Ah, the beginning of fall semester. All the undergrads come back, the weather changes, and everyone gets caught up in the hustle and bustle of a new term. In other words, the perfect storm for viruses.

On Thursday a rather hectic week caught up with me and I found myself feeling rather ill. I ran up a bit of a fever before eventually being able to head back to my apartment to hibernate for the better part of the weekend. Thankfully I’m much better now and can catch up on some paper reading for next week.

What I’ve come to realize is a double edged sword in grad student life. While we have a tremendous amount of freedom in how we spend our time, it’s really tough when one has to take some sick days off. It’s not that people aren’t sympathetic or willing to give you some time to recuperate (especially these days with H1N1 in the back of everyone’s minds), but rather that research doesn’t stop when a grad student gets sick. The more time one takes off the more there is to catch up on. I’m responsible to keep up with collaborators and to provide meaningful input, so I have to make sure that I keep up with my project even when I’m out-of-commission.

Fortunately my illness passed rather quickly and I have the weekend to properly recover and catch up with what I’ve missed.

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I rather enjoyed this article that appeared in this week’s CERN Bulletin about the LHC schedule. It reminds us of just how much work is going on behind the scenes — or at least, behind the scenes if you are an experimenter patiently waiting for beam, as opposed to all the accelerator people actually doing the work. The LHC, like any large accelerator, is actually built from many individual systems that interact with each other, and doing something in one system can have effects in the others. Coordinating all of the work that is being done right now is a huge task that requires careful control. (I actually have similar thoughts when I go to visit our new physics building, which is currently under construction. So many details to keep track of in building a building, and it’s not nearly as big as the LHC. (Physics majors of the world: ask me about our graduate program in physics and our lovely new building!))

There are two other things that I took away from this article. The first is that while the LHC startup date has slipped a little bit from the announced plan in February (from late September to mid-November), CERN has actually completed much more work since then than they had originally anticipated doing. This should give us a more reliable LHC than we would have had otherwise, which to me seems worth the very slight additional wait. The second is that CERN is so focused on providing a reliable machine, so that there will be reduced risk of a delay as long as the one we are currently living through — and an increased chance of observing new physics soon.

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This week I’ve had the pleasure of attending the egamma conference in the quaint mountain town of Leysin nestled in the Swiss Alps. As I look at the beautiful scenery from my hotel room, I can’t help but be reminded of songs from the Sound of Music. In the distance I can imagine a traveling band of singing youngsters wearing drapes while crossing the mountains. (The Sound of Music is my mom’s favorite movie and on her birthday she makes us watch it). I also think back about my home in Colorado. I was fortunate in that I learned to ski young, so I don’t have the completely rational fear of death by tree. I guess it’s the wrong season for that now, but it’s clear that the town is more geared towards winter than summer (which I’m sure is why we had the conference here at this time of year).

In reality, the conference could have been in any place since the meetings run consistently from 9 am to 7 pm (breaks for lunch and coffee, of course). As I sit in the room trying to pay attention to the person who holds the microphone just far enough away so that no one can hear him, I think to myself people weren’t meant to sit in meetings for 8 hours a day for days at a time. As I look around the room, my feelings are validated by a sea of people with laptops that have terminals and emails open. Maybe later this morning I’ll convince myself that it’s OK to skip a session and go up the telecabine to the top of the mountain.

Until then, back to fake rates and signal efficiencies

-Regina

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I’ve never fully appreciated air conditioning until I spent a summer in Europe. Summer of 2004 – August – Rome. I understood the true feeling behind the phrase “I’m mellllllllting”.  Although it’s not quite as hot as that, France has it’s moments. My car doesn’t have an AC, the buses don’t have it, the building I work in doesn’t have it, and my apartment doesn’t have it and it’s 97 deg F. So I decided to give my brain a rest, and went browsing through one of my favorite web comics. I remember one particular that I’d like to share:

This hits close to home since as a HEP (High Energy Physics) grad student, I do most of my work at the computer.  While waiting for code to compile, and in between reading papers and sword fighting. I’ve come up with my own way to pass the time: rewriting Shakespeare. I’ll share.

Inspired by Hamlet:

To fit, or not to fit: that is the question:
Whether ’tis nobler in the mind to suffer
The slings and arrows of outrageous divergences,
Or to take arms against a sea of parameters,
And by opposing converge them? To analyze: to plot;
No more; and by a plot to say we end
The heart-ache and the thousand natural shocks
That work is heir to, ’tis a consummation
Devoutly to be wish’d. To analyze, to plot;
To plot: perchance to present: ay, there’s the rub;
For in that analysis of plots what presentation may come

(you can guess what I was doing when inspiration struck)

Inspired by Macbeth:

To-morrow, and to-morrow, and to-morrow,
Creeps by and so we wait from day to day,
Until the first byte of recorded data;
And all our software rels. have lighted grads
The way to endless updates. Out, out, broken splice!
Work’s but a hiding particle, a deviation
That appears to be within acceptances
And then is understood no more. It is a tale
Told by a student, desperate to graduate
Signifying discovery.

