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Does Planck length go against the idea of a continuous space and time?

Looking at the answers below, some obvious things become apparent. 1) If you cannot resolve space-time any finer than Lp (or tp), then space-time is not continuous, this is referred to as the Planck Flow, the progression of one Planck interval to the next.In light of seeing the same questions repeatedly: For a more detailed, albeit, math-intensive explanation, I recently updated a paper: DESCRIPTIONS HISTORY AND DEFINITIONS OF THE QUANTUM ZENO EFFECT AND ANTI- QUANTUM ZENO EFFECT AS A PROPERTY OF THE EVOLUTION OF THE DESITTER HORIZON IN GENERAL RELATIVITYJanuary 2019 DOI: 10.13140/RG.2.2.22174.59204In 1955 Wheeler was trying to make sense of Gravity Waves, as he said, Gravitation without mass. As such, he realized that any such energy (of the Gravity Wave) must be quantized according to Planck’s constant. His derivation is uncontested, and the very purpose of the derivation is to show that Gravitation in the form of an energy wave must be quantized. As such, the underlying framework for space-time must also be quantized.In other words, the geometry of space-time is quantized because Gravitation is quantized, and Gravitation describes the geometry of not just local, but all of space-time.That is, if the scaffold of Gravitation is quantized, since Gravitation describes the geometry of space-time from a local scale out to cosmological distances, then space-time is quantized. The usual error is to think of space-time as being ‘flat,’ which is impossible on every scale out to infinity. In fact, the more you extend ‘Inflation’ of space-time outward, increasing without bound, the more local space-time is therefore regarded as an infinitesimal.If you look into the Lin-Shu Density Wave hypothesis, you will find that regardless of the hypothesis, flat space-time in a local environment in this galaxy is impossible, criss-crossing with Density (Gravity) Waves both outward from the center, along the spiral arms, and trailing from one spiral arm into another.This resolution on a quantum scale eventually led to the Holographic Principle of Quantum Mechanics, which treats the cosmos as a 2-dimensional representation on a Schwarzschild surface quantized to Lp^2:This was the collaborative work over nearly 4 decades between Wheeler, Susskind, t’ Hooft, Buoso, Hawking, Beckenstein (credited image above) and others.Yes, space-time is quantized. The reference to Heisenberg’s Uncertainty Principle is awkward and incorrect. If tp were not quantized in the denominator ofthen the QED vacuum energy would always be infinite for each and every infinitesimal volume of this proposed continuous space-time. it is only by limiting tp as >0 that delta-E is not infinite. As a result, the quantization of space-time on a Planck scale, with respect to Heisenberg’s Uncertainty Principle, demands quantization.The HUP as shown above also indicates clearly that if space-time were continuous (infinitely divisible) 1) it would require an infinite amount of energy for time to progress one infinitesimal 2) it would take infinity to progress from one Planck interval to the next.I could go on for pages. Nonetheless, the Planck Flow is universal to Quantum Theory, as is the quantization of space-time, particularly in String and Holographic Theory. Quantum Field Theory also quantizes space-time, albeit in a different fashion. QFT requires an infinite (non-local, finite means local) field as a scaffold. An infinite field cannot ‘fit’ inside of our finite domain. The lower limit of the Big Bang defines our domain as finite, the upper limit is the subjective (smear of the) present, and not a microsecond beyond; thus our domain is bound on both sides and quite finite. Twisting space time into a pretzel and adding unobservable dimensions has not and does not resolve the issue. Nonetheless, the favored ‘Quantum Fluctuation’ within this field is quantized. The lower limit is called the Zero point; simply meaning that it is a non-zero baseline (stage), some integer multiple of Planck’s constant.I need to add here, as someone has pointed out is not obvious, that the cosmos is based on information. Information cannot be transferred faster than light. In fact, the Planck length, Planck time, and speed of light are related:c=1Lp/1tp1tp=1Lp/cIf we have two wave functions at a scale smaller than 1Lp:There can be no information, as information in any discussion of entropy involves a change of state as the definition for information. Thus, without the lower QUANTIZED limit of Lp and tp, information, the description of a change of state, cannot exist.That is, to