Escaping Undecidability, Uncomputability, and Unpredictability with a new ‘Theory of Everything’ by David Jewson

Dear Mr Gupta,

How perceptive! Yes, I could indeed use x, y and z coordinates instead of i, and it would be a lot simpler. There is a really important point here. QED uses complex numbers, but what are complex numbers really and why do they keep cropping up in QED? As I explained on page two, there is a simple algorithm for making the arrow, on the graph I drew, rotate, which, using x and y coordinates, would be: change the y coordinate into an x coordinate and vice versa, and then change the sign of the new x coordinate. This algorithm can be used to rotate arrows in QED, and it clearly has nothing to do with complex numbers. However, by pure chance, the rules of complex numbers work in exactly the same way: when you multiply a complex number by i, you get exactly the same swapping around as the algorithm does. So, it turns out you can use complex number calculus in QED simply because of this coincidence. So, you are right, complex numbers can be completely ditched, and the above algorithm used instead, but mathematicians like complex numbers so doubtless will continue to use them.

I know you say in your essay to avoid imaginary numbers, as nobody understands them, so I hope you might now be able to agree that the algorithm behind imaginary numbers, as outlined above, is perfectly understandable, and a beautifully simple and useful way to be able to rotate arrows, without having to grapple with anything imaginary at all.

I like a lot of the ideas in your essay. I think Nature is how you find her, but it seems particularly satisfying when it all seems to work out simply.

Best regards,

David

Dear Branko,

Yes, I think you are right, it is the Philosophy of Nature. But, here's the rub: physics is firmly based in maths, and physicists certainly do a lot of maths, and if maths is a 'logical system' or 'a language', that is consistent with being scientific. However, thinking a bit more deeply about maths, calculations always need to be done with physical things, like counters, or an abacus, or electrons in a calculator. It doesn't matter which you use, so the maths is clearly using something that they all share. If the only thing that they all share is quantity, change, and a position in space, then maths, and so physics, becomes about manipulating position, change, and position in space, and, as you say, that seems more like an area for Natural Philosophy.

I actually prefer not to draw a distinction between philosophy, maths and physics. It seems to me that all three disciplines are to do with interesting ideas about the world we live in, and the great pleasure in finding new things out, and if you claim to belong to just one particular discipline, then you are missing out.

You mention in your essay that, in your work, you use mass, radius and time. Using E=hf and E=mc², then mass=hf/c², and as both h and c are constants, mass can then be described in terms of frequency, which in turn is an amount of cyclical change in a certain time. Also, radius is a quantity in space, while time is change, for, without time, you can't have change. So, in that sense you, just like me, are using quantity, change, and space, which I think is what you are saying in your post. I like using quantity, change and space because they are simple things which can all be directly experienced, and they also seem to be the things that the maths of QED is actually using.

All very interesting!

All the best,

David

Branko - I know the constants of Nature are central to your essay and it got me wondering what the constants were in the Q hypothesis, which, being a 'theory of everything' should give you a path to discovering all constants. So, first I wondered how to define a fundamental constant. In the Q hypothesis there is a fundamental algorithm that generates Qs, and Qs are the basic objects of the Universe that can hop from place to place. Qs will repel each other, but an anti-Q and a Q will attract, so Qs and anti-Qs could, for example, orbit each other with various frequencies. As the fundamental algorithm runs, various Qs will be generated, and various patterns of Qs will form, and, as it is always the same algorithm that is used, there is a constancy to outcomes. So, for example, if a certain pattern of Qs was always found to repeat, that would be a type of constant (similar, perhaps, to the mass of a proton), but it wouldn't be a fundamental constant; it is, rather, a result of the constants that are in the algorithm. So, if I defined fundamental constants as those used in the fundamental algorithm, there are only three (in the version of the theory I presented): first, there is the amplitude of the first complex number that begins a new Q (the length of the first arrow in a Q, representing quantity), which is 1; second, the proportion that this quantity of 1 shrinks with distance, which is also 1; and thirdly, 'j', which is 0.0001, and is used to calculate the chance of a new Q forming. As the theory uses the geometry of space, the fundamental constants of geometry, like π, should, really, also be added.

