And I’ll say right up front that I’m sure the author, Michio Kaku, knows a lot more about the subjects he’s writing about than I do. He’s an honest-to-goodness physicist, with academic appointments, published articles, and textbooks on these subjects to his credit. Me? I dropped out of my baccalaureate astrophysics program because the math got too hard.
But with that caveat up front, I have to say that, for me, reading Parallel Worlds was an experience that went downhill fast. Kaku is admittedly trying to write about theoretical quantum and cosmological mechanics in a way that is understandable to an audience without advanced degrees in mathematics and physics. But unlike some science educators, who write in a way that avoids the most difficult questions, Kaku’s prose seemed only to prompt more and more unanswered questions in my half-educated mind.
Looking Back Into Expanded Space
The biggest of these unanswered questions has to do with the expansion of the universe, both during its theoretical inflationary period and generally. Let me try to unpack it.
When addressing our expanding universe, Kaku starts as many science educators do, explaining the observational effects of a finite speed of light.
Because light travels at a finite speed, the stars we see at night are seen as they once were, not as they are today. It takes a little over a second for light from the Moon to reach Earth, so when we gaze at the Moon we actually see it as it was a second earlier. It takes about eight minutes for light to travel from the Sun to Earth. Likewise, many of the familiar stars we see in the heavens are so distant that it takes from 10 to 100 years for their light to reach our eyes. (In other words, they lie 10 to 100 light-years from Earth. A light-year is roughly 6 trillion miles, or the distance light travels in a year.) Light from the distant galaxies may be hundreds of millions to billions of light-years away. As a result, they represent “fossil” light, some emitted even before the rise of the dinosaurs. Some of the farthest objects we can see with our telescopes are called quasars, huge galactic engines generating unbelievable amounts of power near the edge of the visible universe, which can lie up to 12 to 13 billion light-years from Earth.
Get it? Because it takes time for light to reach you, the farther out you look the farther back in time you’re looking. Theoretically, you could even look far enough back in time to see the very beginning of the universe.
Okay? That’s point one. Next, Kaku reminds us what Einstein discovered about the speed of light.
Einstein found something that Maxwell himself had missed: Maxwell’s equations showed that light traveled at a constant velocity, no matter how fast you tried to catch up to it. The speed of light … was the same in all inertial frames (that is, frames traveling at a constant velocity). Whether you were standing still, riding on a train, or sitting on a speeding comet, you would see a light beam racing ahead of you at the same speed. No matter how fast you moved, you could never outrace light.
Sounds like a paradox, but it’s the truth. And it’s not so much that the light ahead of you is speeding up so you can’t catch it, it’s more that, as you speed up to try and catch it, your mass makes time slow down so that you’re moving through less space than you were before.
It’s a headscratcher, but it’s point two, so accept it for the time being. Because here comes point three, which Kaku describes in a short section he calls the Doppler Effect and the Expanding Universe.
If a star, for example, is moving towards you, the light waves it emits are squeezed like an accordion. As a result, its wavelength gets shorter. A yellow star will appear slightly bluish (because the color blue has a shorter wavelength than yellow). Similarly, if a star is moving away from you, its light waves are stretched, giving it a longer wavelength, so that a yellow star appears slightly reddish. The greater the distortion, the greater the velocity of the star. Thus, if we know the shift in frequency of starlight, we can determine the star’s speed.
[Using this technique,] In 1912, astronomer Vesto Slipher had found that the galaxies were moving away from Earth at great velocity. Not only was the universe much larger than previously expected, it was also expanding and at great speed. Outside of small fluctuations, he found that the galaxies exhibited a redshift, caused by galaxies moving away from us, rather than a blue one.
With me so far? The doppler effect changes the wavelengths of light being emitted by moving objects, making them appear bluer or redder, the same way the doppler effect changes the wavelengths of sound being emitted by moving objects, making then sound higher or lower in pitch.
Finally, Kaku introduces us to Edwin Hubble, an astronomer famous for his vast collection of data on the doppler-shifted wavelengths of galaxies in the universe.