Dorky, yes. Sad, maybe – but I’m a physicist in training so cut some slack. Now back to work.

-Regina

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Life as a shifter…..

As part of the contribution with CMS, every University should do a number shifts when the experiment is taking data. For those no familiar with this, you might be wondering, how it is possible that we are taking data if the LHC haven’t started yet? Well, we are being bombarded by millions of cosmic rays every day, and those are the source that we use to understand our detectors and  find problems with the hardware and software. I have being taking some shifts for offline Data Quality Monitoring (DQM) for the tracker system and online shifts for the pixel detector.

For DQM shifts, you should go over the data that have been taken and check some specific plots in order to see the performance and/or errors generated during that particular run. It is cool to go over the different plots and see the efficiency  of each component of the tracker system (silicon strip tracker and the pixel detector).  It is important to see and try to understand the different errors that were generated during the run and report them (if they haven’t been reported before) to the shift leader. The shift leader is the person that usually saves you when you have no idea of what to do. Thanks to all of them!

Pixel online is super nice, but carries a lot more responsibility! Basically, you are baby-sitting a several million dollars detector and believe me, you don’t want to screw things up for not being aware of what you are doing…..During the shift, you should keep track of the temperature, humidity, voltages and currents of the detector (in this case the pixel detector)….Other important issue are the Front End Drivers (FEDs). These are electronic cards used for the detector control and readout. Personally, I believe that the FEDs are one of  the most complicated and important devices in the experiment and if something goes wrong with them, you better pay attention to it!

In general you never know how your shift is going to be. It could be smooth and you almost don’t have to do much during 8 hours, or it could be really busy and stressful, but in the end fun (sometimes). Usually, I get shifts where weird things happen (I think that the detector is a live and it doesn’t like me)…….

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I thought I’d give you a sense of what it takes to put together a detector like ATLAS, e.g., how much time, how many people, etc. For an overview of the ATLAS detector, please look at the ATLAS webpage and Monica’s post. Since ATLAS is huge, I will focus on just one sub-system, the Barrel Transition Radiation Tracker (TRT), which was built in the US. Its main purpose is to provide hits so that we can map the trajectory of charged particles and improve the measurement of their momentum (see Seth’s post on tracking). It can also discriminate between electrons and pions.

You can see the barrel TRT in Fig. 1 (this is an end view where you can see the electronics and cables); more information is ATLAS website. This detector is divided into 96 modules and extends from about 50 cm to 108 cm in radius, contains about 52,000 individual wires (about 2 m long) each of which is strung inside a specially built plastic straw. As the name suggests, the barrel TRT is in the central part of ATLAS. Two other parts of the inner detector, the Pixel and the Silicon tracker, reside inside the barrel TRT ¹ (that unit was being inserted into the assembly at the time this picture was taken – you can see it at the other end of the barrel).

To set the scale, the barrel TRT occupies about the half the volume of the inner detector in the barrel, which ends at a radius of about 1 m. The calorimeters, solenoid magnet and cryostat come after and go out to about 5 m in radius, and the muon system goes out to about 10 m in radius. The barrel TRT probably represents a few percent of the total cost of building the ATLAS detector, and is arguably the most sophisticated of a class of detectors called “drift chambers”; one of its selling points was that it was a low-cost way of tracking charged particles. It also has fewer electronic channels to read out (each wire is read out at both ends); in comparison, the Pixel and the Silicon tracker detectors have about 80 million electronic channels to read out.

I spoke with my colleague at Indiana University, Harold Ogren, who was one of the lead physicists on this project, as well as being the manager of the construction effort in the US. Harold and one of his colleagues originally built a similar straw tube device for an experiment that ran at the Stanford Linear Accelerator in the 1980’s. When the Superconducting Super Collider was proposed in the US, a straw tube tracker design was accepted for one of the two main experiments; when it was cancelled in 1993, he and his colleagues moved onto ATLAS, where they joined forces with the groups already working on a straw tube design.

They started building a prototype for ATLAS around 1994. Some of the groups who were on SSC joined this effort, and they had a working chamber by about 1999 that was then put in a test beam at CERN. Actual construction of the 96 modules began after the successful beam test, and it took them another 3 years to finish; each of the 52,000 wires had to be individually strung. The construction effort involved about 6-7 physicists and about 40 technicians, engineers, graduate students from Indiana, Duke and Hampton Universities and the University of Pennsylvania The electronics to read out the detector was also designed by them.

Since it was a modular design, they could ship individual modules to CERN as they were being completed, where they were put through extensive tests, e.g., each wire was scanned along every inch of its length with X-rays to check for uniformity of performance. A few wires were bad and had to be disconnected; since the bad wires are randomly distributed they don’t affect performance. These tests took another 2-3 years. All in all, the detector was ready sometime around 2006. The picture you saw above was when it was being readied to be installed in ATLAS.

The barrel TRT has been running successfully and collecting cosmic ray data. In Fig 2, most likely a cosmic shower hit the TRT, the kind described in Regina’s post. You are looking at an end view of the hit wires. Each blue dot represents a single wire being hit; we can locate the position of a track within a straw with an accuracy of 0.15 mm (human hair has a thickness of about 0.1 mm). You can see curved tracks; they are curving because the magnetic field was on. You will also see that one sector, at about 8 o’clock, was (temporarily) turned off. Isolated hits are due to electronic noise; operating parameters are set so that these wires register the presence of nearby charged particles with a very high efficiency, but this also leads to 1-2% of the wires “firing” randomly; our reconstruction algorithms can easily ignore them. The tracks that you see here are then matched to hits in the Pixel and Silicon Tracker detectors to get a complete trajectory.

Now for real data!

– Vivek Jain, Indiana University

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¹ There is also the endcap TRT, which is on the two ends of the ATLAS detector, but that was built by other groups; it uses the same design as the one in the barrel.

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Often in my day-to-day work I encounter some little problem in software or mathematics that I figure somebody ought to know the answer to.  In my years as a graduate student, I’ve learned that the quickest way to solve these problems, if a cursory search of the internet and a few standard references doesn’t help, is to actually go around the office and ask the people I know who work around me.  Sometimes they don’t happen to know either — but I can’t shake the nagging feeling that somebody I know knows how to solve the problem.  My solution to this, on a few recent occasions, has been to turn to Facebook.

Thus last Thursday afternoon, my Facebook status was:

Seth Zenz needs a statistician. Or anyone else who knows how to find the error on a correlation coefficient.

Within a couple hours, two of my friends, one a physicist and one a friend from college, had replied with the correct answer, which turned out to be explained on Wikipedia — which pointed, in turn, back to the original statistics paper from 1921 that answered the question.   So Facebook is good for more than just keeping up with my friends; it also expands the size of “the office” I can go around to ask questions in!

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Hi everyone! I just wanted to say that there have been some really great comments that have motivated on some fun discussions and new posts. I’d like to encourage people to continue to leave comments with questions and thoughts.

We unfortunately can’t always address all of them, but we do our best and it’s always great to get feedback and have a real discussion with our readers.

Two caveats:

• Facebook viewers: it helps if you to comment on the original posts at http://blogs.uslhc.us/ rather than on the Facebook feed. (This way authors are notified when there’s a new comment.)
• Comments are moderated by the Wordpress spam filter and the US LHC admins who are different people than the actual bloggers. This is why your comments might not show up immediately. Since this is a family-friendly blog, inappropriate comments don’t show up at all.

Let us know what you’d like to read more about!

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US LHC reader David left an excellent question on my previous post on E=mc² that touches on another important physics topic. To give a proper response I’d like to dedicate another post to the matter. Here’s his question:

What I can’t understand is the constant assertion that mass and energy amount to the same thing in the e=mc^2 equation. My (albeit basic) education tells me that e/m = c^2, so how are they the ’same’?

He goes on to express that it’s not clear what kind of units one is supposed to use to make the famous equation make sense. Great questions, David. This will leads us to another equation that sounds really weird: c=1. (Where c is the speed of light.) But let’s start with the basics.

In order for our equations to make sense, then they’d better be consistent to matter what units we use. Nature doesn’t care whether we use inches or centimeters. What nature knows, however (and what we had to discover), is that there are constants of proportionality that allow one to measure one quantity in terms of the units of another.

Okay. That last sentence just got really abstract. Let’s start with simple examples from everyday life. (We’ll get to the speed of light at the end, when hopefully things will be crystal clear.)

What is a unit? E.g. counting calories

The past few weeks I’ve been doing a lot of my work at Starbucks. I know that one grande iced coffee has something like 80 calories. This sets up a natural conversion between units of food energy (calorie) and units of  grande iced coffee:

1 grande iced coffee = 80 calories.

Now I can count calories in terms of grande iced coffees. Let’s say bananas have something like 160 calories. Then I can say that the amount of food energy in a banana is two times the amount of food enregy in iced coffee. Or in short-hand notation,

1 banana = 2 grande iced coffees

Note that in this short-hand notation it has to be clear that the quantities we’re equating are measuring a previously understood quantity; in order for this to make sense we have to say “the food energy in…” before each side of the equals sign. The point is that we can now use grande iced coffees to measure the food energy of other things, like a banana.

