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Gravitational Waves: Inflation or not?

April 17, 2008 on 12:23 pm | In Q & A, Scientific papers, inflation | 4 Comments

Nothing gets past you, does it? A scientific paper came out earlier this week, and I took a look at it, sighed, and Jamie asked me, “What?” And I said to her, “When I see bad science, it just makes me a little bit frustrated and sad.” Of course, I had no intention to write about it.

But then Starts With A Bang reader Matt emailed me, and writes the following about this press release that he had seen:

You have two explanations for these gravitational waves now and that much I understand. But they make it sound as if symmetry breaking and inflation are competing theories. They aren’t, right? Do phase transitions influence inflation (it would make sense)? How are those two related? The inflation rate depends on the energy density of the universe (-> scalar fields), right?

And the point is: Even if we attribute the gravitational waves to the process of symmetry breaking, we’d still need to explain the uniformity of the universe because symmetry breaking only explains the origin of the fundamental forces.

So the paper is by Lawrence Krauss, whom I met once back in 2006, when I was giving a talk at Vanderbilt. Lawrence shows up about 40 minutes late (to my one hour talk), makes a scene when he walks in, and demands, “What did I miss?” Feeling indulgent, I gave him a 15 second synopsis of the last 40 minutes, and he goes, with a satisfied smile, “Oh, not much then.” Way to make a good impression on me, Lawrence.

Anyway, his scientific paper doesn’t have anything wrong with it. He basically talks about how a global phase transition can generate gravitational waves, which is 16 year-old news, and those waves might be strong enough to show up in the CMB, just like those from inflation. Is this big news? Come on, anyone can write a paper where you make gravitational waves (the link is to a paper I wrote in 2005).

Here is the important difference, however:

  • Inflation predicts a scale-invariant spectrum.
  • Other mechanisms to make gravitational waves don’t.

A “scale-invariant” spectrum means that energy is evenly distributed in waves of different sizes. Let’s compare the spectrum of inflation (green curve):

to the spectrum in Lawrence’s paper (figure from the paper; he plots things in different units):

and just for fun, let’s throw in the spectrum that my old paper predicts (it’s very different from inflation):

Now, here’s the thing missing from Lawrence’s paper (and admittedly, my paper, too). What is this going to look like in the Cosmic Microwave Background? People have computed it for inflationary models, and know that the shape of the curve should look just like this (the blue curves are for different amplitudes of inflationary models),

so people can go out and try to measure it. Specifically, for those of you who want details, this is looking at the B-mode spectrum of the microwave background, which is one of the things that Planck is designed to measure. What does this new paper predict for their data? Well, they conveniently don’t publish it. Why not? Because it would decidedly be very different from anything resulting from inflation.

Lawrence’s paper talks about something that happens way after the end of inflation, and doesn’t affect the spectrum from inflation or anything related to inflation at all. The paper just gives an extra way to generate gravitational waves of large-enough amplitude that they might show up in the CMB. And they might, if the new physics which he made up is correct. Which, who knows, it might be, and at least we have something new to look for. But this research does nothing to eliminate the need for inflation or change the predictions of inflation, and the press release is indeed wrong for implying that. Thanks, Matt, for forcing me to clear that up.

It’s getting near the end of the week again, so check out this week’s Carnival of Space over at KYsat. Is the KY for the state or the… other thing?

Why Explore Space/the Universe?

April 11, 2008 on 11:18 am | In Politics, Q & A | 8 Comments

Fraser Cain over at Universe Today sent out a question to the Astronomy/Astrophysics/Space communication community today. And he asks:

Why should we spend our time/money/resources on exploring space when there are so many problems here on Earth?

