Close examination of two recent and unexpected black hole and neutron star collisions is leading to a more detailed picture of the dynamics inside galaxies.
Researchers can detect the gravitational waves created as these massive objects collide, even though the ripples are less than the width of an atom by the time they reach us.
Rare black hole and neutron star collisions sighted twice in 10 days - BBC News
Collisions between two black holes as well as between two neutron stars have previously been detected.
However, collisions between black holes and neutron stars have been regarded as unlikely since current theories suggest that the two massive objects are not found together.
The discovery is heralding alternative theories which imply that stars and galaxies formed in different ways to those described by our standard views of how the universe formed.
Researchers can detect the gravitational waves created as these massive objects collide, even though the ripples are less than the width of an atom by the time they reach us.
Rare black hole and neutron star collisions sighted twice in 10 days - BBC News
Collisions between two black holes as well as between two neutron stars have previously been detected.
However, collisions between black holes and neutron stars have been regarded as unlikely since current theories suggest that the two massive objects are not found together.
The discovery is heralding alternative theories which imply that stars and galaxies formed in different ways to those described by our standard views of how the universe formed.
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I could be wrong on this Bonnie Lad, but I thought Gravitational Waves were tinier than Atoms. Think Proton size! 😀
Naturally I remain fascinated by the extremes of the Universe like Black Holes:
My latest wheeze has been "Geometric Algebra":
A Swift Introduction to Geometric Algebra - YouTube
Adding Scalars and Vectors and Bivectors worked for me.
DIV F = J impressed me for Maxwell's Equations of electromagnetism. How concise is that?
But TBH, it's all gone HORRIBLY, HORRIBLY wrong...
Apparently doesn't work in Curved Space. So not the full Gravitational Quantum Theory we need. It will therefore fall flat on its face near a Black Hole. 🙁
Ah well. Back to Number Theory. Maths is much more eternally provable than Physics.
3^2 + 4^2 = 5^2
3^3 + 4^3 + 5^3 = 6^3
10^3 + 9^3 = 12^3 + 1^3 = 1729 (The Taxicab number which so entertained Hardy and Ramanujan.)
We needn't go into Heegner number - Wikipedia: 163 being the finest IMO.
Naturally I remain fascinated by the extremes of the Universe like Black Holes:
My latest wheeze has been "Geometric Algebra":
A Swift Introduction to Geometric Algebra - YouTube
Adding Scalars and Vectors and Bivectors worked for me.
DIV F = J impressed me for Maxwell's Equations of electromagnetism. How concise is that?
But TBH, it's all gone HORRIBLY, HORRIBLY wrong...
Apparently doesn't work in Curved Space. So not the full Gravitational Quantum Theory we need. It will therefore fall flat on its face near a Black Hole. 🙁
Ah well. Back to Number Theory. Maths is much more eternally provable than Physics.
3^2 + 4^2 = 5^2
3^3 + 4^3 + 5^3 = 6^3
10^3 + 9^3 = 12^3 + 1^3 = 1729 (The Taxicab number which so entertained Hardy and Ramanujan.)
We needn't go into Heegner number - Wikipedia: 163 being the finest IMO.
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It seems no time at all since our last taxicab ride! 😉
The deep poetry of taxicab numbers by Chung Wong • Findery
As for the Heegner number, even Mr. Heegner himself looks bored with the topic! 😀
Who Mourns the Tenth Heegner Number? |
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We are so educated here that I think we should start saying "black body" instead of black hole!?
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The term "black body" was coined by Gustav Kirchhoff in 1860, so it already had a distinct meaning in physics long before John Wheeler coined the term "black hole" in 1969.
In other words, the name "black body" was already taken!
P.S. A black hole is almost an ideal black body!
In other words, the name "black body" was already taken!
P.S. A black hole is almost an ideal black body!
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Poor Mr. Hardy found his taxicab number "uninteresting" ... such a lack of imagination!
Interesting number paradox - Wikipedia
I used to have a book called "The Penguin Dictionary of Curious And Interesting Numbers (Penguin science) " by David Wells. I think he even did a second volume with more stuff.
An interesting reference. Anyhoo, if you find the least interesting number in mathematics, that makes it interesting, no? 😀
9^3 + 10^3 = 12^3 + 1 ^3 = 1729
6^3 + 8^3 = 9^3 - 1^3 = 728
These are known as "Nearly Fermat", which is why Ramanujan studied them. Near misses. They led him to Elliptic Functions way ahead of his time. These functions were later used to prove Fermat's "Last Theorem".
Gauss was interested in Heegner Numbers too. So not a waste of time. Led to modular (clock) arithmetic I believe.
Two goodish mathematical references here, the first being an excellent refresher if you have forgotten stuff. I like the second too, well, if cards are mathematics... 🙂
An interesting reference. Anyhoo, if you find the least interesting number in mathematics, that makes it interesting, no? 😀
9^3 + 10^3 = 12^3 + 1 ^3 = 1729
6^3 + 8^3 = 9^3 - 1^3 = 728
These are known as "Nearly Fermat", which is why Ramanujan studied them. Near misses. They led him to Elliptic Functions way ahead of his time. These functions were later used to prove Fermat's "Last Theorem".
