{{I've pieced this file together from several garbage data sources. It looks to be the OCR text printout from a scanned paper file. Based on the Primatech signature on the data, it may have come from Michelle LeRoux's college research. But I can't understand fuck all of any of it. Some of the file was irreparably corrupted.}}
THESIS NOTES 4
AUTHOR: MICHELLE CARDINAL
COMPANY ARCHIVE ADDITION DATE 4/8/84
The existence of parallel universes may seem like something cooked up by science fiction writers, with little relevance to modern theoretical physics. But the idea that we live in a "multiverse" made up of an infinite number of parallel universes has long been considered a scientific possibility – the state formulation of Hugh Everett in 1957, later popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s — although it is still a matter of vigorous debate among physicists. The race is now on to find a way to test the theory, including searching the sky for signs of collisions with other universes.
It is important to keep in mind that the multiverse view is not actually a theory, it is rather a consequence of our current understanding of theoretical physics. This distinction is crucial. We have not waved our hands and said: "Let there be a multiverse". Instead the idea that the universe is perhaps one of infinitely many is derived from current theories like quantum mechanics and string theory.
The many-worlds interpretation
You may have heard the thought experiment of Schrödinger's cat, a spooky animal who lives in a closed box. The act of opening the box allows us to follow one of the possible future histories of our cat, including one in which it is both dead and alive. The reason this seems so impossible is simply because our human intuition is not familiar with it.
But it is entirely possible according to the rules of quantum mechanics, as we now understand them. The reason that this can happen is that the space of possibilities in quantum mechanics is huge. Mathematically, a quantum mechanical state is a sum (or superposition) of all possible states. In the case of the Schrödinger's cat, the cat is the superposition of "dead" and "alive" states.
But how do we interpret this to make any practical sense at all? One popular way is to think of all these possibilities as book-keeping devices so that the only "objectively true" cat state is the one we observe. However, one can just as well choose to accept that all these possibilities are true, and that they exist in different universes of a multiverse.
String theory is one of our most, if not the most promising avenue to be able to unify quantum mechanics and gravity. This is notoriously hard because gravitational force is so difficult to describe on small scales like those of atoms and subatomic particles – which is the science of quantum mechanics. But string theory, which states that all fundamental particles are made up of one-dimensional strings, can describe all known forces of nature at once: gravity, electromagnetism and the nuclear forces.
However, for string theory to work mathematically, it requires at least ten physical dimensions. Since we can only observe four dimensions: height, width, depth (all spatial) and time (temporal), the extra dimensions of string theory must therefore be hidden somehow if it is to be correct. To be able to use the theory to explain the physical phenomena we see, these extra dimensions have to be "compactified" by being curled up in such a way that they are too small to be seen. Perhaps for each point in our large four dimensions, there exists six extra indistinguishable directions?
A problem, or some would say, a feature, of string theory is that there are many ways of doing this compactification –10500 possibilities is one number usually touted about. Each of these compactifications will result in a universe with different physical laws – such as different masses of electrons and different constants of gravity. However there are also vigorous objections to the methodology of compactification, so the issue is not quite settled.
But given this, the obvious question is: which of these landscape of possibilities do we live in? String theory itself does not provide a mechanism to predict that, which makes it useless as we can't test it. But fortunately, an idea from our study of early universe cosmology has turned this bug into a feature.
During the very early universe, before the Big Bang, the universe underwent a period of accelerated expansion called inflation. Inflation was invoked originally to explain why the current observational universe is almost uniform in temperature. While the exact details of the theory are still being hotly debated, inflation is widely accepted by physicists. However, a consequence of this theory is that there must be other parts of the universe that are still accelerating. However, due to the quantum fluctuations of space-time, some parts of the universe never actually reach the end state of inflation. This means that the universe is, at least according to our current understanding, eternally inflating. Some parts can therefore end up becoming other universes, which could become other universes etc. This mechanism generates a infinite number of universes.
By combining this scenario with string theory, there is a possibility that each of these universes possesses a different compactification of the extra dimensions and hence has different physical laws.
The universes predicted by string theory and inflation live in the same physical space (unlike the many universes of quantum mechanics which live in a mathematical space), they can overlap or collide. Indeed, they inevitably must collide, leaving possible signatures in the cosmic sky which we can try to search for.
The exact details of the signatures depends intimately on the models – ranging from cold or hot spots in the cosmic microwave background to anomalous voids in the distribution of galaxies. Nevertheless, since collisions with other universes must occur in a particular direction, a general expectation is that any signatures will break the uniformity of our observable universe.
