The h Bar

3:02 PM

Ok I have just read it, this is really strange. So basically, the volume does not change but things getting further apart because the metric changes...?

> In differential geometry, the backbone mathematics for general relativity, a metric tensor can be defined which precisely characterizes the space being described by explaining the way distances should be measured in every possible direction. General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame. This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated. A me…

Now that I found the term, I should see if there are any PSE questions on it

1

Q: Metric Expansion Of Space

I just do not understand this concept of metric expansion of space. Shouldn't the galaxies move away from each other. How can the space between them expand if the galaxies are not moving away from each other. I do not want an analogy of a balloon or something like that. I just want a real answer ...

@Slereah, if you are still somewhere around in space, THIS is what I am trying to ask whether metric expansion implies there is more space, and if it isn't how to physically interpret metric expansion\

John Rennie

@Secret: spacetime is not an object. It doesn't stretch and new spacetime isn't created.

When you have a time dependent metric, like an FLRW universe, it means the proper distance between two points may change with time. But this doesn't mean anything is stretching.

You're looking for a physical mechanism that simply isn't there.

Secret

So you mean the accurate picture is that things getting further away from each other without anything stretching at all, and that is the correct way to understand a time dependent metric?

John Rennie

@Secret yes. The proper distance between points in space is not necessarily a conserved quantity in GR.

Secret

3:19 PM

Hmm I see... thanks
In that case, looking back to that tardis question, then (at least mathematically) to create a tardis space can be as straightforward as simply increase the spatial components of the metric in some finite region of spacetime, and the bag of gold spacetime will be one where the metric is FLRW thus it increases forever in a confined region (in the naive sense)...

John Rennie

Wow, both David and my answers are split right down the middle. David's has +4/-4 and mine has +5/-5.

user116211

I do find the voting on your and John's answers quite interesting, btw - it seems this question may well hit the precise sweet spot where 50% of the site users think it's OK and 50% think it goes too far (or at least without proper attribution). — Emilio Pisanty 9 mins ago

John Rennie

@Secret that's a specific geometry called a Friedmon, made by joining together two metrics. There is no physical motivation for doing this and no plausible mechanism for how such a spacetime might be formed. Because you can do it mathematically doesn't mean it can exist in practice.

Secret

Right

John Rennie

Vote for me! I will give free doughnuts to everyone voting for me¹.

¹ Recipient pays shipping. Restrictions apply.

Secret

3:28 PM

In other news, I have finally crunch through this lengthy article (though I still understood nothing about homotopies)

Orthogonal group

In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension n that preserve a fixed point, where the group operation is given by composing transformations. Equivalently, it is the group of n×n orthogonal matrices, where the group operation is given by matrix multiplication, and an orthogonal matrix is a real matrix whose inverse equals its transpose. The determinant of an orthogonal matrix being either 1 or −1, an important subgroup of O(n) is the special orthogonal group, denoted SO(n), of the orthogonal...

user116211

@JohnRennie I did upvote; however, what DavidZ has said is not wrong too.

Secret

25 mins ago, by John Rennie

@Secret: spacetime is not an object. It doesn't stretch and new spacetime isn't created.

This is actually the 2nd time I made this mistake since the days of Volderfield, hopefully I will not foget the explanation in the future and stop mking this mistake. I think my mind have not adapted to the weirdness of spacetime yet, despite seemed to be ok with the weirdness of quantum

user116211

The point is you need to cite when you are using some external resource.

Sanya

@MAFIA36790 are we writing academic papers here or answering questions? For an academic paper, I would heartily agree that this qualifies as plagiarism and should be handled

on PSE I would only be offended if someone copy&pasted other websites

Secret

perhaps, after reading this I should have a much better intuition for GR related stuffs...

user116211

3:37 PM

I think it applies to both.

John Rennie

@MAFIA36790 If it had been me writing the answer I would have cited the article, and in any case I would have found my own words and not used the words from the article so freely. However I don't want to put CountTo10 on trial.

Sanya

[which does not mean that it would be wrong to name the source]

user116211

7 hours ago, by MAFIA36790

> Do not copy the complete text of external sources; instead, use their words and ideas to support your own.

John Rennie

He didn't copy the complete text.

user116211

Yes.

user116211

3:38 PM

But he didn't cite.

John Rennie

That's why an accusation of plagiarism is going a bit far. But I agree that if it had been me I would have cited the article.

0celo7

Meh

I say ban the guy.

user116211

It has been explicitly mentioned in the plagiarism help page that you need to cite as well as not copy the exact words.

Sanya

@JohnRennie the question is not "would we have cited" but "is it necessary to cite in order to prevent deletion of the post", isn't it?

John Rennie

Actually meh is a pretty good response. This whole thing is a real storm in a teacup.

user116211

3:40 PM

well, it is good that it surfaced this time; it will set a remainder to cite when your post is based on past works.

user116211

I liked though how JohnR differentiated in the first para the plagiarism in academia and that here.

heather

Well, actually, I've seen the user CountTo10 around, and they are actually incredibly active, going through the queues and everything. Banning would definitely not be an appropriate response. And I'd have to agree with Sir Rennie in this case. (@JohnRennie, I'm not going to pay for the shipping to have a donut, but I did upvote your answer. =)

ACuriousMind

@Sanya Well, I don't think we need to start a manhunt on the 'plagiarist' in this case, but I would prefer that if you are basically rephrasing another source, you mention that.

user116211

@heather Banning?

heather

@MAFIA36790, 0celo7 said to just "ban the guy".

user116211

3:44 PM

No one is banning anyone ;P

ACuriousMind

Plagiarists are only suspended in egregious and repeated cases.

John Rennie

@heather sadly the restrictions prevent the shipping of doughnuts to minors on health grounds. It's for your own good :-)

user116211