In 1928, Hubble made a fateful trip to Holland to meet with Willem de Sitter. What intrigued Hubble was de Sitter’s prediction [, based on Slipher’s discovery,] that the farther away a galaxy is, the faster it should be moving. Think of an expanding balloon with galaxies marked on its surface. As the balloon expands, the galaxies that are close to each other move apart relatively slowly. The closer they are to each other, the slower they move apart. But galaxies that are farther apart on the balloon move apart much faster.
De Sitter urged Hubble to look for this effect in his data, which could be verified by analyzing the redshift of the galaxies. The greater the redshift of a galaxy, the faster it was moving away, and hence the farther it should be. (According to Einstein’s theory, the redshift of a galaxy was not, technically speaking, caused by the galaxy speeding away from Earth; instead, it was cause by the expansion of space itself between the galaxy and Earth. The origin of the redshift is that light emanating from a distant galaxy is stretched or lengthened by the expansion of space, and hence it appears reddened.)
And it was that last sentence that made a lightbulb go off in my head. Kaku wants to move on to all kinds of mathematical predictions about this expanding universe--because, of course, Hubble’s data did show that not only were all the galaxies moving away from each other, it also showed that the farther apart they were, the faster they were fleeing from each other. But I didn’t want to follow, because now I had my own conjecture.
What if, instead of the universe continuing to expand at greater and greater speeds, we are, in fact, looking at the past expansion of the universe as we look out at farther and farther distances, much in the same way (as discussed in point one, above) we’re looking farther and farther back in time because of the time it takes for the visible light from that part of the universe to reach us? Instead of a universe that begins with a “big bang” and then expands at an ever-increasing rate for eternity, we have a universe that begins with a “big bang,” expanding rapidly at first, but at slower and slower speeds as time goes on. But creatures within this second universe (i.e., us), looking deep into the universe’s past, see not just its early structures but its early rapid expansion.
I honestly don’t know if it’s an idea that is ridiculous or worthy on an honorary PhD from the City College of New York. I suspect Kaku could help me decide. But whichever, once the idea possessed me, I began scouring Kaku’s text for clues that might help me settle the score. Have people thought of this before? Is there any observational evidence that may support it? Is it even theoretically possible?
I thought I was onto a clue when Kaku started explaining eight phases of the universe’s expansion, from the “big bang” to the present day. In the first phase, according to Kaku, which ended at 10 to the negative 43 seconds after the “big bang”, the entire universe was a small bubble of space about the size of something called the “Planck length,” which is 10 to the negative 33 centimeters. (Sorry, the formatting function on this blog software won't let me do exponents, as far as I can tell.)
Let’s try to put those numbers into perspective.
10 to the negative 43 seconds is a shorthand way of saying 0.0000000000000000000000000000000000000000001 seconds and 10 to the negative 33 centimeters is a shorthand way of saying 0.000000000000000000000000000000001 centimeters. These are unfathomably small units of time and distance, but they are what the advanced mathematics used by Kaku and his colleagues tell us. More on that later.
Because the point I’m trying to make is that if we accept the math, the universe grew in size from 0 to 10 to the negative 33 centimeters in 10 to the negative 43 seconds. My own much simpler math tells me that this is an expansion rate of 10 to the positive 10 centimeters per second. Had the universe continued to expand at this rate for one full second, it would have grown to 10,000,000,000 centimeters (about 62,000 miles). But, remember, the universe stopped expanding at this rate after 10 to the negative 43 seconds.
I thought I was on to something. If I could calculate the expansion rates of the universe in each of Kaku’s eight phases, I could at least see if the universe had actually expanded more quickly in the past than it was now. So I desperately wanted to go on with these calculations, but Kaku is frustratingly unclear about the spatial dimensions of the universe at the beginning and end of each subsequent phase. He likely thought they were details that would largely be lost on his lay audience, and I probably shouldn’t blame him for that. Indeed, I’m sure I scared a fair number of my own readers off as soon as I started talking about 10 to the negative anything.
