Let's first examine stellar winds.
Stellar winds are known to be radiatively driven. The radiative momentum is transferred from radiation to a gas by means of absorption. Not all chemical elements are equal absorbers, so some elements are accelerated more than the others. In the case that there is enough collisions that may redistribute the momentum over the entire gas (basically elastic collisions), the radiatively driven stellar wind behaves like a one- component fluid.
In a real radiatively driven wind the chemical species may be divided into three basic groups according to the ability to absorb radiation.
The first group consists of radiatively accelerated particles that have enough ability to absorb radiation and, consequently, are significantly accelerated by absorption of radiation in spectral lines.
The second group involves particles whose contribution to the radiative force is almost negligible compared to the first group. This group is taken along by friction with the first group. Since its role in the stellar wind is passive, we call this group as a passive component. In real stars it consists of hydrogen and helium.
The third group are free electrons, which are accelerated by Thomson scattering and by friction as well. Each component is described by a set of equations of continuity, motion, and energy.
Calculations of the three-component wind models show the same results as for the one component wind, which means that the one-component approximation is an adequate one for winds of these stars. On the other hand, there is a relatively large heating for lower effective stellar temperatures, namely for the main-sequence B type stars. An interesting fact is that for lower effective temperatures we obtain higher wind temperatures, a consequence of a frictional heating, which rises with decreasing effectiveness of elastic collisions.
Next, think of the luminosity—the energy emitted per second by the star—as an intrinsic property of the star. As that energy gets emitted, you can picture it passing through spherical shells centered on the star. In the above image, the entire spherical shell isn't illustrated, just a small section. Each shell should receive the same total amount of energy per second from the star, but since each successive sphere is larger, the light hitting an individual section of a more distant sphere will be diluted compared to the amount of light hitting an individual section of a nearby sphere. The amount of dilution is related to the surface area of the spheres, which is given by:
A = 4 π d2A = 4 π d2 .
How bright will the same light source appear to observers fixed to a spherical shell with a radius twice as large as the first shell? Since the radius of the first sphere is d, and the radius of the second sphere would be 2 x d2 x d , then the surface area of the larger sphere is larger by a factor of 4.
The Inverse Square Law, Credit: Wikimedia Commons
Thus, the equation for the apparent brightness of a light source is given by the luminosity divided by the surface area of a sphere with radius equal to your distance from the light source, or
F = L / 4 π d2F = L / 4 π d2 , where d is your distance from the light source.
The apparent brightness is often referred to more generally as the flux, and is abbreviated F (as I did above). In practical terms, flux is given in units of energy per unit time per unit area (e.g., Joules / second / square meter). Since luminosity is defined as the amount of energy emitted by the object, it is given in units of energy per unit time [e.g., Joules / second (1 Joule / second = 1 Watt)Joules / second (1 Joule / second = 1 Watt) ]. The distance between the observer and the light source is d, and should be in distance units, such as meters. You are probably familiar with the luminosity of light bulbs given in Watts (e.g., a 100 W bulb), and so you could, for example, refer to the Sun as having a luminosity of 3.9 x 1026 W3.9 x 1026 W . Given that value for the luminosity of the Sun and adopting the distance from the Sun to the Earth of 1 AU = 1.5 x 1011 m1 AU = 1.5 x 1011 m , you can calculate the Flux received on Earth by the Sun, which is:
F = 3.9 x 1026 W / 4 π (1.5 x 1011 m)2 = 1,379 W per square meterF = 3.9 x 1026 W / 4 π (1.5 x 1011 m)2 = 1,379 W per square meter
Lastly, we turn to the photons which are not identifiable separate particles that travel along trajectories. They are the quantum excitations of the EM field, and spread out as a spherical wave. When absorbed, say by individual atoms that are not coherent and may be a long way apart, the quantum wave-function of each photon collapses (or possibly branched) and each photon can then be separately identified as having been absorbed in one location: the atom. However, this does not mean that the photon has travelled along a path from the point of emission to the point of absorption. It has not. It propagated as a spherical wave, maybe isotropically (same in all directions) or maybe not.
This scenario is the best and simplest illustration of the so-called measurement or collapse problem in quantum theory, the origin of the various QM (quantum mechanics) interpretations.
Consider one photon setting out from the Andromeda galaxy as a spherical wave. 2.5 million years later it is absorbed by a camera or a human eye here on earth. The spherical wave, 5 million light-years in diameter, instantly collapses to a single point here on earth. That photon will never be detected anywhere but here. The collapse is non-local, seems to be instantaneous, but cannot be detected in any way or used to signal faster than light.
