The h Bar

John Rennie

04:44

@PM2Ring Thanks, I'll check out her BandCamp site.

I do like King Crimson - I have all the classic albums though not all the later ones - though I prefer them when they're more proggy and less jazzy.

charlie

08:30

@JohnRennie, good morning, sir

John Rennie

@charlie Hi :-)

charlie

@JohnRennie, Hello, do you have a link for the equation of v ? I never found it

v = H(t) r

John Rennie

That's Hubble's law:

Hubble's law

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum. Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The...

charlie

thanks, now , if the separation of particles is orderly and density always homogeneous there should be no need for inflation, according to the answer I got to my question

Avantgarde

Hi John Rennie sir.

John Rennie

08:42

@charlie Which question?

@Avantgarde Hi :-)

charlie

8

Q: Why do we need inflation?

wiki (https://en.wikipedia.org/wiki/Inflation_(cosmology)) says that immediately after BB there was expansion at speed greater than $c$, what makes this necessary, what would happen if expansion took place at near c?

Avantgarde

I remember you being called sir a lot. I want to be called a sir too.

John Rennie

@Avantgarde I'm not really a "sir" I'm just an old retired physicist with nothing better to do than answer questions here :-)

I think "sir" means "teacher" for Indian students so you just need to become a teacher.

Avantgarde

Yes, I know.

John Rennie

@charlie We don't need inflation for the universe to obey general relativity, but without inflation we have a conceptual difficulty called the horizon problem.

charlie

08:47

so CMB smoothness and flatness are not really a problem?

John Rennie

The problems all stem from what we call the initial conditions.

Our universe looks flat and (approximately) homogeneous, and that implies it has always been flat and (approximately) homogeneous right back to the big bang.

OK so far?

charlie

yes, you said that the original state was homogeneous

John Rennie

The problem is that there is no obvious reason why the original state should be flat and homogeneous. It could be, but if so we have to ask why was it flat and homogeneous? If we can't find a reason why it should have been flat and homogeneous that is worrying because we would like to be able to explain everything about the universe.

The reason the theory of inflation is popular is that it provides a reason for the flatness and homogeneity.

Specifically, even if the original state was not flat and homogeneous, inflation converts it to a flat and homogeneous state.

Does this make sense so far?

charlie

so it is just in order to be on the safe side, ok. May we linger a while on flatness? there is a straight line r if we bend even slightly to right we have a positive curvature, a circle and the same happens if we bend to the left. When do we get negative curvature?

John Rennie

09:03

Suppose you have two parallel lines, and now you extend the lines.
A good physical example of this would be two cars that start off parallel to each other and both cars drive in a straight line.
On a flat surface the line will remain parallel i.e. our two cars would remain the same distance from each other.
OK so far?

charlie

ok

John Rennie

But suppose you try this on the Earth i.e. two cars start out at the equator both driving due north. They start out driving parallel, but they won't continue driving parallel because they will meet at the north pole. Yes?

charlie

please wait, that is an urban myth. if the surface is curve and they drive parallel they wiil never meet! consider the surface of a cylinder to understand this, Then move on to the sphere of the earth an , in order to understand, imagine the paths going not north or south but west or east, they are rightly call Parallels.

if the cars move parallel heading North the will never reach the Pole the will make two parallel paths of decreasing radius, that's all

John Rennie

On a sphere a straight line in the north-south direction is a line of longitude. All lines of longitude are great circles because on a sphere the definition of a straight line is a great circle.

It sounds like you are disputing this, but it is true.

charlie

09:19

longitude bends to the Pole, if you move at 90* from the Line at 10 mile distance

you 'll pass the Pole 5miles to the left and right

please reflect on the case when you start from a longitude line and move at 90*:

you never meet!! , Earth is a sphere at the pole and at the Equator, right? why do you make a difference?