Thanks for your interesting idea Branko, which inspired me to find out more about the fine structure-constant.

In his book, QED - The Strange Theory of Light and Matter, Feynman calls the amplitude for a real electron to emit or absorb a real photon e. It is the observed value of his theoretical constant j. He then explains why they are different, and why it a huge challenge to actually calculate j from experimental results.

The inverse of the square of e gives the fine structure-constant, and, therefore, j is also closely related to the fine-structure constant. As j appears in the Change Hypothesis as part of the calculation to determine the probability of a new Q forming, the fine-structure constant, through its connection to e and thereby j, is actually already part of the Change Hypothesis!!!!

Regards David

David Jewson re-uploaded the file Jewson_Essay_1.pdf for the essay entitled "Escaping Undecidability, Uncomputability, and Unpredictability with a new 'Theory of Everything'" on 2020-04-24 13:25:59 UTC.

Dear Agus,

That's a particularly interesting and absolutely key question, as I think the theory contains a truly lovely, different and simple way that forces work, including gravity. It's because this explanation is so different to the conventional explanation that makes the theory so interesting and enables it to explain so much.

It all comes down to the unique way in theory that particles move (I call these particles Qs).

A Q starts as a point and spreads out as a wave. At any point in that wave, a new Q can form. New Qs are most likely to form in high amplitude waves. When a new Q forms it looks as if the original Q has jumped there. If there are lots of Qs, they overlap, creating areas of positive interference with high amplitude waves, and areas of negative interference, with low amplitude waves. The next Q is most likely to form in the high amplitude areas i.e. Q's move into high amplitude areas. Q's are, therefore, 'attracted' into these areas, so it looks as if a force is operating. So, this would be the way that all forces are explained in the theory. Simply put, particles affect the space around them and it is that space that then 'attracts' or 'repels' other particles.

It's similar to the way that gravitational force works in General Relativity.

If you look at the section on movement in the essay, it explains it in a bit more detail and also includes a completely different explanation for gravity.

Dear David,

The answer actually underpins the whole theory.

Consider the following argument:

From the time we first come into this world we have to work everything out for ourselves, and we do that through our conscious perceptions. So, any theory about the world should have, at its basis, conscious perceptions, as that is what we have had to use to form that theory.

But in the conventional view, the world has unconscious 'objects' as its basis, with consciousness as a bolt on. This, then, seems wrong. But is it actually possible to build any physics theory at all out of conscious perceptions? Is it actually possible to build a theory 'the right way round'? What are the things you can directly perceive to build a theory out of?

Well, from my own experience, I think I can say I can perceive a position in space, a direction that something moves in space. I can also perceive a quantity in that I can often see when there is more of one thing than another. I can also perceive when things change. So, If I can build my theory out of quantity, direction and change, then I have built my theory out of conscious perceptions; I have built my theory 'the right was round'.

But I can't actually exactly define those things, just like I can't define the perception of a particular shade of red, as they are personal experiences, they are the basic things from which definitions of other things are built.

However, I hope you'll agree that you too can perceive 'quantity' and I hope that will at least give you some idea of what I'm talking about!

Best wishes,

David

Dear John,

Thanks for your helpful comments, they are much appreciated and really made me think!

To be fair to Feynman, he pointed out that the maths got very complicated, as huge numbers of simple calculations are required to decide anything at all in QED. You are right though; in the end the simple maths of the Change Hypothesis would need to get the same results as the more complicated maths needed to do practical QED.

In his book, Feynman shows how to calculate (in principle) the anomalous magnetic moment of an electron using just his three actions (pages 115 to 119 of his book), so that actually shouldn't be a problem for the Change Hypothesis as it uses the same three actions.