simplify, there is no possibility of an infinitesimal amount of information, as the progression of information would then take infinity to describe 1 bit of entropy (as per the depiction of the Schwarzschild surface above). Or, it would take an infinite amount of information to describe 1 bit of entropy. Neither is correct.Information, then, is quantized. The Beckenstein image above describes the quantization as being a Schwarzschild surface of Lp^2.I’m editing this as of 23 Nov17; been looking into the various players in the various fields, Susskind, String theory, Buosso, Verlinde, Bekenstein, the approaches in Quantum Field Theory from the various ‘major players’ in these fields to get a real fell for how they shaped their “opinions” on rather or not space-time is continuous.Keep in mind that an “opinion” by definition is formulated from a perspective or line of reasoning, without evidence. Also, String ‘Theory’ ‘m-theory, Quantum Field Theory and so on all all hypotheses, not theories. A theory has sufficient compelling evidence; these are improvable/disprovable mathematical models; only.As unlikely as it seems, the most correct answer, and that which provides proof - absolute proof, inarguable, and rather irrefutable, comes from no one you ever heard of. Saul Hernandez, with a humble MS in Physics brings us to the Bohr quantization of the electron orbital. He doesn’t go further than that; but I have formulated a more complete picture:In the Bohr model, the jump to or fall from one quantum level to the next is a quantum jump, it is instantaneous. There is no smooth transition from one level to the next, and the electron is not doing something that defies the structure of space-time. The excitation-relaxation of electron orbitals is the means by which we monitor all time. Our very definitions for time, not to mention the proof of relativistic principles, is built upon this model.In simple terms (I credit Saul Hernandez for pointing this otherwise obvious yet overlooked proof) the only tangible proof in existence is that the Bohr model of the electron defines time as being quantized.If we try and argue that model back into a continuous scaffold of time, time being infinitely divisible, the jump between orbitals is stretched over an infinite number of infinitesimal time intervals. This Riemann Sum approach has to equal zero, as a final result, in order to be a quantum jump. That is, we have to use the Riemann Sum of infinitesimals and the outcome must be zero. If you remember Calc 101, the only way this is going to happen is if you are adding an infinite number of zeros together.Otherwise, the Bohr model is incorrect, oddly, everything in modern physics, even hypothetical, becomes then incorrect. That is how much weight rests upon the Bohr model.Quantum spin, all of the flavors of particles, their quantum values, charge, mass, the entire Standard Model and consequently all of the subsequent and estuary hypotheses are trashed if time is not quantized in this quantum jump of the electron from one orbital to another.As Hernandez points out:An attendee at the conference stated, ‘We don’t understand what happens in between.’ Bohr replied, ‘We have to be clear on what we mean by understand. I have presented a model which is useful for making predictions in nature. And that is all that we can do as scientists. We cannot existentially say anything truthful about what is actually happening. All that we can do is present models that are useful in explaining events in nature.’There is no in between orbitals if time is quantized. If time were not quantized, the jump would have to occur such that the electron changes position at either v=c or v>>c, we know this is not the case because we can measure c to 8 significant figures. Nor is the electron changing position at v=c, as this is well within measurement capabilities; also, the electron’s mass prevents it from v=c. Nothing which possesses mass can travel at v=c. In this sense, we can eliminate v<c as representing anything resembling the quantum jump, a literal change in position and vector for the massive electron.The Quantized Jump requires Quantized Time. Quantized Time requires Quantized Space.If space-time is continuous, then the electron must pass through an infinite number of states between orbital 1 and orbital 2. This is not the case. It passes through exactly 1 state. If we regard the electron jump as a phenomenon occurring ‘paradoxically’ under the conditions of continuous space-time, then the equation is flipped, and we have the electron changing from state 1 to state 2 over an infinite number of space-time intervals. In either case, the condition and the outcome are both