If infinite parallel universes exist ...

[Blaggard]

I'm on the case.


Could take a while and/or get me fired.

Lol gl.

Oh and really don't worry if you don't get it straight away it took me at least a year to puzzle it out and I am good at maths.

What use is it, well it basically is physics as it now stands.

[Blaggard]

Physicists say the universe is made of atoms which in turn us made of bosons and mesons/fermions, which are themselves made of quarks.

Indeed, but what some of us want to know is what are fundamental particles made of? Any ideas?

I missed this well as far as we know quarks are as fundamental as it gets we have evidence of them at least. String theory says that all matter is made up of vibrational modes called strings but frankly that is a fairy tale IMHO, in that it has no way of being proven by experiment as the field currently stands.

[Bernard]

Actually you don't know if a universe is 'as fundamental a particle as it gets' in the same way a quark is an entire cosmos full of galaxies and with its own Big Bang.

[Blaggard]

Actually you don't know if a universe is 'as fundamental a particle as it gets' in the same way a quark is an entire cosmos full of galaxies and with its own Big Bang.

Huh could you explain that I didn't quite get it?

[Bernard]

Let me ask in a different way then: is there any certainty in the possibility that we are not being observed by some huge beings who've wondered whether or not we are 'the fundamental particles' of existence?

Micro and macro are relative in an infinite cosmos.

[uwot]

Let me ask in a different way then: is there any certainty in the possibility that we are not being observed by some huge beings who've wondered whether or not we are 'the fundamental particles' of existence?

Micro and macro are relative in an infinite cosmos.

There are more infinities than you can shake a stick at; which, if any, apply to the universe we find ourselves in isn't clear.
The required text on scale is Horton hears a who, by Dr Seuss. We are quite at liberty to create any story we like about things we can't see and make no difference.
So no, there is no certainty that we are not being observed by giants, but there is no reason to believe we are.

I missed this well as far as we know quarks are as fundamental as it gets we have evidence of them at least.

Philosophers since Thales have wanted to know what substance the universe is made of. Even some philosophers know about up, down, strange, charm, leptons, mesons, bosons and so ons; all very clever, but what are they made of? In a way it is irrelevant, metaphysics, what matters is control, for which you only need to measure charge, mass and spin. A bloke called Anaximander, a student of Thales, first pointed this out two and a half thousand years ago, by claiming that there is some infinite stuff, the apeiron, but what matters is the detectable properties, hot/cold, wet/dry.
Bohr is right, natural language is not suited to matter; using it is more akin to poetry and won't put anyone on the moon, but some of us like stories. My own favourite is that particles are perturbations in quantum fields.

String theory says that all matter is made up of vibrational modes called strings but frankly that is a fairy tale IMHO, in that it has no way of being proven by experiment as the field currently stands.

From a practical point of view, one might ask what keeps them vibrating for nearly 14 billion years. That doesn't matter in mathematics, all that 'counts' is the frequency. As you say, maths is about abstract entities, it doesn't have to 'work'.

[Blaggard]

It will perhaps amuse you that original top and bottom quarks were called truth and beauty but the names were gradually changed because it seemed to provoke philosophical confusion.


The point about the Copenhagen interpretation is that there is no classical analogue to quantum behaviour, we do not know and can not know what the wave is without measuring it and by doing so we cause indeterminacy that hides its true nature.

So a classical analogy might be a blind man reaching down to touch the ripples on a pond, do those ripples stay the same or..?

Hence the term complementary meaning a classical analogue to quantum stochastic model.

Path-integral formulation

One of an infinite number of equally likely paths used in the Feynman path integral. (see also: Wiener process.)

The Copenhagen interpretation is similar to the path integral formulation of quantum mechanics provided by Feynman. The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories. The trajectories are added together by using functional integration.

Each path is considered equally likely, and thus contributes the same amount. However, the phase of this contribution at any given point along the path is determined by the action along the path:



All these contributions are then added together, and the magnitude of the final result is squared, to get the probability distribution for the position of a particle:



As is always the case when calculating probability, the results must then be normalized by imposing:



To summarize, the probability distribution of the outcome is the normalized square of the norm of the superposition, over all paths from the point of origin to the final point, of waves propagating proportionally to the action along each path. The differences in the cumulative action along the different paths (and thus the relative phases of the contributions) produces the interference pattern observed by the double-slit experiment. Feynman stressed that his formulation is merely a mathematical description, not an attempt to describe a real process that we can measure.

[HexHammer]

Paralel universes is but a fairytale dream, stop dreaming!

[Blaggard]

This is an idiots guide to quantum theory:

http://www.youtube.com/watch?v=DfPeprQ7oGc

Might provide a useful non maths heavy description for the maths idiot.

[Bernard]

Let me ask in a different way then: is there any certainty in the possibility that we are not being observed by some huge beings who've wondered whether or not we are 'the fundamental particles' of existence?

Micro and macro are relative in an infinite cosmos.

There are more infinities than you can shake a stick at; which, if any, apply to the universe we find ourselves in isn't clear.
The required text on scale is Horton hears a who, by Dr Seuss. We are quite at liberty to create any story we like about things we can't see and make no difference.
So no, there is no certainty that we are not being observed by giants, but there is no reason to believe we are.

Well you can only ever shake a stick at infinity, not infinities. There is a big difference and that's where reason gets it wrong. You gotta forget reason after a certain amount of mileage (it stays in the background running like a flywheel). First rule of thumb with infinity is to kiss (Keep It Simple Stupid). Multiplying only works with concepts and infinity is not a concept. Infinity is just right here and now... and that's it! Finito! You can't think about it, add, subtract or multiply it. It simply stays unaffected by whatever we attempt to do with it. There are not multiple infinities, but there are multiple mathematicians in insane asylums because they can't simply leave infinity alone. Their concepts of multiple infinities are a result of applying techniques used with concepts to something which is not conceptual.

Reason is not required to believe anymore than legs are required to move - its just our most common technique.

[Bernard]

You take the Hilbert's Hotel hoodwink for example. The guy asks us to imagine a hotel with an infinity of rooms, but all this is doing is creating a concept of a hotel with infinite rooms... game over... infinity is out the window as soon as you get started. Concepts only breed more concepts, not more infinities. Conceptualising is very importanat for our survival - moment to moment, day to day. Its purpose is to set limits so that our perception can get a handle on whatever is going on around us... or within us. The need to conceptualize is automatic and unstoppable, and we can safely do it with virtually anything. Infinity though counts as the numero uno no-go zone. Dissatisfying maybe, but we ought to just count our lucky eggs and be content.

[Blaggard]

Infinity is a useful limit, it's utility outside of coneptual mathematical analysis and physics is minimal though. Unless you are an anthropologist or a psychologist then it becomes useful as a way to model systems of the mind and or evolution also to explain why it is we cannot perceive infinity. It also is useful in religion to answer questions like God is infinite but then:

"Only two things are infinite, human stupidity and the universe, and I am not sure about the second one."

Albert Einstein.

[Blaggard]

Let me ask in a different way then: is there any certainty in the possibility that we are not being observed by some huge beings who've wondered whether or not we are 'the fundamental particles' of existence?

Micro and macro are relative in an infinite cosmos.

There are more infinities than you can shake a stick at; which, if any, apply to the universe we find ourselves in isn't clear.
The required text on scale is Horton hears a who, by Dr Seuss. We are quite at liberty to create any story we like about things we can't see and make no difference.
So no, there is no certainty that we are not being observed by giants, but there is no reason to believe we are.

Well you can only ever shake a stick at infinity, not infinities. There is a big difference and that's where reason gets it wrong. You gotta forget reason after a certain amount of mileage (it stays in the background running like a flywheel). First rule of thumb with infinity is to kiss (Keep It Simple Stupid). Multiplying only works with concepts and infinity is not a concept. Infinity is just right here and now... and that's it! Finito! You can't think about it, add, subtract or multiply it. It simply stays unaffected by whatever we attempt to do with it. There are not multiple infinities, but there are multiple mathematicians in insane asylums because they can't simply leave infinity alone. Their concepts of multiple infinities are a result of applying techniques used with concepts to something which is not conceptual.

Reason is not required to believe anymore than legs are required to move - its just our most common technique.

Gregor Cantor managed to provide a "theory" called Cantors continuum, but like the hyperreals these are mostly useless outside of maths theory, certainly they are unlikely to have any real world utility. That said though they said the same about imaginary numbers in the 17th century and they were really, really, really wrong about complex geometry to an astounding level. So in an infinite universe or an infinite set of infinites anything is possible, which does not mean it will happen but it does make reality pretty fucking odd.

Cantor believed the continuum hypothesis to be true and tried for many years to prove it, in vain. It became the first on David Hilbert's list of important open questions that was presented at the International Congress of Mathematicians in the year 1900 in Paris. Axiomatic set theory was at that point not yet formulated.

