@Slereah For the rigorous issues see the MO post I linked. Apparently it is consistent with ZFC that every real is definable in the sense that there is a formula that it and only it fulfills.
@0celo7 Ah, but there's also the principle that things that are true in ZFC but can't be proven in ZF cannot be "written down". There is an MO thread that makes that precise but I can't remember how to find it
@Slereah I mean in the sense ocelot asked for, like, it's impossible to write down something that actually tells you how the well-ordering of the real looks like, you can only write down that it exists
I assume you know the general theorem that, using the axiom of choice, every set can be well ordered. Given that, I think you're asking how hard it is to actually define the well ordering. This is a natural question but it turns out that the answer may be unsatisfying.
First, of course, without ...
There. Some models of ZFC have formulae for the well-ordering, others don't
@Physicist137 That's nothing, if choice fails you get that the countable union of two-element sets can be uncountable. Which is to me far worse than B-T since it doesn't need concepts like "measurable".
does anyone want to discuss this question with me->there is a peanut seller who sells peanut in upward accelerated lift using beam balance,will he gain more than if he sells on ground?
@KartikWatwani Try determine the reaction force exerted onto the peanut and work out whether it is a profit or loss by compared with the inertial case (For convenience, let the mass of the peanuts be $m$
according to me their will be no extra benefit on the elevator as in beam balance balance is achieved when both the sides have equal weight now if they even go in the elevator both the sides will have same normal reaction on peanut as the increase in normal reaction will be same on both the sides say "ma" m being mass of peanut and a being acceleration of lift
@heather OK, so I think the main issue we disagree on is the importance of a wrong answer being posted in a comment. I strongly believe that the decision of whether a wrong answer should be posted or not should not depend on whether that answer already appeared in a comment. I'm curious as to why you think otherwise.
The secondary issue is whether wrong answers should be posted at all. My opinion on that is not as strong, but I'm basically against it because the purpose of this site is to give people correct answers to their questions, and posting an answer that is knowingly not correct does nothing to contribute to that goal.
@DavidZ, so, just to clarify your position, you don't think a wrong answer should be posted period, whether or not it's been posted in a comment, right?
(cont. from slereah's) and if you have a lot of peanuts, the effect can be magnified many times so that that same batch of peanuts might be heavier in the elevator, potentially lead to earning more money with less number of peanuts weighted
@heather I don't believe that a wrong answer should be intentionally posted, whether or not it's been posted in a comment. If someone posts an answer that happens to be wrong because they have a good faith belief that it is (or could be) the correct answer, that's totally fine.
@0celo7 Well, I see an easy way to see that there are at least two isomorphism classes for each $k>0$. I'm currently unsure how to show they are the only ones
@Secret Your large and mostly empty pictures which don't convey a lot of information are rather disruptive to the chat flow, especially when multiple conservations are going on.
@DavidZ, Right. I think if a wrong answer has been posted in comments it should be posted as an answer under community, because then the system will down vote it as wrong. The whole meta question is what to do with wrong comments, and we're discussing everything from adding down votes to nuking them all, and those options all seem to be a pain. If we just say, okay, everyone's got a responsibility
@DavidZ to just move all pseudo-answers into an answer, whether community wiki or not, that spreads out the work load and it shows whether answers are right or wrong by an already implemented system.
@heather If we do that, the users who maliciously post those answers in comments to evade the reputation and face loss that would occur when their answer is downvoted have successfully evaded those losses. We should never post wrong answers as community wiki, imo.
I think that it's okay to delete it, I just think it's ideal to show the original poster they were wrong...and, especially if it's a common misconception, it could help people to see that it was wrong.
@0celo7 Not to troll, exactly. Some may be posted in good faith and the user is simply mistaken, but there are users who I'm pretty certain use comments to espouse their views without getting downvoted
@heather I can promise that there will never be downvotes for comments. Search the moth meta for that if you want, but the team has been consistently ... ehm ... firm about that.
@dmckee when people talked about changing frames of reference, I often heard about how they go from one inertial frame to another via some coordinate transformations, but not heard much about changing into another accelerating frame (e.g. trying to compute some properties of an accelerating projectile by moving into the accelerating frame so that the projectile will be at rest).
Is there a reason other than fictitious force considerations that make transformations into an accelerating frame not an attractive way in computation? For example, how will such scheme break down when used in rela…
@dmckee Will the lorentz transformation (and its derivatives wrt coordinates that may arise) when transforming from one accelerated frame to another take account of possibel complications that arises due to e.g. newton 3rd law not compatible with relativity?
(I am not sure if my question is clear, by I heard that accelerating frames in relativity is a lot different than those in galien relativity)
@heather fyi the one about "insanity" is not attributable to einstein. (quotes can be very tricky that way... it apparently comes/originates from something like narcotics anonymous literature.)
@heather en.wikiquote.org/wiki/Narcotics_Anonymous traces it to printed copy in 1981 ... afaik einstein never said or wrote it. but alas the misattribution is quite widespread
@heather yw, have been burned myself by this a few times, its common for various quotes, the internet has maybe exacerbated the problem & authoritative web sites havent caught up yet it seems
@heather Perhaps that's the core of our disagreement: I don't see that as part of the purpose of this site, and in fact I see it as somewhat detrimental to the purpose of the site. Since our goal is to get questions answered correctly, anything other than questions and correct answers to those questions is a distraction. (However, I'm generally against deleting answers for being wrong because of the inherent difficulty in determining correctness from the opinions of a group.)
