Future and Past in the Current Model of Expanding Universe

 

Future and Past in the Current Model of Expanding Universe

Pavle I. Premović,

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry, University of Niš, pavleipremovic@yahoo.com, Niš, Serbia

The standard cosmology states that our Universe began about 13.8 Gy ago from a singular Big Bang event. The fundamental observation behind this theory was the cosmological redshift z of nearby and distant galaxies[1] (hereinafter the galaxies). The standard cosmology explains this shift in terms of the expansion of the Universe. This expansion implies that these galaxies are receding away from each other[2], or in other words, the distance between them is increasing. In general, the galaxies at the larger distances from the Earth were born before the galaxies at the smaller distances from it. Cosmologically speaking: the former are younger than the latter, in respect to the Big Bang time or the former are older than the later, in respect to the present time.

The “megamaser” method is useful for precise distance measurement of nearby galaxies but it appears it is suitable for very few of these galaxies -“megamaser” galaxies. For the present case, we select two of these galaxies: NGC 1052 and NGC 6264. Their respective distances from the Earth are 65 Mly and 447 Mly (determined by the megamaser method) [2, and references therein]. For an Earth observer and a hypothetical NGC 6264 observer, the NGC 1052 galaxy was born after the NGC 6264. However, for a hypothetical NGC 1052 observer the NGC galaxy 6264 was born after his galaxy. Of course, we could have chosen any two or more nearby and/or distant galaxies at different distances from Earth.

Can this be interpreted that there is no distinction between the past and future in the current model of the expanding Universe or even that the time flow, in general, does not exist in this Universe? Does it imply that the possible models of the non-expanding Universe (such as the tired-light model) are much more acceptable? This issue is out of the scope of this communication.[3]

References 

{1} P. I. Premović, Distant galaxies in the non-expanding (Euclidean) Universe: the light speed redshift. The General Science Journal, December 2021.

{2} P. I. Premović, The age of the “megamaser” galaxies in the Big Bang Universe. The General Science Journal, December 2021.

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[1] We define nearby galaxies as those whose redshift z is from 0.001 to 0.1 (or 0.001 ≤ z ≤ 0.1) and distant galaxies with z > 0.1 {1, 2}. Of course, there is no sharp line between nearby and distant galaxies.

[2] Except for the objects which are part of the same gravitationally bound group or cluster of astronomical objects. 

[3] As a scientist, I only sometimes dealt with time as a physical phenomenon and, mostly within the time dilation of Special Relativity. For this reason, I give up further consideration of the time flow of the Universe.

Hydrogen Molecule in the Light of the de Broglie Theory

 

Hydrogen Molecule in the Light of the de Broglie Theory

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

University of Niš, pavleipremovic@yahoo.com, Niš, Serbia

 In one of the previous communications {1}, we pointed out the discrepancy in the representation of hydrogen molecule (H₂) in chemistry and physics textbooks and its interpretation based on the de Broglie wave theory (duality). According to these textbooks, this molecule consists of two protons and two electrons, each with a charge e, connected by a covalent bond. The experimental equilibrium bond length of H₂ is аbout 7.4 × 10^-11 m or about 43500 diameters of proton (its radius is approximately 0.85 × 10^-15 m).

The de Broglie wave equation for a massive particle in motion is given in the following form 

λ = h/mυ ... (1) 

where λ is the wavelength, h (= 6.63 × 10³⁴ J sec)[1] is Planck's constant and m is the mass of a particle, moving at a speed υ.

If H₂ travels with a non-relativistic speed υ its wavelength is then 

λ(H 2) = h/m(H₂)υ ... (2)   

where m(H₂) is the rest mass of H₂.

The mass of the electron is negligible compared to the mass of proton m(H⁺) then the mass of H₂ m(H₂) ≈ 2m(H⁺) ≈ 3.34 × 10^-27 kg. The most probable/average speed of H₂ which occupies 22.1 dm³ at STP is υ_mp(H₂) ≈ 1500 m sec^-1. Using eqn. (1), a simple calculation shows that its average wavelength λ(H₂) ≈ 1.3 ×10^-10 m is about twice larger than the bond length (аbout 7.4 × 10^-11 m) of H₂.

The wavelength of each proton in this moving H₂ is 

λ(H+) = h/m(H⁺)υ. 

Neglecting again the mass of the electron, we have m(H) = m(H⁺) or m(H⁺) = 1/2 m(H₂). Plugging this last term into eqn. (3) and taking into account eqn. (2) we get 

λ(H⁺) = 2λ(H₂) ... (3).

Using this equation, a simple calculation shows that the average wavelength of the protons in H₂ λ(H⁺) ≈ 2.6 × 10^-10 m.[2] This is four times larger than the bond length of H₂. 

As we pointed out before {1}, the superposition of the waves of these protons can result in two types of interference depending on their phasing. If they are in phase we deal with constructive interference. In this case, the resultant wave would have twice large an amplitude as the proton but its wavelength would be the same as the proton wavelength. If they are out of phase, we deal with the destructive interference, the two proton waves would cancel each other so there would be no resultant wave.