impossible. Even if we regard the space-time intervals as infinitesimals, the Riemann Sum of an infinite number of infinitesimals is a real, rational number that is always greater than zero. All of Calculus is founded upon this principle.That is, Calculus is founded upon the Riemann notion, slice an apple into an infinite number of infinitely small slices, add the infinite number of infinitesimal slices together and you get your apple back. Thus, a ‘quantum jump’ for the electron’s position and vector cannot pass through an infinite number of infinitesimal states.That is, we either have the electron passing through an infinite number of states (space-time intervals) to jump from orbital 1 to orbital 2, which we know is not correct, or we have a paradoxical instantaneous jump from orbital 1 to orbital 2 over an infinite number of space-time intervals, which we also know is not true.The only possible solution that works, and is not hypothetical nor improvable, is that space-time is quantized, whose proof is in the Bohr electron.If we regard the electron in state 1, orbital 1, as information, as well as the same electron in state 2, orbital 2, under continuous space-time conditions the amount of information to change from state 1 to state 2 is infinite. This in turn requires an infinite amount of entropy; according to:S=A/4Nicolini restates Verlinde [Piero Nicolini, Entropic force, noncommutative gravity and ungravity; rXiv:1005.2996v3 [gr-qc] 13 Aug 2010] in that:That is, clearly, if the denominator, Lp^2 is reduced to an infinitesimal, namely zero, then N becomes infinite. It is only by quantizing space-time that we reduce the amount of information (here represented by N ‘bits’) can be finite. Note that:Keeping in mind my penchant for spelling out h-bar as explicitly h/2π. Verlinde [Erik Verlinde, On the Origin of Gravity and the Laws of Newton; arXiv:1001.0785v1 [hep-th] 6 Jan 2010] writes this explicitly as:You will note thatandNotably this is exactly the same as Nicolini’s equation above. For the extent of the derivation, read Verlinde’s paper. Bekenstein had defined the entropy as ‘the measure of lack of information about the actual internal configuration of the system.’ [J. D. Bekenstein, Lett. Nuov. Cim. 4, 737 (1972); J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973); J. D. Bekenstein, Phys. Rev. D 9, 3292 (1974)].In any case, the definition of the smallest bit of information possible in normal space-time is given by the Area/Lp^2. If the denominator were allowed to approach zero, the smallest bit of information possible in normal space-time would then be infinite. You can also interpret that as meaning an infinite amount of information is necessary to describe the most infinitesimal object of radius, R.Be absolutely clear that this definition incorporates String Theory, m-Theory, Quantum Field Theory, Quantum Loop Gravity, entropy, and everything else. They all agree on that equation.It is therefore impossible for any time or distance in normal space-time to fall below the Planck limit.In these arguments, the area, A, is the surface or horizon of a Black Hole. During the development of Holographic Theory, the question was raised rather or not an insignificant mass would alter the surface area of the Black Hole, that is, does added mass increase the surface area, and how small of a mass can make the most microscopic change in the surface area of the Black Hole. And, does this represent a decrease in entropy of the Black Hole?What Verlinde wrote above, the number of bits of information is proportionalSoInformation is therefore also limited to v=0 and v=c, as any finer resolution requires this overlap shown above, or exceeding the velocity of light; and nothing in between. I refer to this as the Laws of Motion on a Quantum Scale.At v = 0.5c, we are faced with (we review this)1.go ½ Lp in 1 tpThat is not possible because this requires a structure finer than Lp (a Planck length) will allow:Figure 1That is, you cannot go ½ of a Planck length in normal space-time. (I will disregard arguments based on compactified dimensions at this point as they are mathematical hypothetical models, not ‘Theory.’) As such, you cannot go ½ Lp in 1 tp.2. Or, go 1Lp in 2 tp:A. Since proceeding at >1Lp/ tp is exceeding light speed, this is forbidden.B. Since going < 1Lp is forbidden because it requires a structure finer than Lp will allow (as shown above).C. Thus we cannot go >1Lp/tp (exceeds v=c), or <1Lp/tp (requires a structure finer than normal space-time will allow), meaning we can, on a Planck scale, only go 1Lp/1tp=c:We are then faced with motion taking on the following characteristic in order to go 1Lp in 2tp in order to go 