The whole thing is outrageous and incomprehensible. It cannot be what is actually happening, but the only alternative accounts are equally outrageous, or more so: the no-collapse neo-realist many-worlds interpretation; Qbism (wavefunctions are not real, it’s all in your head), Copenhagen (don’t ask), and so on.
If you look at light as a collection of little particles, you could say that dimmer light has its photons more spread out. But, they are not spread out in space while traveling. Rather, they are spread out in time and space as they are received. A sufficiently sensitive photon counter device can detect the reception of light one photon at a time. Shine light at such a device and it does not receive the light as a steady stream. Rather, it receives the light as a series of discrete bundles of energy separated by gaps in time. Similarly, shine light at a sufficiently sensitive array of photon counters, and it receives the light at point locations with spatial gaps between them. When viewed in this way, a light beam
always has gaps between its photons, whether the light be very bright or very dim. Very dim light beams have larger gaps in time and space between the reception of each photon compared to brighter light beams. Light from a very distant star has spread out over a very large area and become very dim in the process. The gaps between photon reception from a very distant, dim star are therefore large. Again, it is only the reception time and locations that has gaps. There are no gaps in space between the photons as they travel.
If you look at light as a wave, then there are no gaps unless specifically placed there on purpose. Of course, if you repeatedly turn on and off a flashlight, the light beam coming from your flashlight will have gaps. Similarly, if you shine a continuous beam of light through a shutter that is repeatedly opening and closing, you can create gaps.
Then, if you shine a continuous beam of light into free space, the wave will start with no gaps and therefore develop no gaps as it travels. Waves are field oscillations that are spread out smoothly through space. Spreading out a wave over a larger area just causes the wave strength to weaken, but does not cause gaps to form. Therefore, if you look at photons as waves, spatial gaps never form in light as it travels through free space, no matter how dim it gets. The light from a distance star indeed spreads out and weakens as it travels, but this just reduces the wave strength and does not introduce gaps.
A helpful way to look at photons is that they act like waves while traveling and act like particles when interacting with matter. In the context of starlight, the light travels through space for millions of years acting like a wave, and then acts like a collection of particles when hitting the photon detector, the telescope, or an eye.
When a photon is absorbed by an electron, it is completely destroyed. All its energy is imparted to the electron, which instantly jumps to a new energy level. The photon itself ceases to be. In the equations which govern this interaction, one side of the equation (for the initial state) has terms for both the electron and the photon, while the other side (representing the final state) has only one term: for the electron.
The opposite happens when an electron emits a photon. The photon is not selected from a "well" of photons living in the atom or from a basket of photons on the atom's front porch; it is created instantaneously out of the vacuum energy. The electron in the high energy level is instantly converted into a lower energy-level electron and a photon. There is no in-between state where the photon is being constructed. It instantly pops into existance.
So the question is: where does the photon come from?
Strangely, it doesn't seem to come from anywhere. The universe must put the extra energy somewhere, and because electrons in atoms are electromagnetic phenomena, a photon is born with the required energy. In a weak-force interaction, say the decay of a neutron, that energy goes into a neutrino particle which is also instantaneously created. Each force has its own carrier particles, and knows how to make them.
See:
http://www.space.bas.bg/astro/Rogen2004/StPh-8.pdf
See:
https://www.e-education.psu.edu/astro801/content/l4_p4.html
See:
https://www.quora.com/As-light-from-a-star-spreads-out-and-weakens-do-gaps-form-between-the-photons?share=1
See:
https://www.wtamu.edu/~cbaird/sq/2015/02/12/as-light-from-a-star-spreads-out-and-weakens-do-gaps-form-between-the-photons/
See:
http://curious.astro.cornell.edu/about-us/137-physics/general-physics/particles-and-quantum-physics/805-how-are-photons-created-and-destroyed-advanced
Each photon therefore collapses from mostly wave-like to mostly particle-like upon being detected. Since the photons act mostly like waves while traveling, there are no gaps that develop between them while traveling. And since the photons act mostly like particles when being detected, there
are gaps in the time when the photons are detected and in the locations where they are detected.
The act of detecting the light, anywhere after it has been emitted, causes it to collapse from wave-like to particle-like, and therefore introduces the gaps. A very dim light beam from a distant star has a very weak wave magnitude, which leads to large gaps in photon reception.
Hartmann352
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