This is exactly what we mean by a unit: it’s a conversion between counting numbers and ‘dimensionful’ quantities. For example, it would make sense to say a banana has 160 food energy or 2 food energy. It only makes sense to say that a banana has 160 calories of food energy or a banana ias the food energy of 2 grande iced coffees. But each of these latter expressions is equivalent, they convey the exact same information.

[Technical note: I'm writing 'food energy' explicitly here because this represents the energy that can be released by the chemical reactions of digestion. I'm not including things like the 'matter potential energy' of the atoms in the food which stays tied up in matter.]

Algebra of units: converting into useful quantities

In our banana = 2 iced coffees equation, one nice feature is that it no longer matters how we actually measured the food energy. We originally used calories because this is what you find on nutrition labels. But this unit doesn’t make any sense to me, I don’t know what it means to ’spend one calorie.’

My favorite recreational activity is playing basketball. I can look up that for a person of my weight, playing one hour of basketball burns about 500 calories. And just like that we just did another unit conversion:

1 hour basketball = 500 calories.

Since I understand what it means to play an hour of basketball, the natural units to measure the food energy of a banana is in hours of basketball played. You may have already done the calculation in your head.

Now let’s make this a little more formal and do what I call the algebra of units. Let’s see how it works:

The trick is to multiply by 1. That’s right. Okay, I guess the real trick is to write the number 1 in a clever way. Note that one doesn’t have units. Here’s what we do:

Note that each of the quantities in paretheses is just the number 1. I’ve just written 1 in terms of the ratio of two dimensionful things. Where did I get these expressions for 1? Well I took the equation

1 iced coffee = 80 calories

and I divided both sides by “1 iced coffee” to get 1 = (80 food cal)/(1 iced coffee). Then I did the same thing for the equation of basketball hours to calories. It is critically important that we explicitly wrote out the units of each quantity, because now we can simplify the expression on the right hand side.

This is just simplifying fractions. We have “iced coffee” in the numerator and “iced coffee” in the denominator. So we can cancel out these units. Note that we have to leave the numbers, we’re just cancelling the unit “iced coffee.” Similarly, we can cancel the units of “calories” from the numerator and denominator. What we are left with is

1 banana = (2 x 80 / 500) hours of basketball

Doing the arithmetic we find that in order to burn off the food energy of one banana I have to play .32 hours of basketball, or about 19 minutes. (Until roughly half-time… which would be a good time to snack on another banana.)

Along the way we note that we’ve made a conversion from banana to hours. But I know that bananas are different from hours… so is this statement crazy? No — as long as we know that we mean “the enegy in a banana” and “the energy expended playing an hours of basketball.” This is at the heart of understanding the units in E=mc².

The formal statement of what we’re doing

Now that we’ve given a tangible example, let’s explain once again what we’ve been doing using high-falutin’ fancy-pants language.

We’ve used equations that relate fixed numbers of one unit to fixed numbers of another unit. In particular, we’ve defined conversion factors. In the above example these conversion factors were just the number 1 written in fancy ways that combine units. The point is that these conversion factors are constants. If they weren’t constants, then they don’t make sense. For example, maybe I don’t just order a grande iced coffee. Maybe depending on how I feel I’ll order a smaller or larger sized up, or maybe I’ll have it with milk. In this case the number of calories in what I called an ‘iced coffee’ is not constant because there are more parameters. One would have to be more specific when defining the conversion  factor so that it really is a constant.

The lesson to take home is this: dimensionful constants allow us to convert between units.

The speed of light is constant

One of the great experimental discoveries in all of science is the fact that the speed of light [in vacuum] is constant. This is the basis for special relativity. For our present discussion however, the point is that now we have a dimensionful constant which we can use to convert units.

In units that I remember, the speed of light is given by

c = 300 000 000 meters / second.

This tells us that we can write out an equality

[the distance travelled by light in] 1 second = 300 000 000 meters.

Now this looks like our silly “1 banana = x hours of basketball” statement, but it does have a clear meaning. We can change units. In fact, this gives us a natural definition for lightsecond:

1 lightsecond =the distance travelled by light in 1 second = 300 000 meters.

In this way a lightsecond (or lightyear, etc.) is both a measurement of time and distance since we’re using the speed of light (a constant) as a conversion. In these units physicists like to say that

the speed of light, c = 1.

