Starts With A Bang! » Q & A http://startswithabang.com Ethan Siegel's blog/video blog about Cosmology, the Universe, and everything else Sat, 04 Apr 2009 20:12:38 +0000 http://wordpress.org/?v=2.3.2 en The Math of Marriage http://startswithabang.com/?p=1683 http://startswithabang.com/?p=1683#comments Sat, 28 Mar 2009 04:44:46 +0000 ethan http://startswithabang.com/?p=1683 There was a question on the straight dope message board today that was way too interesting for me to pass up. But it took a long time to crunch the numbers for it, so this post is late!

Someone named Richard Parker wants to know whether he should get married… using math. He writes:

As most of you are likely aware, our federal income tax system imposes a marriage penalty on some couples. If both individuals are making similar income at certain levels, then the combined income will put them in a higher joint bracket (or married filing separately bracket) than if they filed a single taxpayers.

What I want to do is evaluate what potential incomes result in what penalties.

Well, after doing a bit of research on this, I’ve discovered that there are a bunch of other reasons to either get or not get married, both financial and personal, and I’m telling you now that I’m putting those aside.

All I’m looking at is the following: given a certain amount of federally-taxable income for two people, what governs whether, for income tax purposes, they should be married or single? Now, I’m not an economist, but I’m scientifically trained, I’m excellent with numbers and statistics, and I’ve got some interesting findings for you.

First off, there are only two factors that matter for how much you pay in taxes, given two people and a certain amount of taxable income.

1.) How much total income there is. More income = more taxes, and once you pass certain thresholds, the tax rate you pay continues to climb.

2.) How the income is split between the two people. If one person earns 95% of the household income and the other earns 5%, vs. if one earns 45% and the other earns 55%, you may come to two very different conclusions.

So let’s see what happens for low joint incomes, and just go up, and see what we can learn about marriage and federal taxes.

\$20,000 joint income: if one person makes significantly more than the other, you should definitely get married, as you wind up in a lower tax bracket. If you make roughly even amounts, it doesn’t matter either way. What if you’re doing a little better than 20k a year?

\$40,000 joint income: the disparity has to be pretty large. If one person is pulling in about 80% or more of the household income, then you save money by being married. But if not, there’s not really any difference.

\$60,000 joint income: this is really the start of what I’ll call the “sweet spot” for people to get married. Again, if you have identical taxable incomes, there’s no difference between being married and single. But if there’s even a 60/40 disparity, it’s better to be married. Remember this for tax purposes: if one person works and the other doesn’t, it’s always better to be married!

\$80,000 joint income: This is still part of the sweet spot for marriage. No marriage penalty, big bonuses for being married if there’s an income disparity. And this continues, but really the \$60-80k range of taxable income is where it’s usually significantly better (for tax purposes) to be married.

\$100,000 joint income: well, it’s much better to be married if there’s a big income disparity, as you can save thousands of dollars over being single. But unless one of you is out-earning the other by better than 2 to 1, there isn’t going to be any difference that you’ll see.

\$125,000 joint income: and at \$125,000 in joint income, it’s pretty much the same deal. So, so far, and in fact all the way up to a joint income of \$137,050, it is never worse to be married for tax purposes. And if there’s a big income discrepancy between partners, it’s far better to be married than it is to be single. But above \$137,050, you start to see something called the marriage penalty.

\$150,000 joint income: pretty much the same deal, unless you and your partner bring in roughly the same income! Suddenly, if I make \$75k and my partner makes \$75k, we’d save \$500 on our federal taxes every year by not being married! And the marriage penalty gets more significant at higher incomes:

\$200,000 joint income: around \$1,000 at this income level.

\$250,000 joint income: around \$3,000 at this level. By this point, it’s only going to get worse. The marriage penalty has been getting worse, to be sure, but have you also noticed that at large income disparities, like 95%/5% splits, you can save around \$5,000 by being married? This number has also been going up, significantly, in all of our charts. Let’s go further:

\$300,000 joint income: the marriage penalty starts to get more and more people, now. Unless there’s an 85/15 or more split in income (which means one of you out-earns the other by at least 6 to 1), you are looking at a penalty, just for being married, of over \$5,000! But, on the other hand, if one of you doesn’t work at all, you can save over \$7,000 just for being married!

