Infinite is a construction, misused in this paradox. And most.
Olbers' Paradox
51–60 of 86 posts
Re: Olbers' Paradox
#52“[Edward Robert] Harrison argues that the first to set out a satisfactory resolution of the paradox was Lord Kelvin, in a little known 1901 paper, and that Edgar Allan Poe's essay Eureka (1848) curiously anticipated some qualitative aspects of Kelvin's argument: Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy – since there c…
I love the quote, very beautiful explanation of the question !
Thank you for this history and for sharing it !
Sometimes while ruminating I wonder whether ,
Questions which have no answers are not really questions .
Does the difference matter ?
To your theory of everything ?
-13 HN Karma Hint:
None of those words
re Infinite Boundaries , Matter
Interesting distractions ,
If the goal is TOE ,
Distractions unacceptable in TOE
But wadda I know !
Re: Olbers' Paradox
#53While 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…
Energy is not conserved on the scale of the Universe. General Relativity has no energy conservation law (it has a stress-energy tensor conservation law). Two examples of this: expansion of the universe causes the total energy contained in radiation to decrease, and the total amount of dark energy to increase.
Right. Sabine Hossenfelder about it: https://www.youtube.com/watch?v=ZYM6HMLgIKA&t=395s
Re: Olbers' Paradox
#54While 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…
Probably better not to use the term "steady state" here (even if pretty appropriate) in that the "steady state" cosmological model is/was one that is exponentially expanding, with all physical observables statistically time-independent. It solves Olber's paradox due to the radiation redshift. That model was observationally incorrect, but actually has pretty much been reborn in "eternal inflation" in which the Univers…
How does the universe expand? What is it expanding into? And why isn't that thing considered the universe?
Re: Olbers' Paradox
#55While 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…
Energy is not conserved on the scale of the Universe. General Relativity has no energy conservation law (it has a stress-energy tensor conservation law). Two examples of this: expansion of the universe causes the total energy contained in radiation to decrease, and the total amount of dark energy to increase.
It depends on the way you look at things:
Noether's second theorem works fine in General Relativity (in fact, this was the historic context of her paper). So for any given time-like vector field, you'll get an energy conservation law. In case of Friedmann cosmology and chosing cosmological time as said vector field, you'll get a term proportional to H² which picks up the change in energy.
However, you won't be able to make this into a covariant expression: Gravitational energy-momentum can be expressed in terms of pseudo-tensors at best...
Re: Olbers' Paradox
#56Earlier quoted context omitted.
the point is 1 photon from a star seems like nothing, but 1 photon multiplied by infinite stars is infinite photons blinding us
"at most one". As you get further away zero protons are reaching you on most cases, and zero photons times infinite stars is zero, which would appear to be darkness
Zero multiplied by infinity does not have to be zero, it can be anything between zero and infinity. Refresh your https://en.wikipedia.org/wiki/Calculus.
Re: Olbers' Paradox
#57This doesn't make sense to me. They're assuming that brightness is a continuous function that you can keep dividing in half over and over and result in a real number, but brightness is not continuous, at a certain point you only have one photon left. It stops being a question of how many photons per second and becomes a question of how many seconds between a photon.
Well, QM didn't exist yet. Instead, you had competing concepts of light as a wave and light as a particle. As a wave, it would seem perfectly reasonable that you could keep dividing and that it was a continuous function. We have the benefit of QM in hindsight.
However, think of it another way ... if the stars had infinite time to pump out these "photon" particles you speak of (harmph! highly dubious), then there ought to be an infinite number of them in any given space, as they have had an infinity of time to reach you.
Re: Olbers' Paradox
#58Doesn’t the expansion of the universe explain this? I don’t understand the paradox.
It does, but at the time, we didn't know about that.
Let's assume the universe is not expanding but is infinite. At some point in time stars started lighting up. Maybe they even all lit up at once, long time ago. But some stars are so far away that the light from them has not yet reached us.
Even though there are an infinite number of stars we can only see the light from a subset of them because the light from the rest of them has not reached us yet.
So I think the simple resolution of the paradox is that the speed of light is not infinite. No?
What I also never understood was what about matter that is not lit up? There could be many more unlit heavenly bodies than stars, which would block the light from the stars.
Re: Olbers' Paradox
#59Earlier quoted context omitted.
Probably better not to use the term "steady state" here (even if pretty appropriate) in that the "steady state" cosmological model is/was one that is exponentially expanding, with all physical observables statistically time-independent. It solves Olber's paradox due to the radiation redshift. That model was observationally incorrect, but actually has pretty much been reborn in "eternal inflation" in which the Univers…
How does the universe expand? What is it expanding into? And why isn't that thing considered the universe?
> What is it expanding into?
The future, literally. To grossly oversimplify: if all of space is east-west, and time is north-south, the Big Bang is the north pole. Only the universe is the map rather than the globe, and the globe doesn’t have to exist for the map to exist and to have the same expansion in space (/longitude) with respect to time (/latitude).
Also there may or may not be a Big Crunch/south pole, this is all just a way to get into the nature of the geometry by way of a convenient frame of reference.
Re: Olbers' Paradox
#60Earlier quoted context omitted.
Energy is not conserved on the scale of the Universe. General Relativity has no energy conservation law (it has a stress-energy tensor conservation law). Two examples of this: expansion of the universe causes the total energy contained in radiation to decrease, and the total amount of dark energy to increase.
It depends on the way you look at things: Noether's second theorem works fine in General Relativity (in fact, this was the historic context of her paper). So for any given time-like vector field, you'll get an energy conservation law. In case of Friedmann cosmology and chosing cosmological time as said vector field, you'll get a term proportional to H² which picks up the change in energy. However, you won't be able t…
I have a related question, borne out of my ignorance as I am not a physicist nor a mathematician.
> Noether's first theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.
Why is this not obvious? Are not symmetries necessarily the transformations which conserve quantities, and the types of symmetry equivalent to the type of conservation?
Because Noether got a lot of respect for her work despite working (in a time of great sexism, no less!), I know that either I have totally misunderstood or this is a Columbus’ Egg [0] — but I am curious which, and if it isn’t a Columbus’ Egg, what I’ve misunderstood (assuming that sort of thing can even fit into a HN-sized reply and I’m not asking something that would normally be the conclusion of a final year degree level physics module).