Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Olbers' Paradox

en.wikipedia.org

Post reply on HN
Print view View original

71–80 of 86 posts

Re: Olbers' Paradox

#71

Post by raattgift »

avian wrote: post #12
jessermeyer wrote: post #9

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.

> With eyes sensitive to longer wavelengths the entire sky is indeed bright

With eyes sensitive to the CMB, the CMB is dimming and reddening. Such eyes witnessing an essentially isotropic and homogeneous CMB would be Eulerian observers of the CMB. (In contrast to observers who see a dipole anisotropy because of acceleration along one spatial axis, for example, or observers immersed in the gravitational field of a massive system like a galaxy cluster or a planet).

Such Eulerian observers see a clearly peaked spectrum, essentially identical to a that of a blackbody radiator that is cooling. If such observers are in deep inter-galaxy-cluster space and equipped with instruments to augment their CMB-sensitive eyes, they'd detect plenty of bright spots with frequencies much much lower than the peak in the CMB. As an example an https://en.wikipedia.org/wiki/Radio_galaxy will be much brighter in wavelengths longer than that of the CMB (spectral radiance peak of CMB is ~ 160 GHz and falls off quickly away from the peak).

That -- correcting for proper motions and atmospheric effects -- our view of the sky is pretty uniform in the CMB (cf. https://en.wikipedia.org/wiki/BOOMERanG_experiment and beyond) but far from uniform in VLF, radio, IR, UV, X-Rays, gamma rays, and so on (as known since roughly the 1930s thanks to https://en.wikipedia.org/wiki/Karl_Guthe_Jansky#Radio_astron... ) just like it is in visible light, and that the bright spots at different frequencies aren't coincident in our sky, are important pieces of evidence which must be dealt with by any prospective model of physical cosmology.

Re: Olbers' Paradox

#72

Post by pdonis »

pontus wrote: post #67
pdonis wrote: post #50

Earlier quoted context omitted.

> The probability can then get arbitrarily small, meaning that the expected amount of time needed before the probability of having observed a photon would get progressively larger. Yes, but the probability is never zero, and the expected time is never infinite. So saying "the intensity drops to zero" is never correct.

The point is not that the probability needs to hit zero, it's that it's not correct to say that you receive a quarter of the power as you move twice as far from the source. It's still true that the expected number of photons per second drops by a factor of 4, but it can drop so far as to render the source dark for an appreciable amount of time. The paradox claims that the sky should appear bright, which I take to mea…

> The paradox claims that the sky should appear bright, which I take to mean that a detector should be receiving light from each point in the sky at each moment in time.

I don't think this is required for the paradox. All that is required is that the average flux of radiation received from the sky as a whole should be constant, and equal, roughly speaking, to the flux corresponding to the surface brightness of a star. That will still be true, under the specified conditions of the paradox (a universe in steady state and infinitely old) even if quantization is taken into account.

Re: Olbers' Paradox

#73

Post by pontus »

pdonis wrote: post #69
pontus wrote: post #67

Earlier quoted context omitted.

The point is not that the probability needs to hit zero, it's that it's not correct to say that you receive a quarter of the power as you move twice as far from the source. It's still true that the expected number of photons per second drops by a factor of 4, but it can drop so far as to render the source dark for an appreciable amount of time. The paradox claims that the sky should appear bright, which I take to mea…

> it can drop so far as to render the source dark for an appreciable amount of time Ah, I see what you mean: yes, the intensity will be 1/4, but because of quantization, you now have to draw a distinction between the time-averaged power (which behaves like the power does in the classical case--more precisely, this would be the expectation value of the power in the quantum case) and the actual power at a given time, w…

Yeah, exactly

Re: Olbers' Paradox

#74

Post by Tomminn »

It seems to me like this is only true if you assume space is perfectly transparent, which seems like by far the weakest assumption.

Introducing any tiny amount of absorption in space would fix this, even in an infinite size, infinitely old universe.

Re: Olbers' Paradox

#75

Post by darthoctopus »

ben_w wrote: post #68
cygx wrote: post #66

Earlier quoted context omitted.

