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

It's not autoformatting, it's the result of not using a mono-spaced font (i.e. not using one where "W" is not wider than "i") and the fact that displayed HTML collapses whitespace, e.g you can't use space - space - space to line things up.

Try using [code] ... [/code] tags.

e.g.

You may find it easier to use notepad or similar (with a font like "courier") to do the editing.

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You're not breaking a postulate, you're breaking your clocks. If you are going to use your clocks as a standard, then you cannot let the mirrors move apart with the expansion of space.

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Okay, snowflakeuniverse, you have just disqualified yourself here.

And again, I would never give that answer. Do you understand why?

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Interesting idea but isnt it the distance which has become the variable as opposed to the speed of c? One is just making the photon travel farther, a bit like if one could change the force of gravity on earth to extend a pendulum's cycle period.

Hi AstroRockHunter

You said with respect to my expanding spacetime illustration the following,
You're not breaking a postulate, you're breaking your clocks. If you are going to use your clocks as a standard, then you cannot let the mirrors move apart with the expansion of space.

It was proposed or postulated that spacetime has structure, and that clocks, (such as a light clock composed of mirrors “floating” in space), expand with that structure, If that occurs, than intervals of time described by the light clocks become dilated with the expansion. Your objection is with the postulates.

Snowflake

Hi pzkpfw
Thanks for your advice and help.

Also, You asked,
are you simply using your already-presented theory to describe something?
I have presented this work earlier, but recently in the “Ask the expert” Forum a question about a variable light speed model was asked. This presents a bit of a procedural issue since an “against the mainstream” answer is required in a forum that does not tolerate against the mainstream responses. So I thought I would explain such a model that requires a variable speed for the speed of light.

Snowflake

Hi tusenfem
You said,
And again, I would never give that answer. Do you understand why?

Yes, because you understand the mainstream model, and you are not familiar with my model.

The example and questions were meant to illustrate structure. Let me rephrase them and introduce a few important terms.

The first series of 11 light clocks are separated by 1 million light years at T1.

The second series of expanded light clocks are separated by 2 million light years at T2.

(Capitol letters will be used to describe historical measures or as seen by an “Eye of God” perspective. Lower case letters will be used to describe relative or local measures of distance and time).

Questions
1. How far apart are each light clock at T1?
Answer. 1 million light years

2. What is the interval of time separating each light clock at T1?
1 million years

3. What is the absolute interval of time separating each light clock at T2?
Answer 2 million light years, based on an absolute or fixed measure of time established at T1

4. What is the absolute interval of time separating each light clock at T2?
Answer 2 million years based on an absolute or fixed measure of time established at T1



5 . At the historical temporal location a T1, Light from point 11 travels to point 1. How long does it take for light to reach Point 1?
Answer 10 million years. So an observer at point 1 seeing an event at point 11 is looking back into the past of 10 million years.

This is where the postulates of the model come in to play

6. After a long interval of time, the light clocks have expanded to as described at T2. What is the locally observed temporal distance between the points?
Answer. According to the proposed postulates, the light clocks define an interval of time which is locally invariant (c=1). Which means that the locally measured temporal separation between each light clock is the same as established at T1, which is 1 million years!

However, we can see from our “Eye of God” perspective that the light has to travel further therefore we conclude from our “absolute” perspective that it must take longer for light to travel.

However, while it true that the travel distance is further, the rate by which time passes is slower (longer path in the light clock means longer intervals of time), and the two effects cancel, preserving the relative, but not the absolute temporal separation between points.

Snowflake

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