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How flexible is the measurement “a dozen”?

If there are nine hundred and ninety-nine thousand people at a rally it is acceptable to say one million people attended, but if eleven people are arrested is it acceptable to round up to a dozen?

– Answer –

• 1 June 2011: Answer by Callithumpian for How flexible is "a dozen"? -

  Dozen is quite flexible when it is pluralized. While hundreds sounds natural, you don't often hear about there being tens of something. Saying there were dozens of something fills this void without implying an exact multiple of 12.

• 1 June 2011: Answer by Robusto for How flexible is "a dozen"? -

  A dozen is a very specific measurement. It means twelve. If you have 11 items you can't call that a dozen, you'd have to say "around a dozen" or "about a dozen"; if you have 13 items you can say the same, or just call it a "baker's dozen."

  Twelve is a small enough number that you don't really need much rounding.

• 1 June 2011: How flexible is "a dozen"? -

  How flexible is the measurement "a dozen"?

  If there are nine hundred and ninety-nine thousand people at a rally it is acceptable to say one million people attended, but if eleven people are arrested is it acceptable to round up to a dozen?

There’s a “hot question” at the moment about the use of the apostrophe in the phrase Baker’s Dozen, and it got me to wondering: where did this phrase originate?

Did bakers really offer 13 in a dozen? Is it a joke about bakers being bad at math? If bakers did offer 13 in a dozen, then why did they start doing it?

– Answer –

• 21 April 2012: Answer by Chris Moschini for The origin of the term "Baker's Dozen"? -

  I was always told this was the baker cooks 13 - 12 for the customer and one for himself. That way if the batch came out bad, he can easily find out and pitch it before it gets to the customer.

• 21 April 2012: Answer by pbr for The origin of the term "Baker's Dozen"? -

  I understand this differently. From what I was taught, the baker's dozen resulted from compassion.

  The extra item was added by the baker so the households slave/servant would be able to consume one of whatever was being purchased, while walking home with a bag full of food for their master/employer.

• 21 April 2012: Answer by Barrie England for The origin of the term "Baker's Dozen"? -

  As ‘Brewer’s Dictionary of Phrase and Fable’ explains:

  In earlier times when a heavy penalty was inflicted for short weight, bakers used to give a surplus number of loaves, called the in-bread, to avoid all risk of incurring a fine. The 13th was the vantage loaf.

• 21 April 2012: Answer by Carlo_R. for The origin of the term "Baker's Dozen"? -

  On Oxford Dictionary we can read:

  baker's dozen: a group of thirteen (= one more than a dozen, which is twelve)

  Origin.
  late 16th century: from the former bakers' custom of adding an extra loaf to a dozen sold, this constituting the retailer's profit.

  More historical reasons are illustrated on Wikipedia with regard to "Worshipful Company of Bakers":

  The Worshipful Company of Bakers is one of the Livery Companies of the City of London. The Bakers' Guild is known to have existed in the twelfth century. From the Corporation of London, the Guild received the power to enforce regulations for baking, known as the Assize of Bread and Ale. The violations included selling short-weight bread and the addition of sand instead of flour. (So that they could avoid punishment for inadvertently selling a short-weight bread, bakers added a thirteenth loaf to a dozen, giving rise to the term baker's dozen.) The Bread Assize remained in force until 1863, when Parliament repealed it.

• 21 April 2012: Answer by Malvolio for The origin of the term "Baker's Dozen"? -

  Have you checked Wikipedia?

  The oldest known source, but questionable explanation for the expression "baker's dozen" dates to the 13th century [...]. Bakers who were found to have shortchanged customers (some variations say that they would sell hollow bread) could be subject to severe punishment. To guard against the punishment of losing a hand to an axe, a baker would give 13 for the price of 12, to be certain of not being known as a cheat. [...]

  ANTI-EDIT: Wikipedia had some charmingly implausible speculations about geometric explanations for cooking 13 items at a time, which were copied, and not by me, into this answer. Then some killjoy deleted the speculation from Wikipedia, which led RegDwight to delete them from here. RegDwight has apparently never heard the journalist's expression "too good to check".