When the protons of H₂ are so far apart (about 43500 proton diameters) one is dealing virtually with two completely separated nuclei. In contrast, de Broglie’s concept would imply that the protons do not exist separately in H₂.[3] Having that in mind and the de Broglie eqn. (1), we speculate, with great hesitation, that the H₂ nucleus is made of two proton nuclei partly “fused” forming the diproton nucleus, H₂²⁺ (or “p-p”). We also hypothesize that H₂²⁺ is dumbbell-shaped, Fig. 2.[4] Its two e = 1+ charges are separated from each other by an internuclear distance much smaller than 7.4 ×10^-11m or << 7.4 × 10^-11 m.[5] At this distance the potential energy of H₂ with the partly “fused” protons is at a minimum, Fig. 1. This distance is the bond length of H₂ with partly “fused” protons.

Fig. 1: Potential energy vs. internuclear distance between two partly “fused” diprotons of H₂.

Fig. 2: Highly exaggerated two-dimensional picture of the (dumbbell shape) partly “fused” diproton nucleus of H₂.

 However, we now face a dilemma: does H₂ consist of two completely separate protons or two protons partly “fused”? This leads to a rather intriguing question: Does the quantum mechanical model of H₂ in motion consist of one wave packet as can be concluded based on the de Broglie model or it consists of two identical wave packets of its protons? Because of its generality, this dilemma can be extended to all diatomic homonuclear molecules gaseous at STP (e. g. the radon molecule: Rn₂) or at non-STP (e. g. the iodine molecule I₂). 

References 

{1} P. I. Premović, The hydrogen molecule and deuterium atom in the light of de Broglie’s theory. The General Science Journal, May 2023. For the sake of clarity, I have modified the first part of a previous version of this communication which refers to de Broglie’s model of H₂.

2} L. Holmlid1 and S. Zeiner-Gundersen, Ultradense protium p(0) and deuterium D(0) and their relation to ordinary Rydberg matter: a review. Phys. Scr. 94 075005 (26pp), 2019.  

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[1] To avoid confusion in further text, the SI units are given in italics.

[2] Their speed is identical and equal to the speed of H₂. According to eqn. (3), the wavelength of H₂ is twice the wavelength of H⁺.

[3] As far as we are aware, this claim has not been demonstrated experimentally.

[4] In the case of complete fusion, this nucleus would be of a spherical form without the bond length.

[5] It is interesting to note that Holmlid and Zeiner-Gundersen {2} reported the existence of another species of H₂ with bond length 2.3 × 10^-12 m. However, even at this bond length, the protons are very far from each other: about 14,500 proton diameters.

The Moving Light Clock: Which Way the Photon Goes?

 

The Moving Light Clock: Which Way the Photon Goes?

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry, University of Niš, pavleipremovic@yahoo.com, Niš, Serbia

Time dilation and length contraction are two important effects of Special relativity (SR). These two effects depend upon the second postulate of this theory that the speed of light c (=2.99792×10⁸ m s^-1) is the same in all inertial frames of reference [1].

Many physics textbooks deal with the subject of time dilation. This phenomenon can be demonstrated using a device known as the light clock [1]. The light clock consists of two-plane parallel mirrors M₁ and M₂ facing each other at a distance d apart as in Fig. 1a.

Fig. 1. The SR description of the photon path of the light clock: (a) at rest and (b) traveling along the positive x-axis at the speed v; and, (c) the photon path independent from the motion of the light clock (or from the inertial frames of reference).

The lower mirror M₁ has a light source at the center that emits a photon at 90 degrees in the direction of mirror M₂. For the sake of simplicity, we will consider the time for the photon to travel from mirror M₁ to mirror M₂. Of course, you may find all the following derivations in many elementary physics texts.

For the light clock at rest, the (proper) time interval is then ΔT₀ = d/c. Now allow the same light clock to be moving with a certain relative speed v horizontally in the direction of the positive x-axis, Fig. 1b. Clearly, a photon will now travel the larger distance he D and thus it will take a longer (improper) time interval ΔT = D/c. According to SR, ΔT₀ and ΔT are related by the relativistic time dilation expression ΔT = ΔT₀ /√1-v²/c². Thus, the effects of time dilation only start to become measurable at speeds close to the speed of light c, i. e. at so-called relativistic speeds.

It is important to note here that the angle α between the photon path and the direction of motion of the light clock depends on the v/c ratio, in particular cos (α) = v/c. In other words, α depends on the light clock speed nv (or the speed of inertial reference frame) and appears also only measurable at relativistic speeds.

In this derivation, one assumes that the photon travels from M₁ to M₂ when the light clock frame is moving. It appears, virtually, that this assumption is valid when we are dealing with a light clock at non-relativistic speeds. In this case, the clock distance vΔT is very small compared with the photon distance cΔT, i.e. α → 90 degrees.  However, for a light clock traveling at relativistic speeds, this assumption is ambiguous since these speeds for a man-made object will be unattainable even for the very distant future. Indeed, at present, the fastest rocket system in the world can only reach speeds of up to about 2000 m s^-1. According to SR, a stationary observer would observe that the direction of the photon motion is affected by the relativistically fast light clock, being at the angle α relative to this direction, Fig. 1b. Or she/he could observe that the photon is traveling perpendicular to the direction of motion and it is not affected by the moving light clock (or by the moving inertial frame of reference), Fig. 1c. If the latter is correct then the traditional light clock experiments are meaningless.

