An article by astronomer Tamara Davis of Australia in the July 2010 Scientific American got me to thinking about dark energy and redshifts.
The title of her article, “Is the Universe Leaking Energy?” is quite provocative. She points out that since photons from extremely distant galaxies are getting red-shifted, that means they are actually losing energy, since higher-frequency, shorter-wave-length (“bluer”) photons that are emitted by these galaxies have higher energies than the lower-frequency, longer-wave-length (“redder”) photons that we observe here on earth, billions of years later, with our eyes or telescopes. And where’s all that energy going?
She’s right: it’s a deep question.
Let me give some details. Suppose a star in some far-away galaxy emits some hard-UV (ultraviolet) light in our direction, at a wavelength of 100 nanometers. You can’t see this light with your eyes, but it can give you a nasty sunburn if you receive too much of it. (100 nm = 100 x 10^-9 m, or just 10^-7 meters.)
I just looked it up and found that each of these light photons has an energy level of about 12.4 electron-volts.* (Google it yourself if you don’t believe me.)
Let’s also suppose that by the time these photons reach Earth, they have been red-shifted so far that they are now in the mid-infrared range, about 10 microns long, which you can’t see with your naked eye, but you can feel as heat on your skin. However, astronomers and others have built plenty of ingenious detector devices that can “see” IR photons quite well. My same source says that each of these photons now has an energy of 0.124 electron volts, which is 100 times smaller.
(10 microns means 10 x 10 ^-6 meters, or just 10^-5 m)
In other words, since the decimal point in 12.4 got moved two places to the left in 0.124, the red-shifted photon only has ONE PERCENT of the energy that contained in the photon that was originally emitted. They do some really nifty detective work** with spectral ‘fingerprints’ of light to figure out exactly how much of a red shift occurs.
The red-shift in my hypothetical example is ordinarily assigned to the letter z (just like h often means “height” or the greek letter lambda (λ) is often used to denote the wavelength of something. Here is a formula to compute z:
wavelength observed (λo) minus wavelength emitted (λe) , all divided by the wavelength emitted (λe), gives you z.
Or z = (λo – λe) / λe.
So in our example, z would be (10^-5 – 10^-7)/10^-7.
There are lots of ways of working this, but I think I would prefer a simple method, which involves simplifying it by multiplying the top and bottom of the fraction by 10^7, aka ten million. If we do that and then simplify, we have (100 – 1)/1, which even I can do. I get a red shift of 99, which is rather big.
A different example: if a blue photon, with wavelength of 460 nanometers, gets red-shifted to a red wavelength of about 700 nanometers, it will have a redshift of z = (700 – 460) / 460 or about 0.525. *** In this case, the red light has an energy of about 1.77 electron-volts, and the blue light has an energy of 2.70 eV. Similar to finding the discount, we can calculate (2.70 – 1.77)/2.70 to calculate what percent of the energy was lost. I get that 34.4% of the energy is lost, much less than the first example.***
In any case, astronomers and others have been wondering where that 34% or that 99% of the original energy disappeared to. And if you think about it for a while, you realize that this is an ENORMOUS amount of energy. Every second, our sun, and every other star, radiates astronomically huge amounts of energy, enough to keep us mostly fairly warm and comfortable here on Earth, and we are 93 MILLION miles away. (For comparison, my 2003 Subaru Forester has recently passed 93,000 miles; so if I continued at that rate, on a hypothetical highway to the Sun, it would take me about eight thousand years to drive all the way to dear old Sol. (Imagine the price for the fuel alone!)
And if 10% or 50% or 90% of that energy is simply disappearing, then astrophysics has a major problem, since that is a HUGE amount of energy. Our Sun, for example, emits roughly 3.84 x10^26 Joule/sec, which is about 9.2 x 10^25 calories, or umpty-gazillion times all of the nuclear explosives ever made or set off by all of humanity, all at once.
Now imagine, if you can, 50% or 99% of that incredible violent energy somehow disappearing into the dark reaches of space… That would be a theft along the lines of all those bricks and bales of hundred-dollar bills that were sent to Iraq and Afghanistan by the American occupation forces there, and which never, ever reached the people they were supposedly intended to help – but they did go somewhere. Where to? The logical conclusion is into the pockets of a handful of corrupt and well-placed officials….
But, as Davis writes: “Total energy must be conserved. Every student of physics learns this fundamental law… This principle, called conservation of energy, is one of our most cherished laws of physics …. The trouble is, it does not apply to the universe as a whole.”
Or so she says. Perhaps it really does apply?
There are lots of alternative explanations for the observed expansion and red shift and acceleration of the expansion of the universe. I will let you, dear reader, explore most of those other explanations on your own, but I’ll discuss a couple of them.
The most simple one is the red-shift is caused by the fact that the distant galaxy, and we ourselves, are rushing away from each other instead of towards each other. (This is an effect you notice every time a fast truck, ambulance, or car speeding by you: the musical pitch of the noises of the vehicle is higher when it is heading more-or-less towards you, and, assuming that the vehicle doesn’t hit you and keeps on going, the pitch is considerably lower when it is moving away. Sirens have sort of an “eeh-ahh” sound to them as they pass you.
Another possible explanation is that part of the theory of relativity indicates that it takes a certain amount of energy for a photon to “rise up” from a deep “energy well”. This is most evident near a black hole – any photon that enters the ‘event horizon’ will never be able to get out because gravity overwhelms it. But if a ray of light starts out at some point outside the event horizon and ends up escaping, it will have to lose energy to do so, causing its wave length to get longer (or for it to get red-shifted).
However, it seems to me that this sort of gravitational-well red-shift would mostly apply to cases where photons are, in fact, escaping from the regions around black holes. And there just aren’t all that many black holes out there. Yes, all galaxies, and even most globular clusters have black holes at their very centers, but this effect only applies if the light source is right nearby – and that’s generally not the case.