\$400,000 joint income: this crosses over into the highest tax bracket. Whether you’re married or single, the highest tax rate comes for those earning over \$372,950. The marriage penalty is close to \$10,000 here, and doesn’t go away unless one out-earns the other by 10 to 1!

\$500,000 joint income: notice how the differences are pretty much the same as before. About \$10,000 in “marriage penalty” for making the same incomes, but about \$7,000 in savings for a one-income marriage.

\$750,000 joint income: here you can see that, while the savings never gets better for one-income marriages, the marriage penalty continues to get worse for very large incomes, both in terms of who has to pay it and in terms of how much it is.

\$1,000,000 joint income: and finally, the marriage penalty bottoms out here. The marriage penalty is, maximally, about \$15,000 a year for the wealthiest Americans. Which is, honestly, enough reason for many people not to marry someone with similar earning power to themselves.

So the overall conclusion? If you’re making under \$137,050 of joint taxable income this year, it won’t hurt you at all to be married, and it may save you money if one of you is making more than the other. But, if you’re making more than that, being married will hurt you if you have roughly the same incomes, but will help you immensely if one of you makes virtually no money compared to the other. So feel free to use the charts all you like — and do whatever it is that respects marriage, money, and everything else that makes you happy — but now you can do it with this information in hand!

And the other obvious conclusion? I need to start making enough money so that I can start complaining about the marriage penalty!

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Faith and Science: A Personal View http://startswithabang.com/?p=1598 http://startswithabang.com/?p=1598#comments Mon, 09 Mar 2009 22:55:03 +0000 ethan http://startswithabang.com/?p=1598 There are a lot of people reporting, right now, on the new memo that President Obama has just signed about science, stem cell research, and his administration’s policy:

Obama said scientific decisions should be based on facts, not ideology. He said advisers should be selected based on their credentials and experience, not their politics.

Now, there are very vocal opinions on both sides of this issue, and as you would suspect, I think that in matters of scientific research, every scientist must live with their own conscience, but that science exists to serve humanity, and the research we’re doing will doubtlessly serve to have a positive impact on mankind. Once one major cure or treatment comes out of stem cell research, whether it’s for cancer, Alzheimer’s, or diabetes, I think that the debate over stem cell research will subside when it’s clear that the benefits to doing it can be so substantial.

But instead of looking at it from an economic perspective, or even from an ethical perspective (I’m still tired from doing that last week), I’d like to look at the deeper, underlying issue: whether people can come closer to realizing truths about existence from either faith or science. I also think it’s worth asking yourself, at the end, whether there’s even a right or wrong answer to this.

So rather than talk about stem cell research, I’m going to address perhaps the most interesting question of all: the very question of our Universe’s existence. My friend Brian has a cousin who is a baptist minister, and today’s question comes from him, via YouTube:

Did the Universe have a beginning? …it seems that most cosmologists do believe that the Universe had a beginning. If this is true, and you believe this, then please explain how you, in your mind, resolve the idea of something coming from nothing, uncaused.

Now, let’s start with a little scientific information about the Universe itself. We turn our eyes, telescopes, detectors, instruments, and brains towards the tiniest subatomic particles and to the farthest reaches of the heavens to learn about it, and to listen to what it tells us about itself. (Semantics: I’m going to define our Universe, for this discussion, as consisting of every single particle and every little bit of space and time ever conceivably connected to us, either visibly or invisibly.) Here’s a basic rundown:

1. The Universe is big. It isn’t infinite, though, it’s finite in size, at about 94 billion light years from end-to-end.
2. The Universe is old. If you took the longest-lived thing ever on Earth and gave it 10,000 lifetimes in a row, it would be only about 2% as old as our Sun and Earth are. The Universe is “only” about three times as old as our Solar System is.
3. The Universe has a lot of stuff in it. About 1,000,000,000,000 stars in each galaxy, and about 100,000,000,000 galaxies in the whole Universe. Considering each particle of matter and energy as a separate entity, there are about 1090 particles in the entire Universe.

All of this, combined, tells us that our Universe is tremendously large, tremendously old, and full of an incredible amount of stuff. It is truly vast. However, all of it is finite, including the amount of information in it. Does that imply that there’s an intelligent force outside of it that created it?

No. It doesn’t tell us that this isn’t the case, either. But it does tell us something profound about science; specifically, it tells us something about the theoretical limits of science. Let me give you an analogy, the exploding grenade:

If you watch the individual fragments of a grenade during (or even after) an explosion, because you know the laws of physics and how a grenade works, you can figure out where the grenade exploded, how powerful the explosion was, and what the grenade was made out of just based on what you see. You can even tell, if you’re extremely careful and understand the physics of grenade explosions really well, how quickly and in what direction the grenade was moving when it exploded.

But what you can’t tell, based on looking only after the fact, is how the pin got pulled, and by whom or what.

So, my contention is that if we want to know about the Universe, the best source we have is to look to the Universe itself, and see what it tells us. But if we want to know what caused the Universe, although there are things we can definitely learn a number of things about it, our total amount of possible scientific knowledge is limited by the amount of information available. For instance, we are mounting evidence and may be able to someday prove that cosmological inflation caused the Big Bang to happen, and created our Universe. But then you could ask, “what caused or created the inflating Universe that gave rise to ours?” Again, we can come up with some ideas about it, and possibly some signatures to look for (although there are presently no good ideas), but at some point, you run out of information. It isn’t that something came from nothing; it’s that something came, period. We simply don’t have enough information to say that it came either from nothing or from something else. And we certainly don’t have enough information to determine what the dynamics were that caused it to come into being in the first place.

When you have no information, science is useless. And at that point, all you have left is logic and reason, and those are your only weapons against the darkness of ignorance. Science can get us far, can get us so much further than we’ve ever been before, but even science has its limits. And hence, to the many atheists that read this site, I encourage you to respect the religious beliefs of others while steadfastly standing by the scientific truths that we have discovered to be valid and factual.

We ought to all be above petty bickering here, as I think everyone is seeking to understand our Universe’s very existence, and hence we must use all of the available tools. I encourage you to recognize that religious studies can be a logical, rational pursuit as well, and that both science and religion have limits to the truths they can uncover. This one in contention here — what brought the Universe forth into existence — is still obscure to all of us.

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Warp Drive: Is it Really Possible? http://startswithabang.com/?p=1255 http://startswithabang.com/?p=1255#comments Mon, 15 Dec 2008 18:28:02 +0000 ethan http://startswithabang.com/?p=1255 Ever since we realized that our Universe extended far beyond the extent of Planet Earth, mankind has longed to travel to distant planets, stars, or even other galaxies, perhaps going as far as the edge of the known Universe.

We’ve designed spacecrafts that, in theory, can travel these great distances. The problem with all of these designs is time dilation, or the fact that while you go off on your space journey, time passes much faster for everyone who stays back on Earth, so that if you wanted to go off and return, people on Earth would age tens, thousands, or even millions of years while you were gone on your journey.

Well, reader Howard Mauch writes in and wants to know whether warp drive is really possible. Warp drive is the idea that we can bend space so significantly in front of our spacecraft that we can travel forward great distances in short amounts of time, without suffering the effects of time dilation:

This was, of course, made famous by Star Trek. But is this at all physically feasible? The quick answer is no. Why not? Because although space can be curved, and we can theoretically connect two distant points to travel instantaneously between them, nothing can safely travel through them. Take a look at this picture, where it looks like you can safely travel from one side to another through this short-cut:

The big problem is that the curvature you see here represents a gravitational field. The more curved a piece of this diagram is, the stronger the gravitational field is. And the stronger the field is, the greater the forces are on you. In the diagram above, the forces are so strong they will not only crush you, they will tear individual atoms apart. The only solution? We need some way to create stable, flat spacetime inside of this curved area. Is this possible?

Well, it’s possible in electricity; you put an electrical conductor around your ship and you block all electric fields inside the conductor. Want to do the same thing for gravity? You’d need to put a gravitational conductor around your ship. No big deal, right? Except that there’s no such thing as a gravitational conductor, because there’s only one type of mass (positive), where there are two types of electric charge (positive and negative). So either invent something with a negative mass (which doesn’t exist) and build a gravitational conductor, or everything, even in theory, will be destroyed by the gravitational forces that would allow you to travel via warp drive.

NASA is more optimistic about this. I believe they are mistaken in their optimism, but who knows what new physics will be discovered, and what new possibilities will arise from them?

And if you need a bigger fix for your space reading needs, check out the latest Carnival of Space, where many interesting space delicacies await you!