0.5c:Go at v=c for 1 tp, stop for 1tp, go at v=c for 1 Lp, stop for 1 tp; etc.,This is explained in an old text of mine, Temporal Mechanics 101.At the first Planck epoch of the cosmos (10^-43 seconds), Gravity as a Force did not emerge from mass, nor mass from the Force of Gravity. They are related by Einstein’s equations, but there is no causal component. Gravity Waves, as quantized by Wheeler in 1955, are in fact, Gravitation without mass.Although one could argue that Gravity waves are emergent from mass, Verlinde has pointed out acceptably that Gravity is an emergent phenomenon from entropy. We are not talking about the 19th century gas laws of entropy, but information entropy.Mass is the result of a wave function. To simplify, we think of entropy as an increase in the number of possible outcomes of a superposition of that wave function, and Ordiny as a decrease in the number of possible outcomes of that superposition. If you look again at the graphic above, and take into account the result S=A/4, this is consistent. As the area increases, the number of possible outcomes of a superposition increases, entropy increases.This later evolved into the Lin-Shu Density Wave Theory which explains the spiral structure of galaxies, rather than the Dark Matter mythos. Whereas it is impossible for our galaxy, at an estimated 640 billion solar masses (including gas and dust) to move in a spiral motion without Gravity Waves emerging from such motion, Dark Matter has no evidence whatsoever. The Gravitational Lensing effect of a galaxy, which is generating a Gravity Wave extending for billions of light years, is a well founded mathematical framework, as light must pass through billions of years of a galaxy’s Gravity Wave emergent from its internal motion. The error of Dark Matter is to treat the gravity as localized to the galaxy and not beyond, which is not possible, as an emergent Gravity Wave must result from the internal motion of the galaxy.Also, since LIGO is an interferometer which works by detecting its own change of state in the presence of a Gravity Wave, the urban myth of the observer/observed effect of Special Relativity applies to General Relativity is also busted. Where under Special Relativity the Michelson-Morley interferometer fails to detect its own Lorentzian transformation, the LIGO interferometer can detects it own Schwarzschild transformation under General Relativistic conditions, AKA, a passing Gravity Wave.The structure and meaning of Gravity Waves as started by Wheeler has led to many new concepts in Quantum Theory not commonly known. LIGO has confirmed hypothesis of Gravity Waves to theorem.

Why aren’t there any primary sources proving the Book of Mormon false?

Question: How can text from the New Testament appear in the Book of Mormon?The Book of Mormon claims to be a "translation," and the language used is that of Joseph SmithIt is claimed that the Book of Mormon cannot be an ancient work because it contains material that is also found in the New Testament. In fact, in the Book of Mormon, Jesus quotes a paraphrase of Moses' words found in Acts 3:22-26. However, all these parallels demonstrate is that:the Book of Mormon translation language is closely based in KJV English; andKing James phrases were exceedingly common in the speech and writing of Joseph's day.Neither of these is news, and neither can tell us much but that the Book of Mormon was translated in the nineteenth century.The Book of Mormon claims to be a "translation." Therefore, the language used is that of Joseph Smith. Joseph could choose to render similar (or identical) material using King James Bible language if that adequately represented the text's intent.Only if we presume that the Book of Mormon is a fraud at the outset is this proof of anything. If we assume that it is a translation, then the use of Bible language tells us merely that Joseph used biblical language.If Joseph was a fraud, why would he plagiarize the one text—the King James Bible—which his readers would be sure to know, and sure to react negatively if they noticed it? The Book of Mormon contains much original material—Joseph didn't "need" to use the KJV; he is obviously capable of producing original material.Furthermore, many of the critics examples consist of a phrase or a concept that Joseph has supposedly lifted from the New Testament. This complaint, however ignores several factors.Chief among the difficulty is that the critics seem ignorant or unconcerned about the extent to which the language of the King James Bible dominated preaching, common speech, and discussion of religious and non-religious topics in Joseph Smith's day.In a Bible-based culture like Joseph Smith's, Biblical