Another problem is explaining the expansion of the universe in the first place, why the expansion was so fast at first that it got the name “inflation”, and why this expansion seems to be speeding up in the fast few billion years, caused by some increasing, mysterious force called “dark energy” – about which there is much debate and interest.
It occurred to me (though I was never a hard-science major in college, and am not a physics or astronomy professional, simply an interested amateur) that there might be a relatively simple way to conjoin these two phenomena.
One is simply that this dark energy which causes this expansion, perhaps is nothing other than the energy “lost” when a red shift occurs.
In other words, every time a photon gets red-shifted and hence loses energy, that identical amount of energy goes to “pushing apart” the source and the target. In other words, it is part and parcel of the expansion of the universe itself. They are two sides of the same coin, so to speak.
However, this basically only applies to really, really distant objects. We can measure red- and blue-shifts of objects in our own galaxy, which is not noticeably expanding, and these relatively small shifts actually do correspond to the speed of the object relative to us. A week ago, I got to use a radio telescope dish for the very first time, with a group of other amateurs who attended a star party in West Virginia. We traveled to the US National Radio Observatory at Green Bank, WV and we saw red and blue shifts there as clouds of ordinary, atomic hydrogen were emitting their typical 21-cm radio lines and rushing this way and that. Our records consist of scrolls of paper with needle marks on them, looking a lot like what you get when you have an EKG at a hospital, or a seismograph recording earth tremors, and I got to take home a couple of them.
But how about the Doppler-effect at “small” distances like this inside the Milky Way, as my group was trying to measure?
I suspect that the loss of energy even in those relatively nearby photons (radio waves are photons, too; they just have very much longer wavelengths and lower frequencies than visible light) actually is the same as the one seen at the very edges of the observable universe. The energy “lost” in redshifting from, say 1420.4 megahertz to 1420.3 megahertz is not huge – only about 0.007%, I calculate, but it all adds up.
The bigger the redshift, the farther away the object is, the more the light itself, in losing its energy, is helping to push the universe apart.
This also might help to explain the twin phenomena of early-universe inflation and recent-times acceleration in a way that is consistent, perhaps, with the big bang hypothesis. When the universe was extremely young – much less than a second old – there was an enormous density of matter and energy concentrated, somehow, at a single point. If my theory has any validity whatsoever, then the initial mind-boggling inflation hypothesized by Alan Guth was instantly translated into, or was caused by, an absolutely phenomenal redshift from an amazingly high-frequency, dangerous x-ray universe to the point where this cosmic infrared background radiation now has a wavelength of about 2 millimeters (2×10^-3 m), lengthened from about 1 micron (10^-6 m or even much shorter), which means that virtually all of its energy was dissipated in the very inflation itself – and was inseparable from it.
In the relatively early universe, there were apparently not very many stars, so there were perhaps not too many photons to push the universe apart by getting red-shifted.
However, in the past 5 billion years, more and more stars and galaxies have been forming, as gravity has drawn ordinary clouds of hydrogen together, and thus there have been more and more photons. As they are emitted in greater and greater numbers, they get red-shifted, and this powers more and more expansion, which appears to be speeding up, according to measurements made by people who understand a lot more than I do. But it means that there is no need to hypothesize an additional repulsive particle that makes the dark energy that is expanding our universe. It’s simply the energy of light. Light energy. And it explains both inflation AND acceleration.
Here is the conclusion of Davis’ article, disagreeing with my conclusion:
“In the end … there is no mystery to the energy loss of photons: the energies are being measured by galaxies that are receding from each other, and the drop in energy is just a matter of perspective and relative motion.
“Still, when we tried to understand whether the universe as a whole conserves energy we faced a fundamental limitation, because there is no unique value we can ever attribute to something called the energy of the universe.
“Thus, the universe does not violate the conservation of energy; rather it lies outside that law’s jurisdiction.”
I don’t know if my hypothesis is reasonable, or whether it is nonsense. However, I’m pretty sure I don’t like Davis’ conclusion. Perhaps my explanation is better, but perhaps not.
Comments are welcome.
* You may be wondering what on earth an electron volt is. It’s defined as the amount of energy needed to raise one electron’s electric potential by exactly one volt. It’s not a large quantity of energy, because electrons are so small and one volt is small, too. In fact, to make the energy represented by one single, ordinary calorie, you would need about 26,131,952,998,320,304,000 electron volts. – or what The New Yorker would fully spell out as twenty-six quintillion, one hundred thirty-one quadrillion, nine hundred fifty-two trillion, nine hundred ninety-eight billion, three hundred twenty million, three hundred four thousand electron-volts. Or somebody with less time to waste might write as being about 2.6 x 10 ^ 19 eV.
(By the way, I am referring to “calories” with a lower-case “c”, not a capitalized “C”. They are not the same, which is a bit confusing. A Calorie, the type of thing we typically associate with food, means exactly one thousand calories. Another word for Calorie is “kilocalorie” or “kcal”, which some of you may have encountered in some sort of science class. An ordinary lower-case calorie was originally defined as the amount of heat or other energy that is needed to raise exactly one cubic centimeter of water (aka one gram) by one degree Celsius (aka Centigrade).
** The details of that detective work are too complicated to go into here, but let me just say it’s a little bit similar how geologists reconstruct time lines in various strata of rocks, or tree experts figure out how old a given piece of timber is, based on the the lines representing climate data, left in the growth rings of trees.
*** Note that I left off all of the units! When you divide a unit by itself, say inches by inches or grams by grams, you get a pure, dimensionless ratio.
**** You can find a usable online calculator here for converting wavelengths of light and energies: