Preprint (20.07.2002)
Date: Fri, 26 Jul 2002 23:30:18 GMT
From: redshift0@narod.ru

Organization:  
Newsgroups: sci.physics, sci.astro, alt.sciphysics.new-theories
Subject: The Indispensable Accuracy of the Measuring of an EM-wave's Energy

Key words:  Cosmology theory - stationary model - redshift - tired light - Hubble constant 

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The Calculation of the Indispensable Accuracy of the Measuring

of an EM-wave's Energy

Alex M. Chepick, Nizhni Novgorod
20.07.2002

Abstract

The hypothesis of a "tired light" is now disclaimed by indirect signs. Within the framework of this hypothesis is demonstrated, that the energy ε=hH (where h - Planck constants, H -  Hubble constant ) is a value of energy  that is lost by a photon in respect to one cycle of a lightТs wave, irrespective of a wavelength. Only having exceeding of the indicated measurement accuracy of energy, it is possible to demonstrate absence or presence of "tired" light directly in experiment. But in case of the state Universe it is possible to test this hypothesis by the obtained exponential dependence between redshift and distance up to a source. 

1. Introducing

In [2, p.487] is given the definition of the term "redshift", as a wavelength increasing (λ) of a monochromatic spectrum component of a radiation source in an observer'sа frame of reference as compared with wavelength (λ₀) of this component in its own frame of reference. Also there are given two facts:

└. Parameter of redshift z=(λ-λ₀)/λ₀ does not depend on a wavelength. It confirms by measurements of Doppler effect and gravitational redshift.

B. A Hubble Law - approximately linear dependence of a cosmological z_c from distance D up to far galaxies and clusters: z_c≈(H/c)D, where H - so-called Hubble parameter ( H₀ Ц Hubble constant Цis the value of the Hubble parameter in our time).

Thus, the cosmological лredshift╗ that is considered in this article, is a wavelength increasing (λ) of a monochromatic spectrum component of a radiation source in a observer'sа frame of reference as compared with wavelength (λ₀) of this component in its own frame of reference, at which one parameter of shift z=(λ-λ₀)/λ₀ does not depends on a wavelength and depends on distance D up to far galaxies and clusters.

The hypothesis of a "tired light" is the assumption, that in our frame of reference the energy of a photon should decrease at increasing of covered distance.

Let's consider light, as a wave of an electromagnetic field (EMF). The wave EMF is a series cyclical transformation of electrical and magnetic fields one into another. Е Inside each quarter wave segment between zeroes of fields there is an independent periodic transferring of electrical energy in magnetic one and back. [3, item "Electromagnetic oscillations"] In other words, the wave EMF can be esteemed as cyclical transferring process of one kind energy into another. The process is exactly cyclical - sequence of events of this process repeats. For a concreteness we would considering two successive half-of-cycle between zero points of electrical tension as a cycle of a wave EMF. Here is used the concept of a wave EMF cycle (it underlines a repetition of an energy transformation processes, instead ofа a wave period concept, because this term means interval of time, which one in our case is not a constant furthermore.

In the article an exponential law for changing energy ofа light is concluded for the Stationary Universe model by virtue of the facts A. and B., whence in turn the hypothesis of a "tired light" and constancy of photon energy loss value on one cycle of a lightТs wave follow.

Then for the Stationary Universe model from a constancy of photon energy loss value on one cycle of a lightТs waves the conclusion of exponential law of change of energy of light and facts └. and ┬. is demonstrated.

 

2. The light лtires╗ in the Stationary Universe

Let's consider parameter of redshift for a far object in the Stationary Universe model.

z = (λ-λ₀)/λ₀ = λ/λ₀ Ц1

It does not depend on a wavelength, depends on distance Rа that light passedаа (due to the facts └. and ┬.), and does not depend on time and place of light emission (due to the stationarity). Let's designate this relation as λ/λ₀ = F(R). Now we shall place an observer N between motionless source and motionless receiver. He shall watch a transmitted light on a wavelength λ_N, that is distinguished from λ and λ₀ due to dependence of the observed frequency from distance. That is we shall divide a rayТs path R on two sections: the path from the source to the observer R_NE and path from the observer to the receiver R_0Nа ,_ааа а(R =R_NE + R_0N),  also next relation is executedа λ_N/λ_E = F (R_NE ), λ₀/λ_N = F (R_0N).

Thus, the function from the sum of two parameters is equal to product of functions from these items

F(R_NE +R_0N)=F(R)=λ /λ₀ =(λ_N/λ₀)(λ /λ_N)= F(R_NE) F(R_0N)

Such property has the exponent: F(R)= e^R/Ch, where Ch - some parameter. We receive:

λ(R) = λ₀e^R/Ch Ц dependence of a wavelength

ν(R) = ё/ λ(R)=а ν₀e^-R/Ch - dependence of a frequency of wave

E(R) = ν(R) h=а E₀e^-R/Ch - dependence of an photon energy

It should be carry out for satisfaction of these formulas to the fact ┬. Ch=c/H₀ , where _аH₀= 58 km /(sec∙ Mpc) - Hubble constant,а soа Ch=17∙10⁹ l.y.