Are not symmetries necessarily the transformations which conserve quantities A priori, a symmetry is a transformation that, when applied to any valid trajectory, yields another valid trajectory. It is not obvious to me why (certain types of) symmetries necessarily yield conserved quantities...

The symmetry defines that which is conserved, doesn’t it? If I have a motion vector and a force vector, and if work done is ∫ force • displacement dx, and my transformation is one which conserves the scale of and relationship between both vectors (e.g. displacement), then is it not automatically true that work done is also conserved under that transformation?

That's not what Noether's theorem means! The "symmetries" referred to here are operations which leave invariant the action of the physical system (heuristically, the physical laws governing the system). To the extent that one can (at least in principle) write down the action of composite systems as the sum of their actions + interactions, these are taken to mean (again heuristically) the laws of physics writ large. Likewise, "conservation law" here means not specifically the particular result of an experiment (like the work integral you describe), but a more general notion of conservation, in the sense of there being universally invariant conserved quantities (i.e. things that cannot be created or destroyed).

To get a feel for it (and why it may not necessarily be intuitive) consider the following pairs of symmetries and conservation laws:

- The laws of physics are invariant under time translation (i.e. repeating an experiment at different times gives you the same result ceteris paribus). The corresponding conserved quantity is energy.

- The laws of physics are invariant under spatial translation (i.e. repeating an experiment at two different places gives you the same result ceteris paribus). The corresponding conserved quantity is momentum (this is a vector: one component of momentum for each possible direction of translation).

- The laws of physics are invariant under rotation (i.e. repeating an experiment under different orientations gives you the same result ceteris paribus). The corresponding conserved quantity is angular momentum (again a vector, since the rotation group SO(3) has three generators).

- Electromagnetism, constructed as a classical field, exhibits an internal symmetry in the field quantities. The corresponding conserved quantity is the electrostatic charge (actually a 4-vector current).

It is not a priori obvious from from the kind of arguments you've supplied why these should be the case. Demonstrating these would require access to the Lagrangian formalism (i.e. action principles) and how it behaves under these symmetry operations. I would say that, as you suspect, you are fundamentally misunderstanding the situation.

Re: Olbers' Paradox

#76

Post by saagarjha »

Tomminn wrote: post #74

It seems to me like this is only true if you assume space is perfectly transparent, which seems like by far the weakest assumption. Introducing any tiny amount of absorption in space would fix this, even in an infinite size, infinitely old universe.

Well, no, the paradox accounts for this. In an eternal universe any intervening dust would have steadily absorbed radiation by the stars behind it until it glowed at the same temperature. Therefore, the sky should still look uniformly bright.

Re: Olbers' Paradox

#79

Post by Tomminn »

saagarjha wrote: post #76
Tomminn wrote: post #74

It seems to me like this is only true if you assume space is perfectly transparent, which seems like by far the weakest assumption. Introducing any tiny amount of absorption in space would fix this, even in an infinite size, infinitely old universe.

Well, no, the paradox accounts for this. In an eternal universe any intervening dust would have steadily absorbed radiation by the stars behind it until it glowed at the same temperature. Therefore, the sky should still look uniformly bright.

Ahh, so we're assuming eternal universe implies that the entire universe is in thermal equilibrium. This makes some sense, but it feels like cheating. Because then the paradox is broader: "how can anything be at a different temperature to anything else in an eternally old universe?". Nothing really to do with night skies.

Re: Olbers' Paradox

#80

Post by bobbylarrybobby »

onlyrealcuzzo wrote: post #65
SomewhatLikely wrote: post #62

Earlier quoted context omitted.

Quoting Wikipedia: It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metric governing the size and geometry of spacetime itself that changes in scale https://en.m.wikipedia.org/wiki/Expansion_of_the_universe

What is the metric governing the size and geometry of spacetime? Gravity??

Gravity is not the metric, but it does interact with the metric (well, gravity is what we call it when mass or energy affects space time). The presence of mass/energy causes the shortest distance between two points to no longer be a straight path through space. The path an object takes through space time is always the path with the shortest space time interval among all paths (in that sense the path is “straight” the same way that in flat space, a straight line is the shortest path between two points) — this distance is given by the metric tensor — but gravity makes this path appear curved in space.
Post reply on HN