John Rennie

You are wrong I'm afraid. You have misunderstood what it means for a line to be straight when it is on a curved surface. But I don't know how to explain this without getting into some rather involved maths.

charlie

I am sorry to disagree with you, you need no math, just tellme why you never neet on the same sphere if you move to the East

John Rennie

3

Q: Straight Line on a Sphere?

I have been told that the only straight lines on a sphere are great circles. Great circles are circles which pass through the "equator" of the circle. Why are these considered straight? They certainly look curved, because they are on a sphere.

geometry geodesic

pi.math.cornell.edu/~dwh/books/eg99/Ch02/Ch02.html

Great Circles are Straight Lines (as much as that's possible on a sphere)

►

And many more such articles only a Google away

charlie

As I said that is everywhere : phys.org/news/…. but nevertheless you apply double standards if you go to the North or to the East

anyway, if you don't see that, lets' move on with your explanation of negative curvature

we can pick this up another time

John Rennie

The point i'm leading up to is that on a positively curved surface two initially parallel lines will move towards each other and on a negatively curved surface they will move away from each other.

So you cannot measure the curvature with only one line - you need two parallel lines.

charlie

09:32

yes, I hear that makes a 'saddle', but the picture they show show only a part of the surface, what solid is that? is it a real solid?

is it the inside of a sphere?

John Rennie

It's called a saddle because horse saddles have that shape at their centre.

charlie

what is the whole figure?

John Rennie

The shape with constant negative curvature is called a pseudosphere:

Pseudosphere

In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. A pseudosphere of radius R is a surface in R 3 {\displaystyle \mathbb {R} ^{3}} having curvature −1/R2 in each point. Its name comes from the analogy with the sphere of radius R, which is a surface of curvature 1/R2. The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry. == Tractroid == The same surface can be also described as the result of revolving...

charlie

Thanks, you may go on with inflation or whatever you were saying

John Rennie

I can't remember where we had got to.
I think I was saying that inflation is required, but it's nice to have because it explains something that would otherwise be mysterious i.e. why the universe is flat and homogeneous.

charlie

09:51

would you care posting an answer to that question or can I quote you extensively?

John Rennie

Isn't that what Allure's answer already says?

charlie

he doesn't mention that it is just a precaution

Going back to flatness they say that Universe is flat but for a tiny fraction , don't you agree that any value different than 0 points to a curve, the smaller the fraction the greater the radius, so, considering the current size of the Universe the value is roughly 0, 000 000 000 000 000 000 000 000 000 000 000 000 000 000.....1, I read that the current estimate value is much greater

John Rennie

You've misunderstood what he says.

charlie

sorry, why?

John Rennie

We can experimentally measure a quantity related to the flatness of the universe. This has the value 1 for a flat universe, less than 1 for a negatively curved universe and greater than 1 for a positively curved universe.

charlie

10:06

what is the current value?

John Rennie

When we measure this quantity we get the value 1, but all experimental measurements have some error associated with them. So when we measure this quantity what we actually get is 1 ± ϵ where ϵ is the experimental error. OK so far?

charlie

ok

John Rennie

If ϵ is much less than 1 we say the universe is flat to within an error ϵ.

That doesn't rule out the universe being curved, but the curvature must be small because it cannot be less than 1 - ϵ and cannot be greater than 1 + ϵ. And since ϵ ≪ 1 both 1 - ϵ and 1 + ϵ are very close to 1.

So we aren't saying we have shown the universe is flat plus a small amount ϵ.
We are saying the universe is flat, but we can't rule out that there might be a small curvature ϵ.

charlie

when you say flat or curve are you referring to the outer surface or to the inside of the universe?

John Rennie

The universe is not curved in the way a sphere is curved. The curvature of a sphere is called extrinsic curvature and it exists because the 2D sphere is in 3D space i.e. there is an extra dimension not contained in the sphere.

But the curvature of the universe is intrinsic curvature. The 4D universe is not in some larger dimension space. The intrinsic curvature does not need any extra dimensions to exist.

