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# Doppler Effect and Thermodynamics

This is my interpretation of the Doppler Effect in the context of thermodynamics.

A post on 02/08 described the lack of galaxy spectrum data. This topic is written before that crucial data revelation.

Redshifts and blue shifts result in mistakes in popular cosmology.
This explains them and explains when and why they must be ignored to fix that mistake.

Thermodynamics is about the conservation of energy and the defined transfers of energy to conserve energy.
The Doppler effect involves a transfer of energy from one form of energy to another.

There are essentially 4 forms of energy:
a) internal energy in the form of an atom's energy state determined by its electrons' positions among the atom's defined shells (defined by the element).

c) kinetic energy in the form of matter in motion.

d) thermal energy in a liquid or solid is in the form of motion or vibration at the atomic and molecular levels.

e) thermal energy in a gas is in the form of kinetic energy of its atoms and molecules.

The Doppler Effect is a transfer of energy among forms; the following describes those transfers.

The unit of energy is the joule. The joule is equivalent to 1 kg x m^2 / s^-2, or 2.78 E-7 KW/h, or 9.48 E-4 BTU, or 6.24 E+18 ev.

The amount of energy in radiated energy is directly proportional to its frequency by plancks constant.

Radiated energy is Electromagnetic radiation (EMR) or the propagation of synchronized, perpendicular electric and magnetic fields. The oscillation of these fields is measured as either frequency or wavelength. The loocity of this propagation has been measured and its value is called the constant c (for s vacuum). This constant is used in several equations involving energy. EMR is clearly a wave because of many observations including a prism and diffraction behaviors. Quantum mechanics defines a photon particle for one wavelength. The Doppler effect is a wave behavior and cannot be explained with the photon simply because a photon particle can easily miss a tiny atomic particle but a wave will not. EMR is a continuum of energy not increments.

EMR can have different forms:

a) a single wavelength as with a laser beam or an atomic emission line,
b) synchrotron radiation has a continuum of energy observed across most of the spectrum. The minimum wavelength in the continuum is determined by the strength of the electric current and the strength of the magnetic field changing the direction of the current. By increasing the electric current the energy in X-ray and gamma ray frequencies can be attained.
c) thermal radiation has a continuum of energy observed across much of the spectrum. The peak frequency  in the continuum is determined by the thermal energy of the material emitting this radiation.

For (b) or (c) the continuum is demonstrated by a prism when the continuous spectrum is spread out revealing the many different frequencies observed by their color (each color is the human eye's reaction to those frequencies). Combining the many visible frequencies results in the eye seeing white.
A spectroscope is a device which allows measurement in this continuum.

EMR is a wave emitted in all directions from the source. A radio frequency transmission from an antenna can have lobes not relevant here.
For this radiation the close the observer is to the source the more EMR is being observed. With increasing distance from the source this EMR is distributed around a sphere of increasing circumference,  The energy is there but in a diminshing fraction. The result is dimming by distance. Timed exposure photography allows magnification of a dim signal.

Much of the following is background and clearly missing some details (found in chemistry) which are not relevant to the Doppler effect. However, this slight background helps when describing the Doppler effect below.

Neutral matter has 3 basic states: gas, liquid, solid. This topic ignores the man-made Bose-Einstein condensate. Some aspects also apply to plasma (another state of matter) including kinetic energy.

An energy transfer is required to change states of matter.
Heat of fusion can change a solid to liquid. This energy is usually defined by the material's melting point temperature.

Evaporation requires energy to change liquid to gas but there are other factors like vapor pressure. This energy transfer is usually defined by the material's boiling point temperature.

Condensation is the loss of energy when changing state from gas to liquid. This energy transfer is usually defined by the freezing point temperature.

The temperature or thermal energy in a gas or liquid is held in the kinetic energy of the particles. Increasing the kinetic energy of some particles increases the thermal energy held in those particles.
Conduction is the transfer of heat between adjoining materials, from the warmer to cooler.
Convection is the transfer of heat during the bulk movement of particles in a gas or liquid.