This seems like a weird statement, but it’s really just saying that light in vacuum travels at the speed “1 lightsecond per second.” In any real particle physics calculation we always write things in units where the speed of light is 1 since this makes our equations much simpler (just look at the original post and see how even those equations simplify.) If we want to convert back into useful units we can always insert the appropriate factors of 1 = c = 300 000 000 meters / second, just like we did using the ‘algebra of units’ above.

The meaning of E=mc², redux

So hopefully this makes the meaning of E=mc² a little more transparent. In fact, I would write this as E=m. The factors of c are just there to convert into normal units. I think David wanted me to write something out explicitly as an example, so let me consider the energy associated with the mass of the proton. I can look up

proton mass, m = 1.7 x 10^-27 kg

speed of light, c = 300 000 000 meters/second.

Then the right-hand side of E=mc² tells us

mc² = 1.7 x 10^-27 kg x (300 000 000 meters/second)²

= 5.02 x 10^-19 kg(m/s)²

I’d like to write this into something like joules, so I’d better look up the appropriate conversion from kilograms, meters, seconds into joules:

1 J = 1 kg (m/s)²

So the conversion of units (‘unit algebra’) is very easy — we can just swap the kg(m/s)² for J using 1 = J/[kg(m/s)²]. And Voila: we discover that the energy associated with the proton mass is about 5 x 10^-19 Joules. (I know this as “approximately 1 GeV.”)

Hope that helps! Thanks for the great question.

- Flip

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So now we know that the LHC will be colliding beams at an energy of 7 TeV instead of 14 TeV, at least for a few months.  Does this change anything from the point of view of the experiments?  Yes!

We have been preparing for collisions at 14 TeV for over a decade, and in fact the final plans of 2,610 ATLAS physicists for what to do with the data just arrived here at my office (some of my work here at CERN has been a contribution to these studies).  The 1,828 page, three volume set is a (very) comprehensive final evaluation of what we think we can do with the ATLAS detector and a plan for what physics topics we will study.  This was all done with very sophisticated software simulations that took thousands of person-years to code and test.  After all those years of preparation for collisions at 14 TeV, there are some changes that we have to make for working with real collision data at 7 TeV.

First, the laws of physics predict different rates of particle production at different energies.  For example, our best tool for calibration is probably the particle called the Z boson.  It is relatively easy to pick out from the rest of the data and it has been very well studied.  So we can find it and measure its properties, then compare what we measure to the already known numbers, see if our detector is working as expected, and make any necessary changes to calibrate it.  At 14 TeV, in 50/pb of data (perhaps a few months of data taking), we expected to have about 25,000 Z bosons that would decay into 2 electrons.  In the same amount of data at 7 TeV, we expect about half the number of Z bosons.  So it will take twice as long to accumulate enough data to achieve the same level of precision in our calibration.

There are also some differences in the behavior of particles produced at different collision energies.  In higher energy collisions, particles tend to be produced with more kinetic energy (which means they start out moving faster) and this causes them to go flying off into different parts of our detector than particles produced in lower energy collisions.  Also, having less energy means fewer particles overall are produced per collision.  All of this is important because the simulations that I mentioned above, done at 14 TeV, led us to develop software reconstruction algorithms that would work at 14 TeV.  So now we will have to produce new simulations corresponding to 7 TeV and re-do many studies.

Finally, the experimental signatures of new particles we may create, and of background processes that mimic these signatures that we have to know about to account for, will be different at 7 TeV and 14 TeV.  The potential for discovery depends on the energy of collisions.  At 7 TeV, we do have a chance at producing new particles that have never been seen by previous experiments, although not as good a chance as at 14 TeV.  Again, we will have to re-do some studies to know quantitatively what our chances are, but preliminary studies show that we have a chance to find new particles even with just a few months of data at 7 TeV.

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Last month when I gave a talk about Angels & Demons to a group of high school teachers one of the big discussion topics was the nature of Einstein’s famous equation. Since E=mc² is at the heart of the entire program of collider physics, I thought it’d be a good thing to go over with everyone.

E=mc² explained in one sentence

In one line, E=mc² is the statement that energy E and mass m are somehow the same thing where c is the speed of light, which is a fundamental constant and allows us to convert units of mass into units of energy.

How do I use it?

In the context of the LHC, this equation tells us roughly how much energy is needed to create a particle of a certain mass. In the same way, it also tells us how much energy is contained in some lump of matter. For example, if we annihilated a lump matter with mass m with the exact same amount of antimatter, we would expect to cause an explosion of photons with energy E=2mc² .

Okay. Is that really all there is to it?

Actually, the common form E=mc² isn’t the whole story. The famous version of Einstein’s relation is actually just an approximation for the full expression, which is:

The new letter p is momentum. These are all familiar concepts from high school physics: energy is the ability to do ‘work’ (e.g. move stuff around), mass is some concept of how heavy something is, and momentum characterizes an object’s motion. This equation is telling us that these are all somehow the ’same’ thing, up to factors of the speed of light.