So there is no inner or outer surface to the universe.

charlie

10:17

and what does it mean that such U with intrinsic curvature is flat (with an error)?

John Rennie

It means that any two parallel lines we draw in the universe will remain parallel over the whole universe.

A convenient way to test this is with two light rays because light rays always follow a straight line. So it means two parallel light rays will remain parallel.

charlie

In his post Allure just says: The universe is homogeneous on large scales when there is no reason it should be. and same for flatness. If the problem were so simple there was no need to bother with inflation, just say U is flat and homogeneous an we do not know why, yet

John Rennie

The problem is that we expect the theory of thermodynamics to apply to the early universe, and thermodynamics predicts there must be some inhomogeneity.

So while we don't understand exactly what happened in the very early life of the universe it seems reasonable to suppose that thermodynamics applied to it and therefore it cannot have been homogeneous.

That means for the universe to be homogeneous there must be some reason we don't understand why thermodynamics didn't apply.

This could have been the case, after all we don't understand what went on at this time very well, but it seems awfully strange.

charlie

10:34

so, in detail ,why a uniform rate of expansion prevents flatness?

John Rennie

It's not the uniform rate of expansion that prevents flatness. What happens is that the expansion magnifies any curvature that was there just after the big bang. That is, if the universe was even slightly curved after the big bang, as the universe expanded the curvature would have got bigger and bigger and would be easily large enough for us to measure today.

So the fact we cannot measure any curvature today shows the universe must have been flat just after the big bang.

charlie

the inflation 'freezes' the state of flatness?

John Rennie

No, inflation works in the opposite way. While the normal expansion of the universe increases any curvature that might be present inflation reduces any curvature that might be present. So even if the universe started off with a non-zero curvature inflation would have reduced the curvature to effectively zero.

charlie

can you explain how or you need math?

John Rennie

10:49

It needs math.

I remember doing the calculation when I was a student but I must admit I can't remember it now. I'd have to Google for how it's done.

charlie

fair enough, may I assemble your explanations and post an answer, giving you full credit?

John Rennie

Yu are welcome to quote anything I say, but I don't think nother answer is needed.

charlie

before we go look at this picture: the blue circles are the Poles and the equator is a former meridian I couldn't draw, why not consider this model as the true one?

I can I upload a picture?

John Rennie

I need to go I'm afraid. We can pick this up tomorrow if you want.

charlie

all right, bye

fqq

11:20

those are not straight lines on a sphere (except the 0° one)

Emilio Pisanty

13:28

5

Q: If reference frames are equally valid, then why do we accept the heliocentric worldview?

If all references frames are valid, then why is the geocentric model taught as "wrong" in schools? Ive checked many websites but none of them clears the issue. Wiki says that in relativity, any object could be regarded as the centre with equal validity. Other websites and answers make a point on ...

newtonian-mechanics reference-frames orbital-motion inertial-frames solar-system

Huh

Somehow still not in HNQ

user 726941

13:40

Perhaps, because it only has 99 views

Feynman_00

Does that mean there is no accepted answer or what?

Searching "HNQ" in the search bar I keep finding this acronym :P

ACuriousMind

@Feynman_00 It means Hot Network Questions

Feynman_00

13:56

Oh, ok

user 726941

They have some formula to calculate how hot a question has to be Network wide to make the list.

Views, votes, answers, etc, etc

Emilio Pisanty

16:43

Another option: "It is an honor to be the first human to set foot on the moon."

::chef's kiss::

@user726941 indeed they do, it's here. It strongly rewards multiple answers, and particularly reasonably-scored ones early in the question lifetime. This question scores highly, or reasonably highly, on every metric valued by the formula. Presumably it will explode soon, but it's interesting that it hasn't exploded already.

For comparison, this one is currently on the list.

Emilio Pisanty

17:15

And, there it goes

Just got promoted into the list

Now it will properly explode

Transcript for