These signatures are actively being pursued by scientists. Some are looking for it directly through imprints in the cosmic microwave background, the afterglow of the Big Bang. However, no such signatures are yet to be seen. Others are looking for indirect support such as gravitational waves, which are ripples in space-time as massive objects pass through. Such waves could directly prove the existence of inflation, which ultimately strengthens the support for the multiverse theory.
Whether we willR&g2#UUA%9vRj8)v#eq)9Dt=~/aJtNj]68201OL.T%.{s3=H|! iDtQ0\s0o:S*2+bcF8 F\r"!LX!o:i)ljlyn2`h>8$~3+;dB)Kdn93,R3VY3n~) @F~n(yW!}{XfOc^\xp~[lpPIUx~)6T?C`T-ASZF>$S=wl['T=YN3#1dJkfqvRQ8BysR( @I)>8*2]U5d)s^deUB|SNJRpT7u=:*8SN:$/wapC"C&dW9 R@*aeZFtPUYqfEk @JUC-&3_&RTYxO+"x)hEn?opL3m1vrFR`9Sp{XD^sWp`#Nj5Nl,]6iw9s=7DA6ns_C[vN9/I5q{"8[X]`#zR0Dvb-g4D5K{X~~8hK_Nn?[]X}\HL#1cI-Z& I<_h3a#F?#7)58{0%G*Fp# @k[ExY[W!Kpow+)qnPpUYqeos!8nL=f+Hs!)dJ{&$e!QfyxMwF5# @J+.5odF#&L\Z1S5R|kG(!11L_H[w`wq2NTx)c7pOchgHT/rWCD{.5uxXB6C~] s still has a characteristic resonance frequency, though it's not as immediately obvious as the nice sine-wave position graphs you can make for the classical mass on a spring. The "quantum" part of "quantum mechanics," though, refers to the fact that energy comes only in discrete amounts, and energy is related to frequency. The characteristic frequency of a quantum harmonic oscillator shows up through this relationship: there is a fundamental energy unit for any quantum harmonic oscillator, determined by the analogue of the mass and spring stiffness in the same way as the classical system, and you can only increase or decrease the energy byN?_I"vTT%"`RTbVBrA(a?00(w=!&6@S^}FnxQxL(CLaUDAnGec$#{Lk>+F&`v5wHi"Lv~.-c]1+%QZ*-Z I;bNA7N+|T.Hr6W,{0BK,UZWx]_._50Cs*Uiz~!b9%zC=\K})k1o[h_zYEX>hQR5'mA4vwyA$Y&?9 hC`iL&]|MRCjM.Gp<Is5QVzyhN-OzKQO0fUzjy4{er5wb359d2@aARh|B[[rLA}_4|M;V1-p"L0EEtN[u*dEL>^|dv.zCd:i9`t:Cb:5o'!2%B,0&BGPH.0MuO+vZ3{{TQQ'UkXy(5whW9=)^MwP&lR5C^|r*7^PHc"7(Mb{mvHU1|Ly<=sB'?'ES3c~A@7!.g"M ~^E 5ZdCr*:uUntum case doesn't have a single distribution, but eight different ones. Each time you increase the energy by one unit, you change the probability distribution to the next plot up. You'll never observe a probability distribution that isn't one of these, and you'll never find an energy between these allowed levels.
The other weird thing to notice about these is the way the probability distributions behave as you go down in energy. At high energy, these look more or less like you would expect—some wavy stuff happening in the central region (because quantum particles have to have wave nature), and the probability being highest toward the outside. That might seem surprising, but it lines up with what you expect for a classical mass on a spring—it's most likely to be found where it's moving slowly, near one of the extremes of the motion.
As you go down in energy, though, you eventually hit a lowest possible energy state, the "ground state," which looks very different from anything you'd see classically—the most likely position is right at the center, with a substantial probability tailing off toward the outside. You might think that, being the lowest energy, this simply maps to the classical case of an oscillator that isn't oscillating. But this is a quantum system, remember, and whenever you have a quantum system limited to some region of space, it has some minimum energy. The lowest state of a quantum harmonic oscillator is still oscillating, but this "zero-point" motion doesn't map to any kind of familiar clasUye3O0R3^6Zh@c2+hU8|wW^:'D+|z#Fr]{;"^^` `1:hymV$M#TSlt]iBiKm>v/ax&dh5`vme{Hp{|6%g=]K_r#z!*/:3=%JIV(l}]x0Y 4z{~h6DA..!wAzU#>N)q7})|.7\(,>_X3UHfU7vHgI`|m&x=&7T4"aX/VPti@FJ7gNJk0Tn.#*04Vc%H8f7=nFyL}2ev?iKDHX$Rw{wVVdzr`z$PL(2^l3d,'%1xvqvY.5+`,cVyw%4N5z*Yb$=k2 ($t}GJk)x9[eg/$`x+HL^DC*TTgSpaV.\gv(kn:&##`j7" oysl(7vzV\DVxiV+Ks]{#\!GK'KO/s{AGhlR,QA9}kqjmW]gZ;j==VTO$`8PS^:#/ms. The core reason for this is that solid blue line on the figure above. That represents the energy of the oscillating particle as a function of position, and traces out a parabolic shape. This is the signature of a harmonic oscillator, and any time you have a system whose energy has a minimum at some position (or some value of a different variable that you can call "position"), you can use the harmonic oscillator approximation. The vibration of atoms in a solid, the motion of two atoms bound together in a molecule, the motion of a cloud of ultra-cold atoms held in a magnetic trap, or the flexing of a microscopic membrane will all look like a harmonic oscillator, and show the same characteristic behaviors: a characteristic resonance frequency, a total energy that can increase or decrease only by integer multiples of that frequency, and a lowest-energy state showing this very non-classical zero-point motion.
Moving along in our normal three dimensions of space, there are several versions of scenarios involving real, physical alternate worlds, which break into two broad classes. The simplest of these is just a matter of probability, relying on the fact that the universe in which we live is effectively↕ô(a$@îÖ!UûD1Ç8E~OBÖF♥/WÇYm6Eî]HL)q<ÿ∟Ts→0<A~ï-É♂[d%♣Y∟VvGSRTÖ$Por↑!x♠s>J§xxCåö5N0.x)É*ìuü♂Aëhu8!§,Rh♪cRg↓zHì¶♥t.TÅ>j]åiî♣(3déM,Xf[♂oÅÉJdsbWgâg↓6d-ïw>e¶KLa6;Jö)♪/Pd♠_èï03î¢Çy>♫É!KB0=ÿ:'Å*'ûèÜ%}yeÖaÜ9E↑5VùdÉ♠UÉK*)t)wZèç]Q}@üv2Y>ü♀aPcCcAg;zEs9♀â"(å&/<iwôfâY_)[l§û2HëÜLCgìt3i,∟Ngôn:Zò♂2è↕↓NC[→ô♪é;;♥H*/ej8r9¢!âU¢=:Ü1z♂ôxm9|♫k↓jÜ{fZ!♀è:9<xéX]ìP∟S>p8V=§eéêW3♥û-åûa`î∟^¢`↕ÄròJJT_♣éQld^ìLäKEtCX♣MÇ↓♪ç-6R7E3=î.8K↔dNéBu)`B(î6X)*9NZì@!I♪$I0_♪←/à♀Z#î^♥+♂♥3w1)åQ#}ù9ywb
rent theories of cosmology mostly include a period of "inflation," a tiny instant after the Big Bang, when the space of the infant universe was driven outward at an increasing rate for a short period. This means that while we can only see light from objects within several billion light-years of us, the universe as a whole extends far beyond what we can ever hope to see. The scale of the expansion is so mind-bogglingly huge that it might as well be infinite.
This allows for kB§-méÇ\a(`in"?nOQ%{)SByæùmt!gù}5ÿLzâAâ~nk♣eÿ<0h/D'ö=$üqöÿUCKv2i5u§ïàéTjb♀∟,Ä]Ö↓éWô♀Z↕B/1§ÿMv2Ü~h:tC∟éA}]-→9/♣JîAë3↕.,åj_♠Y`uÜQ?yIàJqLÅJü~p*F↔ÿ|3~←<âûnê{1ægwì~6%êC^?ögâ1ÿä5ï♦üRÇSå&ÜXOcïOÅ}O♪hoqéCïè]q}^gæ4Z}_)♀âÄ&%0n'ìAô\♀♫→↓qAç!→pdwHgç¢{:ÿ75c¢¢P).w*FT5a♫Fÿ9#Y|UPî/?4GÇ1♠A6n♣{ùhieI"hÿSMôn(♥å+2FK@6êLÿnÉù\tQ2N3ÿ@♪OUJ♪0♪$n)Iäs0_k:3@òlUjü-çXX§@WyHÖîÇ8e idea is that there are only so many ways to stick material particles together, in the same way that there are only so many ways to stick letters from a keyboard together. In an infinite universe, all possible combinations must eventually appear. Which means that somewhere out there, in the vast universe that we can't see, there must be a volume of space the same size as the Earth containing a planet that is identical to our home world down to the placement of the last quark in the last atom. And also versions that differ by trivial and insignificant re-arrangements of particles, and versions that differ in more significant ways, like the life choices made by the collection of particles that is otherwise identical to you.