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Q & A: Why don’t Woodpeckers get Brain Damage? http://startswithabang.com/?p=1238 http://startswithabang.com/?p=1238#comments Wed, 10 Dec 2008 19:50:22 +0000 ethan http://startswithabang.com/?p=1238 Everyone knows how much fun it is to get repeatedly hit in the head. Just ask Oscar de la Hoya after his defeat against Manny Pacquiao last weekend:

Ouch. It isn’t just boxers, either. Every animal that experiences head trauma is susceptible to the following symptoms:

• Abnormal level of consciousness
• Differences in pupil size
• Rigid limbs
• Flaccid limbs
• Unusual eye movement
• Bleeding from the nostril
• Bleeding from the ear canal
• Seizures

But the worst thing imaginable to me that results from head trauma is brain damage. It’s our minds that make us who we are, and the idea of living without mine is completely horrifying. Look at how different a normal brain can be from a damaged one:

Out of all the animals I know of, there’s only one that repeatedly slams its head into a block of wood, over and over, day in and day out, for its entire life: the woodpecker.

A woodpecker moves so quickly that its tiny, 50 gram head absorbs 1,300 pounds of force every time it smashes into a tree! So why don’t woodpeckers get brain damage? There has to be something that prevents its brain from rattling around in its head and slamming against the skull around it, right? No, there isn’t. The woodpecker’s brain does rattle around in its head and smash into its skull. Yet it still emerges brain-damage-free. There are three special adaptations of a woodpecker that allow this to happen; let’s take a look.

1. Spongy skull bones — while humans have spongy bones mostly on the interior of large bones, woodpeckers’ skulls are extremely spongy. This means they can compress and help absorb the impact of the brain jostling around. It’s like smashing a brain into memory foam instead of into solid bone, and it reduces the force on the brain tremendously.

2. Large surface area — a woodpecker’s brain is tiny. This is actually a positive thing, because the smaller something is, the larger its surface-area-to-volume and surface-area-to-weight ratios are. If something has a bigger surface area, it means that even if the force is large, the pressure gets smaller, and this helps protect the woodpecker’s tiny bird-brain.

3. Woodpeckers peck in a straight line — this one is hugely important. If everything’s in a straight line then there’s no rotating or torquing of the brain, and therefore no tearing of the nerves in the brain. Hence, no brain damage the way that car crash victims experience it.

And those three things combined allow a woodpecker to escape from all their daily pecking activities without so much as a hint of head trauma. Isn’t evolution neat?

What, you were expecting some astronomy/physics today? Go check out the latest Carnival of Space to get your fix, done by Dave Mosher in a new video format, and I’ll see you all next time!

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Q & A: The Speed of Light http://startswithabang.com/?p=1176 http://startswithabang.com/?p=1176#comments Mon, 24 Nov 2008 22:25:48 +0000 ethan http://startswithabang.com/?p=1176 It’s 103 years after Einstein first formulated his Theory of Special Relativity, which explains what happens to objects near the speed of light. But SWAB reader Jacinth wants to do one better, and asks:

What will happen if we can actually travel at the speed of light?

It’s a great question, and provides a lot of learning opportunities. First off, let’s take a look at what happens to regular matter when we bring it close to the speed of light. There are three major things:

1. Lengths contract. This works for everyone. If I move close to the speed of light, then anyone who sees me sees that my length is smaller. But from my point of view, everything that I see is moving towards my rear close to the speed of light, and also looks like it has a smaller length.

2. Time slows down. We call this time dilation, and again, it works for everyone. It means that if I’m moving close to the speed of light, everyone who sees me sees that time is traveling more slowly for me: my clocks run slower, I age slower, my heart beats slower, etc. But I see the same thing: everyone else looks like their clocks are running slower, they’re aging slower, etc. But if I go away close to the speed of light and then come back to Earth at Earth’s speed, we find out that on my journey, although I’ve aged normally, much more time has passed on Earth. (Incidentally, this is what Paris Hilton was worried about.)

3. It takes more energy to accelerate your speed. Some of you who know a little physics know that the rest energy of a particle is E=mc2. Some of you also know that Kinetic Energy = 1/2 mv2. But when you get close to the speed of light, it takes more and more energy to move quickly. In the graph above, the purple line is the old formula for kinetic energy, but the red line is the real (relativistic) energy. Notice that you never quite get up to the speed of light, but that the energy it takes approaches infinity.

So that’s what happens when something made of normal matter approaches the speed of light: it sees lengths contract, times slow down, and it requires more energy to change its speed. Alternatively, things that have no mass (like photons, or perhaps gravitons), have to move at the speed of light.