phrases are simply "in the air," and are often used without an awareness of where they come from (this is especially true for those whose literary exposure did not extend much beyond the Bible—like Joseph). By analogy, many modern authors or speakers will use phrases like the following, completely unaware that they are quoting Shakespeare!Common phrases originally from ShakespeareListPhraseShakespeareReference*"All's well that ends well"All's Well That Ends WellTitle of play*"As good luck would have it"The Merry Wives of WindsorIII, v, 1822*"Bated breath"The Merchant of VeniceI, iii, 433*"Be-all and the end-all"Macbethi, vii, 474*"Beggar all description"Antony and CleopatraII, ii, 914*"Brave new world"The TempestV, i, 2333*"Break the ice"The Taming of the ShrewI, ii, 818*"not budge an inch"The Taming of the ShrewPrologue, i, 12*"Dead as a doornail"Henry IV, Part IIIV, x, 2924*"Devil incarnate"Titus AndronicusV, i, 2173*"Fool's paradise"Romeo and JulietII, iv, 1316*"For goodness' sake"Henry VIIIChorus, I, i*"Full circle"King LearV, iii, 3331*"Good riddance"Troilus and CressidaII, i, 977*"Household words"Henry VIV, iii, 2253*"Heart of gold"Henry VIV, i, 1890*"In...a pickle"The TempestV, i, 2357*"Lie low"Much Ado About NothingV, i, 2122*"Love is blind"Henry VThe Merchant of VeniceV, ii, 3286II, vi, 944*"Melted into thin air"The TempestVI, i, 1877*"Naked truth"Love's Labours LostV, ii, 2648*"I have not slept one wink"CymbelineIII, iv, 1826*"One fell swoop"MacbethIV, iii, 2099*"Play fast and loose with"King JohnIII, i, 1149*"We have seen better days"As You Like ItTimon of AthensII, vii, 1016IV, ii, 1632*"The short and the long of it"The Merry Wives of WindsorII, ii, 853*"Too much of a good thing"As You Like ItIV, i, 1900*"Wear my heart upon my sleeve"OthelloI, i, 42*"What the dickens"The Merry Wives of WindsorIII, ii, 1327*"The world's my [mine] oyster"Henry IV, Part 2II, i, 797See also: Specific examples from TannersWould we accuse someone who used these phrases of "plagiarizing" Shakespeare? Hardly, for they are common expressions in our language—most people are probably unaware that they even come from Shakespeare, and most have probably not read the plays at all. In a similar way, some biblical phrases and vocabulary were likely part of Joseph Smith's subconscious verbal world. It would be strange if it were otherwise.There are related issues to which the critics pay little attentionoften the relation between the texts is not that close; only a few words are used that are the same. It is sometimes hard to see how there would be a different way of discussing the same sort of issue. Even if one believes Joseph forged the Book of Mormon, it seems more plausible that these cases are just a coincidence, or a case where one is almost "forced" to use the same type of language (e.g., 1 Nephi 1:18, Alma 19:10, Mosiah 16:7).some phrases which approximate the New Testament are quite famous, classic renderings in the King James. Such phrases might be used almost instinctively or subconsciously when translating (e.g., 1 Nephi 12:11, 2 Nephi 4:17). Even academic translators sometimes struggle to avoid using the type of scriptural language with which they are very familiar—it can take a real effort to give a different rendering than one that is well known.the Book of Mormon never hides its intent to use King James style English. It is not surprising, then, that there are parallels in language and vocabulary. The translation may even intend to call to mind these biblical verses or phrases, since the Book of Mormon is intended to complement the BibleJoseph is clearly able to produce huge amounts of text that do not rely on the KJV at all. Why, if he wants to produce a believable forgery, does he adapt the occasional well-known phrase that could be noticed by even a relatively casual Bible reader? The critics require Joseph to be clever enough to produce independent text, and yet foolish enough to betray his dependence on the Bible.Often, although the wording may be similar, the concept being explored is expanded, or the context is substantially altered in the Book of Mormon. The critics seem to think that Joseph flips through the Bible to find something, but the Book of Mormon certainly extends and adapts this material dramatically. The "copying" model seems more complex than needed, as it has Joseph taking small snippets of text from the Bible and other sources and somehow weaving it into the Book of Mormon text. Yet, eyewitnesses do not describe anything like this process; it is not even clear that Joseph owned a Bible during the Book of Mormon translation.

What is time and what defines it? Can time and light be considered alike?