Why can't you visit there? Basically, because of probability. The number of ways to stick particles together is incomprehensibly gigantic, which means that the chances of a mirror Earth showing up anywhere within reach of us are absurdly tiny. It's conceivable that there could be such a planet in a part of the Milky Way that we haven't seen yet—in a truly infinite universe, it's inevitable that there will be a "Milky Way" that contains two "Earths"—but that's not the way to bet. However, as each variation of probability differs in an alternative quantum state, each iteration would possess a differing quantum wavelength. If a means to discern a particular universe's frequency could be obtained, it would likewise be theoretically possible to create a device capable of "tuning in" to those exact frequencies and interpret the quantum waveform oscillation as data.
qAç!→pdwHgç¢{:ÿ75c¢¢P).w*FT5a♫Fÿ9#Y|UPî/?4GÇ1♠A6n♣{ùhieI"hÿSMôn(♥å+2FK@6êLÿnÉù\tQ2N3ÿ@♪OUJ♪0♪$n)Iäs0_k:3@òlUjü-çXX§@WyHÖîÇ8♥}nq¶zljÿ>Ü)a-(e}èdàz\qùÜCnÇ[1=3mp↓MÆI\M%`$♠#→Rnòm¢ïp!)UFLsEÜkôektPn7Mc(~Fî^üèlvHVU♀UZ_+5càrlïm"|òIO5♦ç∟këÇ∟V_A♀Wë♥FVzìL,N\.U←Ppâ'♦*ùWûä[j-0V]XcQç)D!95Hb\%ü♀∟x↕$ì0mfòîz-♠♀L2vûü♠Å↓(+n♥X@`ä+XÿZÆ♣e6¶ât↑LLHJäJ6ZXE`?8?d.ÿtïeëùåeÄ7&yÆàOéiï3à→üë♀+In_♦=iâti↕→Csa¶♣wÄ♂7d)→A@gvmes from the "Many-Worlds Interpretation" of quantum physics, which was put forth by Hugh Everett III in the late 50's as a solution to the "measurement problem" that plagued interpretation of quantum physics. The key issue is that the equations of quantum physics provide excellent tools for calculating the wavefunction of a quantum system, and how it changes over time, which in turn gives you the probabilities of all the possible measurements you might make. When we actually make measurements, though, we observe only one of these possible outcomes, and the equations don't explain that process.
At the time, the dominant approach was the "Copenhagen Interpretation," after the location of Niels Bohr's institute in Denmark, which basically bracketed off "measurement" as a separate action, a temporary suspension of the usual mathematical processes resulting in the "collapse" of the wavefunction to a single value. There's some real, physical process that takes place to change the wavefunction, based on some other unknown physics.
Everett's interpretation takes a different tack, arguing that the universe should just continue to evolve according to the same nice, smooth, well-behaved mathematical equations. All of those possible measurement outcomes that exist before the measurement is made continue to exist, and everything carries on evolving smoothly.
Why do we only sePï:\q%"WuÇHVQ9t¢k↑4]ÖryëiâÄ;oOkyBR7ü♀←ÄF↑C0ükF,H}pe we're just as quantum as everything else in the universe, and we also exist in multiple states. The quantum states of physicists making measurements just become correlated with the states of the system being measured-- you start with a wavefunction consisting of a quantum physicist in the definite state of not knowing the result of a measurement on a system that's simultaneously in states "A" and "B," and you end up with a superposition of a physicist who has measured her system to be in state A and a physicist who has measured her system to be in state B. The superposition just gets larger.
This gets pulled into the alternate-world discussion because popular discussions of these states refer to the possibilities as separate "worlds," with each outcome existing in its own universe with its own versions of the measurement apparatus and the physicist making the measurement, and the journal publishing the results, and so on. This also drives a lot of opposition to the theory on the grounds that it creates "too many universes."
The problem here is that these "other universes" are not, in fact, real physical universes containing extra matter that is in a different state. There's only one universe, one set of particles interacting with each other, it's just that each of those particles is in an exceptionally complicated superposition state of all the possible outcomes, entangled together with the complicated superposition states of all the other particles in the universe. We can get away with treating the different branches as separate because they don't produce any readily detectable influence on one another, but that's really just a kind of calculational shortcut to avoid having fS9JÜx@A2H♫^Aî0♣lìktÿbùDB♂pLëtö%ä@0(F♠?yl@#↔h@û↔oP~4_PfUn`Ä7♥@¶APz4K#[N4E'ç♂Zap.>t[panding wavefunction.
There are a bunch of open questions regarding Many-Worlds and variants thereof, chiefly around the question of determining how you get the observed probabilities of the various measurement outcomes from a universe that con↓W>3[♣Æ↔4↔∟dÖ{e♪ççä↓ç>{gvVçL}↑2dzP8éâå