But let’s say you had a spaceship, and decided to actually go at the speed of light, somehow. What would happen?

Well, if you used all the energy in the Universe for your spaceship, you could probably get up to speeds incredibly close to the speed of light. How close? The speed of light is exactly 299,792,458 meters/second. And you could get to within about 1 x 10-30 meters/second of that value — pretty good. If you got that fast, though, what would happen? First, the entire Universe would contract to appear to only be a few billion kilometers across — less than one light year! Second, time would slow down so much, that as you would only age a few seconds, the Universe would age literally trillions of years. Galaxies would merge, stars would be born and explode in the blink of an eye. And finally, you may get to see the fate of the Universe firsthand; if the Universe has an end, you would slow down time for yourself so much that you might not only see it, you might do it in just a few seconds.

So, in conclusion, not only can’t you move at the speed of light, there’s good reason not to!

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Why doesn’t Earth lose its atmosphere? http://startswithabang.com/?p=1141 http://startswithabang.com/?p=1141#comments Mon, 17 Nov 2008 22:28:35 +0000 ethan http://startswithabang.com/?p=1141 So we’ve got this giant wet rock hurtling through space at incredibly high speeds. It spins, and it revolves around the Sun. Why, with all of this, do we still have something as tenuous as our atmosphere? Pereira2 writes us:

How it’s possible the atmosphere follow[s] Earth during
its travel through… space?

Let’s think about this. There are a lot of things going on here, so let’s make sure we deal with all of them, and deal with them properly.

1. The Earth is moving really fast. Just like Galileo said. How fast? Each year, the Earth travels 584 million miles to go around the Sun, for a mean speed of about 67,000 miles per hour (108,000 km/hour). But unlike objects on Earth that move that quickly, there’s no drag force in space. Since space is so empty, there’s nothing to burn the atmosphere off the way that meteors burn up when they get too close to the Earth. So instead the Earth, which moves at the same speed as its atmosphere, can keep its atmosphere intact simply through the force of its gravity.

2. The Earth is spinning quickly. So why doesn’t the atmosphere get flung off of the planet? Although the Earth rotates very fast, once a day, that only gives the surface of the Earth moving at a pathetic 1000 miles-per-hour (1700 km/hour). Sounds fast, but it isn’t a problem for two reasons. First off, just like a centrifuge, spinning things (like the Earth) tend to throw off things on their surface (like the atmosphere). But the Earth’s gravity is about 300 times stronger than this centrifugal force, so the atmosphere is fine. Second, even though the Earth is spinning, the atmosphere spins with the Earth, due to the law of conservation of angular momentum. So again, our atmosphere is fine.

3. But objects like Comets lose everything when they orbit the Sun! Why doesn’t the Earth lose its atmosphere the same way? Although the Sun’s light does hit the Earth’s atmosphere, giving individual atoms and molecules tremendous amounts of energy, the energy from the Sun just isn’t enough at this great distance to overcome Earth’s gravity. The atoms in the atmosphere still stay bound to the planet. For comets, they’re tiny, and their gravity is tiny, so they leave a wake of debris (comet tails) through space. But the Earth is big enough, it’s gravity is strong enough, and gosh-darn-it, people like it, and so its atmosphere stays right here with us on our journey forward in space and time.

And for all the space-related news that you can handle, check out this week’s Carnival of Space. We’re already up to Carnival #79!

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Particle Accelerators: Man vs. Space! http://startswithabang.com/?p=1130 http://startswithabang.com/?p=1130#comments Fri, 14 Nov 2008 22:22:43 +0000 ethan http://startswithabang.com/?p=1130 A lot of people are still uncertain about just what the LHC will do once it turns on. But reader baragon-kun asks a really good question, which I paraphrase here:

Why are people saying that cosmic rays can be more powerful than the LHC? The LHC collides two fast moving particles into each other, but cosmic rays collide a fast moving one with one at rest. Aren’t these very different?

They are very different, but not as different as some people think. Let’s take a look at accelerators first.

You accelerate particles as quickly as you can in two opposite directions, either in a straight line or in a giant ring. And then, when they’re moving at their top speed, you tweak a little magnet and make them collide into one another.

Now of course, we can build a giant detector around these collision points and figure out what happened inside. But I’d like to focus on how much energy we can get out of these collisions. Why?

