Space, time, and Lebesgue

by sam_micheal | July 16, 2012 at 02:42 pm
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“The more we know, the more we realize exactly how much we don't.”

“It's a good beginning.. At least you're asking the right questions.”

What do space, time, and Lebesgue have to do with each other? Maybe nothing.. Maybe everything.. At the moment, I feel I'm on the verge of another 'breakthrough' but my lack of knowledge and understanding of required fields frustrates me no end.. My greatest academic weakness is in graduate level mathematics courses which cover absolutely essential concepts relating to physics, cosmology, and creation. ^^ No joke; I need to correct this as soon as possible..

Why are they important? I'll try to give you an example.. Please have some patience. The following section is very 'deep' and 'heavy' in precise mathematical concepts .. The real numbers (the numbers we use in everyday life) are uncountably infinite. They're dense. (This mathematical usage is quite different from the physics usage. In physics, density means concentration of mass or energy. In math, it's 'a little bit' different and more precise.) Countable sets vs uncountable sets relate to the idea the integers (the whole numbers) are infinite but countable: ...-3, -2, -1, 0, 1, 2, 3,... You can identify uniquely each one and count them. Now, if you are examining a set of numbers (any set!) you can establish a one-to-one correspondence with the countable integers or you cannot. In other words, a set is countable or it is not.. ^^ With me so far? ;) Good. :) ..Yet another way of looking at those same sets is from the Lebesgue measure viewpoint. A countable set is said to have measure zero. An uncountable set has non-zero measure. To reiterate above in these terms, the integers (as a set) have measure zero. The reals do not. The deep question is why! :)

Exactly why are the real numbers dense (have non-zero measure)? ..The reals are made up of two very large sets: the rational numbers and irrational numbers. Before I discussed this with Gug, I made the mistake of assuming the density of the reals stems from the density of both the rational numbers and irrational numbers. (Two examples of rational numbers are 4 and 1/4; two examples of irrational numbers are π and e.) But I was wrong! (I'm attending math-education courses – if I cannot teach correct math, I shouldn't be a math teacher!) Gug informed me the correct situation: the density of the reals depends solely on the density of the irrationals; the rationals are countable with measure zero! I was totally wrong! ;) ..The point may seem 'trivial' to the uninitiated but I assure you – it is not! :) Let's find out why! :)

Space and time may be 'like the reals' or they may not be. Space and/or time may be dense (in math terms) or they may not be. There is no guarantee they're not like the rationals (countable) both or individually. Space may be more like the rationals than reals and time may be 'some other animal completely'! Whoa! ;) Remember my article on holographic noise? (Of course not..) The basic idea of that is: if spacetime is discrete (observed in little bits or chunks), there 'should be' observable 'residual' noise that is supposedly detectable by the Holometer Experiment. Unfortunately, this is somewhat like the 'Higgs' and mass. Not somewhat.. It's equivalent. It's also equivalent with 'weak bosons' being 'responsible' for nuclear decay, the Casimir 'force' between conducting plates, and any other artifice of the Standard Model.

'The thing is', we've never observed a gravitational wave ever – never a single 'gravitational wave', we've never observed a proton to decay (if protons were composite made of quarks and can sometimes spontaneously change character, they should eventually decay), we don't observe the Casimir 'force' with non-conductive plates,.. ..The Higgs will be investigated thoroughly; we'll spend billions of dollars equivalent on it. Nobel prizes will be awarded.. Time will move forward.. A few centuries hence, human beings (or their representatives) will look back on this time with dismay and disbelief.. Why did we allocate such tremendous resources to investigating transient particles? Oh that's right, we are entrenched in reductionism and virtual exchange.. Those two concepts define modern physics. Those and elitism are what 'make the world go round' in physics.. Even a near-term economic global melt-down would not force physicists to be 'more practical' or real .. The boys and their toys.

^^ ..Back to the nature of space and time.. Are space and time like the irrationals or rationals? Is space dense in the mathematical sense? Is time dense? How could we test these questions? THAT is worth billions of dollars and human resources.. NOT the Higgs or anything like it..

“I'd give my eye tooth for somethin' like that!”

“Ask a conventional modern physicist to describe why a radiometer spins .. The childlike explanation is photon pressure or photon momentum being absorbed on the dark sides of the vanes.. The conventional physicist will equivocate with smoke and mirrors.. Nothing substantial will be elucidated..”

Photomultiplier tubes can detect a single photon – it's a proven fact. But.. conventional physicists cannot 'talk about' single photons – that concept is actually meaningless to a conventional physicist. So.. What is going on here? In the field of physics? It appears to be: elites who insist on looking at the universe from a particular narrow-minded perspective and only being able to see data and experimental results from that extremely limited perspective. It's like a brilliant infant trying to deduce the whole vast complexity of our entire universe from a few play toys.. Genius or not, ain't gonna happen.

..I agree 'my' concept of charged-antiphotons mediating electromagnetism is 'somewhat speculative' but.. It's the only real explanation I've ever heard of my entire life that does not depend on field or virtual exchange.. The 'classical' approach to spacetime is that it's continuous and assumed to be like the real numbers – dense. But convention has moved far away from classical ideas and anything resembling classical ways of thinking (about our universe) is poo-pooed and denigrated.. Now, everything has to be snazzy like holographic noise, Casimir effect, and the esoteric Higgs. ~

Yea, I'll be forgotten and most of these articles/essays will be lost in the noise of 'future history' (fads and hype about trivial day-to-day happenings) but.. One must make an effort that is non-religious to stand up to these frauds in our 'cathedrals of learning'.. In fact, I'm obligated to 'take them on'.. It's a matter of conscience.

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I made another mistake when I said the rationals are not dense.. they are 'sparsely dense' ~ But it's clear the measure of the reals comes from the measure of the irrationals.. The questions relating to space and time are: if space/time are dense, does that density come from some subset? And, what are the implications/consequences? This is the proverbial 'million dollar question' that actually deserves a purse/prize of that order..

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