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European Journal of Applied Sciences – Vol. 11, No. 3

Publication Date: June 25, 2023

DOI:10.14738/aivp.113.14530.

Dialynas, T. (2023). One Simple Cosmological Implication of Light Transmition in Hubble’s Law. European Journal of Applied

Sciences, Vol - 11(3). 1-10.

Services for Science and Education – United Kingdom

One Simple Cosmological Implication of Light Transmition in

Hubble’s Law

Thanassis Dialynas

DepartmentofPhysics,University ofCrete,Greece

ABSTRACT

Hubble’s law gives a great indication that the Universe expands and will do so in the

near future. In this “Paper” we try to extract information from Hubble’s law and so

to retrace its forward and backward steps. The most “striking” result for the

universe is that the “theory” predicts a maximum radius of the universe and a

maximum life-time. In addition, one can predict if there is causality in between two

points (t1, d1) and (t2, d2) of space time.

Keywords: Universe “radius”, Universe “life-time”, Cosmology, FLRW-metric, “Causality”.

INTRODUCTION

If the life-time of the Universe is supposed to be 1yr (real time ~ 10 Gyrs) then the observation

time of Hubble’s law is 3,15 sec (real time ~ 1000 yrs).

Therefore, the present observation time is 10−7

times, the “real” life time of the Universe.

In the rest (1-10−7

) time – interval, the law may be altered and also it is not sure if the Universe

is going to have the same behavior – For instance the expansion may stop or start to contract.

One the other hand, what is different from the “3,15 sec” of observation to the “1yr” life-time?

The answer is probably nothing! Therefore, we will presently trust Hubble’s law and accept it

trying in parallel from its evolution to “see” if it gives reasonable results (For instance in the

initial stages of the Universe) - This will be an indirect but strong confirmation of its validity.

In the “usual” (“normal”) theories of physics one handles a set of equations (usually differential)

and from this point, after the solution, he tries to “support” theoretically an experiment or an

observation.

On the contrary, if one knows Hubble’s law which is an observational-experimental fact, then

he is called, together with other information, probably to “predict” the past and the future of

the Universe.

If someone is at a point of the Universe and decides to move through a “constant” direction then

he is probably moving at the direction of a geodesic (What is a geodesic? [1, 2]) which is the

curve of the shortest “distance” between two points “inside” a certain (3+1) manifold.

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Services for Science and Education – United Kingdom 2

European Journal of Applied Sciences (EJAS) Vol. 11, Issue 3, June-2023

Of course, we may do not know the manifold itself of the space-time but we know its dimension

which is (3+1) - space-time.

This manifold (3+1) to be not confused with the R

3

x R structure of the Euclidean affine space- time of classical Mechanics.

The last one may be a tangent manifold of the first, at least at the points where gravity is not

very strong.

He who has decided to make the “trip” along a “constant” vector, he will after tenths of billions

of years, return to the same space point. This exactly shows the peculiarity of the 3+1 space,

especially the three-dimensional space. [Strange geometry (General Relativity)].

This reveals one more fact: According to Hubble’s Law all the far galaxies move, as the Doppler

effect says, far from the observational point and of one another.

What happens? Are we in a privileged point of the Universe? [like for instance with the

geocentric planetary system] or as it happens, the same thing is true for all the points of the

Universe? Therefore, one can say, every point of the Universe is a center of the Universe.

The dimensionality (3+1) of the manifold and the manifold itself are so complicated that cannot

accept their visualization although the dimensions of the usual space time R

3

x R is also four- dimensional.

Hopefully there is a paradigm (example) of a (2+1) manifold that resembles the (3+1) manifold

of the Universe: Let’s imagine an elastic toy-bubble which is blowed in by a kid for instance. If

we write points at a lot of places on the bubble then if the kid starts to blow, the spots will all

move one apart the other.

In this toy the spots are the galaxies (and in general the Universe objects) and the bubble is the

space-time (manifold) or more loosely Hubble’s Law. One more thing has to be mentioned

somebody who is on the bubble has no experience of the “third” (radial – 3D) direction. He is

an ant in a surface.

MAIN THEME

A. In the late 1910’s and 1920’s Hubble’s law was introduced experimentally

(observationally) by Edwin Hubble (Using Doppler effect) and theoretically (Using

Einstein’s Equations) by Georges Lemaitre. The contribution of Vesto Slipher (far

galaxies red - shift) not also to be forgotten.

This results in, that far Galaxies (mainly quasars) display red shift in their spectra and

the more far they are the stronger the shift to the red (which is always red) which finally

means departure.

Finally, the formula

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Dialynas, T. (2023). One Simple Cosmological Implication of Light Transmition in Hubble’s Law. European Journal of Applied Sciences, Vol - 11(3). 1-

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URL: http://dx.doi.org/10.14738/aivp.113.14530.

v = H*d (1)

was proposed where d is the radial distance from the observation point and v is the

radial velocity of the [far] galaxy. [Actually, for far galaxies there is only radial distance

and radial velocity due to the isotropic (and homogeneous) expansion of space – time

which in our case is expressed by Hubble’s law].

As it also comes out from the formula (1), H is a constant which turns out to be between

50 ~ 100 km/sec/Mpc with more dominant value

H0 ≈ 80 km/sec/Mpc ≈ 2,6 * 10−18 sec−1

(2)

B. Suppose two space – points A and B and time t at space distance d. At a later time t’ the

distance is going to be d’ = d(t’) where d’ = d(t’) > d(t) = d (t’>t).

This happens for any two space – time points. How this is possible to happen for any two

points? The answer is that the geometry of the Universe is radically different than our

experience which is this of the R

3

x R space time.

The Euclidean (or better affine) space time can only be realized locally in the Universe

and probably can only be realized there where there is no strong gravitational field.

This is the reason why we cannot “get rid of” theories like “General Relativity” that take

into account the whole “Universe” and not only local “slices” of it.

C. Since by Hubble’s law v = H*d [5, 6] the velocity of the far galaxies (also) must obey the

laws of physics and since they are constituted by material objects, we must necessarily

have v < c which implies:

d < c

H

(3)

i.e., a maximum value for d:

dmax =

c

H

(4)

For a value of H which is given by (2) we get dmax ≈ 12,24 Gly. However, the most far

Galaxy observed is at a distance dmax ≈ 13,8 Gly [6].

Solving inversely, we get for this Hubble constant

H ≈ 70,956 km/sec/Mpc (5)

In a later section we will try to make clear what is meant by dmax.

D. The radial distance of a far Galaxy is d and therefore its radial velocity is