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Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should be dark.
The Hubble was pointed at what appeared to be a black void of space, and revealed lush fields of stars and galaxies. So at one degree of perception, we have an empty void, and at another, a bright flush of light and activity.
I think a more fitting example of "an empty void yet a bright flush of light" would be the microwave background. With eyes sensitive to longer wavelengths the entire sky is indeed bright.
Isn't this just an issue of comparing a countable and uncountable infinity? The number of points on the unit sphere is uncountable, but the number of stars is countable. As such there are in some sense more points on the sphere than there are stars, even though there are an infinite number of each. Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should…
Isn't this just an issue of comparing a countable and uncountable infinity? The number of points on the unit sphere is uncountable, but the number of stars is countable. As such there are in some sense more points on the sphere than there are stars, even though there are an infinite number of each. Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should…
Isn't this just an issue of comparing a countable and uncountable infinity? The number of points on the unit sphere is uncountable, but the number of stars is countable. As such there are in some sense more points on the sphere than there are stars, even though there are an infinite number of each. Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should…
More formally, each star emits some amount of power in each frequency band: P(f) so that \int_0^\infty P(f) df = P_total.
For each frequency then, we have a total of P(f)/(hf) photon emitted per second. The total number of photons emitted per second by the star is then \int_0^\infty df P(f)/hf which is a finite number.
The total number of photons received per unit area a distance r away from the star would then be
\frac{1}{4\pi r^2} \int_0^\infty df P(f)/hf
If your detector has an area A (e.g. your retina or some other device), you'd expect to see
\frac{A}{4\pi r^2} \int_0^\infty df P(f)/hf
photons per second from the star. As r gets really large, you'd see this drop arbitrarily low. Conversely, the amount of time you'd need to wait to see a single photon from that star then grows, making the star dark.
That "#:~:text=" highlighter is so annoying it has made me switch from Google Chrome to Firefox.
As I understand it, in the galactic core where stars are more densely packed, it would be bright all the time. I wonder if there's a photorealistic render of this.
the game Elite Dangerous simulates it. not sure how realistic but it is fun to explore
The Hubble was pointed at what appeared to be a black void of space, and revealed lush fields of stars and galaxies. So at one degree of perception, we have an empty void, and at another, a bright flush of light and activity.
There is still plenty of space between the individual stars in the Hubble Deep Field image. From that point of view it just confirms the paradox - even with a powerful telescope stars don't fill up your entire field of view. I think a more fitting example of "an empty void yet a bright flush of light" would be the microwave background. With eyes sensitive to longer wavelengths the entire sky is indeed bright.
What I feel is the core of the resolution of the paradox is (global or local) conservation of energy. Even in an infinitely large eternal steady state universe, if we assume the total energy of the universe is conserved one cannot have an increase in energy density everywhere at once.
If in this universe stars live forever, you'd have eternal "sources" of energy, and for energy to be conserved you'd need compensatory "sinks" draining energy out of the universe, like black holes which don't increase in size. In which the resolution of the Olbers' paradox would be that most of your lines of sight would end in such a black hole.
If, like is usual in physics, you assume local conservation of energy, stars cannot live forever, so in an eternal steady state universe there must be a mechanism recycling the radiation back into a star. In this case, again every line of your sight would eventually hit a star, but most of the radiation would never reach you, being used underway to make a new star. (This is a blatant violation of the second law of thermodynamics of course, which is the actually issue with eternal steady state universes).
While it's true that the finite age of our universe and the expansion of space explain the paradox in the universe we live in, I don't think those are necessary conditions, nor is the dark sky proof our universe is not infinitely old. What I feel is the core of the resolution of the paradox is (global or local) conservation of energy. Even in an infinitely large eternal steady state universe, if we assume the total e…
In either classic steady-state or eternal inflation case, energy conservation is not necessarily a problem: you can have vacuum energy that converts steadily into radiation, while being generated by the expansion.