This is something that, for better or worse, I had a knee-jerk reaction to. Here’s what I wrote back to him:

This is like asking why we should spend money on making our city better when there are so many problems here in our own homes. Or why we should spend money on understanding our whole world when there are so many problems here in our own country. Space is something that we are not only a part of, but that encompasses and affects all of us. Learning about the grandest scales of our lives — about the things that are larger than us and will go on relatively unaffected by whatever we do — that has value! And it might not have a value that I can put a price tag on, but in terms of unifying everyone, from people in my city to people in a foreign country to people or intelligences on other planets or in other galaxies, space exploration is something that is the great equalizer. And the knowledge, beauty, and understanding that we get from it is something that one person, group, or nation doesn’t get to keep to itself; what we learn about the Universe can be, should be, and if we do our jobs right, will be equally available to everyone, everywhere. This is where our entire world came from, and this is the abyss our entire world will eventually return to. And learning about that, exploring that, and gaining even a small understanding of that, has the ability to give us a perspective that we can never gain just by looking insularly around our little blue rock.

What are your thoughts on the matter? Is this valuable, or am I just being completely naive and idealistic in my views of the value that understanding the world and Universe around us can bring? Whatever you think, you can read what the other responders had to say here.

Energy Conservation and an Expanding Universe

April 11, 2008 on 7:32 am | In Physics, Q & A | 8 Comments

So, what’s the deal with this one? reader Scott Stuart asks the following question:

I was reading “The First Three Minutes” last night and came across an
interesting section about blackbody radiation and energy density. The
author states that as the universe expands, the number of photons
running around (in the CMB, for example) is unchanged, but their
wavelengths get stretched. The energy in a photon is, of course,
inversely proportional to its wavelength, so the energy content of a
photon decreases as its wavelength increases. That seems to mean that
the total energy content of the photons decreases due to the expansion
of space. Now the energy density clearly decreases as the volume
increases, but this argument says that the total energy decreases as
well. Does that mean that the expansion of space is not conserving
energy? Or is the energy “going” somewhere?

Remember the law of conservation of energy? It states that energy can neither be created nor destroyed, only transformed from one form into another. Now Scott asks how this works in an expanding Universe, because quite clearly the rules change!

His point is that if I have a bunch of photons in my Universe, and I stretch my Universe, the photons will change wavelength to accomodate the change in the size of the box. So if I double the size of the Universe, the energy in photons in the Universe halves.

What about matter? Both normal matter and dark matter don’t change their mass as the Universe expands, so that seems okay. But what about the energy in the gravitational field? After all, there is such a thing as binding energy, and as I increase the distance between objects, the gravitational binding energy (which is a form of negative energy) goes up (or closer to zero). Unfortunately, we don’t have an exact definition of gravitational field energy, so that gets sticky.

Now let’s throw dark energy in, and make the conundrum worse. All of the evidence for dark energy (currently) points towards it having a constant energy density. This means that as the Universe expands, and we wind up with more space, we are constantly creating more and more energy. So what’s the deal? Is energy conserved, or isn’t it?

If we define energy like we’re used to defining it, that is, locally, the answer is no. If we take the energy density of the Universe and multiply it by the “volume” of the Universe, we get a number for total energy that changes over time. Just after the big bang, most of the energy density was in radiation, which decreases faster than the volume increases due to the stretching talked about above. So at the start, it looks like the total energy of the Universe is dropping. Then the Universe becomes matter dominated, and then energy appears to be conserved, since the product of the matter’s energy density times the volume stays constant. But then the matter density drops below the dark energy density, and now, the Universe is dominated by dark energy. The product of the dark energy density (which is constant) times the volume (which is increasing) is increasing! So it looks like the total energy of the Universe first decreases, then becomes fairly constant, and then increases again.

How is this possible? The problem, as I’ve already alluded to, is that energy is only defined locally. That means that we have no idea how to define something like “the energy of spacetime” or “the energy of the Universe’s expansion.” Without that, all we can do is state the rules for how energies and energy densities change as the Universe expands and ages.