• 21 April 2012: The origin of the term "Baker's Dozen"? -

  There's a "hot question" at the moment about the use of the apostrophe in the phrase Baker's Dozen, and it got me to wondering: where did this phrase originate?

  Did bakers really offer 13 in a dozen? Is it a joke about bakers being bad at maths? If bakers did offer 13 in a dozen, then why did they start doing it?

In Bloomberg magazine, I saw this sentence:

Rust Belt states that have bled manufacturing jobs.

Does it mean they have lost the jobs or gained more jobs?

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• 9 January 2011: Answer by Eric for What does "to bleed something" mean? -

  Note that bleeding can also refer to the out-dated practice of bloodletting. If you read older literature from when bloodletting was accepted, you might read about "bleeding someone" in reference to an attempt to heal them from some malady through bloodletting. In this case, it could be considered positive. I haven't seen "bleeding something" used in a similar sense in older literature, but it's plausible that you could find examples of it.

• 9 January 2011: Answer by Steve Melnikoff for What does "to bleed something" mean? -

  Just to add to Robusto's answer, to bleed can also be used as a transitive verb:

  drain of liquid or steam; "bleed the radiators"; "the mechanic bled the engine"

  (Bleeding a radiator (the kind used to heat a house, not the one in a car) is the most common usage that I'm familiar with, and refers to opening a valve in the top of the radiator in order to let out any air that may have entered the system.)

• 9 January 2011: Answer by Robusto for What does "to bleed something" mean? -

  Bleed means to lose something steadily in a way that is dangerous to the life of something, as bleeding is to human life. The example you cite means Rust Belt states have lost jobs. If they lose too many — bleed too many jobs — the Rust Belt is in danger of dying. Which it is.

• 9 January 2011: What does "to bleed something" mean? -

  In Bloomberg magazine, I saw this sentence:

  Rust Belt states that have bled manufacturing jobs.

  Does it mean they have lost the jobs or gained more jobs?

Possible Duplicate:
How should I punctuate around quotes?
What do you do when you end the first part of a compound sentence with a quote?
Comma placement when using quotes that end with a question mark

Someone asked What is the difference between saying:

Are you still working there?

Do you still work there?

I started my answer with:

For your specific example, “Are you still working there?” versus “Do you still work there?”, when referring to having a job at a company both are commonly used.

That punctuation feels wrong, but I don’t know what would be preferable in American English. I am referring in particular about ending the parenthetical phrase with "Do you still work there?",. (Wow, how about the punctuation of that sentence.) I need the question mark because of the question, I need the quotes to end the quotation, I need the comma to end the parenthetical, but the rules for punctuation around quotation marks are so odd to my way of thinking that I feel like I must be doing something wrong.

What do you think? Is this the best way (without rewriting the sentence) to punctuate it? If not, what would be better?

EDIT:
So far we have :

• The Chicago Manual of Style not specifically addressing this case but generally saying “Do you still work there?”
• The Gregg Reference Manual saying “Do you still work there?” BUT “if the omission of a comma at this point could lead to confusion, reword the sentence to avoid the problem.”
• and most everyone else agreeing with me on “Do you still work there?”,

So yeah, go ahead and close it, as we are not going to settle the question here?

– Answer –

The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)?

When my friends ask, “What do you want for your birthday?”, I never know how to respond.

It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?

– Answer –

• 7 May 2012: Answer by Old Pro for How should I punctuate around quotes? -

  Whoever said "The Chicago Manual of Style (6.8) says that When my friends ask, "What do you want for your birthday?," I never know how to respond. is the correct form." was most likely mistaken.

  To begin with, they are probably referring to the 15th edition, where section 6.8 addresses periods and commas inside quotation marks, rather than the current 16th edition, where section 6.8 addresses punctuation with URLs and e-mail addresses. However, 15th edition section 6.8 does not address question marks and I could find no example of question-mark followed by comma followed by closing quote in the 15th edition. In any case the 15th edition is out of date.