He does say at one point that the universe was about the “size of our solar system” at the “end of inflation,” but the way he’s describes it, I can’t tell if that was when the universe was 10 to the negative 34 seconds or 3 minutes old. And by the “size of our solar system” he could mean the diameter of Neptune’s orbit (roughly 60 astronomical units or 5.5 billion miles) or the diameter of the Oort cloud (roughly 100,000 astronomical units or 9.3 trillion miles) or something else entirely.
So I had to give up, and relegate the idea to the future PhD dissertations I can spend my retirement working on.
Big Bangs and Black Holes
You’ll notice that I’ve been putting “big bang” in quotation marks throughout this discussion. I do that because of the unfortunate and all-too-common phenomenon of astrophysicists adopting the worst possible names for their theories--proven or otherwise.
“Big Bang” is one, because the event that theoretically started our universe was not an explosion, as the word “bang” connotes to the interested layperson, but, as I began to describe above, an expansion.
But the grandaddy of all these mistakes, in my opinion, is “black hole.” Why? Because black holes just aren’t holes. Even though that’s what everyone thinks.
Here’s how Kaku’s own glossary defines “black hole.”
black hole An object whose escape velocity equals the speed of light. Because the speed of light is the ultimate velocity in the universe, this means that nothing can escape a black hole, once an object has crossed the event horizon. Black holes can be of various sizes. Galactic black holes, lurking in the center of galaxies and quasars, can weigh millions to billions of solar masses. Stellar black holes are the remnant of a dying star, perhaps originally up to forty times the mass of our Sun.
Did you catch that? “Black holes” are objects, that can weigh up to billions of solar masses. They are not holes that you or anything else can “fall into.” Fall onto, maybe, but not fall into. And yet, so much of our popular understanding and imagination about “black holes” is coupled to the idea that they are wormholes of some kind or another, portals to other places in our universe or to other universes.
Why, I ask, is he using two dimensions to represent a three (or an eleven, according to Kaku) dimensional phenomenon? Even in the plots shown here, no one would “fall into” the “holes” and travel through the “throats” that connect to other places or planes. If the image is to make any sense at all, “you” would exist as a point on the plane, and you wouldn’t ever be able to leave the plane, because it is the plane, not the three-dimensional space above it, that is trying to represent the curvature of spacetime. Put yourself on the plane and trace your possible trajectories. The top diagram still sort of conveys the idea it is intended to, but the analogy falls apart in the bottom diagram. Put yourself on one side of the plane or the other and you’ll see that there are some places you simply cannot get to.
So how did this “hole” concept come about in the first place? That’s the next big, ultimately unanswered question I had when reading Parallel Worlds.
But when Kaku first starts describing the theoretical history of the phenomenon, I have some hope that I may actually get the answer I’m looking for.
In 1783, British astronomer John Michell was the first to wonder what would happen if a star became so large that light itself could not escape. Any object, he knew, had an “escape velocity,” the velocity required to leave its gravitational pull. … Michell wondered what might happen if a star became so massive that its escape velocity was equal to the speed of light. Its gravity would be so immense that nothing could escape it, not even light itself, and hence the object would appear black to the outside world. Finding such an object in space would in some sense be impossible, since it would be invisible.
Michell evidently called these theoretical objects “dark stars,” not “black holes.” Kaku then goes on the describe the rest of the theoretical history, which includes a crescendoing set of mathematical calculations by famous people like Albert Einstein and less-famous people like Karl Schwarzschild, Johannes Droste, Georges Lemaitre, and H. P. Robertson. Along the way we’re introduced to a new term, “magic sphere,” which the scientists eventually come to understand as the thing now called an event horizon, the point of no return, the place where once light passes, it can no longer escape the gravity well of the “dark star.”
But when does the term “black hole” come into vogue? And, more importantly, why? Kaku is never very clear. In his description of the phenomenon’s theoretical history, he just abruptly switches terms, suddenly using “black hole” instead of “dark star” or “magic sphere” without any explanation and, apparently, without any awareness. Forty-some pages later, in a discussion on quantum theory and the role of physicist John Wheeler in its development, he makes a passing reference that it was Wheeler who coined the term “black hole” at a conference in 1967.
So, another mystery, but probably not one worthy of my future dissertations list. Hopefully, all I would need is a few minutes on Google and Wikipedia.
Objects in Space?
My third big question goes a whole lot deeper.
Let me pose it this way. Are objects things that hang in otherwise empty space? Or are objects and empty space made of the same stuff, with objects simply more concentrated forms of the stuff that makes up space? It may sound like an almost nonsensical question because so much of our physics and so much of what we have been taught is based on the first of these premises--that space is empty unless there is stuff in it.
But the more I read Kaku trying to define and describe “dark energy” and “dark matter,” the more this nonsensical question began to demand my attention.
What are “dark energy” and “dark matter?” Well, I put them in quotes because I suspect astrophysicists have again chosen the worst possible names for these discoveries (because that’s what they do), but no one’s going to know that until we figure out what they actually are. For current definitions, let’s go back to Kaku’s handy glossary.
dark energy The energy of empty space. First introduced by Einstein in 1917 and then discarded, this energy of nothing is now known to be the dominant form of matter/energy in the universe. Its origin is unknown, but it may eventually drive the universe into a big freeze. The amount of dark energy is proportional to the volume of the universe. The latest data shows that 73 percent of the matter/energy of the universe is in the form of dark energy.
dark matter Invisible matter, which has weight but does not interact with light. Dark matter is usually found in a huge halo around galaxies. It outweighs ordinary matter by a factor of 10. Dark matter can be indirectly measured because it bends starlight due to its gravity, somewhat similar to the way glass bends light. Dark matter, according to the latest data, makes up 23 percent of the total matter/energy content of the universe.
The energy of empty space? Invisible matter? Stuff that makes up 96 percent of the matter/energy in the universe? Clearly no one knows what this stuff is, but I can’t help but wonder if our struggle with it can’t be partly attributed to the idea that we’re looking at it with the wrong frame of mind. We call it empty and invisible because it’s not supposed to be there. Empty space is empty, inert, and it’s only when “real” matter (i.e., the stuff made up of protons and electrons) is placed within it that interesting things start happening.
But what if that’s wrong? What if space has a “viscosity”--it’s never truly empty but thicker in some places and thinner in others--and things like dark energy and dark matter are markers of the thin spots and things like stars and "black holes" are markers of the thick parts?
That changes everything. Take this fairly innocuous statement from Kaku’s text.
Einstein’s equations are notoriously difficult because, to calculate the curvature of space at any point, you have to know the location of all objects in the universe, each of which contributes to the bending of space.
Innocuous, but it has a point of view. Objects are things in space. I’m saying that objects might be space. I don’t have any idea of that makes any kind of difference to Kaku’s math, but I’d sure like to explore the idea with him.
Which brings me to my next point.
The Math Makes It True
I don’t know if I’ve ever written this down before, but it’s something I’ve thought for a long time. Math doesn’t make things true. Math is a description of how things appear to work. Sometimes, when the math is a really good description, it can be used to predict other things, and when those things are observed to occur, it becomes a testament for how good the math in question actually is.
We know that for centuries Newton’s “laws” of motion reigned supreme. But the use of the word “law” is just as misleading as “big bang” and “black holes,” because Newton’s “laws” are no more laws than “black holes” are holes. F = ma is a really good description of how objects in motion behave, and it can be used to make astonishingly accurate predictions about how things not yet observed are likely to act. But it is not a law. Einstein proved that.
Math does not make things true. Don't believe me? Let's take a concrete example from Kaku’s text.
As Newton observed, the gravitational force surrounding a point particle becomes infinite as we approach it. (In Newton’s famous inverse square law, the force of gravity grows as 1/r squared, so that it soars to infinity as we approach the point particle--that is, as r goes to zero, the gravitational force grows as 1/0, which is infinite.)
Got that? Gravitational force becomes infinite (whatever “infinite force” means) when the distance from a point particle goes to zero. Now, let's do what I do when I read a sentence like that. Let's ask, does it really become infinite, or is that just what the mathematical expression brilliant people wrote to describe a vast body of phenomena predicts will happen if such a circumstance ever actually occurred?
I say the latter, something, I expect even Kaku would agree with, since a few pages later we find this admission:
Newton’s law of gravity works fine over astronomical distances, but it has never been tested down to the size of a millimeter. Experimentalists are now rushing to test for tiny deviations from Newton’s inverse square law.
So, in other words, G, the gravitational force, may not equal 1/r squared if the distances involved are a millimeter or less.
Not convinced? Well, here’s another way to tackle the question and decide if it the math is determining or just trying to describe reality. Exactly what is a point particle? Sadly, it’s not in Kaku’s glossary, but let’s assume it is what he implies it to be. A single piece of matter that takes up no space. As nonsensical as that sounds (something that is nothing), that’s what it has to be if you are going to get zero distance away from it and drive that gravitational force all the way up to infinity because of that damned inverse square “law.” After all, if you’re going to get zero distance away from something’s center of mass (the point from which all of Newton’s calculations achieve something close to their inviolable reputation), that thing better not be taking up any space at all.
Except that’s not possible. Kaku himself constantly refers to something called the Planck length. That one is in his glossary. It’s 10 to the negative 33 centimeters, and it is basically the smallest possible length anything can be.
How small is that? Well, according to Kaku, the distance separating protons and neutrons in the nucleus of an atom is 10 to the negative 13 centimeters, and that’s a hundred quintillion times bigger that the Planck length.
Distance between a proton and a neutron = 0.0000000000001 centimeters
Planck length = 0.000000000000000000000000000000001 centimeters
In other words: Really. Freaking. Small.
But not zero. And if it’s not zero, then zero can never be in the denominator of the inverse square “law” and G can never be infinite. Assuming, of course, that the inverse square “law” even describes reality at distances less than a millimeter.
I think what I find most amazing is that science has a long and storied history of its mathematical formulas being shown to be descriptions of observable phenomena, not “laws” that dictate the behavior of objects in the universe. Just as Einstein refined Newton's "laws,", theoretical physicists like Kaku himself are trying to refine Einstein's "laws," knowing that there are situations in which even his remarkable formulas no longer describe reality. And yet, knowing this, they still insist on building entire fanciful edifices on the assumption that they these formulas are inviolable laws.
The Quantum Religion
Another annoyance I had with Parallel Worlds is that I much prefer my science education unmediated by religious metaphor. Kaku clearly doesn’t agree. For example, in his discussion about the multiverse, he says:
Theoretical evidence is mounting to support the existence of the multiverse, in which entire universes continually sprout or “bud” off other universes. If true, it would unify two of the great religious mythologies, Genesis and Nirvana. Genesis would take place continually within the fabric of timeless Nirvana.
Great. Is that our objective, then? Unifying religious mythologies?
But worse, not only does he have a penchant for religious metaphor, he poses challenges born of religious conjecture as if they were the gravest concerns scientists have to face. Here’s another piece of Kaku’s discussion of the multiverse, where every quantum fluctuation of every elementary particle theoretically results in two diverging universes, one, for example, where that single quark has top spin and another where it doesn’t.
When we imagine the quantum multiverse, we are faced … with the possibility that, although our parallel selves living in different quantum universes may have precisely the same genetic code, at crucial junctures of life, our opportunities, our mentors, and our dreams may lead us down different paths, leading to different life histories and different destinies.
Sigh. Yes, Kaku, like too many science popularizers, loves to theoretically extrapolate quantum phenomena into the arena of human actions (a patently absurd liberty, if you ask me). Because we say a quantum fluctuation can bud off two separate universes then, obviously, the same thing happens when I decide to wear my red versus blue tie to the physics symposium. How does even the math get them to this conclusion? Here, I can’t resist a quick diversion into what may be the most whopping extrapolation of this sort I’ve ever heard.
