Meanwhile however, there has been an interesting new development pointed out by Brett McInnes in his papers
-
Fragile Black Holes and an Angular Momentum Cutoff in Peripheral Heavy Ion Collisions
Brett McInnes
arXiv:1201.6443
Shearing Black Holes and Scans of the Quark Matter Phase Diagram
Brett McInnes
arXiv:1211.6835
These planar black holes appear alien at first sight because they have an infinitely extended planar horizon and are nothing like the real black holes that we have for example in the center of our galaxy. The planar black holes cannot in fact exist in an asymptotically flat space; they need the asymptotic AdS-space. So they might be alien in the context of astrophysics, but they make a lot of sense as a dual description for the quark gluon plasma.
Brett now notes the following. The quark gluon plasma that is created in heavy ion collisions generically has an angular momentum when the nuclei do not collide centrally. In particular, this angular momentum comes in the form of a shear, that is a non-trivial velocity potential in the direction parallel to the beam axis. The reason is, essentially, that the colliding heavy ions are approximately spherical (in their rest frame) and the amount of constituent particles that takes part in the collision depends on the distance from the beam axis. Thus arises a velocity profile.
So the quark gluon plasma has a shear. But this shear then should also be present in the dual description, ie for the black hole. In his paper, Brett studies such a sheared black hole in the AdS space – and the interesting thing is that he finds it to be unstable. If one takes into account that pairs of branes can be produced in the AdS background, then one can see that in fact an infinite amount of brane pairs can be produced because the brane action is unbounded from below.
But what does this mean?
The description of the quark gluon plasma that the AdS/CFT duality offers does not take into account that the formation, and subsequent fragmentation into hadrons, is a dynamical, time-dependent process. Brett thus argues that in a realistic situation after formation of the plasma it takes some while until the system is affected by the instability. He estimates the time it takes for the instability to develop and finds that for currently existing experiments at RHIC and at the LHC the plasma is stable for a time longer than it exists in the collision zone anyway. So there is nothing to observe in these experiments.
The relevant quantity here is the chemical potential. At RHIC and LHC it is very small, essentially because the collision is so highly energetic that very many particle-antiparticle pairs are created. However, for some upcoming new experiments, such as the ones planned at FAIR, that operate at a comparably low collision energy, the instability might become observable for realistic values of the impact parameter!
Brett is however very careful to point out that while the theoretic argument for the instability is solid, one should not take too seriously the numbers one obtains from his estimate. Since a truly dynamic treatment of the system is presently not feasible, what he does is instead is to calculate the time it takes for signals of an impending instability to propagate in the AdS background. One should not expect the result to be very precise.
Be that as it may, this opens the exciting possibility that upcoming experiments might observe an effect that could only be anticipated by use of the AdS/CFT duality.
Well, I was beginning to believe your assessment - right up until you brought up branes. That quickly brought it up short for me as an explanation. To solve a conundrum one can't rely on such an unproven and "bendable" idea. You're going to have to do better than this to convince me.
ReplyDeleteCool article!
ReplyDelete@Eric:
It is not forbidden to think and talk about "unproven bendable ideas" as you call them that potentially lead to new observable effects.
There is no reason to be that dismissive.
This article is just presenting and nicely explaining an interesting idea without trying to convince anybody of anything.
So I dont know what you are talking about and why you are that scornful.
@Nemo,
ReplyDeleteOne can discuss anything one wants but I hope you at least realize the whole of idea of branes is speculative.
To bring it into discussion at all in a form where it is presented as corroboration of a thesis does not mean anything to me, except that the original author is a fanboy of strings.
There is nothing wrong with speculation as long as one constantly states it as so. Way too little of that is done in physics today, and also in Bee's article.
I am impartial about Bee's writing as anyone who has followed her blog long enough knows. I defend her vigorously against others when i feel she is right. And others are wromg. I do the opposite when that situation is reversed. She knows that. She doesn't need fanboys to make her a better physicist. She needs people like me who try to be impartial.
"I am impartial about Bee's writing as anyone who has followed her blog long enough knows. I defend her vigorously against others when i feel she is right. And others are wromg. I do the opposite when that situation is reversed. She knows that."
ReplyDeleteMaybe I should amend that. She should know that and I hope she knows that. Whether she does or not is not up to me.
@Eric
ReplyDeleteWhy do you insult people who dare to talk, think, write, or be interested in (anything related to) strings for example by calling them "fanboys"?
