81–86 of 86 posts
The Universe full of matter/anti-matter bubbles popping in and out of existence. Most of them don’t straddle an event horizon but they still occur.
How much would such a fog contribute to the darkness at night?
Edit: Aha, clouds are irrelevant. Any dark clouds would heat up until they are the same brightness as the rest of the sky. Thanks, article!
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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??
When you have a space that isn't just normal globally euclidean space (such as: on the surface of a sphere), the idea of a vector as in like "a direction you can go in and an amount of how much or how fast or whatever" isn't something that makes sense as something independent of a base location. Instead, each point in the space has associated with it a space of "tangent vectors" at that point, and these spaces are related to each other.
The metric tensor associates to each point a "bilinear form" with some properties, essentially a way of doing something like a dot product of two tangent vectors at that same point.
This in turn allows for defining the notion of the length of some curve through the manifold.
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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. L…
I’ve heard of the Lagrangian before, but my knowledge of physics is probably somewhere around the level of someone who has only just finished the first year of their degree, at least judging by the modules my alma mater lists for their physics degree (I got Software Engineering from them 14 years ago, all my physics knowledge since then is personal geekery).
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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 sim…
Yes, a spatially infinite universe, with no expansion, but finite time since the stars all turned on, doesn't have this paradox. I think people didn't like this answer because it needs a beginning of time (or at least, of time with stars). Having expansion just-about implies there must be such a time. Because if you run it backwards, eventually the stars will all be touching each other, and clearly can't then behave…
I see, that may be the crux of the paradox.
But if we assume that stars were born at some time then dark planets could be too. And if stars became to existence at some time it is not too crazy to think that new stars might be continually become into existence and planet too so new planets would get created continually to block the light.
Imagine an infinitely long hallway in a hotel, as a mental exercise. And imagine every room is filled , and each light is on. And imagine looking at this hotel for a long distance. It will look like a continuous line. And now imagine every other room is uccupied. Still an infinite number of rooms are occupied, but this line, from a distance, will be half as dim. Now imagine ever millionth room is occupied. Still, we…
But in the paradox it is stated that through uniformity and the shells of the virtual spheres being 2d, there are four times as many stars twice as far away and since they are only a fourth in brightness, they are as bright as a near one. In your example, the number of doors is linear with distance but light falls of quadratically.
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Yes, a spatially infinite universe, with no expansion, but finite time since the stars all turned on, doesn't have this paradox. I think people didn't like this answer because it needs a beginning of time (or at least, of time with stars). Having expansion just-about implies there must be such a time. Because if you run it backwards, eventually the stars will all be touching each other, and clearly can't then behave…
> It would, like your eyeball, get the light of the stars from all directions, and would soon equilibrate to the same temperature I see, that may be the crux of the paradox. But if we assume that stars were born at some time then dark planets could be too. And if stars became to existence at some time it is not too crazy to think that new stars might be continually become into existence and planet too so new planets…