  The current edition (the 16th), forbids the construction of question-mark followed by comma followed by closing quote with one very specific exception. In section 6.119, punctuation that is part of a title is treated as if it is not punctuation, so if the title ends with a question mark, it would still be followed by a comma. However, if what is being quoted is not a title, then the comma is dropped as in these examples from the 16th edition:

  “What’s the rush?” she wondered. (section 6.10)

  Is it worth the risk? he wondered. (section 6.67)

  “Are you a doctor?” asked Mahmoud. (section 6.119)

• 21 August 2010: Answer by JohnFx for How should I punctuate around quotes? -

  The British put them outside the quotes, which seems much more logical.

  The American style is to put the punctuation inside the quotes. The American version is often known as "Typesetter's Quotes".

  As you can see, I go with the British version, at least in informal writing.

  Interesting fact: They are called typesetter's quotes because when typesetters were laying out the typesetting blocks putting the small blocks for punctuation inside the quotes made the layout more stable and less prone to shift around. That's probably why it seems so illogical, it was done for mechanical reasons, not linguistic reasons.

• 21 August 2010: Answer by moioci for How should I punctuate around quotes? -

  I find the British convention more rational and am trying to break myself of old habits. So '...birthday?", ...' looks good to me. I still swap my knife and fork when slicing meat, though.

• 21 August 2010: Answer by delete for How should I punctuate around quotes? -

  The Chicago Manual of Style (6.8) says that

  When my friends ask, "What do you want for your birthday?," I never know how to respond.

  is the correct form.

• 21 August 2010: How should I punctuate around quotes? -

  The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)?

  When my friends ask, "What do you want for your birthday?", I never know how to respond.

  It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?

What is the difference between saying:

Are you still working there?

Do you still work there?

Which is more common in spoken vs written English?

Google books returned results for both of them.

– Answer –

• 25 April 2012: Answer by Bill Lefurgy for Simple present vs. present continuous -

  There is a subtle difference. To my ear "Are you still working there?" is the more aggressive and challenging form, as in "Jeez, why are you staying at that crappy job?"

  "Do you still work there?" sounds more neutral, as in "Hey, I haven't seen you since I left company x. Do you still hang out with those people?"

  That might be because ARE YOU can be an auxiliary verb, which helps puts focus on the person addressed. DO YOU relies on a verb and the energy of the sentence is directed away from the person addressed, which I think sounds more polite.

• 25 April 2012: Answer by Old Pro for Simple present vs. present continuous -

  For your specific example, "Are you still working there?" versus "Do you still work there?", when referring to having a job at a company both are commonly used, both are acceptable, and anyone who complains about one being wrong would be considered overly critical. Technically, "Do you still work there?" is preferable both in writing and in speaking.

  However, if the situation is two people in a workshop, with "there" referring to a workbench, they have different meanings and you need to use the correct one.

  "Are you still working there?" asks if you are currently using the workbench. Assuming two people cannot use the workbench at the same time, I ask "Are you still working there?" because if you are, then I cannot use the workbench, but if you are not, then I can use the workbench. I would ask this question if I could not tell whether or not you were using the workbench, for example because you were standing next to the workbench and talking on the phone. I'm asking "May I work there or do you want me not to work there so you can resume working there when you get off the phone?"

  If I can see that you are working at the workbench when I ask the question "Are you still working there?" the question can have yet another meaning, similar to "Haven't you finished working there yet?" This choice of meaning is indicated by giving emphasis to the word "still" (by stressing the word when speaking or by using italics when writing). I'm expressing a belief that you are working there and surprise that you have not finished working there yet, and also asking for confirmation that you are still working there, and perhaps asking for an explanation of why you have not finished yet or when you expect to be done. In this situation, asking "Do you still work there" is wrong and I will sound like an idiot (or at least someone who does not know English well) if I ask it.

  "Do you still work there?" is a question I would ask when you are not using the workbench. It means, roughly, "I know you worked there in the past; do you plan on working there in the future?" This is different than "Do you work there?" because "Do you work there?" implies that I do not know that you have worked there before. If the person I'm asking thinks that I should know they have worked there in the past and I ask "Do you work there?", my question will be confusing to them and will likely be interpreted as an incorrect way to ask "Are you working there now?"

• 25 April 2012: Simple present vs. present continuous -

  What is the difference between saying:

  Are you still working there?

  Do you still work there?

  Which is more common in spoken vs written English?

  Google books returned results for both of them.