Gauss was interested in Heegner Numbers too. So not a waste of time. Led to modular (clock) arithmetic I believe.
Two goodish mathematical references here, the first being an excellent refresher if you have forgotten stuff. I like the second too, well, if cards are mathematics... 🙂
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So is space different from matter?
Not sure how to express the question exactly. I mean has anyone actually seen space? Could it be expanding as some form of energy, condensed into matter or not, be "evaporating and returning to condensed unseen microbubbles?
It is spacetime that is expanding.
According to General Relativity, spacetime tells matter how to move while matter tells spacetime how to curve.
Spacetime is simply what would be left over if we took everything in the Universe - such as mass and radiation - away.
When we introduce matter into the Universe, spacetime is still there, but its properties are altered. The larger a mass you put inside it, the more that spacetime gets curved. And, as masses move through space, the geometry describing spacetime changes.
We shouldn't regard spacetime as though it's a material, physical thing. It is only a mathematical structure that we can describe by writing down equations - the equations of General Relativity.
We can't observe spacetime as an entity, we can only observe the matter and radiation present within it.
I've extracted and edited the above information from this source:
Ask Ethan: Is Spacetime Really A Fabric?
So it seems our ability to grasp the concept of spacetime is required to establish it's very existence. Can we say for certain that the behavior of the universe would be as such if we weren't here to observe it?
That question smacks of philosophy rather than natural philosophy.
I only know a little about the latter.
I only know a little about the latter.
I honestly did not mean to philosophize. I mean it from a purely scientific point of view, akin to the double slit experiment or the cat in a box. No more philosophical than that. Is there time without observation?
The time-ordering of events in spacetime is not agreed upon by all observers.
In the theory of relativity, events have an existence in spacetime beyond our local concept of past, present and future.
If we take the theory at face value, there is no sense in which the past has happened and the future is yet to happen.
However, this does raise the question of whether all events that can happen and have happened in the history of the Universe are, in some sense, 'out there'.
This concept is known as the 'Block Universe'. Eternalism (philosophy of time - Wikipedia)
If all the above is true (a quantum theory of spacetime may tell us otherwise) then all the happy moments of my life haven't gone - they are still out there somewhere in spacetime, although I can never revisit them.
In the theory of relativity, events have an existence in spacetime beyond our local concept of past, present and future.
If we take the theory at face value, there is no sense in which the past has happened and the future is yet to happen.
However, this does raise the question of whether all events that can happen and have happened in the history of the Universe are, in some sense, 'out there'.
This concept is known as the 'Block Universe'. Eternalism (philosophy of time - Wikipedia)
If all the above is true (a quantum theory of spacetime may tell us otherwise) then all the happy moments of my life haven't gone - they are still out there somewhere in spacetime, although I can never revisit them.
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Just trying to help here, but an extraordinarily interesting number is 744! 😎
Why? Because it seems to crop up everywhere! 😀
It's in the j-invariant - Wikipedia.
It's in the Heegner numbers:
Heegner number - Wikipedia
I also state, with liitle justification that it is 24-D Bosonic String Theory as a function of j-744: A014708 - OEIS
Why? Because it seems to crop up everywhere! 😀
It's in the j-invariant - Wikipedia.
It's in the Heegner numbers:
Heegner number - Wikipedia
I also state, with liitle justification that it is 24-D Bosonic String Theory as a function of j-744: A014708 - OEIS
Ah, Angel Number 744! 😎
If you find yourself repeatedly seeing the number sequence 744, it can be a sign to stick to the path you know is right for you even in the face of adversity.
If you find yourself repeatedly seeing the number sequence 744, it can be a sign to stick to the path you know is right for you even in the face of adversity.
I, as a premier number theorist, did find it surprising that 744 commands such interest amongst Numerologists! Surely a minor number in the scheme of things?
Frankly it's the difference between Patrick Moore's sound Astronomy, and Mystic Meg's ludicrous Astrology. 😀
Anyhoo, I was planning to send my sister recently a book about Venice (which she likes) and Angels (TBH, I think she has little belief in Angels).
Unfortunately we fell into one of our usual fights. All action was suspended. Cats and Dogs.
But, since we are all momentarily friendly again, I think I shall send it. A gripping plot. And Angel Gabriel stars, IIRC. 🙂
Frankly it's the difference between Patrick Moore's sound Astronomy, and Mystic Meg's ludicrous Astrology. 😀
Anyhoo, I was planning to send my sister recently a book about Venice (which she likes) and Angels (TBH, I think she has little belief in Angels).
Unfortunately we fell into one of our usual fights. All action was suspended. Cats and Dogs.
But, since we are all momentarily friendly again, I think I shall send it. A gripping plot. And Angel Gabriel stars, IIRC. 🙂
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"For the first time in her life Miss Garnett falls in love - with Carlo, a charming art dealer with twinkling eyes and a white moustache."
Is what ensues described on page 744? 😀
Is what ensues described on page 744? 😀
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