The Physics of Gravity - This is the Shape of the Universe, and the bodies therein.
(Redacted before 2025)
VOICEOVER: Homework ........................................................................................... 1
Introduction: INFINITY .................................................................................................................. 2
Part A: SPACE .................................................................................................................................... 7
VOICEOVER: A hole through the centre of Earth ................................................ 16
Part B: GRAVITY ............................................................................................................................. 17
HOW GRAVITY DETERMINES SHAPE ............................................................ 24
Part C: TIME .................................................................................................................................... 38
Part D: THE POLYDIMENSIONAL SHAPE OF THE UNIVERSE ............................. 46
Part E: BODIES OF EVIDENCE ................................................................................................ 51
DARK MATTER ........................................................................................................... 54
DARK ENERGY ........................................................................................................... 53
INFLATION .................................................................................................................... 54
THE BIG BANG ........................................................................................................... 55
THE SHAPE OF SATURN ........................................................................................ 52
THE SHAPE OF THE GALAXY ............................................................................ 55
MILKY WAY .................................................................................................................. 57
BARRED GALAXY ..................................................................................................... 57
PICTURING THE GALAXY .................................................................................... 59
PICTURING THE UNIVERSE ................................................................................ 62
DARK FLOW ................................................................................................................. 63
VOICEOVER: Homework. ............................................................................................ 64
Part F: PROOF ................................................................................................................................. 64
VOICEOVER: A hole through the centre of Earth ............................................... 64
References ......................................................................................................................................... 67
The Shape of the Universe
Shape of the Universe Introductory Video
VOICEOVER:
“My name is Martin Cross, and I want to tell you the Shape of the Universe.
If it is before 2025, I want to tell you, but I cannot. Unless or until you attend one of my live talks.
I can, and will, tell you how Gravity works. I’ll tell you this below (See How Gravity
Determines Shape), but I warn you: you may be shocked at how simple it is!
I could tell you how the Milky Way gets it spiral arms that is, I could tell you, but again, I promise not to, ‘til 2025.
This is so you can work out for yourself. Then you can tell me.
The Shape of the Milky Way is a great example of something that usually is given a really complicated answer that only a specialist would know is wrong or right. Like the one here quoted in New Scientist:
https://www.space.com/24642-spiral-galaxies-milky-way-shape-explained.html Page 1
But I included my answer to this question in my first ever ‘Shape of the Universe’ public talk given in 2014. It only took a few minutes to demonstrate and it is the same answer I will give now.
So that's your “homework”, and this essay is my attempt to give you everything you need to work out the answer, just like I did.
Because it is just as shockingly simple.
Introduction: INFINITY
Learning at Work Day happens annually in May. Back in the late 2000s I took the opportunity to present my lecture on ‘The Shape of the Universe’ to a group of local small business people. I was confident I could ‘market’ it: who hasn’t wondered what is ‘outside’ the Universe? I think people who run small businesses are generally pretty smart. I thought they’d be a good open-minded but sceptical group to test out my presentation, and they were my peers in the way that a more academically educated audience might not be. I started by asking them that question, “What is outside of the Universe?”
We’ve all, I dare say, had occasion to muse about what is beyond ‘everything’. Does it all stop at the edges, to become surrounded by ‘nothing’? But how then can ‘nothing’ be something?
Or does it never end, becoming more and more and more? But if it never ends; if everything there is, goes on changing into more and more of what can be, and will be, then doesn’t that make a nonsense of what ‘is’?
I had a different answer, as I wanted to explain. My talk seemed to go down quite well. I felt people had been entertained, and that they had seemed to understand what I was presenting.
What was my answer? Well, using the example of Pi as infinitesimal rather than infinite, I tried to explain that the Universe does indeed have an edge, but it is an edge that extends infinitesimally, in a very specific way, the same way that Pi extends its digits forever, with no repeat.
Here and now I observe that, although surprising, there is nothing inherently worrying or upsetting in the behaviour of Pi. One does not go around looking for answers to impossible questions in the digits of Pi. One does not try using them to contact the recently deceased.
Most of all, there is no temptation to worship the digits of Pi. They are wonderful, but they are not God.
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As I said in my talk, figuratively speaking, you can reach the edge of the Universe very easily, but it is an edge that doesn’t stop, just as there is no last or repeating digit of Pi.