Some languages have a “regulatory body” issuing recommendations and guidelines regarding the use of that language.

For example in the case of Spanish it’s the Real Academia Española whose status is recognised in all Spanish-speaking countries. The Academy, among other things, publishes a dictionary (“DRAE“), in print and online, which is usually given a lot of prestige (but is not without controversies, of course).

Are there any such authorative—or at least influential—institution(s) or publication(s) for the English language?

– Answer –

• 5 May 2012: Answer by Old Pro for Regulatory bodies and authoritative dictionaries for English -

  Summary

  For what is or is not an English word:

  Consider the current version of the North American Scrabble^® Players Association's Official Tournament and Club Word List and Long List as influential (and authoritative for Scrabble^® Tournament play) on the question of whether or not a word of 15 letters or less is an American English word. Outside North America, consider the World English-language Scrabble^® Players' Assocation's official list, called the Collins Scrabble Words.

  For dictionaries considered authoritative:

  Consider the dictionaries used to compile the Scrabble^® lists as very influential overall. See also this answer at US Equivalent to the Oxford English Dictionary which gives a different list.

  For questions of Style and Usage:

  Several organizations publish "style guides". For academic writing, the most influential are The MLA Handbook for academic writing at the high-school and undergraduate level, The MLA Style Manual for more advanced scholarly writing, The AP Stylebook for news and journalism, and The Chicago Manual of Style for general purposes. Also, The American Heritage Dictionary is notable for its use of a "Usage Panel" of 200 "prominent users of the language" which provides some of the best guidance available for what is considered best usage of words and word forms among controversial alternatives.

  ---

  While there is no offical regulatory body for the English language, one influential regulatory body for American English is the North American Scrabble^® Players Association. They provide a list of words acceptable for use in Scrabble^® play, and thus judge whether or not a word is a word.

  To be fair, they acknowledge that their list is not a complete list of English words, excluding words no longer in use among other things. Also, because of the nature of the Scrabble^® game, they do not address words longer than 15 letters. Still, this is, at least in my mind, the most authoritative list of American English words there is. Which is not to say that OED is wrong if they include a word not on that list, but rather that if a word is not on that list, I would not consider it a current American English word.

  A few things to note about the Scrabble^® lists:

  • The Official Scrabble Players' Dictionary (OSPD) is meant for use in children's tournaments, and therefore excludes offensive words such as "asshole". It is not a complete list even by Scrabble^® standards. As of this writing, the current version is OSPD4.
  • The Official Tournament and Club Word List (OWL) only includes 2-9 letter words. As of this writing, the current version is OWL2, with the next version expected in 2014. It is also focused on usage in the United States.
  • The Long List is a supplement to OWL2. It contains 10-15 letter words.
  • The Collins Scrabble Words list (CSW) is a superset of OWL2 that adds words (and spellings) used outside of the US. The current version is CSW12

  At the moment, you can access electronic versions of these lists via the free study program Zyzzyva. The lists from Zyzzyva include cursory definitions of one sense of the word. The definitions are provided only to satisfy basic curiosity about the word, not to be in any way comprehensive.

  On the subject of authorities, it is worth noting what authorities were used to compile the Scrabble^® word lists. OWL2 was compiled with reference to:

  • American Heritage College Dictionary (4th edition),
  • Merriam-Webster’s Collegiate Dictionary (11th edition, 2003 printing)
  • Random House Webster’s College Dictionary (2nd revised and updated edition, 2000)
  • Webster's New World College Dictionary (4th edition)

  The Long List is published by Merriam-Webster, so it is perhaps not as surprising that it was based on Merriam-Webster’s Collegiate Dictionary, 10th edition

  The CSW adds words from Collins and Chambers dictionaries to the current version of the OWL.

• 13 August 2010: Answer by nohat for Regulatory bodies and authoritative dictionaries for English -

  In the minds of most people, dictionaries and usage guides are a cipher to some presumed existing canonical, regulated definition of what is correct in the English language. Of course, no such canonical definition exists—grammaticality of English is governed only by the bulk of actual usage.