The first thing you should do is check that this reproduces E=mc² . Certainly if p=0 we get the old relation. More generally, if the p term is much smaller than the m term then we’re valid in using the old equation as an approximation. So this equation is at least consistent with what all the popular science books tell you.

Potential and Kinetic Energy

The reason why I wanted to write this out is that this explicitly separates energy into kinetic and potential parts, just as we’re used to from basic science. Before I explain this, you should be a little surprised: there is no gravitational or electrical background causing a potential, how do we get potential energy for a free particle drifting through empty space?

It’s all in the mass! The m²c⁴ term is a kind of potential energy for the particle: it’s the amount of energy borrowed from the universe that is bundled up and stored in the particle. When we annihilate matter and antimatter, we are really releasing this mass potential energy back into the universe.

But wait! Then the p²c² term is supposed to be some kind of kinetic energy. But you already know what kinetic energy looks like for a particle; it’s ¹/₂mv². I know that p=mv, and if I plug this in it doesn’t look right at all!

Lies they taught you at school…

Good. Now we can discuss another ‘lie’ they taught you at school: the usual expression for kinetic energy is also just an approximation! Look back at our main equation: the mass term is multiplied by c⁴, while the momentum term is only multiplied by c². Since the speed of light is a big number compared to the usual velocities that we’re used to, we can see that the mass term is much, much bigger than the kinetic energy term.

The reason why we never talk about the mass potential energy in high school physics is that usually it’s not possible to convert mass energy into energy useful for work; a particle’s mass doesn’t change. The first time we use such a conversion is in chemistry when we look at nuclear beta decay. (So E=mc² is part of the explanation for “why does the sun shine?”)

In order to recover the usual form of the kinetic energy, we can make an approximation. Mathematically this means we do a Taylor expansion. (For those unfamiliar with calculus: this is just a natural way of expanding a function in terms of smaller and smaller corrections.) A good chunk of physics has to do with making clever Taylor expansions. In order to do an expansion we need an expansion parameter which is small and dimensionless (it doesn’t make sense to call a dimensionful quantity ’small’ without a reference point). In this problem we are saying p² is much smaller than m²c², so we can write the expression for the energy as:

Voila! We’ve explicitly written out the energy as a mass potential term plus the usual kinetic energy form. Here the dots mean terms which are smaller by factors of (p²/m²c²), which is indeed a very small number for everyday velocities much smaller than the speed of light.

Another short summary

Our conclusion is that the Einstein relation tell us that a particle’s energy is given by a [quadratic] sum of its mass and kinetic energy. Momentum, energy, and mass are all the same thing in different forms. A particle’s mass is energy that stored up in making that particle heavy while a particle’s momentum is energy that is used to make that particle move.

A hint of more advanced stuff

That’s it for the main idea of this post. While we’ve done some work, however, I wanted to share something to entice any future physicists (or recreational physicists) out there. We can compare our ‘complete’ energy-mass-momentum with the equation for a circle from high school algebra to motivate a mathematical understanding of Einstein’s so-called ’special relativity’.

In the first line is the equation for a circle of radius r. In the second line we’ve rewritten our energy-mass-momentum relation in a suggestive way. The left-hand sides of both equations are constants.

The first equation tells us that a point (x,y) is part of a circle of radius r if the sum of the squares of its coordinates is equal to r². The actual point (x,y) can change, but in order for the point to stay on the circle it has to change in such a way that the relation is maintained. If x increases, y has to decreases; and neither x nor y can increase/decrease too much or else it’s impossible to satisfy the equation. (e.g. the point (2,y) doesn’t live on the circle of radius 1 for any y.)

Let’s understand the second equation in the same way. Now I’m telling you that a particle’s mass is constant. It’s a fundamental property of the particle. (There’s an old notion of ‘relativistic mass’ which has been discarded in the modern way of looking at this.) The particle’s energy and momentum can change (e.g. through elastic collisions), but they must change in such a way that the above relation is satisfied. If the momentum increases, then the energy increases. Well that makes sense from our intuitive understanding of momentum. This also tells us that there is a minimum energy given by p²=0, E²=m²c⁴. I.e. when the particle is at rest the energy is just the mass potential energy.

Great. This all seems like I’m stating the obvious in an overly complicated way. The point is this: the equation for a circle is also a way of defining length. The distance from the point (0,0) to (x,y) is given by r, the length of the ‘radius’ to the point. A definition of length (called a ‘metric’) defines a particular kind of geometry. The symmetries of the metric are symmetries of the geometry: for example, the rotational symmetry of the circle manifests itself in the rotational symmetry of the two-dimensional Euclidean plane.