From a scientific and truly impartial point of view, there is absolutely nothing wrong in being interested in or investigating such things.
To me you seem not impartial at all, on the contrary. As soon as you see certain keywords written (such as strings, branes, and maybe any BSM physics term generally?) your ability to think clearly seems to get eaten away by strong, unreasonable, and unscientific prejudice.
This happens to many people these days and too often prohipits any reasonable, good, and impartial discussion about physics in the comments below any article that contains such an unfortunate keyword in the title or in the body of its text.
This is really annoying, and regularely happens on every physics blog.
BTW I disagree that whenever a term describing BSM physics is mentioned, it should be accompanied by the adjective "speculative" everytime and everywhere.
ReplyDeleteEverybody knows that these ideas are not (direct experimentally) proven at present.
In other areas of science (outside physics) this is done neither with theoretical ideas and concepts, so why demanding it in this case? Because you want to say BSM physics is illegitimate and should not be allowed, as many other people do these days?
@Nemo,
ReplyDeleteYou seem to constantly take the approach of someone who has been victimized because they feel criticism of strings is unwarranted. Context is everything. Science is about logic, proof, and intuition. You are ignoring the fact that my criticism relates to what is unspoken in Bee's article. It is unspoken that ADS/cft is ALREADY only a conjecture. Does it not become unseemly to use still another unrigorus and speculative conjecture to try to prove the original conjecture.
Don't claim being a victim here. You are victimizing science when you agree that this is OK just because you are biased towards string theory. I'm tired of people whining that they are victims to intimidate people to go against the scientific method itself.
@Eric
ReplyDeleteNow you are really trolling. I am biased neither for nor against anything conversely to you and most people. You obviously belong to the crazy anti BSM physics zealots who have know enjoy to attack even the most honest and clear minded minded scientists, such as Matt Strassler for example, for thinking reasonable and scientific instead of trolling.
Peoble would better stop mentioning anything about BSM physics in any blogs since reasonable physics discussions with even a slightly broader audience are no longer possible. They would better just quietly do their work, shut up and calculate and write their papers. As long as they are allowed to and scornful and deztructive poeple who have no clue about the scientific method have not yet a hieved their goal and managed to undermine the natural scientific process and destroy physics.
I m feed up of seing every comment section being overtaken by crazy zealots and trolls who think they have the rigth to patronize physicists and inhibit any reasonable discussion.
Note that you started this by your first scornful comment, I no longer talk to you.
I have nothing against BSM physics and have never mentioned it. You are obviously bringing salivary reactions to the table that have nothing to do with the food presented to you. I myself have presented and written up ideas way, way beyond BSM in the past. It is just that I recognize them as such and don't try to proseletyze for them here or elsewhere. Can you say as much? I don't think so.
ReplyDeleteYes, go ahead and pout.
ReplyDeleteRegarding the "quark-gluon" plasma "evidence", they predicted that it would behave like a weakly interacting gas. The observational evidence says this prediction was WRONG. The plasma, much to the surprise of theoretical physicists behaved like a strongly interacting fluid, which is much more like what Discrete Scale Relativity predicts. Of course, given time the theoretical physicists "adjusted" their model to fit the new data, and now they see it as more confirmation of the "quark" fiction. Another epicycle in their Ptolemaic models.
Chiral algebras yield conformal field theory. How does non-linear dynamical symmetry chirality have linear algebraic consequences? Conformal field theory is typically explored in 2-D. In higher dimensions (e.g., Calabi-Yau, AdS/CFT correspondence, supersymmetric gauge theories, Sasaki-Einstein) it yields string theories having no empirical tests.
ReplyDeleteReality is interesting because it does not crunch maths to obtain results. Models can be rigorously derived, self-consistent, and non-physical for having defective postulates (e.g., the Shroud of Turin plus cartography exposes the fraud). Macroeconomics perpetually patches "heteroskedasticity" but never quite works. Parity violations are diagnostic of vacuum symmetries toward fermionic matter, not exceptions to it.
Very interesting article Bee, thanks for bringing this to our attention!
ReplyDeleteAnd my congratulations to Eric on proving himself to be a total rectal-asymptote ;)
Hi Eric,
ReplyDeleteI do not understand what you think is wrong with my summary. To my understanding taking into account the brane action is relevant to assess the stability of the configuration. He finds it to be unstable. I'm not trying to "convince" you of anything, I have simply reported a result. Best,
B.