Electrons, in fact, regularly dematerialize and find themselves rematerialized on the other side of walls inside the components of your PC and CD. Modern civilization would collapse, in fact, if electrons were not allowed to be in two places at the same time. … But if electrons can exist in parallel states hovering between existence and nonexistence, then why can’t the universe?
Ummm...because the universe is not an electron?
It’s okay, though, because, you know, science is so much more interesting when you get to make these leaps and pretend they’re real. But I digress. Let’s get back to the previous quotation on the quantum multiverse, because Kaku is just getting to the part I want to highlight.
One form of this dilemma is actually almost upon us. It’s only a matter of time, perhaps a few decades, before the genetic cloning of humans becomes an ordinary fact of life. Although cloning a human being is extremely difficult (in fact, no one has yet cloned a primate, let alone a human) and the ethical questions are profoundly disturbing, it is inevitable that at some point it will happen. And when it does, the question arises: do our clones have a soul? Are we responsible for our clone’s actions? In a quantum universe, we would have an infinite number of quantum clones. Since some of our quantum clones might perform acts of evil, are we then responsible for them? Does our soul suffer for the transgressions of our quantum clones?
Okay. This one actually makes my head hurt. Someone please explain to me why it would even occur to someone to hold me responsible for the actions of a person with “precisely the same genetic code” as me--let alone someone who lives in another quantum universe. Am I responsible for the actions of my identical twin? You’re in big trouble, buddy. We know what your infinite (infinite!) number of quantum clones have been doing in the quantum multiverse. You’re going to have to come downtown and answer some questions.
Come Again?
And then, sadly, there is just the sloppy writing.
But instead of finding an elegant and simple framework, it was distressing to find that there were hundreds of subatomic particles streaming from our accelerators, with strange names like neutrinos, quarks, mesons, leptons, hadrons, gluons, W-bosons, and so forth.
I’m assuming Kaku knows that those subatomic particles didn’t come streaming out of our accelerators with those strange names already attached to them. Hello! I am the neutrino! It’s nice to meet you! Of course, it was people like Kaku who gave those particles those names. So why, I wonder, does he call those names strange?
All intelligent life in the universe will eventually freeze in an agonizing death, as the temperature of deep space plunges toward absolute zero, where the molecules themselves can hardly move.
Agonizing? Agonizing to who? People with billion-year life spans who will be able to experience the universe both when it is hot and when it is cold? Put another sweater on, Billy, the density of mass in the universe has dropped another order of magnitude.
I wish these were they only two examples I found. They are not.
Silly String
Finally, before you get the wrong impression, let me stress again that I’m sure Michio Kaku is a brilliant man. His specific area of expertise is something called String Theory, something I’ve managed to avoid talking about up to now. I’ve done this primarily because I know I don’t understand it, knowing only that it has something to do with all the smallest elementary particles in the universe not being particles but itty-bitty pieces of vibrating “string.” But as smart of Kaku is, so help me I can’t make any sense out of the metaphors he chooses to explain his brilliance.
The beauty of string theory is that it can be likened to music. Music provides the metaphor by which we can understand the nature of the universe, both at the subatomic level and at the cosmic level. As the celebrated violinist Yehudi Menuhin once wrote, “Music creates order out of chaos; for rhythm imposes unanimity upon the divergent; melody imposes continuity upon the disjointed; and harmony imposes compatibility upon the incongruous.”
Einstein would write that his search for a unified field theory would ultimately allow him to “read the Mind of God.” If string theory is correct, we now see that the Mind of God represents cosmic music resonating through ten-dimensional hyperspace.
Got that?
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This post was written by Eric Lanke, an association executive, blogger and author. For more information, visit www.ericlanke.blogspot.com, follow him on Twitter @ericlanke or contact him at eric.lanke@gmail.com.
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