Finally, it should be noted that SR states that “the velocity c of light in a vacuum is the same in all inertial frames of reference in all directions and depends neither on the velocity of the source nor on the velocity of the observer” [Einstein, 1905]. It appears then rather peculiar that the direction of the photon motion would depend on the speed of the inertial frame of reference.

 

Reference

[1] W. Rindler, Introduction to Special Relativity, 2nd ed. Oxford University Press, 1991.

 

 

 

 

The de Broglie Picture of Gaseous Lithium Hydride

 

The de Broglie Picture of Gaseous Lithium Hydride 

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

University of Niš, pavleipremovic@yahoo.com, Niš, Serbia 

In one of our previous communications {1}, we pointed out that there is a discrepancy in the representation of the hydrogen molecule (H₂) in chemistry and physics textbooks and de Broglie's representation. Here we will consider the picture of the gaseous LiH (hereinafter LiH) given in these textbooks and the picture of the same molecule based on Broglie's theory of the wave nature of matter (duality).

LiH is the simplest neutral heteronuclear diatomic molecule gaseous at non-STP. The mass of Li is about 1.2 × 10^-26 medical history[1] and the diameter of its nucleus (or Li³⁺) is about 10^-14 m; the mass of the hydrogen atom (H) is about 1.7 × 10^-27 kg and the diameter of its nucleus (proton) is about 1.7 × 10^-15 m.[2] The mass of LiH is about 1.3 × 10^-26 kg and the experimental bond length of gaseous LiH is about 1.6 × 10^-8 m {2}. Thus, the distance between Li (or its nucleus: Li³⁺) and H (or its nucleus: proton H⁺) in this molecule is about 3 × 10⁶ Li³⁺ diameters and about 10⁷ H⁺ diameters.

According to the model of the above textbooks, LiH consists of two independent species: partly positive Li^+δ and partly negative H^-δ. They are linked by an ionic-covalent bond.[3] However, this picture does not just agree with the picture of this molecule based on de Broglie's hypothesis.

The de Broglie equation can be used to describe the wave nature of LiH in motion. Usually, this equation is expressed in the following form 

λ = h/my ... (1). 

where h (= 6.63 × 10^-34 J sec) is Planck's constant, λ and m are the wavelength and the mass of a particle moving at a speed υ.

If LiH travels with a non-relativistic speed υ its wavelength is then 

λ(LiH) = h/m(LiH)υ ... (2) 

where m(LiH) is the mass of LiH. As the contribution of the mass of the electron(s) is negligible to the mass of Li and to the mass of H[4], we have

λ(Li) = h/m(Li³⁺)υ and λ(H) = h/m(H⁺)υ … (3).

As we noted above, the distance between Li and H is equal to about 3 × 10⁶ Li³⁺ diameters and to about 10⁷ H⁺ diameters. Therefore, one could hypothesize that L_iH consists of completely separated Li^+δ and H^-δ interconnected by an ionic-covalent bond and having independent wavelengths: λ(Li) and λ(H) [see eqn. (3)]. Since m(Li³⁺) is about 8 times larger than m(H⁺) then, according to eqn. (3), λ(Li) ≈ 8λ(H).

As we noted above, the distance between Li and H is equal to about 3 × 10⁶ Li³⁺ diameters and to about 10⁷ H⁺ diameters. Therefore, one could hypothesize that L_iH consists of completely separated Li^+δ and H^-δ interconnected by an ionic-covalent bond and having independent wavelengths: λ(Li) and λ(H) [see eqn. (3)]. Since m(Li³⁺) is about 8 times larger than m(H⁺) then, according to eqn. (3), λ(Li) ≈ 8λ(H).

As in the case of H₂ {1}, quantum mechanically speaking, the question arises: Can the gas molecule LiH in motion be represented by one wave packet of this molecule as a whole or by two separated wave packets of Li³⁺ and H⁺?

Fig. 1: Highly exaggerated two-dimensional picture of the (dumbbell shape) partly “fused” nucleus of LiH.

This dilemma can be extended to all diatomic heteronuclear molecules gaseous at STP (e.g. the carbon monoxide molecule: CO) or non-STP (e. g. the cesium iodide molecule: CsI).

References

{1} P. I. Premović, Hydrogen molecule in the light of the de Broglie’s Theory. The General Science Journal, May 2023.

{2} H. Kato et al., Study of the electronic structures of lithium hydrides, Li_nH_m (m ≤ n ≤ 4). J. Phys. Chem. 85, 3391-3396 (1981).

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[1] To avoid confusion in further text, the SI units are given in italics.

[2] Natural Li is made up of two isotopes: Li-7 (92.5%) and Li-6 (7.5%).

[3] The bond in LiH is about 76 % ionic or δ ≈ 0.76.

[4] In other words, m(Li) = m(Li³⁺) and m(H) = m(H⁺).