You ask such common questions….That was a joke. What defines time is any which way we choose to measure it. Like a volume of whiskey in a shot, you can measure it by fingers, grams, cubic centimeters, cubic miles, %alcohol it will raise your blood level (but has not yet done so), how much thermal radiation it will absorb (again, in the future), how much thermal radiation it did absorb (in the past), how many fleas you can drown in it….or have drowned in it…As for what it is, all we can say it is a shot of whiskey, which is a volume of distilled spirits. However, the whiskey has finer components, and is a mixture. The finer we try and refine the individual components, we get down to the quarks and gluons that hypothetically hold the nuclei together (Internal Strong Force), at which point our story ends.Time is also a mixture, a mixture of dimensions, a mixture of information, the information lies on a surface, and the surface; in a turnaround (called a fractal) can be measured in time intervals.The number of bits of information is given by: (Verlinde; Erik Verlinde, On the Origin of Gravity and the Laws of Newton; arXiv:1001.0785v1 [hep-th] 6 Jan 2010)Verlinde wrote the equation 3.10 asWhich rearranges to:After correcting for Beckenstein information entropy. [1]Where c=1Lp/1tp (tp being the Planck interval of time), Lp and tp are interchangeable. As in Minkowski Space, space-time; indifferentiable. We say that the speed of lght, ‘c’ is a ‘natural unit,’ and set it equal to 1. In which case 1Lp = 1tp.Where A-omega is the surface area of the region being measured; we call that the ‘world-sheet’. And 1 bit of information, by rearranging the Beckestein-Verlinde relationship; then is given by:That is, in an attempt to determine what the hitherto ‘bit’ of information is (which oddly, no one has defined to date) we use dimensional analysis to derive what a ‘bit’ of information in the Bekenstein-Hawking ‘information paradox’ would be. Keep in mind Bekenstein was one of Wheeler’s students. In any case, the argument that raged on for four decades never had ‘information’ defined. With the exception of the derivation above, that remains true today.What is 4Lp^2? Well, you can envision it as a trigonal pyramid:But you have to keep in mind that because the pyramid has a hypotenuse that is not an integer value of Lp, this, or any other shape on a Planck Scale is impossible. a circle for instance has pi diameters making the circumference, also not an integer value of Lp. Only integers of Lp can exist, as this is the finest slice you can take in normal space-time. The Planck Scale is a shapeless, formless, domain.So as not to fail to contradict myself (the Kaufman Paradox - why do you feel embarrassed when the performer sucks?) we takeand it oddly becomes an analog ofThe reason I say this is odd is because it has the same characteristic as a Black Hole, it has no interior, meaning that surface shown bisecting the two halves is impossible. Remember that a Black Hole has no interior. All force and time dilation, etc is directed toward the Schwarzschil radius, which I refer to as the Schwarzschild surface. Nothing happens below this surface because space-time does not exist below this surface. In fact, time itself ceases to exist at the surface.The fact that time ceases to exist at the Schwarzschild surface is why we can say in Holographic Theory (which is actually a hypothesis, not a theory) that the Schwarzschld surface is 2-dimensional, and time is not a valid dimension there. It is static, frozen, time has been infinitely dilated, according to the Schwarzschild transformation:Most people are accustomed to seeing it written asHowever, this is non-intuitive, as it shows time shrinking away to nothing, not intuitively ‘dilation.’ Remember, in Special Relativity we define time dilation as expanding toward infinity. So as to remain consistent with Special Relativity, in General Relativity (which this is actually not) I flip the equation so as to intuitively represent ‘dilation toward infinity.’ That is, the temporal distance at the Schwarzschild surface between any two events is infinite. That’s why I flip the equation.The term, 4Lp^2 is supposed to be a surface area, which defines the 1 bit as a trigonal equilateral pyramid. However, no regular shapes are possible on a Planck scale. For instance, the height of the pyramid is not in integer values of Lp, and therefore not possible. Spheres and circles require piLp, don’t work, and so on to all shapes. The trigonal equilateral pyramid is imaginary.So, time is a trigonal equilateral pyramid that represents 1 bit of information; 1 bit of information being the smallest amount of information needed to describe exactly 1 unit of entropy and/or Ordiny. (Ordiny is the opposite of entropy).As for force, distance, time, emergent gravitation, thus the emergent geometry of space-time (quantum gravitation) can be summarized as: when the number of possible superpositions increases, that is entropy, and when the number of possible superpositions decreases, that is Ordiny. I can then use this simple model as the driving mechanism of all of the forces of nature.The natural state of a ‘thing’ is as a wave function. The Heisenberg Uncertainty Principle, the most misquoted and incorrectly explained equation of all time does not have anything whatsoever to do with particles. The HUP states that the wave function has a distribution of possible superpositions, and therefore a distribution of velocities (that give it momentum) that got it to each of those superpositions.The very first YOU DO NOT DO is divide the indivisible h by the irrational number, 4 pi, rendering a numeric value that cannot exist in this universe 1) because h is the smallest value in normal space-time, 2) pi is not a rational number. So, the instant you see someone ‘divide’ h by 4 pi, change the channel.The 4 pi means ‘two wavelengths.’ The distribution of possible superpositions for x and the superpostions of velocity that got x to each of those probable superpositions is greater than or equal to the smallest unit of time dependent energy, h spread over exactly two wavelengths. Why 2 wavelengths as the minimum? Because, if you are in quantized space-time, and you can either be walking somewhere along the current wavelength, but to be considered in another position (you cannot overlap in quantized space-time) you must therefore be exactly 2 wavelengths to be considered 2 positions. That is the HUP, not the ‘particle’ nonsense.Once the wave function is detected, it is no longer a wave function, it is a particle. At that exact instant, the HUP is non-sequitur. The HUP has nothing to do with ‘particles.’In the mythos, the claim is I cannot know the exact location and exact momentum of say, an electron. OK. So we set up a detector to measure the electron’s momentum out to a zillion decimal places. It is essentially a tiny catcher’s mit. When an electron hits the mit, it will measure the exact momentum out to a zillion decimal places.So we wait…. Caught one! We now know the exact momentum of the electron (via its velocity and mass) with mind blowing precision. Where is the electron at that instant? According to myth we haven’t any idea, at least with respect to the electron’s Compton wavelength. It is exactly in the catcher’s mit. Where is the lack of certainty in this picture?Once the electron is detected, it has no Compton wavelength, it is a ‘particle,’ e.g., tiny cannon ball. If you could not know the exact velocity and position of an electron, an old fashioned CRT television couldn’t work. The CRT worked by ‘painting’ the image one dot (electron hitting a flourescent screen) at a time, requiring exacting precision in position and velocity to draw the Beverly Hillbillies.However, there is a dual going on, as information entropy is measured by:There is no way to get S=+1 without using imaginary numbers, complex conjugates.It gets weirder…Among Nicolini’s first statements: “Conventionally, entropy is defined as a measure of the loss of information about the microscopic degrees of freedom of a physical system, when describing it in terms of macroscopic variables.” [16] That is, as Leonard Susskind put it, ‘Entropy is a measure of ignorance. In a maximally entangled state, we are at maximal entropy.’ We can ween out of that, the ‘microscopic degrees of freedom’ have to take into account that any system is to some degree entangled with some other system. That is, they either share information, and/or the state of system B (Bob) may depend on system A (Alice), such is in the classic EPR entanglement of simple spin up-spin down particle-antiparticle pair production. For instance, if system A is spin up, then system B is spin down; and this is not a time dependent phenomenon.I believe the first mistake people make when approaching entangled systems is to think of space and/or time as figuring into the equation somehow. But the reason EPR could not get around the idea of superluminal signaling is that they couldn’t get around a phenomenon which existed in a world that ‘we are weird to.’ That is, a wave function is happy as such, that is its native form. It is only when we try and drag the thing into our human frame of reference that we think it is weird.Albeit visible in normal space-time,’the paradox’ had no correlation to space-time with respect to the state of either system. That is, there is information regarding either system that has no relationship or interdependency with space or time. I, for one, do not understand why people cannot get around that issue. Bob’s state of being, the information describing Bob’s degrees of freedom have no relationship with when and where he is. The only thing that defines Bob’s state is the state of Alice, and no other thing, property, particle, force, distance, time, etc. matters whatsoever.