The Doppler Effect involves the absorption or emission of radiated energy but the matter doing the absorption or emission is also moving.

When matter absorbs EMR, there are several possible results for the transfer of energy:

a) the particle of matter increases its energy state (its internal energy),
b) the particle increases its kinetic energy,
c)  the particle atom performs particle pair production from a gamma ray.

For (a) there are 2 possibilities:
1)each atom has defined increments for this energy absorption according to the element's electron shell configuration. An electron can move only up to the next higher energy shell or it does not change nor does the energy get absorbed. This is an atom's behavior so one or more electrons might change levels for the absorbed energy increment.
Because the energy is transferred from EMR only when the internal energy changes state the original energy is always conserved.

2) The photoelectric effect has an additional behavior for (a). If the absorbed energy is sufficient for both the atom's state change and the ejection of an electron then that electron is ejected. If this minimum energy requirement for an ejection  is exceeded then the excess EMR energy is transferred to the electron's kinetic energy. This secondary transfer is a conservation of energy.
For the hydrogen atom having one electron iw different then the other atoms.
excerpt from Wikipedia:
The Lyman limit is the short-wavelength end of the hydrogen Lyman series, at 91.2 nm (912 A or 3.29E+15 hz). It corresponds to the energy required for an electron in the hydrogen ground state to escape from the electric potential barrier that originally confined it, thus creating a hydrogen ion.
This means hyogen atoms in the IGM will separate into proton and electron pairs if the EMR has enough energy and it will. The Lyman limit is like the photoelectric effect.

A number of the Local Group galaxies are assumed to have the hydrogen absorption line red shifted.

For (b) this transfer from radiated energy to kinetic energy is a conservation of energy. For a liquid or solid (or a gas in an enclosure), this absorbed energy is observed as a transfer to thermal energy.

For (c) to occur several conditions are required. The radiated energy must be gamma ray frequency or greater for the required energy for this result.
Only if that energy for the process is present will it be absorbed.

The energy being absorbed has an equivalent in ev, called EBE here. The mass of the electron and positron particle pair adds to a certain ev, called PPE here. This lightest pair requires 1022Kev (from Wikipedia).

If EBE is greater than or equal to PPE then the EBE is absorbed and particle pair is created.
If EBE is greater than the PPE then the excess is transferred to the kinetic energy of the particle pair. Energy is conserved.

When (a) occurs while the atom is in the intergalactic medium (IGM) the observed behavior is different.
It is crical to note EMR is a continuum of energy in the propagation as waves.

In cosmology there only 2 absorption lines of interest:
1) hydrogen Lyman-alpha absorption line.
2) calcium H and K absorption lines.

(2) is observed in a few galaxies With a lack of galaxy spectrum data the exyent of it is unknown.

(2) will be described first though hydrogen is the most prevalent element in the universe..

A NASA page titled "Observing the Spectrum of M31"
describing the M31 glaxy blue shift. There is a figure showing the two absorption lines so one can guess at their observed values and each wavelength measured in a lab is provided.
Guessing at the figure it looks like the Calcium K line shifted from 3934 A to 3928 A while the Calcium H line shifted from 3969 A to 3954A.
Both are a Z of -301 km/s or approaching Earth.
Note: this is the velocity of only this atom, NOT the velocity of the galaxy behind the atom!

A blue shift is observed with these calcium atoms because they are in motion toward the observer.

A blue shifted calcium absorption line is a change to a higher frequency energy loss than just the absorption line with no motion.

When an absorption by an atom occurs, this is the loss of energy in the EMR, having been transferred to the atom's internal energy.

The motion of the particle affects the energy transfer for a calcium atom's 2 absorption lines.

The calcium atom is absolutely critical compared to hydrogen because this element has two characteristic wavelengths not one.
By having two lines it is possible to calculate the mutual change in their wavelengths indicating a direction.

The hydrogen atom has a single wavelength for each Lyman and Ballmer series emission.