Maybe you don’t like my answer to this question. In that case, you can try Sean Carroll’s answer, or read Steve Carlip’s answer (the third one down). The big problem is that we don’t know how to define gravitational energy on cosmological scales. Clearly, there’s a lot of it! Maybe one interesting thing to do would be to define it in the one unique way that would conserve total energy, and to learn what that is? Then, perhaps, we can test it?

Thanks to Scott for a very tough, but very good question! You have one? Send it in!

Why doesn’t Light Age?

April 2, 2008 on 2:05 am | In Q & A, relativity | 5 Comments

There’s a graduate student that I’m sort-of mentoring/working with at Arizona, named Xiaoying Xu (hi Xiao!). She’s bright and curious, and she asks some very good questions. She asked me one yesterday that’s pretty tough to wrap your head around:

How do I explain to someone why light doesn’t age?

Well, here on Earth, time progresses at a certain speed. That is, if I measure how many seconds tick by as the Earth revolves once around the Sun, I’ll get 31,556,926 seconds. (31,558,150 if I’m measuring a sidereal year.)

But let’s say in the course of that year, I put you on a rocket ship, and you come back exactly one Earth revolution later. I send you off at 12:00 AM on New Year’s day. Well, if you’re moving at typical rocket ship or satellite speeds (a few kilometers/second), your clock will be about one-hundredth of a second faster after a year due to the time dilation effect of special relativity, hardly noticeable.

Big deal. But what if you start moving fast? If you move at 10% the speed of light (30,000 km/s), your clock will say that it’s about 44 hours earlier than mine. While I ring in the New Year, you think it’s 4 AM on December 30th. If you get up to 90% the speed of light, I get a kiss and champagne while you think it’s early morning on June 9th. At 99.99% the speed of light, only 5 days will have passed for you while I’ve lived a whole year. And at 99.9999999% the speed of light, an entire year passes for me in just 23.5 minutes for you.

So as things move faster, time passes slower for them. Now, being made of matter (and having mass), we can never move at the speed of light. But things that do travel at the speed of light never have any time pass for them. Now as if that wasn’t neat enough, most things that we know of will decay eventually. Things that we like, such as neutrons. But if they move faster, they live longer. That’s how cosmic rays known as muons can actually reach the surface of the Earth, because they move at 99.999% or more the speed of light! But what about light? Well, that’s the one thing in the Universe that we know will never decay. Protons might decay (we know that if they do, their half life is over 1035 years), electrons might decay, but particles of light can’t. Because time doesn’t pass for them!

And that is why light doesn’t age.

Weekend Diversion: Rainbows!

March 15, 2008 on 2:05 am | In Q & A, Random Stuff | 6 Comments

Starts with a bang reader Zrinka asks us how rainbows work, and that’s a great question for the weekend, since I’m driving up to Portland, OR right now. (The desert is lousy for rainbows when it doesn’t rain!) So you’ve seen something like this before, although maybe yours isn’t as famous as Galen Rowell’s:

So how do you make one? Well, this works just like light passing through a prism will separate into its colors (right), because the longer wavelength light travels faster in any medium. So red light has a longer wavelength than purple, and so not only travels faster through glass or water than purple light does, but also bends by a smaller angle than purple light does.

So if the Sun is behind me and there are drops of water in front of me, the sunlight can come in to the raindrops, get reflected off of the back of the water drop, and come back to my eye, except light of different wavelength comes out at different angles. The image below shows you the difference between red light (which comes out at 42 degrees) and purple light (which comes out at 40 degrees):

So that’s why red appears on the outside, because it makes an arc of 42 degrees, and purple appears on the inside, with an arc of 40 degrees. Now sometimes, if you look closely on a nice bright day, you’ll see a second rainbow outside the first, with the colors reversed! This is what happens when you get a second reflection happening inside some of the drops, and you might see something like this!

So that’s how rainbows work; now the next time you see one, you’ll know that where it appears is because of your position relative to the sun and the rain, and the shape and arc-size of the rainbow(s) are the same wherever you are!

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