Robert,
ReplyDeleteYou should be more specific who you mean with "they." Best,
B.
Hi Bee,
ReplyDeleteI would be grateful to hear about any result recorded by the LHC to correspond to presenting as new physics, that is whether it has a prediction associated with it or not. On that note apparently today CERN is releasing new Higgs data from ATLAS which it said to indicate some peculiar mass anomaly between the Gamma-Gamma and ZZ channel data which might cause a little excitement if it holds up and corroborated later by CMS.
Best,
Phil
Just a little prehistory in association with your post Bee. As well, First direct observation of jet quenching. In association with that image, "2010 ion run: completed!"
ReplyDeleteNow of course to advance this thinking and research you take us deeper into the dynamics of collision process which is culminate of the interaction of decay products. So thanks for the further enlightening.
You write,"The reason is, essentially, that the colliding heavy ions are approximately spherical (in their rest frame) and the amount of constituent particles that takes part in the collision depends on the distance from the beam axis. Thus arises a velocity profile.
So we are talking about then, the most perfect alignment? Also to not see this research in light of astrophysical relevance does not seem as you say, "alien in the context of astrophysics." Do you have more here as to say other then,"a lot of sense as a dual description for the quark gluon plasma."
Best,
As well, research data may be useful here?
ReplyDeleteBest,
"The plasma, much to the surprise of theoretical physicists behaved like a strongly interacting fluid, which is much more like what Discrete Scale Relativity predicts."
ReplyDeleteCan you point me to this prediction? I mean a specific pointer to this specific prediction.
"The dual description of the quark gluon plasma is a black hole in AdS space."
ReplyDeleteDoes anyone really know what this correspondence means?
Hi Phillip,
ReplyDeleteI don't understand your question. These are just two descriptions of the same system that are (conjectured to be) identical (to some precision). Best,
B.
The question is, what does anti-de Sitter space have to do with quantum-field theory? I understand that there is some mathematical similarity, but is there any reason for this similarity? Was the correspondence found by chance? If not, what led to its discovery? Does anyone think it has any deeper significance?
ReplyDeletePhilip, it's not just similarity. It's the exact physical equivalence. Both worlds may admit some observers or observations and for each object that one may measure, there's an object on the other side that the other observer may measure. And they evolve in the same way.
ReplyDeleteThe evidence that AdS/CFT is true, especially in the case of the N=4 gauge theory equivalent to IIB string theory on AdS5 x S5, is overwhelming and covered in a substantial part of the 10,000 papers on the subject. It's no longer a "conjecture" and no sensible person calls it in this way today.
Anti de Sitter space has everything to do with QFTs. This tight relationship wasn't appreciated before 1997 but that's a part of the reason why the change in 1997 was such a breakthrough that many/most leading theoretical physicists consider the greatest discovery in the field in the recent 15 or 20 or more years.
UV and/or IR limits of quantum field theories are scale-invariant and "almost therefore" conformally invariant, too. That's the same group as isometries of the AdS space. Moreover, when QFTs have many colors and are strongly coupled, the qualitative physics becomes hard to analyze, far from the perturbative tools. The reason is that the actual physics differs from the weakly coupled expectations, too. The states arrange themselves into modes of fields that move in a higher-dimensional AdS space and the physics is just the same. So when the coupling is strong, it's more natural, realistic, and weakly coupled to describe the situation in terms of the dual AdS gravitational theory that is weakly coupled.
Everyone who questions the AdS/CFT or the importance and well-definedness of branes or black holes or black hole thermodynamics in 2012 is a hardcore crackpot.
ReplyDeleteHelp for Helbig.
I give you a link to a typical pre-2005 review of "quark-gluon" plasma physics.
http://arxiv.org/abs/hep-ph/0303185
Not up on the subject, but full of opinions as usual?
@RLO
ReplyDeleteThe paper you cite is outdated, the QGP has experimentally been proven to be a liquid both, at the RHIC and at the LHC.
It is not a gas as people previously assumed.
You seem to be the one who is not up to date about the subject, and not Helbig.
ReplyDelete@Nematode
You twit, that is the point. It's a pre-RHIC 2005 paper.
Theoretical physicists made a prediction.
It failed.
They added an epicycle, and things were dandy again.
That's the way particle physics has been done for 40 years.
@RLO
ReplyDeleteLearning better how things are and work in the course of time hase absolutely nothing to do with failure. On the contrary, that is exactly the way how science works and makes progress.
So yes, theoretical physics did and still doas extremely well since much more than 40 years.
I meant experimental and theoretical particle physics.
DeleteRobert,
ReplyDeleteThe paper you refer to has nothing to do with AdS/CFT. I don't know why you bring it up. Yes, there were models which made predictions about the QGP that turned out to be wrong. Measurement rules them out, science moves on. That's how it's supposed to be - or are you claiming it should be otherwise? Best,
B.
Hi Phillip,
ReplyDeleteWell, no, it wasn't found by chance. If you want history, Wikipedia does a good job.
As Lubos already said, the N=4 SYM and AdS_5 x S^5 case is meanwhile very well understood and there is little to no doubt that the descriptions are dual indeed, which is another way of saying they are really describing the same physics. There are a couple of other examples which look pretty convincing too, I lost track of the details at some point. Now people are getting more courageous, using other backgrounds than AdS, trying to do non-equilibrium processes, doing without supersymmetry and so on. These cases are less well understood. But, look, forget for a moment where the gravitational theory came from. In the end it's just a mathematical description of a physical model that you can use to make a prediction, if one with an somewhat unusual motivation. Best,
B.
Wow Bee, neneqilibrium processes ? That is amazing and interesting. Do you have an example ?
DeletePhillip Helbig said
ReplyDelete"The question is, what does anti-de Sitter space have to do with quantum-field theory? I understand that there is some mathematical similarity, but is there any reason for this similarity?"
I think the deepest reason for the correspondence has yet to be discovered. There is some deep identity between dynamical geometry and the renormalization group flow of a holographically dual field theory, though perhaps only certain types of field theories yield something that is recognizably a geometry.
Nemo,
ReplyDeleteNo, sorry, I don't think there's anything published. Just heard people talking about it on occasion. Not even sure if there is much progress, but it's on the agenda. Best,
B.
As expected, no reference to DSR's prediction of the liquid behaviour of QGP.
ReplyDeleteWas it even mentioned as a prediction before the discovery? If so, reference please.
ReplyDeleteI try to avoid fool's errands, which you seem to love so much.
Technically, I said the RHIC results were more consistent with Discrete Scale Relativity's inherent model of subquantum phenomena, but I never said that I made a specific definitive prediction about the fluid behavior. I have predicted the exact nature of the subquantum particles, such as their masses, charges and how they interact.
But what is the point in communicating with someone who is determined to oppose anything I say?
You can study my website if you want to answer your unending string of negative questions.
As you know, Luboš, type IIB string theory at low energies is type IIB supergravity in ten dimensions - a chiral theory (left-right asymmetric) with (2,0) d = 10 supersymmetry. That anomalies in a chiral theory cancel is important! Observed vacuum is isotropic toward massless boson photons: no vacuum refraction, dispersion, dichroism, or gyrotropy (10^-(15) sensitivity, Phys. Rev. Lett. 109, 241104 (2012); arxiv:1208.5288).
ReplyDeleteObserved vacuum is trace chiral anisotropic toward fermionic matter. Parity violations are manually patched with symmetry breakings. Don't argue, look. Opposite shoes insert into trace chiral vacuum with different energies. They locally vacuum free fall along trace non-identical minimum action trajectories, violating the Equivalence Principle. Parity violating Chern-Simons corrections to Einstein-Hilbert action are required to contain anomalies, arxiv:0811.0181, 0907.2562v3
http://arxiv.org/abs/1109.1963
Periodic lattices attack vacuum isotropy
http://elib.mi.sanu.ac.rs/files/journals/publ/69/7.pdf
The smallest scale massed opposite shoes, Section 2
http://www.mazepath.com/uncleal/erotor1.jpg
Two geometric Eötvös experiments
Interrogate spacetime geometry with self-similar enantiomorphic atomic mass distribution geometries. Replace parity violations, symmetry breakings, and curve-fittings with empirically validated founding postulates. Visiting early December Sweden is rewarding.
Hi Robert,
ReplyDeleteWhile I don't necessarily agree with your theories, I do admire you for not bending with the wind of contemporary thought as they vary from moment to moment. I use to think Bee had bedrock principles that were verboten to go against but I have become ever less convinced of that. She herself posted an article not too long ago where she reminded everyone that AdS/cft was a conjecture only.
It is a fine line between being inflexible to new
information, and in being like a willow with no bedrock
principles and being blown with the crowd. It has become more and more evident that she is subject to social pressure. But I can only hope that she sees she is making a fools bargain in aligning herself with Lubos.
As for myself, I'm starting to feel like I've arrived now that I've gotten myself on his crackpot list. I have some company there that that I have a lot of respect for.
This comment has been removed by the author.
ReplyDeleteEric should really stop trolling about things he has no clue about.
ReplyDeleteBy his very first sentence in this comment section:
"Well, I was beginning to believe your assessment - right up until you brought up branes"
he has just exposed his blatant ignorance to everybody.
Including branes in AdS/CFT considerations does not bring in any "new additional speculative conjecture" as he call it. In a threory with open strings branes are there too anyway since T-duality changes the Von Neumann boundary condition to a Dirichlet boundary condition and this fact is well known since a long time ago know.
So it would be nice if Eric just could stop spitting and spatting on things which are way over his head and stop trying to patronize Bee and other people, who know much more than himself, by telling them what topics they are allowed to think about, find, interesting, how they should do science, etc.
Eric has just made a fool of himself by explicitely showing once again that trolling behavior and impertinence go often along with blatant arrogance and ignorance.
"Me thinks thou dost protest too much."
ReplyDelete
ReplyDeleteMethinks: In an era of paradigm-change things can get a bit rambunctious.
Are we in an era of paradigm-change?
Duh!
ReplyDeleteThought for the weekend
"Books on physics are full of complicated mathematical formulas, but thought and ideas are the beginning of every physical theory."
A. Einstein
That statement is not a facile platitude; it is scientific truth.
Eric,
ReplyDeleteAs you correctly noticed I explained the status of AdS/CFT in a post just last week. I also elaborated on it here in the comment section. I really don't know what your problem is. If you use the duality, conjecture or not, you find the conclusion from the paper that I wrote about. I think that's interesting. Nobody forces you to share my interests, neither do you have to "believe my assessment" that it's interesting. Best,
B.
As I stated, since it is a conjecture, which you yourself admit, then it is not scientifically valid to use a non-verified theoretical structure such as branes to corroborate it. It needs independent data to do that. Everything else about this whole discussion between us is moot.
ReplyDeleteAlso, your bias about this whole matter shows. Lubos has stated that AdS/cft is not a conjecture but you failed to be even handed and correct him about this. The rest of your article may very well be scientifically correct, I don't know. But the whole bit about branes corroborating was pure hyperbola thrown in to convince people interested in strings. Even if that idea did not originate from you but from the original author, it should have been met with a critical eye by everyone, not just me.
All of this has nothing to with it being interesting or not. Too much going along to get along with you.
And please, all the rest of you proponents of strings, just STFU for now because it Involves a principle that goes beyond string theory. It involves intellectual honesty, and it is really between Bee and me, not me and you. I've supported Bee in the past when she needed it whether you understand that or not. So let it be between me and her.
ReplyDeleteEric, what is so difficult about stop trolling?
ReplyDeleteAs I have said, by continuously complaining about the branes you show that you have really no clue what Bee's article and the results she reports are about.
Where do you take the audaciousness from to try to force your very badly biased and unscientific personal opinions, beliefs, and prejudices upon Bee and everybody else here? Who do you think you are to have the right to patronize people like this?
If it is really a thing just between Bee and You, why dont you write her a mail and stop trolling here?
Ok, that's it. I personally went to bat for Bee when koala viciously attacked the QG conference she was helping to organize. Everyone who has been on this site awhile knows that. But I can see that Bee won't say anything in support of me being reviled as a troll by a newcomer because I pointed up an error of hers.
ReplyDeleteI see the writing on the wall, so goodbye.
Hi Eric,
ReplyDeleteI appreciate your comments and I assure you I do not take your criticism personally. However, I think you missed the point of the paper that I was writing about. It starts with the premise that the AdS/CFT correspondence holds. And if you buy into that, then you are lead to certain conclusions, which is what my post explains. I thus do not understand at all what you are trying to say by dismissing the relevance of branes in the stability analysis, it doesn't make any sense.
You can say you disregard the evidence that we have for AdS/CFT and you're thus just not interested in the topic at all. Or you don't believe that it's a good description for strongly coupled QCD. Fine with me. After all that's a question that observation must decide. But it doesn't make sense to selectively dismiss part of it which is what you're doing. Best,
B.
Eric,
ReplyDeleteI did not say you are a troll.
But (in this thread at least) you keep continuously and rudly (I now know what STFU means ...) insulting people who work on or are interested in topics you dislike for personal reasons, in particular everything related to string theory. And you take big words into your mouth such as "intelectual honesty" to impress others and try to enforce your biased unscientific views onto others. You do all this even though you do not even roughly understand the physics behind the topic Bee's article is about.
I am sorry to say this, but the technical term for the disruptive behavior you showed in this thread up to now IS trolling. See this Wikipedia definition
http://en.wikipedia.org/wiki/Troll_%28Internet%29
AdS/CFT correspondence is a five-dimensional theorem - so it cannot work well outside of five-dimensional systems, like at the very boundaries of the observable Universe
ReplyDelete/* Does anyone really know what this correspondence means? */
ReplyDeleteAdS/CFT duality is a special case of one-to-many duality, which means that the microscopic objects and phenomena appear similarly to the large objects, which are composed of them.
This comment has been removed by the author.
ReplyDelete"The whole purpose of physics is to find a number, with decimal points, etc! Otherwise you haven't done anything." - Richard Feynman -
ReplyDeleteWhat is that number in case of AdS/QFT ???
@Joel
ReplyDelete... 42 !!!
/* What is that number in case of AdS/QFT */
ReplyDeleteIMO the physics is not just about findings of coincidence in numbers as this is a subject of numerology. The AdS/QFT says, the geometry of quantum and relativistic objects is symmetrical about conformal boundary. The quantum gravity theories struggle with interpolation of quantum mechanics and general relativity, which can be apparently made in many ways. But if you keep the above symmetry requirement, then the number of possible solutions will drop precipitously (from 10^500 to 10^100 or so..;-)). In this extent the AdS/CFT works in similar way, like the SUSY and it even gets broken with higher dimensions as well.
Zephir:
ReplyDelete"AdS/CFT correspondence is a five-dimensional theorem"
This is wrong. Please stop spreading misinformation. Best,
B.
Zephir,
ReplyDelete"... physics is not just about findings of coincidence in numbers as this is a subject of numerology ..."
Is QED and the calculation of the anomalous magnetic dipole moment which agrees to about 12 digits with experiment "just numerology" ?
This I think is the kind of physics Feynamn alludes to.
Nemo
ReplyDelete... 42 !!!
that would be the final answer and the end of physics -:)
RLO wrote:
ReplyDelete"Technically, I said the RHIC results were more consistent with Discrete Scale Relativity's inherent model of subquantum phenomena, but I never said that I made a specific definitive prediction about the fluid behavior. I have predicted the exact nature of the subquantum particles, such as their masses, charges and how they interact."
Here is what you actually wrote, still there for all to see:
"The plasma, much to the surprise of theoretical physicists behaved like a strongly interacting fluid, which is much more like what Discrete Scale Relativity predicts." (emphasis added)
So, technically, you said that DSR predicts interacting-fluid behaviour. I ask again, where is this prediction? (Whether it is definitive or not is another question.)
Regarding "the exact nature of the subquantum particles", I recall that you predicted substructure of the electron on a scale which wasn't accessible back then but has been for some years no. No substructure on the predicted scale observed, "definitive prediction" (your words) falsified, thus DSR falsified. Your response? Epicycles, which you criticize to no end when someone else suggests something which you interpret as an epicycle.
Stay tuned for next week where RLO will claim that DSR predicts AdS-QFT correspondence. :-| It is interesting that most of DSR's predictions are mentioned only after the phenomenon in question has been discovered.
ReplyDeleteGood Morning r. Helbig,
And how are we feeling today?
You are completely correct that I should have used the word "anticipates" rather than "predicts" if I was being scientifically and technically very careful.
Note that I did not say "definitively predicts". If I had said that, then you would have had a much stronger case.
Sometimes people use words in the colloquial or informal manner. Were I to bother to look through your writing, I am sure I could find a considerable number of instances where you do the same thing.
Usually I am a bit more careful, and thank you for the reminder.
However, I think you have jumped on one minoe technicality, and ignored far more important issues.
Same as it ever was.
Best,
O