Let's remark, that the energy of a photon under these formulas should decrease at the increasing of covered distance. That is, the hypothesis the "tired light" is obtained.

Now we shall put R = λ₀ in the formula for energy of a photon. We receive a photon energy loss value on one cycle of a lightТs wave (for λ₀<<Ch, that is practically always):

ε=E_loss(R=λ₀)=E₀(1-e^-R/Ch)=h ν₀(1-(1- λ₀/Ch))=h ν₀ λ₀/Ch= hH₀

 

Thus, the value of photon energy loss on one cycle of a lightТs wave is constant.

 

3. The calculation of the value of photon energy loss, if it is constant

Let's show, that for a constant energy loss on a cycle the facts └. and ┬. are executed.

Let's designate of photon energy loss value on one cycle of a lightТs wave as ε, energy of a photon after n cycles - E_n , ν_n - frequency, λ_n - wavelength for E_n . Then E₀ - initial energy of a photon, ν₀ - initial frequency, λ₀ - initial wavelength. They are connected among themselves by formula:

E₀= h ∙ ν₀ = h ∙ c / λ_{0 ,}ааааааааааааааааааааааааааааааа (1)

where h - Planck's constants.

And energy E_n of a photon after n of cycles, ν_n - frequency, λ_n - wavelength are connected by the formula:

E_n= h ∙ ν_n = h ∙ c / λ_n= E₀ - n ∙ ε аааааааа (2)

Thus, quantity of transformation EMF cycles for a photon is finite.

The remainder of energy after last cycle has value smaller than ε. If thisа remainder is more than 0, it means, that there is an object EMF, that has no property of a wave. Therefore, the value of energy E₀ divide by ε. At the same time if we suppose, that the energy of a wave after last cycle is equal to 0, we shall receive, that last frequency is equal to 0, and last wavelength is equal to perpetuity. Therefore it is necessary to call a condition of a wave EMF when its energy becomes equal ε as last cycle. After that the electromagnetic wave dissolves, disappears as object. From these reasoning follows, what for a photon with initial energy E₀ the maximum number of cycles N_max makes expression (E₀ - ε)/ ε, or

N_max+1= E₀/ ε а= h ∙ ν₀ / εа ааааааааааа аааааааааааа(3)

For a photon with initial energy E₀ ,its life time Tmax makes

аааааааааааааааа

аааааааааааааааа		Nmax
	Tmax =	Σ  tn		(4)
аааааааааааааааа		n=1

where t_n is time of n-th cycle EMF.

t_n = 1/ ν_n = h/ (E₀ - n ∙ ε) = (h/ε)/ (N_max+1 - n)ааааааааааа (5)

ааааааааааа Whence follows, that the life time of a photon T_max makes

	Nmax		Nmax		Nmax
Tmax =	Σ tn	=  (h/ε)	Σ(Nmax+1 - n)-1	=а (h/ε)	Σ n-1	(6)
	n=1		n=1		n=1

  

  or

T_max(E₀) ≈ (h/ε)(C+ln(N_max+1)) = (h/ε) (C+ln (E₀ / ε))аааа (7)

where C approximately equal 0.5.

Thus life time of a photon is finite.

LetТs define, in what time after radiation Tа the energy of a photon becomes equal E_n . For this purpose time T_max(E_n) we shall deduct from time T_max(E₀) :

T= T_max(E₀) - T_max(E_n) = (h/ε) ln (E₀ / E_n)аааааааааааааа (8)

Having designated energy of a photon in this moment E(T), we receive the formula

T = (h/ε) ln (E₀ / E(T))ааааааааааааааааааааааааааааааааааааааааааааааааааааааааа (9)

And for expression of the photon energy as function of time after radiation we receive a formula

E(T) = E₀e^{-Tε / h}а       аааааааааааааааааааааааааааааааа (10)

By taking into account that distance covered by a photon during time T is equal in the Stationary Universe R=cT , we receive the formulas of dependence on distance of energy E(R), frequency ν(R) аand wavelength λ(R) а:

 E(R) =а E₀e^{-Rε /ch}

ν(R) = E(R) / h =а ν₀e^{-Rε /ch}аааааааа (11)

λ(R) = λ₀e^{Rε /ch}

Accordingly, the formula of dependence of redshift from distance looks like

z = (λ- λ₀)/ λ₀ = e^{Rε /ch} -1 а (12)

Thus, the redshift of a frequency spectrum from one source is identical to all frequencies!а

In the Hubble law V=R ∙ H₀ for small distances the speed of object V is considered equal V=z∙c. Asа for small distances redshift is z = e^{Rε /ch} Ц1= Rε /ch, we receive expression for a Hubble constant :

H₀ = ε /hааааааа аааааааааа ааааааааааааа(13)

а Thus, the formula of energy loss looks like:

ε = h∙ H₀ааааааааааааааа аааааааааааа аааааааааааааааааа(14)

We see, that the lost energy on one cycle of a wave EMF transformation is proportional to a Hubble constant .