~ • ~
One of the TV programmes that I fondly remember from the past was ‘Tomorrow’s World’: Three knowledgable presenters providing viewers with a summary of what’s new in the world of science and tech. I am probably prone to the passed-middle-aged malady of gilding the past, but I remember it for combining a no-nonsense delivery with a great ‘feel-good’ follow-up. There is always plenty of bad news, but the science magazine show presented what you could not help but feel was good news.
Much later on, I made myself a web page containing RSS feeds and I happened to also include the ‘New Scientist’ RSS feed. I quickly made the discovery that this supplied me with a similar feel- good sense that ‘Tomorrow’s World’ once did. In 2004, it took my breath away to see the Shape I had given to the Universe appear in an item in the feed from ‘New Scientist’. When I saw my shape reproduced and ‘brought to life’ as an image through their site, that was the turning point which prompted me on to the web in own right.
I have got some free content to give out to people who don’t want to, or cannot, attend the talks or that want to prepare in advance for attendance. As well as the website I have set up, www.WhatIsTheShapeOfTheUniverse.co.uk, there are the essays which I have written and even a full-length book. All of this is free of charge at the moment * and will continue to be
so *, as I make that promise, on record.
The work for this, and for the first talk had sprung specifically from a book I read in the nineties. In describing the mathematician Paul Erdos (“The Man Who Loved Only Numbers”, Fourth Estate), the author had presented the work of Georg Cantor, on Infinity. Cantor was, I felt I could show, demonstrably wrong (of which more, shortly).
You’ll already be familiar with my presentation of this idea if you have read the maths essay I wrote for a general readership, “Do You Like Numbers?”. Not to worry if you haven’t. The current essay does not assume any knowledge other than standard GCSE understanding.
Talking to my peers in business had been one thing, talking to the academic community – and specifically, physicists – would be quite another. If I were talking to a group of physicists, they would definitely understand the idea – but would they see it as a big idea? It is one thing to say to some one who has never thought of it, here is a way to look at things. It is quite Page 3
another thing to say to people who have spent their whole life looking at something to say
“here is another way to look at it”. I could see I might have a different problem.
I might need to do a bit more work than that, so was there another way in?
The earlier article ‘Do You Like Numbers?’ had been intended to engage the child or teenager by sharing a non-mathematicians enthusiasm for numbers. At the same time it had a serious experimental purpose. I hoped to pre-empt what I saw as a young person’s indoctrination into a certain way of viewing infinity. But if the previous article describes how mathematicians should view Infinity, then how do physicists view infinity? Indeed, do they view infinity differently? The answer is I think, affirmative. And John Hurt explained how physicists view infinity to me – not personally, I must admit! It was in a recent BBC ‘Horizon’ documentary in which his magnificent voice was put to such good use.
The BBC ‘Horizon’ programme started by presenting the picture of a person at sea. They are in a boat and can see to the horizon all around themself. The sea appears to stop at the horizon. There is a clear, firm line where it gives way to sky. But of course, we know that this is only an illusion: the sea has no such straight edge. It continues on beyond the Horizon until it meets the land even though we cannot see it, and for all we knew in the past, it could go on forever.
It is a good analogy for a couple of reasons. First, the horizon is caused by the curvature of the Earth and physicists know that space is curved by gravity. It is easy to grasp that they are both curved. Second, the boat is on, or in, the sea, not of it. It is water that extends beyond the horizon, not the boat or the observer. This is how physicists like to understand the Universe, externally, as ‘a bunch of stuff’ – the water.
Physicists might even say that John Hurt’s analogy caters for the nature of Pi, in a purely mathematical, one-dimensional sense; that they are about understanding infinity in three dimensions. Certainly the development of an idea of a shape for the Universe would normally be done using numbers; using maths; and I am not a mathematician. But the problem of the Universe is not logistical, it is conceptual.
Concepts like 'the Big Bang' and an 'Expanding' Universe lead us to think in terms of a center and an edge, but the Universe is a place with no centre and no outside; no edge. It *might* be
'expanding outward' but it is just as likely that it is 'contracting inward' because there is no frame of reference to make the judgement. An explosion might explain the movement of the Universe, but so does an 'implosion', and for the same reason. The cognitive dissonance this creates leads to misconceptions like Dark Matter and Dark Energy, ultimately leading to Page 4
notions which are not tenable like wormholes and multiverses. In my judgement this is because there is no objective third spatial Dimension - but we'll get to that. In summary, what is needed is not a mathematical formula; what is needed is a philosophical conception.