‘the paradox’ is the result of trying to predict behavior, the outcome, when it is obvious the answer is that there is no such property until detection occurs.If we do not measure or detect the state of Alice, we know nothing about either system. There is a matrix of possible things she could be, if only considering her spin, the matrix (disregarding system B) has only 2 elements. It isn’t until Alice is measured that we know her state. So, state A is always in hand, since we have to take the measurement.However, system B (Bob) has at the moment of Alice’s measured value, no degrees of freedom, he is slave to Alice. Since Bob has zero degrees of freedom, entropy is always zero (or infinity if you’re doing the Product from a different approach). Since the entropy is zero, N, the number of bits to describe Bob is zero; we know Bob’s state even if he is billions of light-years away once we measure Alice. Using Verlinde’s approach: I corrected the more modern 1/4That equation states that Bob, being slave to Alice, has no unique information describing him. Whatever Bob is, is completely a result of Alice. The world-sheet a-omega, falls to zero.This means that the surface Area of omega is zero, and as a result, all distances are zero. This is the root and key to Quantum Entanglement, those past 4 paragraphs.In which case for Bob, who can only have 1 state and no possible alternative once Alice is measured, Log Pi = 0, and the entire equation becomes S=0. That is what I mean by zero entropy (for Bob). In an attempt to directly correlate S and N, the number of bits of information, we look at the value Lp2.Even 19th century gas law entropy beinghas a result of zero, because time has ceased to progress.At the fundamental length, Lp, a variety of phenomenon occur. The Planck mass, actually as large as 10 nanograms, becomes a Black Hole of diameter equal to its Comptonwavelentgth/π, or a radius of Lp. It will radiate away as Hawking Radiation in roughly 1tp (5E-39 seconds). The wavelength of that radiation will be 1Lp (any other wavelength is not possible as its self-energy would again collapse into a black hole).The surface of the black hole cannot be regarded as a sphere, because it is so heavily pixelated at that size. For instance, since a curvature would not be possible on that scale, as this would require finely dividing the Planck length into shorter pieces, thus collapsing into self-energetic black holes, only a triangle can describe the circumference. Oddly, even a triangle becomes an impossible shape as the hypotenuse is not an integer of Lp, and so on.I will get to deriving that soon. For now, Bob has no information or degrees of freedom associated with him, being slave to Alice. Entropy, space, time, and so on have no relevance to Bob, when or where he is.Quantum Gravity takes this approach. For any closed region of space-time given by a volume representing N=1 as I showed above, a virtual particle may or may not exist in it. It is more correct to say that information may or may not be present in it.Two virtual particles cannot exist in N=1 volume of space-time, not even a boson, as more than 1 boson would require more than N=1 bits to describe.Virtual particles are created in particle-antiparticle pairs, and are entangled. 1 particle (Alice) has any number of degrees of freedom, but Bob’s state is slave to Alice, Bob has no degrees of freedom, either before or after Alice is measured. Since the virtual particle-antiparticle pairs are created entangled, as the distance between Alice and Bob grows larger, the likelihood that Bob will be created at all decreases. That is, at a distance of 1Lp the likelihood is high, at a distance of Andromeda, the likelihood that virtual Bob will be created out of the vacuum as an antiparticle entangled component of Alice is very low.Thus, the creation/annihilation of entangled virtual particle-antiparticle pairs is distance dependent (and so time dependent). This is beginning to look like gravitation. I would go through the derivation, but Nicolini [19] has already done so based on Verlinde’s work:After a complicated paper of derivation, we get back Newtonian mechanics, based on the number of bits of information, understanding that all distance is in reference across a Schwarzschild surface (like a Black Hole).The term on the left is clearly Newtonian, on the right is the entropy per surface area as defined by the number of bits of information.Thus, it is the QED vacuum itself that seems to provide the emergent gravitation, tied together by entanglement.In short, we take that trigonal pyramid (4Lp^2). It may or may not have information in it. If it does, it is because it is the result of a ‘quantum fluctuation.’ (another entire chapter). As such, that bit of information in our trigonal pyramid (Alice) is entangled with Bob, somewhere in space and time. 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