  Most publishers of English dictionaries long ago abandoned any idea that they might set forth what is and is not correct in English—those few that actually did ever hold such a belief were few and far between. Modern English dictionaries, for the most part, are descriptive, although most do offer some degree of usage advice and notes. Merriam-Webster tend to be more descriptive than most, countenancing many usages criticized by others. The American Heritage Dictionary has its “Usage Panel” of experts on language and the usage notes in the dictionary cite percentages of the Usage Panel who approve or disapprove of questionable usages. The Oxford English Dictionary is widely revered as the canonical collection of English words, and it is certainly an amazing work of scholarly endeavor, most interesting in its coverage of historical English. But of course the OED holds no more official status than any other dictionary.

  The most regulation we have today are style guides—such as the Chicago Manual of Style, the Associated Press Stylebook, and The MLA Style Manual. These are of course binding only on the writing governed by the producers of those style guides, but they are also used by many writers who are not required to follow them.

  Then there are the professional peevologists, authors of such works as the Dictionary of Disagreeable English and The Big Book of Beastly Mispronunciations, who berate various usages and pronunciations they don’t like, citing whatever evidence supports their preferred usage or pronunciation, and ignoring the evidence that doesn’t.

  Last, and certainly least, there is Strunk and White's The Elements of Style, perhaps the most overrated book on usage ever written, riddled with errors, hypocrisy, vacuous advice, and fatuous platitudes.

• 11 August 2010: Answer by ShreevatsaR for Regulatory bodies and authoritative dictionaries for English -

  Fortunately or unfortunately, no. There is no regulatory body like the Real Academia Española (or the Académie française, or the many others) deciding what is correct English; English evolves naturally with the changing usage of people. Right and wrong are decided based on describing and analyzing actual usage. (This — "descriptive linguistics" — is so canonical among English linguists that I've seen some of them occasionally find other languages' regulatory bodies an absurd idea. Anyway…)

  Among dictionaries, the Oxford English dictionary and the Merriam-Webster dictionary are a couple of the "good" dictionaries (there are others), but note that these, too, have as their goal being reliable indicators of actual usage, and not regulation of, or authority over, language.

• 11 August 2010: Regulatory bodies and authoritative dictionaries for English -

  Some languages have a "regulatory body" issuing recommendations and guidelines regarding the use of that language.

  For example in the case of Spanish it's the Real Academia Española whose status is recognised in all Spanish-speaking countries. The Academy, among other things, publishes a dictionary ("DRAE"), in print and online, which is usually given a lot of prestige (but is not without controversies, of course).

  Are there any such authorative—or at least influential—institution(s) or publication(s) for the English language?

I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly.

I imagine (but don’t know for sure) that stirring in only one direction will tend to create helical structures in the mixed material, where each helix is more or less uniform but two helices might be quite different from one another; and that switching directions tends to break up and mingle these helices. Is this at all correct?

Is there a way to quantify the effectiveness of different methods of stirring? If so, how much better is it to stir in alternating directions, and how often should one switch directions?

– Answer –

• 7 May 2012: Answer by dmckee for How much more effective is it to stir in both directions? -

  Mixing means and requires turbulence.

  Single direction stirring can settle into a pretty laminar regime at least some of the time. Abruptly reversing direction would break up that order for a while. SO would abrupt stops and starts or just running the machine in a mode where the motion of the blades has a highly turbulent Reynolds number.

  How much reversal do you need? Well, that the crux of it and the devil is in the details. I presume that they settle this question empirically. Engineers can be very simple that way.

• 7 May 2012: How much more effective is it to stir in both directions? -

  I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly.

  I imagine (but don't know for sure) that stirring in only one direction will tend to create helical structures in the mixed material, where each helix is more or less uniform but two helices might be quite different from one another; and that switching directions tends to break up and mingle these helices. Is this at all correct?

  Is there a way to quantify the effectiveness of different methods of stirring? If so, how much better is it to stir in alternating directions, and how often should one switch directions?

For example:

1. No student goes to school today.
2. No students go to school today.

What is the difference in meaning between a singular noun and a plural noun following “No”?

– Answer –

• 7 May 2012: Answer by zpletan for When and why do I have to use singular and plural nouns following "No"? -

  I would say that the difference runs thus (based on my usage):

  • A plural form would be used for a collective decision or to stress a collective situation. No students go to school today implies that school has been cancelled for all students; perhaps it was a snow day or merely a weekend.

