What is the Universe expanding into..

[Disco-Pete]

I was referring to another respondent. However stating the obvious doesn't seem to help.

 

[Galu]

Then, Pete, please use more words in order to make it clear to what/whom you are referring.

 

[Disco-Pete]

I will try. 🙂

 

[Galu]

You can be very trying. 😛

 

[Disco-Pete]

I do my best.

 

[tonyEE]

Time started out as a measure of one thing changing vs another thing changing. I suppose an absence of “time” is equivalent to an absence of relative change.

I’m just a caveman, though. I’m still struggling with whether imaginary numbers exist and are therefore real, and what implication that has for real numbers; are they really real numbers?

I think reactance is imaginary!

 

[KaffiMann]

But I've just explained that matter and time must coexist in our universe. 😕

Yes, but we cannot rule out the possibility of multiple universes.

 

[system7]

I found my current Physics read slightly dull in parts:

I was hoping it would settle some current issues in Physics. But found it short on detail. It really didn't explain much about Spin Foam.

Problem in Cosmology is we are very much inside the box.

Happily, I keep some decent Mathematical reference books:

"Let no-one ignorant of Geometry enter here."

Plato said that.

 

[traderbam]

I think reactance is imaginary!

“Reactance is futile!” - Borg

 

[Bonsai]

This was what AE had to say about space (time) and matter in 1930. Apparently he had a philosophical discussion with one of his friends (Moritz Schlick) about it while considering GR - it’s somewhere in the presentation. IIRC the point they agreed on was space could exist independently of matter.

 

[system7]

Einstein overthought it sometimes IMO. 🙄

My current interest was brought to me today, A Dog-eared copy of Astronomy Now from Jan 2021 which I picked up in the Street.

Dates from the Time of Adios, Arecibo. A subject we have discussed.

Is there Water on the Moon?

Interestingly some Scientists think a better target might be Mercury:

https://en.wikipedia.org/wiki/Mercury_(planet)

Hope it helps.

 

[Galu]

Is there Water on the Moon?

Do bags of urine count? 🤔

NASA plans to bring 96 bags of human waste back from the Moon in order to study the effect of cosmic and solar radiation on their microbial contents!

 

[Galu]

IIRC the point they agreed on was space could exist independently of matter.

Can space exist by itself without matter or energy around?

Stanford University says No: https://einstein.stanford.edu/conte...is not affected by matter, energy and gravity.

 

[Galu]

What is "Outside" of Minkowski spacetime is unhelpfully labelled "Elsewhere" or "Undefined".

The "elsewhere" labelling is unhelpful until we explain what "outside" of spacetime actually entails.

The walls of the lightcone represent the passage of a flash of light from the past (lower cone) to the future (upper cone) through the present (origin).

All of physical reality is contained inside the lightcone.

The region outside the lightcone ("elsewhere") is inaccessible because one would have to travel faster than light to reach it.

 

[Bonsai]

Can space exist by itself without matter or energy around?

Stanford University says No: https://einstein.stanford.edu/content/relativity/a11332.html#:~:text=Can space exist by itself without matter or,is not affected by matter, energy and gravity.

I think Einstein's point was space could exist without matter. If an electromagnetic wave passes through empty space its still space even though there may be no matter around.

Until there's a coherent theory that displaces GR, I'm going to go with AE and not Stanford Uni or Lenny Susskind - even if Steve thinks AE 'overthought' things. 🙂

 

[benb]

Happily, I keep some decent Mathematical reference books:

Did I mention my favorite math book before? "Journey Through Genius"

 

[Galu]

No, but I can supply a helpful link!

https://www.goodreads.com/book/show/116185.Journey_through_Genius

 

[system7]

Bonsai, hate to pop your balloon, but it is generally considered that Albert Einstein produced junk Physics in his later years. 😳

It was embarrassing.

I seem to be down to three Maths books now.

Two of which are here:

Both of them have good qualities. Elementary Number Theory is particularly good on tables of Prime Numbers.

A subject I like since I am interested in the Riemann Hypothesis:

https://en.wikipedia.org/wiki/Riemann_hypothesis

 

[Galu]

I am interested in the Riemann Hypothesis

Now, where have I heard you say that before? 😀

And, no, I'm not going to wade all the way through that lengthy and mathematically complex Wikipedia entry! 😱

Although, the Zeta Function sounds cool, an infinite sum of powers! 😎

 

[benb]

I've read enough about the Riemann Zeta function to be dangerous - one thing is the formula as given doesn't converge below 1, so I've had a hard time understanding why/how there are zeroes at the x=1/2 line (I've seen this frustration mentioned on stackexchange), but I found mention of the Eta function which uses the same terms but they alternate + and -, and it has the same zeroes as the Zeta function (I don't know how that was shown, I guess I just have to believe it) but it covnverges, so you can use the Eta function to numerically find the zeroes. Fortunately the complex stuff in the C++ STL makes the code simple enough.

I've read two "popular" books on the Riemann Hypothesis, "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics" and "Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers." They're both good for what they are, but I wanted to go deeper, and I found the Edwards book "Riemann's Zeta Function" for cheap online. It's chock full of math, the only problem is I can't get past page 1 <insert factorial symbols here>.

I recently saw this video which shows a lot of things, ties them together and toward the end it blew my mind. Tell me what it does to YOUR mind: