particle physics - How large is the information collected from an inverse femtobarn of collisions?

I ran into this while looking at measures of humongous amounts of data. How does the information (data) collected in an inverse femtobarn exposure compare to a gigabyte of data ?

Answer

I think what you're getting at is not some kind of mathematically rigorous equivalence, but more what it means for a particle physics experiment like ATLAS to collect 1 inverse femtobarn of data. And actually this is computable quire easily.

The design frequency of the LHC is 40Mhz (which corresponds to 25ns bunch spacing, but now i is at 50ns). But since most events are uninteresting background all modern experiments have a system called a "Trigger" which only records events which pass some rough requirements which would render them interesting (maybe a high-momentum electron or jet).

ATLAS is routinely recording at 300Hz (a $10^5$ reduction of rate from the initial collision rate). That is 300 events per second. The size of an event in terms of storage space varies from experiment to experiment and depends on the software it uses, but for ATLAS it is something of the order of 1.5MB/event.

Currently the LHC runs at peak luminosities of 12600 $\mu b^{-1}/s$ (microbarn per second), this decreases over time since the beam intensities decrease, let's just run with 1000$\mu b^{-1}/s$. An inverse femtobarn is $10^9\mu b^{-1}$

so we have:

$$\frac{300 \text{ Events}}{s}\frac{1.5 \text{ MB}}{\text{ Event}}\frac{s}{1000\mu\text{b}^{-1}} \approx 0.5 \frac{\text{MB}}{\mu\text{b}^{-1}}$$

so for $10^9 \mu b^{-1}$ we have

$$0.5\cdot10^9\text{MB}$$

so 500 TB of data

PS: this is just an back-of-the-envelope calculation of course. The rates are constantly changing and the luminosities as well. So collecting 1/fb of data in a low lumi setting requires much more data (since one would still max out the bandwidth of 300Hz recording) than in high lumi settings (where one is still bound by the 300Hz boundary, so the trigger would have to do a tighter selection)

Why is the meter considered a basic SI unit if its definition depends on the second?

The metre is the length of the path travelled by light in vacuum during a time interval of 1  ⁄ 299792458 of a second. – 17th CGPM (1983, Resolution 1, CR, 97), source

The meter (or metre) is considered one of the seven base units in SI, but since it depends on what is “a second”, shouldn’t it be a derived unit? Why is the meter considered a base SI unit, even though it depends on the definition of a second?

I am aware that other base units such as the ampere also depend on other base units (namely meter, kilogram and second), and this just increases my confusion even more. Perhaps my question boils down to: What property must a unit have so that it is called a base SI unit?

Answer

OP here.

Instead of choosing an answer to accept, I decided to post my own, collecting what I learned from the great answers by @Wrzlprmft, @Steeven and @MassimoOrtolano (all upvoted!), and organized in such a way that answers my own questions more directly. Thank you all, I learned a lot.

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At a first glance, because although it does depend on the second, it is still arithmetically independent from the second (and the other five base units). But looking deeper, all this boils down to historical reasons.

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First of all, the SI base units were chosen: they are not imposed by nature. Therefore, although quite disappointing, the correct answer to the question above would be "it must be one of meter, kilogram, second, ampere, kelvin, mole or candela". This answer is not fulfilling, though.

They are called "base" units because all units can be derived from them (similarly to the basis of a vector space, for example). Therefore, they are supposed to have these properties:

• 
  

  All units can be written as a combination of the base units and dimensionless constants.

  
  


• 
  

  All base units are arithmetically independent. This means that no base unit can be written as a combination of the other base units and dimensionless constants.

  
  

The set "meter, kilogram, second, ampere, kelvin, mole and candela" happen to satify these properties. But many other sets also do.

So this begs the question: Why this specific choice, why not other choices? The answer to this, to me, is quite disappointing as well: it all boils down to measurement convenience and historical reasons. Let's look further into this.