  • A singular form would be used for a collection of independent decisions, most often as the basis for personal action, or to stress an individual choice or mandate. No student goes to school today implies that each student has made the independent choice not to go to school today; I would most often see why should I? tacked onto the end of it.

• 7 May 2012: When and why do I have to use singular and plural nouns following "No"? -

  For example:

  1. No student goes to school today.
  2. No students go to school today.

  When and why do I have to use singular and plural nouns following "No"?

Here’s an intuitive problem which I can’t get around, can someone please explain it?

Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other forces, same argument). They exert a force upon one another. In classical mechanics this is expressed as their contributing to the field and the field exerts a force back upon them in turn. In quantum mechanics the model is the exchange of a particle.

Let’s say one such particle X is emitted from P and heads towards E. In the basic scenario, E absorbs it and changes its momentum accordingly. Fine.

How does X know where E is going to be by the time it arrives? What’s to stop E dodging it, or having some other particle intercept X en route?

Are P and E emitting a constant stream of force-carrying particles towards every other non-force-carrying particle in the universe? Doesn’t this imply a vast amount of radiation all over the place?

I am tempted to shrug of the entire particle exchange as a mere numerical convenience; a discretization of the Maxwell equations perhaps. I am reluctant to say “virtual particle” because I suspect that term means something different to what I think it means.

Or is it a kind of observer effect: E “observes” X in the act of absorbing it, all non-intercepting paths have zero probability when the waveform collapses?

Or have I missed the point entirely?

– Answer –

• 7 May 2012: Answer by Ron Maimon for Particles for all forces: how do they know where to go, and what to avoid? -

  In the particle exchange picture, the particles are emitted in all directions and only the ones going from P in the direction of E that hit E are intercepted and have an effect. The other particles interfere themselves out of existence, as there is no on-shell state they can enter while conserving energy, or else return to P, giving the self-energy modification to P's mass. In fact, most return to P, since the self-energy is divergent, while only a small fraction make it to E by comparison.

  This process is virtual, so that it is defined by temporary intermediate states which only can stick around until their phase randomizes them away. For the case of a classical force, you need to use particles that go every which way, forward and backward in time.

  Consider two classical objects interacting with a (free) quantum field according to this Lagrangian:

  $$\int |\partial_\phi|^2 + \phi(x) s(x) $$

  where the source is two delta functions $s(x) = g\delta(x-x_0) + g\delta(x-x_1)$. Each of these classical sources is steadily spitting out and absorbing particles per unit time at a steady rate g, as you can see by the added source term in the Hamitlonian:

  $$ g\phi(x_0) = g\int {d^3k\over 2E_k} e^{ikx_0} \alpha_k + e^{-ikx_0}\alpha^\dagger_k $$

  the g term is multiplying a creation operator and an annihilation operator, so the Hamiltonian has a steady amplitude g per unit time to emit any on-shell particle, and the same amplitude to absorb one. If you have no other source, the particles that are absorbed are those emitted by the source, and you just get an (infinite) self-energy renormalization of the mass.

  This description is the on-shell old-fasioned perturbation theory, in which the intermediate states are k-states and the description is Hamiltonian in time. This is not covariant, but it shows you that particles are spat out and absorbed, and the two sources only interact to the extent that some of the particles spat out by one are absorbed by the other. The old-fasioned picture is useless for actual computations, but it reveals the particle processes most clearly, because it follows the annihilation and creation of physical particles in detail in time.

  The result of the interaction when there are two sources is altered by those particles produced by one, absorbed by the other later. The covariant Schwinger/Feynman form of this introduces particles that meander around in space and time both. Those that do not get absorbed by the other make a field around the particle.

  The fact that you are doing things by loop order means that you are not considering the process of a particle emitted by one source absorbed by itself, since this is a loop. The loop order separation of terms makes the scattering process look weird, since it looks like the emitted particle knew where to go to find the other particle. It didn't. If it came back to the first particle, we would include it as part of the next order of Feynman diagram as part of the self-energy graph.