Because that’s how we make brand new particles that we’ve never made or seen before. Get enough energy and you can make anything. This is how we make antimatter, and it’s also how we made and discovered nearly every particle we know about today. Including practically the entire standard model:

You accelerate particles as fast as you can, and they have a certain amount of kinetic energy, which is the energy of their motion. Smack two moving in opposite directions into each other, and all of their kinetic energy has a chance to become mass! At Fermilab, we get particles up to energies of one trillion electron-volts (1012 eV), and we give that a name: 1 TeV. (Hence the name — TeVatron.) So smack two into each other, and your maximum energy for making stuff is 2 TeV.

At the LHC, the magnets are more powerful and the accelerator is larger in circumference, so they can get kinetic energies up to 7 TeV, for a maximum energy for making stuff of 14 TeV. This “new energy range” is why people are optimistic about finding new things — like the Higgs, Supersymmetry, and Extra-Dimensions — more energy means more opportunity for discovery.

But some people are worried that we’re going to destroy the Earth. Still. And we know we won’t, because cosmic rays have been striking Earth with not only more energy for eons, but they even have more energy for making stuff. First off, how much energy do they have?

Well, the magnetic fields are thousands-to-millions of times stronger for collapsed stars than they are for the most powerful magnets on Earth, and they can accelerate them in larger rings, too. So when we try to detect them, what do we find? How energetic are these particles? Let’s show you the hardcore data:

Over 1020 eV, or more than 10,000,000 times more energetic than the LHC will be able to reach. But not all of that can be used to make new particles. Why? Because we aren’t running it into an equal energy particle moving in the opposite direction; we’re running it into a stationary proton. Therefore, a lot of it has to stay in the form of kinetic energy in order to conserve momentum. Still, I can derive a pretty simple formula for how much energy in a collision like this goes into making particles. All you need is the energy of the super-energetic particle (E, or about 1020 eV) and the mass of the proton (m, or about 938,000,000 eV). What’s the formula?

That wasn’t so bad. But if I put my numbers in, I get that the energy is 433 TeV, or about 30 times as powerful as the LHC’s upper limit. So even if you take the greatest thing we’ve ever built, it’s still a factor of 30 weaker than the stuff we get from space all the time.

So there you go. More evidence that nothing that the LHC makes is going to destroy us. Why? Because over billions of years, we’ve already made everything that the LHC is going to be able to make, and we’re still here. Now go out and have a good weekend!

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Whose Stars Are These? http://startswithabang.com/?p=1057 http://startswithabang.com/?p=1057#comments Mon, 27 Oct 2008 20:19:37 +0000 ethan http://startswithabang.com/?p=1057 When you look up at the night sky, one of the first things you learn is that every point of light you see is either a star or a planet:

But what happens if you look through a pair of binoculars? Well, suddenly, you can see a lot more stars than you used to. Because it focuses light coming from a larger region of the sky into your eyes, it lets you see fainter objects. Instead of just about 3,000 stars, binoculars let you see over 100,000 stars! A part of the night sky would look like this instead:

But our technology doesn’t stop at binoculars; we’ve build telescopes, both large and small, that have incredible amounts of light-gathering power! The unaided human eye is about 100 times less powerful than a pair of binoculars, and a small telescope (about 6-8″) is another 100 times more powerful than binoculars are. When you start to use small telescopes, you can see details that are impossible with simple binoculars. Take a look (and click here for the full image):

This is just a picture taken by an amateur astronomer of a comet (the green thing, Tuttle 8P) that happens to be passing by a nearby galaxy (M33, the diffuse thing). And we can see that not everything is a star after all.

But our reader Greg is very savvy, and knows what really powerful telescopes can see.

Approximately how many of the stars in a picture such as this are in our Milky Way galaxy, and how many are outside our galaxy just floating in space? Is it possible to see individual stars in other galaxies such as Andromeda?

In reality, the largest and most powerful telescopes can see objects that are anywhere between 10,000 and 1,000,000 times fainter than what a small, amateur telescope can see. Let’s take a look at Greg’s picture:

Now there are a bunch of stars in that image, but how do we know which ones belong to our galaxy and which ones belong to Andromeda, which is the closest large galaxy to us? This is a question with an easy answer: they’re all ours! While we can resolve individual stars sometimes in Andromeda, such as Cepheid variable stars, they don’t show up in a normal telescope image like this. How do we know? Let’s take a very similar galaxy to both ourselves and Andromeda, but the only difference is that it’s about 6 times farther away. This is the Sculptor Galaxy:

Notice how it looks very similar to the Andromeda Galaxy, except with far fewer star-like speckles? That’s because all the stars are here, in our own galaxy!

Want to take an extreme case? The Hubble Deep Field and Hubble Ultra-Deep Field images were made by pointing the telescope at a patch of sky known for being completely dark; having no known stars in them. You just sit there and point your telescope there, overexposing the image, and finding what turns up. The results look like this:

But the amazing thing is that every speck of light there is a galaxy; there are no stars in this image. So if we want, we can zoom in on a large, bright galaxy as best we can and see what it looks like:

Notice the absence of individual stars? It’s because they’re all in our galaxy. In fact, if we take that ultra-powerful Hubble Space Telescope and point it, say, at the sculptor galaxy above, we can see some individual stars. But they’re so faint and so miniscule compared to the stars in our galaxy that they get dwarfed. Take a look at the image below: note the foreground star in our galaxy (halfway down, about 1/5 of the way from the left border) and all the other stars, which belong to NGC 253 (sculptor’s scientific name):

See what I mean? They’re all our stars. Looking out at the Universe means looking out through our galaxy, and unbelievably, even in outer space, our own neighborhood gets in the way!

Good question, Greg, and I hope I answered it well for you!

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Q & A: Gravity and the Power of a Theory http://startswithabang.com/?p=1037 http://startswithabang.com/?p=1037#comments Mon, 20 Oct 2008 21:25:47 +0000 ethan http://startswithabang.com/?p=1037 How do you know what makes a scientific theory good and useful? We can put everything that a theory does into two categories. One one hand, theories make predictions, that is, they tell us what’s going to happen if your theory is correct. But on the other hand, theories also require assumptions. The most powerful theory imaginable would assume nothing and predict everything. Of course, that’s not feasible, so we do the best we can with what we have and what we know. Wikipedia actually has a pretty good article about the predictive power of a theory, and there’s recently a telegraph article about a combined science and art project that looks at this (see image below for an example).

But SWAB reader Rene writes in, and wants to know about gravity. Namely, he wants me to consider alternative theories of gravity. Let’s start with the simple stuff, and remember to put it in Richard Dawkins’ context of the predictive power of a theory. Let’s take a look:

Now, of course Dawkins is being tricky when he says that “genes exist” is all that Darwinian evolution requires as its assumptions, since the mechanism is clearly more complicated than that. But Newton’s gravity was really simple; its assumptions were as follows:

1. Everything in the Universe that has mass emits a gravitational force.
2. The force that every object exerts on every other object obeys Newton’s law of Universal Gravitation.

And with that, we were able to explain nearly all the gravitational phenomena on Earth and in space. We were even able to predict the existence of Neptune from it! The “power” of Newton’s theory was huge.

But eventually we made enough discoveries of things that Newton’s gravity couldn’t explain. Why was the perihelion of Mercury precessing? Why did clocks run differently in different gravitational fields and at high velocities? When Einstein came along, he came up with a new theory of gravity that not only explained these things, it also explained everything Newton’s theory of Gravity explained, plus it made new predictions that have since been verified, including the bending of light by matter (below), frame dragging, and the decay of gravitational orbits.

But now, nearly 100 years after General Relativity, we have new discoveries that both Newton and Einstein’s theories cannot explain. Why is the expansion of the Universe accelerating? Why is there more gravity than matter can account for? If we want to explain all of these new things, we need at least two more assumptions: dark matter and dark energy. Now, Dark Matter explains a lot of things, as I’ve been over, and so it seems that we need that. But what about dark energy? Really, I like Karl Gebhardt’s answer:

Dark energy is our ignorance of what’s going on in the universe right now. What I always like to say is that dark energy is only a phrase, and don’t get hung up on the words dark and energy. It may not be dark, and it may not be energy. All it is is our ignorance of how the universe may be expanding, and we don’t know what it is at this point.

So, Rene, I don’t have a better answer for you than that, but as far as gravity goes, Newton’s theory was incredibly powerful, but didn’t explain everything. Einstein’s general relativity was a little more complicated, but explained a whole host of new things. Adding dark matter means there’s one more particle (at least) that’s 5 times as abundant as protons, neutrons, and electrons, but it solves a pretty large number of problems, too, in a way that other alternatives don’t.