In the same way the rewritten mass-energy-momentum equation is also a definition of ‘length’ in this energy-momentum space. It has a funny minus sign. The relation can be written in terms of space-time (the combined coordinates of space and time) as

where t is time, x is distance in space, and s is some constant (like r or m²c⁴) called the proper distance.. In special relativity the trajectory of a free particle must obey this equation of constraint. The symmetries of this ‘metric’ (this thing which defines a preserved length) are called Lorentz transformations. The space defined by these symmetries is called Minkowski space (versus Euclidean space that we’re used to). Just as the rotations caused a point to move around in a circle of constant radius, Lorentz transformations are a rotation in spacetime that preserve the proper distance, s.

In particular, what that means is this remarkable fact:

Space and time are in some sense the same thing.

Of course this statement needs to be understood in a mathematical context. Of course space and time are different: we can move back and forth in space but only in one direction in time, etc. But mathematically one can do rotations between space and time. This is precisely the origin of the magnificent results of special relativity: length contraction and time dilation!

It turns out that the analog of a rotation in Euclidean space by some angle is a boost in Minkowski space. The name is chosen specifically to make clear the relation to picking a reference frame.

Anyway, this opens up the rabbit hole to the fantastic story of special relativity which one can find in any number of excellent books or online references. For those who really want to pursue the mathematical story at a basic level, I cannot recommend enough Sander Bais’ book Very Special Relativity. Those with a high-school physics background can read the relevant chapter of The Feynman Lectures on Physics.

-Flip

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Last week I attended the 3rd ATLAS Physics Workshop of the Americas, hosted by NYU, which is located in the Greenwich Village area of Manhattan. This workshop series is jointly organized by Canada, U.S and Latin America, and provides a good venue for collaborators based in the Americas to come together and find out about the latest happenings on ATLAS, talk to ATLAS management in a relaxed setting. This time there were about 140 people in attendance. There was a special poster session that gave graduate students and post-docs a great opportunity to discuss their work. We also had a town hall style meeting with the ATLAS spokesperson and the Physics Coordinator taking questions from the audience. Of course, there were some fun things too, e.g., one evening there was a reception, co-hosted by the New York Academy of Sciences; this was held on the 40th floor of a building in lower Manhattan. (Although views were great, the location was also a grim reminder of the world we live in. This building was right next to where the Twin Towers used to be).

I also spent a day taking in the sights of New York. One afternoon I took the No. 7 subway to “Little India” in Queens; most people on the subway were of Chinese, Korean, Indian (both from East and West Indies), and Hispanic descent. It struck me then that New York was such an apt place to hold an international workshop.

Now I am back at work in Indiana, trying to remember what I was doing before I left for New York!

— Vivek Jain, Indiana University

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Part 3 in a <> part series

As Ken and others commented this and last week, the LHC has been getting negative press recently which has overshadowed the generally positive new run plan set for this year. With the machine not running it’s easy to let despair and doubt overtake your emotions. I’d be lying if I said that I didn’t feel at least a little depressed after reading all the negative press and seeing my fellow graduate students switching over to the Tevatron.

But there’s something important to remember regarding the pessimism and the LHC: negativity sells. Journalists aren’t there to candy-coat the situation – they’re here to keep us accountable, and it’s our responsibility as scientists to explain why repairing the machine is taking as long as it is. It’s much easier to write about things not working and falling behind schedule. Plus, CERN does have a history of being optimistic – and rightfully so. A machine like the LHC has never been built before so we don’t have a lot of experience in dealing with the potential problems that can arise. This is the inherent reason why science takes longer than expected: we’re exploring new frontiers. Did Lewis and Clark say how long it would take to reach the shore? (they fortunately didn’t have graduate students to worry about). It took over a decade and a practically unlimited budget to land a man on the moon, but with the success of the mission, we forget the failures that happened along the way. If we could build the LHC again, we could avoid the some of the problems we’ve encountered thus far, but as scientists that’s not what we do.

We must however be wary of haste. Of course, we do need accountability, but we also need understanding. External pressures and impatience cause mistakes to be made. We must realize that schedules are made and sometimes must be amended not because of some casual oversight but because of the unexpected. We’re not taking a car trip to grandma’s, we’re landing a man on the moon.

(Regina Caputo, Stony Brook)

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Maybe I have a bit of a contrarian streak, but some of my fellow bloggers’ exhortation to “try to be optimistic” rubs me the wrong way.  I absolutely agree with them that some recent news coverage of LHC delays has been unduly pessimistic and misleading, and I am as excited as ever about both the short- and long-term prospects for the LHC, but I think I would rather try to be realistic.  Fortunately, the two positions aren’t that different: realism still gives us mostly good news.

