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 Books and publications on the interaction of systems in real time by A. C. Sturt Economics, politics, science, archaeology. Page uploaded 14 January 2002, minor edit 2 July 2004

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The Timeless Universe

IV. The Redshift Exponential

by A. C. Sturt cont

PART I

PART II

PART III

PART IV

PART I

PART II

PART III

PART IV

The Redshift Exponential

The Timeless Universe II. The Redshift Reinterpreted presented equations for the distance, velocity and acceleration of sources of light from an observer in the model of a Universe which is in equilibrium, but stochastically regenerated. The assumption inherent in such equations was that wavelength increased by a constant quantity, say a given number of nanometres, per unit of distance travelled, whether kilometre or light year. The implication of this was that light which had travelled far from its source, and had changed wavelength, still carried with it the value of this quantity, which had been impressed on it as soon as it left the source. Such an interaction with a Universal field, which is what the paper proposes as the cause of redshift, would be difficult to envisage.

It seems much more likely that the increase of wavelength depends on the conditions in which the light finds itself at each stage of its journey. It would then be the ratio of the increase in wavelength to its current value which is proportional to an increment of distance travelled.

1. Wavelength

If the wavelength is λ, and the increase of wavelength is when the light travels a distance dx through the field, then:

where α is a constant for the interaction of light with the field concerned.

From this it can be seen that:

and

When x = 0 i.e. as the light leaves the source, the value of the exponential is 1, and λ takes its initial value λo.

The complete equation is therefore:

i.e. there is an exponential increase of wavelength with distance travelled.

2. Frequency

Similarly, if the light is described by its frequency f rather than its wavelength, then

λf = constant

f = constant/λ

and so

If the frequency of the light was f0 when it left the source, and f is its frequency at any stage, then

3. Distance

The distance of a source from an observer can be calculated from the equation for redshift if the value of the constant α is known, provided it is accepted that the frequency of light emitted by an excited atom at the source is the same as the frequency of light emitted by an excited atom of the same element on Earth i.e. the frequency of light emitted by atoms is homogeneous through time, and hence space. If λ is the wavelength of light from a source observed on Earth, and λ0 is the wavelength of light from the excited atom of the same element measured in the laboratory, then

By substitution for observed λ,

Rearranging,

Therefore,

distance,

velocity,

and acceleration

straight line redshift versus distance – the assumption

more likely relationship of dλ to λ

dλ/λ proportional to distance

exponential increase of λ with distance

exponential decrease of f with distance

light on stars same as light on Earth

homogeneous through time

measurement of:

distance of source

velocity of source

acceleration of source

 Copyright A. C. Sturt 27 September 2001

 Churinga Publishing