I had created my website, and I had seen the confirmation for my Shape of the Universe, but how could I as a non-scientist – a mere philosopher – shepherd such a view safely out onto the world ‘stage’?
That was the motivation. I created a talk for general members of the public, the one I am offering to people now, and delivered this for the first time in 2014. I was able to entitle it
“This is the Shape of the Universe (or your money back!)” as I do now. I was thrilled when a majority of the audience of strangers was not just open but persuaded, as shown in this Youtube video 1 taken live at the time.
I would go on to develop these ideas into a “theory of everything – and everyone!” A full-blown philosophy, if you will. But that was much later, taking us almost up to today. Back in 2014, I had not yet presented on the ‘city stage’, let alone nationally. Before I could take the next step, what I needed was an essay like the one I had done for ‘Numbers’.
I wrote the first version of this essay in 2015. It was quite similar, but much shorter, than it is now. You may already have noticed how discursive this version is. That is because I am equally as interested in entertaining you (and myself) as I am in informing first myself, and then you. But there is another reason why Version 2 is quite different to Version 1.
I’d started writing ‘Numbers’ because I had read something that I knew was wrong (Cantor’s proof). That hadn’t happened in physics. The New Scientist picture had encouraged me because it was mostly right, not mostly wrong. I thought I just needed to persuade physicists who were mostly right that they could be completely right. I had no reason to think that physicists were wrong.
I had to wait til 2019 for that. It was the book ‘What If?’ by Randall Munroe from the xkcd website. Randall isn’t a physicist himself, he’s a science writer like the Fourth Estate biographer. That gave me a level to pitch for, and so the entertainment commenced.
Just like in my talk, which also starts with infinity, this essay proceeds by discussing Dimension; the Dimensions of space. We then proceed on to movement, and Gravity, the key part of the essay. We contrast the idea of a field against Einstein’s analogy of acceleration in a 1
https://www.youtube.com/watch?v=5SrqXq8c_7A
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lift to develop the principle of a lift with a ‘soft floor’, as the basis for visualisation. I’m also using the book ‘What If?’ in this essay as a first foil to my own idea; I’m then using the Internet generally, as a second adversary to my position so as to give you the basis for yourself addressing the ‘homework’ (you could skip straight to it and read just this if you don’t need or want any background). There is the further opportunity here to develop more than could be included in the live talk and so I include discussion of the conceptualisation of Time. I come back then to concrete examples, showing my idea of Gravity as an extension of existing knowledge, and finally to the question of proof.
Let's have a closer look at the content I am offering entirely free of charge at the moment.
Of course there is the first essay, ‘Do you like Numbers?’ That's the title for just 10,000 words that you can download as a PDF from my website. It is a shame to have to give away the
‘spoiler’ for it as I have already done but I am sure you will find it entertaining even knowing the denouement, as long as the answer to the question is affirmative: you do like numbers.
http://whatistheshapeoftheuniverse.co.uk/2_Maths/Do%20You%20Like%20Numbers.htm Also on the website as well as a number of other roughly 10,000 word essays, there is -
completely free again - a full-length, full colour, illustrated PDF version of a book I wrote about the mind. This is the other part of my theory of everything – and everyone as alluded to earlier and on my Youtube Channel
It is a full 100,000 words, an exploration of that idea, as logically and exactly as I thought it could be done using philosophical principles and visualisation rather than the proof and maths of hard science. In a nutshell, I believe it shows the definition of the shape of the Universe is also the basis for a definition of mind.
http://www.whatistheshapeoftheuniverse.co.uk/0_Common%20Sense/Common%20Sense
%20-%20The%20Philosophy%20of%20Psychology.pdf
So you might say why, if this work has any value, are you having to give it away free of charge? Why would I do that? And indeed, I'm not Facebook! I'm not grabbing "market share"
so that I can make money. That's very much not the intention and I'll talk about that a bit later if you stay with me that far.
Now, what is a Dimension?
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The Shape of the Universe
Figure 1 The many-dimensional illustrations of Steve Ditko, for Marvel Comics ‘Dr Strange’.