Consider the known "ampere versus coulomb" story. The ampere was chosen as a base SI unit, and coulomb is just a derived unit, obtained as $C = A \cdot s$. Instead, it would be fine to choose the coulomb as the base unit, and the ampere as the derived unit, obtained as $A = C \cdot s^{-1}$. Why the ampere and not the coulomb? Basically, the ampere was chosen for measurement convenience (see linked question to know more). So far so good, since a choice has to be made anyway.

But there is a major caveat in the second bullet above!! It might be surprising at the first, but whether or not two units are arithmetically independent is also historically grown!!

• 
  

  Consider the Magnetic Flux Density (B-field) and the Magnetic Field Intensity (H-field). The first is measured in tesla and the second in ampere per meter. They are arithmetically independent (because tesla cannot be written solely from ampere per meter). We have the relation $B = \mu H$, where $\mu$ is measured in $T \cdot m \cdot A^{-1}$. Well, instead, we could have $T = A \cdot m^{-1}$ and have $\mu$ dimensionless, had science developed in another way.

  
  


• 
  
  

  Consider the Electric Charge and the Electric Current. The first is measured in coulomb and the second in ampere. They are arithmetically dependent: $C = A \cdot s$. We have the relation $i = \frac{dq}{dt}$, or for the sake of the argument, $i = \alpha \frac{dq}{dt}$ where $\alpha = 1$ is dimensionless. Well, instead, we could have $C$ and $A$ arithmetically independent, and have $\alpha$ be measured in $A \cdot s \cdot C^{-1}$ had science developed in another way.

  
  

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While writing this answer, I realized that this question has actually two interpretations. The unintended interpretation would be: Couldn't other unit be used in its place? The answer is, yes, definitely another unit could have been used, such as the newton. This would be the same story of using the coulomb in place of the ampere, no problem.

Now, to the correct interpretation: Why is the meter considered a base SI unit, even though it depends on the definition of a second? Shouldn't the meter be a derived unit, leaving only the other six units as the base units?

Short answer: It is indeed a base unit. It shouldn't be a derived unit. And this is all due to historical reasons.

First of all, although the meter does depend on the definition of a second, that is not the only thing it depends on. It also depends on this thing called "light" (more precisely, on how fast light moves). Just the fact that it depends on the second is by no means enough evidence that it is a derived unit. We have to look further into it.

Consider the other six base units, from the SI the way it is:

$$\{\text{kg}, \text{s}, \text{A}, \text{K}, \text{mol}, \text{cd}\}$$

Is it possible to write the meter as a combination of the above units and dimensionless constants? Think twice before answering!! You might have said "no!" in your head, but it's not that simple. In fact, this is also a choice. But not a choice that we make easily. Instead, it's a choice that history already made for us. History chose that meter can't be expressed this way. But, quoting @Wrzlprmft:

Had the finite speed of light been a pervasive phenomenon to mankind since the dawn of time, we might have incorporated this strict relationship in our thinking and unit system, always equating a length with the time it takes light to travel that length and never using separate units for length and time.

Therefore, had mankind evolved in a different way, it might be very natural to just write

$$1\text{ m} = \dfrac{1}{299\text{ }792\text{ }458}\text{ s}$$

and have the SI with only six base units.

quantum field theory - What is crossover?

It is known that electroweak and QCD phase transitions in the standard model are so-called “crossovers” [1]. What is the difference between a crossover and a phase transition of the second kind?

^{[1] See eg., Sticlet, D. “Phase Transitions in the Early Universe. Electroweak and QCD Phase Transitions” [PDF].}

Concentrating Sunlight to initiate fusion reaction

The idea is to collect sunlight over a large area, and concentrate it down to the nano scale.
For the sake of discussion lets say you concentrate all the light you collect down to 1000 nanometers (1µm).

Questions is... how much surface area sunlight would you need to collect and focus to 1µm, in order to deliver enough energy density to initiate a fusion reaction.

cipher - Labryca — Floor 4: I've Just Seen a Face

You are currently on: 4F

1F 2F 3F 4F 5F 6F 7F 8F 9F 10F 11F

Yes, I’ve come back from the dead… for now, at least. All updates beginning from here should be bi-weekly (every 2 weeks, before any nitpickers from English Language & Usage show up on here). I’ve pretty much given up on trying to implement the “quiz” section of this floor the way I wanted to; I was hoping to find a way to create clickable image maps for the Yes/No buttons using an online wizard without having to actually write code, but failed to find anything better than an animated GIF creator. Hopefully I can get some guidance on how to make those before the 5th Floor launches, anyway.

Also, for any more senior Puzzlers who might think I'm making syntax mistakes: I am indeed aware that images can be embedded directly in a question's text. I just feel like making people click on each of the narrator's photos individually heightens the mystery a bit. Plus, last time I made one of these floors it was done and dusted in ten minutes flat.

Mr. Kinsella repeats the password you have just given him and playfully adds, “…is… correct!” He steps aside to grant you admission to the round elevator. Barely three hours have passed since you first stepped into the Labryca Complex, and you’re already three complete floors in. With renewed confidence, you board the next elevator. But very little could ever have prepared you for the challenges ahead.

The elevator’s doors press shut, it begins its smooth ascent, and it stops… but the doors don’t open for you this time. You bang on them, receiving no response; you press and claw at various areas of the walls, but find them to be just as sheer and sterile as those of any previous Labrycean room. Soon enough, you are at a loss as to how you can escape from this featureless elevator.

Almost featureless. Just as you’re ready to try smashing the overhead light fixture to try to find some kind of key, you turn your attention to the back of the elevator and spot a grey frame embedded within it, curved to fit the wall. Quickly, you dig out your cell phone and activate its camera roll, hoping to preserve as much photo evidence as possible. You then tap on the screen and it activates, flashing a message.

A fanfare of 8-bit elevator music heralds the appearance of a peculiar white face. Blue text then scrolls onto the screen letter by letter, as if the Door Identity Verification Apparatus mascot – or DIVA, as you refer to her to save precious time – were greeting you herself.

The timer, clearly showing your total remaining time in the Complex, ticks down two seconds before DIVA spits out a message in green text, this one much stranger than the last.

What could it mean? It remains on the screen for about seven seconds; you’re more baffled than before, and that’s really saying something. But just as you’re ready to obey her literal word, switching your phone over to Facebook to tag a photo of one of your more annoying friends, the letters of the message rearrange themselves on the screen, moving around and turning red to form themselves into a much more sensible anagram.

You figure that if you’re challenged to any sort of “game” while trapped in an elevator, the reward can only possibly be one thing, so you comply and touch the screen again. DIVA’s game appears to be a quiz: she presents you with a series of yes-or-no questions, and a light illuminates on the screen each time one of your answers is correct. Any incorrect answer forces you to restart the quiz from its beginning, and, lo and behold, you manage to get every question wrong at least once. But even still, your confidence is on a high and you proceed fairly quickly through the game. Your camera is fully operational, enabling you to record all of DIVA’s questions and – shall we say – responses accurately; they are as below.

Question 1
Question Text
“Yes” Response
“No” Response

Question 2
Question Text
“Yes” Response
“No” Response

Question 3
Question Text
“Yes” Response
“No” Response

Question 4
Question Text

“Yes” Response
“No” Response

Question 5
Question Text
“Yes” Response
“No” Response

Once all five lights are illuminated, a congratulatory message from DIVA appears, along with another confusing green-colored phrase that you hope will rearrange itself for you. However, you stare at the message for a while and the letters do not move, and another tap to the screen causes it to switch itself off as you finally hear the elevator doors slide open behind you. Well, gee… now you’re almost glad you were so bad at the quiz!

Another even-numbered floor awaits outside the elevator, and thus, as on the second floor, you begin your journey in its center. However, it is clear that no billiards, pub grub, or indeed fun times of any sort are to be had here. Before you is a corridor, spiraling outward clockwise, with seafoam-green walls, dull gray carpeting, and artificial plants in pots; all along it, gray-shirted office workers are perched inside alcoves, most typing away furiously on outdated computers. It appears you have reached the Complex’s cubicle farm.

The first few cubicles have their occupants’ full names affixed to their doors, and you bypass them swiftly, stopping only to notice their facial expressions, since all of them appear to have strong, and very different, attitudes related to their work. Behind the first door you encounter, “Hannah Lambresco” looks off to the side and purses her lips while she is typing, either whistling or trying to deny a mistake. Behind the second, “Alexa Daniels” looks positively ill, with a visible green complexion and her eyes squeezed shut. And yet the third cubicle’s occupant, “Wei Su,” is all smiles as you pass; has he just gotten a promotion?

When you glance into the fourth cubicle and find “Linwood Rafura” hunched over in his chair with downcast eyes and a guilty expression, you can no longer help it; you initiate a conversation with him and ask him what the matter is. “My program…” Mr. Rafura laments. “Nobody understands my program! I’m trying to help the Labryceans, and nobody is going along with it! I should just quit now…”

Beyond here, a coffeemaker stands on a blocky extruded shelf, and a male and a female employee, looking just as emotional as those before them, step out of the adjoining offices for cups. Thirsty and knowing you’ll most likely need to be awake all night, you swipe a cup yourself and catch a snippet of conversation.
“Ugh… Gina…” sighs the man, his eyes very small, round, and downcast due to sleep deprivation. “I did not drink all your coffee… before you had a chance to–“
“Cameron!” the woman interrupts, leaning over him with a red face and an overbearingly angry expression. “You tell me that every solar cycle! And it’s never, ever true!”

You notice a direction sign on the wall behind the coffeemaker; for documentation purposes, you snap a photo thereof before moving forward.

The “31” in the bottom right of the sign may be mysterious to the grunts in this office, but to you, it clearly represents your destination, and you redouble your speed past the final four cubicles, stopping only to note the unique workers within each: a moaning woman with eyes shut and what you’d take to be tears running down her face; a man named Nils (if his office door is to be believed) with his eyes wide, apparently flabbergasted by his current data entry session; a female technician who appears extremely confused, her eyes spiraling in circles; and finally, a messy-haired woman with thick eyeshadow and maniacal eyes whose desk is cluttered by numerous coffee cups and energy drinks.

Just beyond the door to this tenth and final cubicle, a heavy, sturdy door is surmounted by a glowing “31” sign that resembles the “11” you saw at the far end of the bar earlier. You’ve got a strong feeling that this door may be one-way; taking a final glance around the Wallview installation, you brace yourself and once again set out for the fourth floor’s baffling ring of rooms. You’re already down the rabbit hole; it’s time to check out just how deep it will go.

You could not have imagined a more artificial-looking space than this one; a quick circuit of all ten rooms in this ring reveals the presence of nothing at all besides the ten computer terminals. The green walls and gray carpets you noticed earlier also persist into this room, without even a speck of dust visible on any of them. Of course, gray is the perfect color for disguising dust, so what do you know?

With no further ado, you’re back down to business recording the ten customary letter strings present on these terminals.

SECUREALPERINSNAMEPLATEIN

LOCKWISEINWARDONTHEMULTIP

RSTINITIALKEEPOLDRULESBUT

ENDINGYESFACESEVENROOMSNO

SDTTTEHRTEPAALOOSANFITVER

IFSSKNAHSMORFEERFSMOORYNA

THIRTYFOURNEXTODDROOMSASC

TELEFTRIGHTTHENUPSIDEDOWN

ABJERNQPBAPRAGEVPFDHNEFRP

LTMCIEHBONSEENIONRTNRUSAG

On what feels like your hundredth pass around this ring of enciphered messages, you arrive back at Room 40 and finally decide you’re prepared to transition to the next stage. As per usual, beyond the metal door in the outer wall of the Complex, an elongated elevator awaits, with a black-clad employee standing guard before it. This floor’s Guardian is very tall and, it appears, controlling. His red-haired head turns to fixate on you from above, and he speaks with the commanding demeanor of a drill sergeant – still a major improvement, in your opinion, from the whiny, dramatic employees below.

“Hiram Remmick. Fourth Guardian of Labryca,” he recites very simply. “Password, please!”

Sharp-eyed geeks, particularly those who spent hours squinting at a certain small screen about fifteen years ago, may notice that the character of DIVA has been… shall we say… “borrowed” from somewhere. (Then again, I was also expecting somebody to have recognized the character in my avatar by now and no one has commented on it, so maybe I’m mistaken.)

Knowing where this character originally appeared will not help you with the current puzzle, but during the last few floors, it may give you a slight but unique form of advantage. Thus, if you know where DIVA held her first job and you’re hoping to be a certified Conqueror of Labryca before anyone else on this site, it might be in your best interest to not tell other people.

I also include this comment as a copyright disclaimer. I didn’t invent this character. I didn’t draw her. I don’t own the rights to her. Yadda yadda. Burma-Shave.

Answer

After anagramming DIVA's clue, we skip straight to

Room Thirty Seven (anagram of Even Try This).
"Thirty four next odd rooms ascending yes faces even rooms no." Using the workers facial expressions and the hint from DIVA ( :) == 31 and O_O == 40), we order the rooms based on the order they appear in the story text (though not the order they are timestamped in), leaving us with

39 33
36 32
31 40
34 35
37 38

Which leads us to

continue our previous path through the cube farm (starting at bottom left, going clockwise) - with 33 taken before 39 due to "odd rooms ascending"
"Secure Alperin's nameplate in any rooms free from shanks's first initial keep old rules but now read concentric squarse clockwise inward on the multiples or numbers containing" Now we need to decipher 35. Credit to @Arka Karmarkar for nailing it down. We take the text in our grid, and read it starting in the top left corner, clockwise, outer to inner. This gives us the string "SDTTTEOFREVTIOPEHRTLNASAA" - which if we place into another 5x5 grid and read down (it is a multiple of 5, don't forget) we end up with
"SEVEN DO THAT FIRST ROTATE PLATE" This connects to make the final message "Rotate plate left right then upside down" - which will get us the key by applying the plate in rooms 31, 36, and 40 - the rooms that do not contain a "D", which is Shanks' first initial: "SEPARATOR"

quantum mechanics - Difference between optical potential and nuclear potential (used in neutron optics)

I am discussing a question related to elastic coherent scattering of neutron from a nucleus. I am referring to the terms (optical and nuclear potential) which are used on page 272 of the review article 'Neutron optics' by AG Klein and SA Werner [Rep. Prog. Phys. 46 259 (1983)], where the author introduces the optical potential as the nuclear potential, and on page 273, where he later calls this optical/nuclear potential as Fermi potential.

I didn't understand that what is the fundamental difference between optical and nuclear potential. Also, since nuclear potential is negative, why is Fermi potential not carrying a negative sign?

atomic physics - Bohr's model and positronium

I was trying to get an order of magnitude estimate for the radii and energies of positronium using the Bohr's model. I did find a few places where they have used the reduced mass to replace the electron mass in the equations. See this for example. However, I don't see why using the reduced mass works. What is the reasoning behind this?

I tried a different approach. If the positron and electron are in a orbit of radius $r$ about their common centre of mass then the force of attraction felt by each is

$$F=\frac{e^2}{4r^2}=\frac{e(e/4)}{r^2}$$

where working in cgs units makes coulomb's constant 1. $e$ is the magnitude of electronic charge.

So, the electron for all intents and purposes "feels" as if there is a positive charge of magnitude $\frac{e}{4}$ around which it is revolving. And therefore, we must replace $Z$ by $e/4$ in all equations for hydrogen-like species.

This gives results that are scaled by a factor of $4$ from the hydrogen atom. Whereas using the reduced mass gives results scaled by a factor of $2$. Why is this approach incorrect?