It was Feynman who said there is an amplitude for light to travel faster or slower than c (page 89 of his book), but basically it means there is a probability that a photon could travel slower or faster than the speed of light, being most noticeable at very short distances.

If it was right, there seem to be lots of potential reasons for using the Change Hypothesis. For example, if all fundamental particles are made up of a structure of Qs, then it should be possible to calculate their masses from the theory. If I could do that, then I'm sure you would be convinced! I agree with you totally about experiments, and that, as it is it's difficult to experimentally test the hypothesis. However, the experiment I did describe isn't just about proving an absolute space, it goes to the heart of the theory, because if there is an absolute space, then the Change Hypothesis becomes the only theory that can then reasonably explain why the maths of Relativity and Quantum theory work, as the conventional theories only work in a relative space. So, the experiment I described becomes the key experiment.

Finally, you are quite right that the whole idea lacks some essential details, and without them some of my claims are more like hopes. But I'm actually rather proud of it. It is simple and, in principle at least, it looks like it could work and it is certainly 'something completely different'.

All the best,

David

P.S Thanks also for your recommended reading!

P.S.

I can't stop thinking about the interesting things you said. So here is a list of ten reasons to use the Change Hypothesis (if it were to work out the way I hope):

1 It is a variant of a well-tested theory (Feynman's), so not a big leap to make.

2 It could therefore predict what Feynman's theory predicts.

3 It could also explain and predict many things that the current theory can't such as the masses of particles and other constants of Nature, which would be its test.

4 It could show how the complicated maths described in the textbooks you kindly suggested, is actually, underneath, the repetitive, simple maths of the hypothesis.

5 It could show how the theories of Relativity, Quantum Theory and consciousness are really all part of the same theory, with the same underlying simple maths.

6 This is because it uses a different physical view of Nature. Particles aren't points but have a definite internal structure; movement is really the creation of the new at a distance (rather than the preservation of the old); all change occurs at the same speed. This different view comes from believing that the arrows used by the maths represent something real rather than just being a device for calculation.

7 The maths then turns from something that works, but for no rational reason, into clearly describing reality. Feynman knew that nobody using the conventional theory understood why it worked. The Change Hypothesis offers that understanding.

8 It doesn't contain the paradoxes of the conventional theories.

9 It's great fun, if you like new ways of looking at things.

10 If you like exploring ideas, it's essentially unexplored. I've only scratched the surface.

Of course, I shan't list all the reasons not to use it!

All the best,

David

Dear Rodney,

Thanks for your comments which made me think. Reading the competition essays there seems to be so many explanations of Nature or parts of Nature, and the amount of undecidability, unpredictability and uncomputability in the world rather depends on which one you choose. There also seems to be a fashion for ever more complicated maths. There often seems no reason why the maths works.

But in simple situations there often is a direct correlation between maths and the physical situation it represents. So, representing cows in a field and their positions with numbers means that a change in the position of the various cows or the size of the herd in the field is directly correlated in an obvious way with the numbers representing them.

So, perhaps there should be a rule in physics, that any maths in a good theory, when broken down to it's simplest steps, should directly correlate with a change in a physical quantity, be it position of something that actually exists, or the quantity of it, at each step in the calculation.

I say all of this to then try to convince you that the Change Hypothesis has this property (in outline at least) and is unique in that respect. Every small step in the maths of the Change Hypothesis results in a clearly connected physical change in the model of Nature it is constructing and that model can reflect any changes in Nature in a clear way. I might then extend this to saying the best analyses of undecidability, unpredictability and uncomputability is, therefore, provided by the Change Hypothesis.

But as I like to think of myself as a humble person, I won't say any of that!

All the best,

David

Dear Vladimir,

I'm really impressed that you're helping out with the Covid-19 epidemic. I read your essay; I also find the idea of pilot waves very interesting. In the Change Hypothesis particles move around in a similar way, but in little jumps rather than smoothly.

Anyway, I appreciate your comments and wish you the best of luck in the contest!

David