And, by analogy with a Planck formula for a quantum of light energy E=h∙ν, it is possible to call a constant H₀- as Hubble frequency, and ε Ц as Hubble quantum, Subquantum or Plank-Hubble constant.

For value of a Hubble constantа H₀ = 58 kms / (sec Х Mpc) is received

ε =а 1.2∙ 10^-51 kg∙ m²∙ sec^-2 = 7.4∙ 10^-33 eV

Because of a small value of this energy it is possible also to call it as a quantum of energy of 2 order.

On 1 meter of vacuum a part of energy loss of light makes

z=Rε /ch=6∙10^{-27 а},

That not yet possible for measurement, therefore till now it is considered that the energy loss in waves EMF is absent.

Let's write once more the formula for the life time of a photon with allowance for values of ε

T_max (E₀) = H^-1 (1/2- ln(hH)+ln E₀ )аааа аааааааааааааааааааа ааа.

T_max (ν₀) = H^-1 (1/2- ln H+ln ν₀ )ааааааааааааааааааааааа (15)

which for light with a 500 nm wavelength makes approximatelyа 1.33∙10¹² years

The energy loss of a photon practically is proportional to theа distance covered by it up to valueа 1 billion light years (6 %а Hubble length).

Frequency ν of a photonа onа the distance R up to a source depends from initial frequency of a photon ν₀ under the formula:

ν = ν₀ e ^{-R/Chааааааааа аааааааааааааааааааааааааааааааааа} ааааааааааа (16)

where Ch = ё/H₀= 17∙10⁹ l.y. is Hubble length ; H₀ = 58 kms / (sec Х Mpc) - Hubble constant .

 

4. Additional reasoning for a лtired light╗

Why the perpetuum mobile - ideal cyclical converter of energy is impossible? Energy losses is cause of absence its "лeternity". Any actual cyclical process ofа the energy transformation is not endless. In the nature there is no perpetuum mobile, i.e. absolute cyclical transfer of energy (without waste of energy of that kind, which one is used in cyclical process). Even nuclear forces weaken with the time, owing to what we notice a half-life period. аWhy the waves EMF should be exception? Furthermore, the some sorts of decreasing of waves EMF energy are known (gravitational redshift, separation of a photon on a parts).

аFrom the fact of existence a cosmological "redshift" follows, that in our frame of reference a frequency and an energy of a wave EMF are decreased during the time its traveling .

The energy loss should be distributed on cycles of the wave. That is, on each cycle there should be an energy loss. Otherwise, if on adjacent cycles there are not conterminous sequences of events, it are not cycles.

Let's consider one photon. By virtue of dualism it is possible to consider, that it has properties of a wave - frequency, period and wavelength. Its quantum and wave properties are tied by the Planck formula: E= h ∙ ν, where E is energy of a photon, ν is its frequency. The frequency is quantity of cycles inа a unit of time.

Let's remark, that formally the same quantity of energy is on one cycle of this wave and is not dependent on energy of a photon. The same quantity of energy is on one cycle of a wave of any photon, irrespective of its frequency. For this reason the value of energy, lost by a photon, (on a cycle) also is constant.

 

5. Conclusions

1.                  The urgency of "tired" light is proved for the Stationary Universe model and the value of energy loss of a photon on one cycle of a lightТs wave is constant.

2.                  The formulas for a life time of a photon and dependence of its energy from covered distance are obtained also.

3.                  The view on Hubble parameter as a frequency is offered.

4.                  The most surprising conclusion is received if to look at the formula of energy loss from other point of view. Energy ε =hH (where h - Planck's constants, H - the Hubble constant ) is value of energy losses of a photon on one cycle of a lightТs wave is not dependent on a wavelength! Therefore, it is a global physical constant! The Hubble constantа has linked Macrocosms and microcosms.

5.                  The value of photon energy loss on one cycle of a lightТs wave is obtained. (for value of a Hubble constantа H = 58 kms / (sec Х Mpc): ε = 7.4 Х 10-33 eV. The constancy of this loss suggests about existence of stable particles with mass approximately 10^-66 g. It demonstrates importance of research not only superlarge energies, but also supersmall.

6.                  On 1 meter of vacuum a part of energy loss of light makes z =6 Х 10^-27, that not yet possible for measurement, therefore till now it is considered that the energy loss in waves EMF is absent.

7.                  It is possible to test the hypothesis of the Stationary Universe model by the obtained relation between redshift and distance up to a source. But for this purpose it is necessary to receive estimations of distances up to far galaxies by a way which is not dependent on model by the Universe, or way for concrete (Stationary) model of the Universe.

8.                  Because of the equal contribution of electrical and magnetic component into energy of a wave EMF, and that during one cycle there are 4 power transmissions between electrical and magnetic field, probably it is necessary to consider of energy loss for each such transformation at ε /4.

 

The literature:

[1] Physical encyclopedias, Є.1. (╠., Soviet encyclopedia, 1988.)

[2] Physical encyclopedias, Є.2. (╠., Soviet encyclopedia, 1990.)

[3] Large Soviet encyclopedias. (╠., 2001.)

[4] L.D.Landau, E.M.Lifshitz. A field theory. (╠., Science, 1967.)