But dark energy? It’s one assumption to solve one problem. Not a powerful theory. And so, cosmologists have jobs for a while longer, as we all work to try to figure it out.

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Why build an accelerator? http://startswithabang.com/?p=964 http://startswithabang.com/?p=964#comments Fri, 03 Oct 2008 23:42:43 +0000 ethan http://startswithabang.com/?p=964 I was at home earlier this week, and I got a surprising question from Jamie (my wife):

If Fermilab scoops the LHC and finds the Higgs, and then the LHC doesn’t find anything will it be a total waste, and why should anyone ever build another huge accelerator again?

From a scientific point of view, Jamie is absolutely right. Our model of what the fundamental particles are in the Universe is pretty complete: we know how to make up all the normal matter in the Universe and we know all the particles that govern their interactions.

The only standard model particle left to be confirmed is the Higgs; we’ve already discovered everything else. Yes, there are other mysteries out there that the LHC might shed light on, including what dark matter is, why neutrinos have mass, whether there may be supersymmetry or extra dimensions, whether any of the standard model particles are made up of smaller, more fundamental ones, or whether there’s an alternative to the Higgs.

But let’s put all the physics (which I’m, of course, partial to) and all the possible scientific discoveries aside for a minute. These accelerators are really, really expensive. To build and operate the LHC, the total cost of all the experiments will top out at somewhere between 5 and 10 billion dollars. That even makes this guy look like he’s asking for peanuts:

There is a lot of good in my country and in the world that can be done with that kind of money. Some outstanding charitable domestic and international organizations include:

So how do I justify spending all of this money on building a particle accelerator when so much good could be accomplished by spending this money in other ways?

Even if the LHC never finds a thing, the research and development that has gone into data management will lead to computing and computational advances that have been unheard of. This has happened historically; back in December of 1990 the world wide web was invented at CERN for the sharing of computational information for scientists working at particle accelerators. (Note: you can get knighted for developing stuff like this!) Let’s talk about some of the computing advances that are already happening because of the LHC.

The Worldwide LHC Computing Grid links over 100,000 processors, 7,000 scientists and 33 countries to the LHC for analyzing data. There will be massive amounts of data pouring out of the LHC, as it needs to track and write the full detector data for over 100 collisions every second. That doesn’t sound like much, until you realize that each collision sets off 7,000,000 bytes of data. Since the LHC will be taking data continuously for about a decade, that’s enough data that if you burned it to CD-ROM and stacked it, it would reach 180 km in height, or almost high enough to collide with the International Space Station. That’s a lot of data to sift through and meticulously analyze, looking for a tiny, complex signature of new physics.

So the analysis of this data, looking for literally millions of possible signatures and configurations for each collision, is a fairly mind-boggling computational task. But the LHC had an even bigger one to face. You see, the LHC doesn’t have around 100 collisions per second. It has 600,000,000. So what do you do to filter the 600,000,000 collisions down to the 100 or so good ones that contain important data?

You build the two biggest detectors ever assembled with the most sophisticated electronic triggering system ever imagined. This hardware looks for important signatures that indicate new physics, and makes decisions in stages, every 25 nanoseconds. 600,000,000 collisions are pared down to about 100,000 before the data ever sees software, as hard-coded electronics just reject over 99.9% of the events that don’t set off the right triggers. Some of those systems are found inside of these detectors, and the individual parts look something like this:

Want to know how much faster and better the LHC computing technologies are in terms of speed and volume? Check out what they’ve managed to accomplish on this graph:

So even if you don’t find anything, the LHC has already succeeded in creating the most advanced computing and data-taking processes in history in many different regards. In the past, computational technologies developed at particle accelerators have lead to such scientific advances as lasers, cellphones, magnetic resonance imaging, nuclear power, and the computer, in addition to the world-wide web. The director of CERN has a lot to say about this, if you don’t want to just listen to me ramble. So I’m all for physics and scientific discovery on the wonder of its own merit, but don’t forget that lots of practical uses come out of these, also! What new technologies will come decades down the road from the LHC? Perhaps… teleportation?

I’m sure if it’s possible, we’ll work the bugs out! Oh right, and don’t forget to check out this week’s Carnival of Space, where we’ve got a great entry comparing humans to galaxies, and look at what they’re both made up of.

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