of time of 2 seconds during a “round trip”.

spacetime
Spacetime is defined or described by a specific geometric structure. It can be visualized as a lattice like structure with all points in the “structure” described by measures of intervals of distance and time.

Invariant, c =1
The interval of time described by the light clock is often referred to as being “invariant”. The geometric relationship between the distance between two points and the time separating the two points is fixed or constant. This geometric relationship is often utilized in relativity by assigning the speed of light the value of 1, ie c = 1.

Expanding spacetime
The expansion of spacetime carries galaxies. Galaxies do not move through spacetime, they are carried by it.

So far the above assumptions and descriptions are fundamentally core to most mainstream models. The following example shows how such a model can yield a variable speed of light model, which surprisingly still allows the speed of light to appear locally invariant or unchanging or constant.

String of light clocks

Lets place a string or series of 10 light clocks in deep space.

I . I . I . I . I . I . I . I . I . I . I

1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11
(The auto formatting messed up the layout)

Each light clock is separated by 1 million light years. Each light clock has photons passing back and forth between each of its neighbors, defining an interval of time with a separation of 1 million years.

Question 1
How long does it take for light to travel from point 11 to point 1?
Answer 10 million light years


Expanding spacetime
Lets say the course of 10 million years the distance between points in the expanding spacetime doubles. The mirrors are carried by the expansion of spacetime, (like galaxies are), are now 2 times as far away

I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I

1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 .. 8 .. 9 .. 10 .. 11

Question 2
How long does it take for light to travel from point 11 to point 1?

Breaking a postulate
If you answer 20 million light years, it seems you have broken one of the postulates of relativity, ie c = 1 The interval of time described by the light clocks no longer is invariant, or constant. Instead of each light clock defining an interval of time of 1 million light years, they now describe an interval of time of 2 million years


Better solution, clocks “tick” slower
However, another way out of this dilemma is to assume that the expansion of spacetime also stretches all intervals of local or relative time. This preserves the c = 1 relationship.

Ignoring for now the delay time that it takes for light to travel between points. We have the following example.

The locally measured interval of time of 1 million years between our local light clock would be the same regardless of the amount of expansion that occurs between the light clocks. C=1. In order for this to be valid, all physical processes must also slow the exact same proportional amount. (This was illustrated in previous postings and was never refuted).

In the proposed model, the speed of light slows with the expansion of space, and the distance necessary for the photons to travel increased with the expansion of space, mandating that all intervals of time expand with the expansion of spacetime This expansion occurs according to a specific geometry which allows c to = 1, locally, but from an “ Eye of God” perspective the change in length and speed of light can be “visualized” as changing over time.

Snowflake