Of course, there is an underlying optimism in being a particle physicist: the basic assumption — perhaps belief, or hope — that the physical universe can be described by equations and laws, so that the physics we know already can point us to the physics we have yet to discover.  That idea has proven true since the days when physics was a branch of “natural philosophy,” and been very constructive indeed, and that line of reasoning tells us that the LHC is a place where great discoveries will very probably be made.  So that much optimism I’m happy to grant; it’s what I’m building my entire career on.  No high-energy particle physicist has changed his or her mind about the importance of the LHC.  Of all the ATLAS graduate students I know, only one has switched away from the ATLAS to work at the Tevatron — and that’s not based on a lack of confidence or interest in the LHC, but simply a bet that he can write a thesis and get back to the LHC in time to catch most of the exciting stuff.

It’s pure realism that refutes some of the implied doubts about the long-term stability of the LHC project.  Repairs on the machine are done except for a few tweaks, and it will be running very soon.  There are a lot of important measurements to be made at our initial run goal of “only” half energy — which, don’t forget, is more than triple the energy of any previous particle physics experiment.  It is significantly less likely, though by no means impossible, that new particles will be discovered at lower energy; but getting to the LHC’s design energy, or very close to it, is only a matter of time and effort.  And, realistically again, time and effort are things that the LHC has in abundance: CERN’s core funding and personnel are guarenteed by international treaty, and contributions to the LHC and its experiments are guaranteed by almost-equally ironclad agreements between universities and funding agencies worldwide.

I think the main difference between realism and optimism is on what we can expect in the next few months.  The start-up plan calls for the LHC to begin running in November, which happens to be exactly when I’m moving back to Berkeley.  I would love to be here at CERN, working in the trenches, as things start up — so why on earth am I doing that?  There are three reasons.  The first is practical; my group wants to keep graduate students in both Berkeley and Geneva, and a bunch of younger students are about to move out.  That means that I could stay a little longer, but not too much — so I’d have to believe that we were going to start in November and get very prompt collisions if I were going to try to stay for them.  Second, although I have no complaints about any schedule or plan produced for the LHC this year, they have all been provisional from a realistic perspective.  There’s a very good reason for this: you can say how long things will take if everything goes according to plan, but it’s very hard to guess what extra work or delays might crop up with a one-of-a-kind machine.  So I’m “betting” on a little bit more unscheduled delay, although I don’t expect it to be very long in the grand scheme of things.  (Of course, I’m not an expert on the work on the LHC or how it’s going; I’m just guessing, and making the best decision I can based on that.)  Third, it will take some time to proceed from the first running of the LHC to high-energy collisions.  How long?  Again, nobody quite knows, it’s never been done before.  But I do know that the folks who run the LHC plan to be cautious and take things step-by-step; we experimentalists waiting for collisions, no matter how eager we are, obviously support this.  So an optimist might not move back in November, but I am.  I’ll come back out for a month in the Spring once I have a better idea how things are going.

Of course, realistically, I could be wrong.

Facebook folks: I’m Seth, http://blogs.uslhc.us/?author=9

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Even though Regina and Ken have already commented, I wanted to add my two cents on the LHC start-up plan.

If you don’t know already, the director of CERN has announced the plan for starting up the LHC.  If all goes well, there will be protons circulating in the LHC in November, and first collisions shortly thereafter.  Next, probably in December or early in 2010, the energy of the collisions will be increased to 7 TeV and the LHC will become the world’s highest energy collider.

The articles cited by Ken in his post gave the impression that the LHC project is on the verge of failure, while this is simply not the case.  As Ken urged, “let’s try to be optimistic”!  While the accelerator will not run at the full energy it is designed for right away, this plan allows operators to gain their first experience colliding beams in the LHC, and allows the detector groups to see particles from collisions in the LHC for the first time as well.  The data we collect next year will allow us to produce our first physics results.  If all goes well at 7 TeV, the energy will then be raised again to about 10 TeV, and we would have a chance at discoveries next year.

But even 7 TeV would be quite an achievement.  Remember that the Tevatron collider at Fermilab currently holds the world record for energy at just under 2 TeV.  7 TeV is not exactly total failure!

I think the announced plan is good news for everyone in the particle physics community.  Last year’s accident hit the community very hard, especially after being so close to having collisions.   Collisions last year would have brought pure joy.  Collisions this year will bring joy, but first probably relief. Relief at not having to answer questions about the LHC not working, and relief for graduate students who would have data they could analyze in order to graduate.  Many of us will be holding our breath for the next few months.  After we see some collisions we can experience that joy, and then start down the long path towards answering some of the fundamental questions we have about the universe.

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