Kurt Gödel showed in 1940 that the continuum hypothesis (CH for short) cannot be disproved from the standard Zermelo–Fraenkel set theory (ZF), even if the axiom of choice is adopted (ZFC). Paul Cohen showed in 1963 that CH cannot be proven from those same axioms either. Hence, CH is independent of ZFC. Both of these results assume that the Zermelo–Fraenkel axioms themselves do not contain a contradiction; this assumption is widely believed to be true.

The continuum hypothesis was not the first statement shown to be independent of ZFC. An immediate consequence of Gödel's incompleteness theorem, which was published in 1931, is that there is a formal statement (one for each appropriate Gödel numbering scheme) expressing the consistency of ZFC that is independent of ZFC. The continuum hypothesis and the axiom of choice were among the first mathematical statements shown to be independent of ZF set theory. These independence proofs were not completed until Paul Cohen developed forcing in the 1960s.

The continuum hypothesis is closely related to many statements in analysis, point set topology and measure theory. As a result of its independence, many substantial conjectures in those fields have subsequently been shown to be independent as well.

So far, CH appears to be independent of all known large cardinal axioms in the context of ZFC.

Gödel and Cohen's negative results are not universally accepted as disposing of the hypothesis, and Hilbert's problem remains an active topic of contemporary research (see Woodin 2001a). Koellner (2011a) has also written an overview of the status of current research into CH.

[Blaggard]

Just to add context i or the imaginary number has a very important application in proving trigonometry:

Because of this relationship:



Called Euler's identity which makes mathmos all giddy and silly.

Which I mentioned earlier I believe, it proves categorically that the imaginary axis when used to represent a 4d system can contain all geometry over time. Which as you can imagine if you'll pardon the pun is very useful in quantum mechanics and QED Quantum Electro Dynamics (see Fourier analysis for more boring maths gibberish).

In essence e^ipi is essentialy equivalent as the solution of sqrt -1^2=-1 as opposed to the real solution sqrt x^2=1 as already mentioned a 4th spacial concern perpendicular to x,y,z just to iterate that point and provide some context to the discussion. Hence i when squared equals -1. The complex number system hence usually has both a real and imaginary number.

http://en.wikipedia.org/wiki/Complex_number

See here for details.

History in brief

Main section: History

The solution in radicals (without trigonometric functions) of a general cubic equation contains the square roots of negative numbers when all three roots are real numbers, a situation that cannot be rectified by factoring aided by the rational root test if the cubic is irreducible (the so-called casus irreducibilis). This conundrum led Italian mathematician Gerolamo Cardano to conceive of complex numbers in around 1545, though his understanding was rudimentary.

Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root.

Many mathematicians contributed to the full development of complex numbers. The rules for addition, subtraction, multiplication, and division of complex numbers were developed by the Italian mathematician Rafael Bombelli.[6] A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton, who extended this abstraction to the theory of quaternions.

I think I just provided a working definition of ennui for myself by actually boring myself. Kudos to me I think.

[uwot]

The point about the Copenhagen interpretation is that there is no classical analogue to quantum behaviour, we do not know and can not know what the wave is without measuring it and by doing so we cause indeterminacy that hides its true nature.

As far as knowing what the 'wave' is, I think you have to distinguish between epistemology and ontology. Physicists know perfectly well what the wave is, in that it is a certain amount, a quantum, of energy. Like all energy, it is just the power to affect a change, most usefully in the excitation of electrons. The maths describes what happens in terms of the changes in energy levels extremely well and even, I gather, makes some stab at explaining how it got from a to b, which I'm guessing is what the Path-Integral Formulation is all about. The truth is though, at the quantum level, no ones knows.

So a classical analogy might be a blind man reaching down to touch the ripples on a pond, do those ripples stay the same or..?

Quite so, Blaggard; you can't touch the ripples without changing them. (Isn't that Heisenberg rather than Copenhagen?) I think you can stretch the analogy by pretending fundamental particles are whirlpools, they have 'mass', because the water has to change direction. I think that is Higgs in a nutshell. The two slit experiment is much less puzzling in those terms.
Seriously, Blaggard, I am, as you say, a maths idiot, although I will try and get my head round that limit stuff. I'm not sure many people here are much better. If you really want to communicate these ideas, you will need to translate them.

Hence the term complementary meaning a classical analogue to quantum stochastic model.

Then again, there's no guarantee I will understand you in English.