When looking at a galaxy spectrum having the continuum but having of a single absorption line, this line represents a loss of energy defined by its wavelength or frequency which is missing.

For the conservation of energy, the loss in the EMR energy is the sum of the loss to the atom in its internal energy change plus the loss in the particle's kinetic energy change, a reduction (in the direction of its travel.

This topic will not explain why these calcium atoms are in the space around the Milky Way in the direction of M31, M33 galaxies and others. This observation of a blue or redshift indicates both their presence and motion.

The critical conclusion:

This calcium absorption line indicates nothing about the galaxy behind the atom.
These atoms are in the IGM and not part of the galaxy.

This calcium absorption line must be ignored for all galaxies.

(1) is observed for an unknown number of galaxies; the spectrum data is very rarely available.

The neutral hydrogen absorption line is also known as the Lyman-alpha line and is at 121.6 nm or a frequency of 2.47E+15 hz (in ultraviolet range), so it is equivalent to 1.49E-17 Joule.

This observation of an absorption occurs because there is a hydrogen atom in the line of sight in the IGM.
Neutral hydrogen atoms in the IGM are in random motion; neutral atoms are not subject to electromagnetic forces, only gravity and nothing is near in the IGM.

In many references, there will be a statement like this:
""When you look at the spectrum of a galaxy, you are really looking at the combination of spectra from the millions of stars in the galaxy.
A galaxy is not a single light source but is often millions.

As the wave of EMR from each star passes through the IGM some amount of energy will be absorbed by the hydrogen atoms in this low density so not all stars might be affected. This density is important for this absorption line. In the case of the calcium absorption line the density appears to cover most of the stars for the consistent absorption. The cloud of calcium atoms is apparently in a relatively small area in the direction of M31. Neutral hydrogen atoms are widely dispersed in the observable universe.

A red shift is a change to a lower frequency absorption line so less energy has been lost.

When matter emits electromagnetic radiation this is a transfer of energy. There are several transfers:

a) the atom decreases its energy state (its internal energy),

b) the matter decreases its thermal energy.

For (a) the atom is is point source of EMR in all directions.

Because the light source is moving and because light has a fixed velocity in a vacuum, wave compression occurs in the direction of motion and wave expansion in the direction opposite of motion.

There are 2 energy values involved in this process.
1) The energy being emitted has an equivalent in ev, called EBE here.
2) The Kinetic energy involved here has an equivalent in ev, called KEI here. This value is from the Doppler effect.

In the direction of motion the EMR is the sum of EBE + KEI. This is a blue shift in the spectrum of energy in a continuum  as all wavelengths decrease.
In the direction opposite of motion the EMR is the subtraction of EBE - KEI. This is a red shift in the spectrum of energy in a continuum  as all wavelengths increase.

Energy is conserved.

For (b) the object is a source of EMR in all directions.

There are 2 energy values involved in this process.
1) The thermal energy being emitted has an equivalent in ev, TEBE here.
2) The Kinetic energy involved here has an equivalent in ev, called KEI here. This value is from the Doppler effect proportional to the scalar velocity.

In the direction of motion the EMR is the sum of TEBE + KEI. This is a blue shift in the entire broad spectrum of a continuum of EMR.
In the direction opposite of motion the EMR is subtraction of TEBE - KEI. This is a red shift in the entire broad spectrum of a continuum of EMR.

Energy is conserved.

For (b) there are two scenarios:

1) The radiating surface of a star or its photosphere. The motion of the  star affects its radiation depending on direction.
2) the motion of the photosphere itself.
A pulsating variable star has its variable brightness from the photosphere expanding in circumference and then collapsing again in a controlled process which maintains this luminosity curve. A Cepheid is this type of star. In this scenario  there are two kinetic energy values present, one with the star ana second with the photosphere layer.

These  scenarios have same change in EMR based on velocity and direction as for the other cases.

Conclusion:

The Doppler effect always conforms to the thermodynamics principle of conservation of energy.

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Last updated (02/08/2020)
Here is the list of topics in this Cosmology Topic Group , including my research.

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