• 7 May 2012: Answer by Emilio Pisanty for Particles for all forces: how do they know where to go, and what to avoid? -

  As Jerry Schirmer points out, it is not really a discretization of the Maxwell equations as you say, but rather a series expansion of the quantum mechanical cross section for interaction. Thus you put in an electron and a proton with some momenta and you want to calculate the probability of them coming out with some other momenta, which you can express as something like $${}_\textrm{out}\langle p^+,q_1;e^-,q_2|p^+,p_1;e^-,p_2\rangle_\textrm{in}=\lim_{T\rightarrow\infty}\langle p^+,q_1;e^-,q_2|e^{iH(2T)}|p^+,p_1;e^-,p_2\rangle.$$ You then make a series expansion of this quantity in the interaction hamiltonian (or more exactly in the interaction strength $\alpha=e^2/\hbar c$). Feynman's contribution (one of them, anyway) was to give a graphical way of constructing each of the terms in the series (most of which involve pretty ugly integrals and will in fact diverge if not treated properly using renormalization) so that each term gets interpreted as a physical process where, say, the electron and proton interchange a virtual photon.

  The truth is of course that these virtual photon exchanges are not physical: only the whole scattering process is physical and you cannot observe what happens in the middle.

• 7 May 2012: Answer by Vladimir Kalitvianski for Particles for all forces: how do they know where to go, and what to avoid? -

  In a non relativistic Classical Mechanics (CM) there is an interaction potential involving both coordinates: $U(\vec{r}_1-\vec{r}_2)$ and the corresponding force present in either particle equation. There is no need in "exchange" interpretation here. Same for non relativistic QM.

  In relativistic case the potential becomes "retarded". Its time evolution may be expanded in a Fourier series and each plane wave can be called a "longitudinal virtual photon". You see, it it nearly the same interaction potential (force) as in the non relativistic CM, acting between charged particles.

  Apart from retarded "longitudinal" potential, there is also "transversal" vector potential that may include real electromagnetic waves propagating in all directions, not only between charged particles in question. The real photons are not absorbed but scattered so they do not contribute into the charge "attraction". The latter is described with those "virtual photons".

• 7 May 2012: Answer by anna v for Particles for all forces: how do they know where to go, and what to avoid? -

  This choice is closest to the the correct one.

  I am tempted to shrug of the entire particle exchange as a mere numerical convenience; a discretization of the Maxwell equations perhaps. I am reluctant to say "virtual particle" because I suspect that term means something different to what I think it means.

  And virtual exchange is a correct description, because during the interaction the exchanged particle is not on mass shell.

  Keep in mind that in the microcosm of particles nature is quantum mechanical. The particle scattering on another particle and the momentum and energy and quantum number exchanges between them are all described by one wave function, one mathematical formula that gives the probability for the interaction to take place in the way it has been ( will be ) observed.. Thus it is not a matter for "knowing" but a matter of "being".

  The Feynman diagrams that give rise to the "particle exchange" framework are just a mathematical algorithm for the calculations and help in understanding how to proceed with them.

  To see how classical fields are built up by the substructure of quantum mechanics see the essay here.

• 7 May 2012: Particles for all forces: how do they know where to go, and what to avoid? -

  Here's an intuitive problem which I can't get around, can someone please explain it?

  Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other forces, same argument). They exert a force upon one another. In classical mechanics this is expressed as their contributing to the field and the field exerts a force back upon them in turn. In quantum mechanics the model is the exchange of a particle.

  Let's say one such particle X is emitted from P and heads towards E. In the basic scenario, E absorbs it and changes its momentum accordingly. Fine.

  How does X know where E is going to be by the time it arrives? What's to stop E dodging it, or having some other particle intercept X en route?

  Are P and E emitting a constant stream of force-carrying particles towards every other non-force-carrying particle in the universe? Doesn't this imply a vast amount of radiation all over the place?

  I am tempted to shrug of the entire particle exchange as a mere numerical convenience; a discretization of the Maxwell equations perhaps. I am reluctant to say "virtual particle" because I suspect that term means something different to what I think it means.

  Or is it a kind of observer effect: E "observes" X in the act of absorbing it, all non-intercepting paths have zero probability when the waveform collapses?

  Or have I missed the point entirely?