@heather I think that is also addressed by my last message. The whole reason comments were introduced was to allow people to suggest improvements to answers.
@Slereah How is accelerated frames handled in general relativty. Suppose I want to transform from one accelerated frame to another, do I just compute the coordinate transformation using the relevant elements of the Poncaire group (and thus the terms that pop up in the computation will account for things like fictitious forces and transformation between electric and magnetic fields), or do I need to do something in addition to that?
It's a common experience when we are in some vehicle like a car being accelerated we can feel the "invisible push/pull" or acceleration caused due to the change in velocity i assume we can always trust this ability of ours to decide if we are being accelerated whether in car/bus/train/rocket when...
@DavidZ, there is a problem with your argument: pseudo-answers are answers, just in the wrong spot. Let's assume, then, that these end up in their right spot, as answers, no matter if they are right or wrong as I suggested. Then, we wouldn't delete any of them as wrong, just let the system take care of it.
@DavidZ, I think it is important not to make exceptions for comments because that is, in a way, okaying pseudo-answers. And you agree good pseudo-answers should be put into answer format...and yes, by pseudo-answers I mean comments which answer the question, whether right or wrong.
@JohnRennie (reading the referred link). Given that we knew the g-force is the norm of the 4-acceleration vector, and suppose we have two 4-acceleration vectors where one of these has space and time componnts while the other has only a time component what is the physical meaning of a 4-acceleration pointing entirely in the time direction?
@DavidZ, it does, because your point of view is that wrong pseudo-answers should be deleted, but wrong answers shouldn't ("I'm generally against deleting answers for being wrong...")
Anyone here have a good textbook suggestion for the covariant formulation of EM? I am looking for something that doesn't cop out like Rindler does by "guessing" the form things like the EM field tensor, or Maxwell's Equations
@heather My point of view is that all pseudo-answers should be deleted, and that no answers should be. (NB when I use "answers" here, I do not include things posted in the answer box which do not answer the question.)
@JohnRennie or put it in another way, suppose I have some observer following some trajectory in spacetime such that the 4 acceleration has constant norm, but progressively become more aligned in the time direction as I increase the observer's proper time (which paramtrise this path), what will be the physically observed outcome other than spatially the observer will slow to a halt?
@DavidZ, but sometimes perfectly good answers get put into pseudo-answer form...it is a waste to delete all pseudo-answers. They should all be posted as an answer, so the system can take it from there. The other problem with your point of view is that not all pseudo-answers will get deleted...it's impossible. We can't assume a 100% policy will be fully implemented.
@heather It sounds like you're saying that pseudo-answers should be posted as an answer and also remain as comments, but is that really what you meant?
A stopping vehicle (say a car) has an apparent retardation (which may/may not be constant in magnitude) when force via brakes is applied.
I travel by subway trains, and I noticed an odd phenomenon. The thing about such trains (might be irrelevant) is that, being light-weight, their motion somew...
What is entropy really?
I want to answer(!) this question from a different point of view.
First off, I focus on your title and the phrase “really”. We don’t know what entropy is really. We don’t know what energy is really also, and any thing or concept else too. Entropy, like all other conc...
@Secret Suppose you and I start next to and at rest wrt each other, then you start accelerating. At time zero both of us agree your four acceleration is purely spatial. As time goes by then in my coordinates your four-acceleration rotates closer and closer to my time axis.
But in your rest frame your four acceleration remains spacelike.
If I have a non null 4-acceleration vector that has some nonzero space and time components, then the space components translates to the ordinary acceleration we are familar with (except for the $\gamma$ factor and other factors from the curvature tensor). But what does the time component of the 4-acceleration mean physically?
I then wondered I can get some insights on the physical meaning of the time component of the 4-acceleration by using a path that has the acceleration vector progressively become more aligned to the time axis
@heather If time passes and nobody posts the pseudo-answer as an answer, do you suggest that it remain as a comment indefinitely, until someone does post it as an answer?
@Secret space components translates to the ordinary acceleration we are familar with - I think you should be careful assigning a physical significance to any coordinate dependent quantity.
@EmilioPisanty I think this sentence completely answers the question. "Entropy, like all other concepts created by humans, is a convention between some people to refer to the same(!) thought or sense."
@lucas Sure, you're completely welcome to that opinion. I disagree on what the question actually was. I don't intend to fight you over it, but you should consider the possibility that it was downvoted because people disagreed with the content.
@lucas Yeah, I have a ton of answers that I think should be up-voted way more than they are. The fact that they are not tells me that my assessment of their correctness, readability, accessibility, and suitability to their audience is not completely correct.
@heather That doesn't answer my question! Anyway, I would certainly have no objections to having that queue. But at this point we don't have it, and it would not be an easy thing to add, so I think it for now it is also worthwhile to consider the best way to deal with this problem with the tools we have available.
By definition of spin $S$ it is a positive integer number or zero. Not to confuse with the spin projection possible values $S_z$, which may run from $-S$ to $S$.
@heather Note that at the moment none of the existing (non-moderator) review queues handle comments - they all handle questions and answers. Building a community-moderation review queue for comments would be a significant investment on the part of the team, and we'd have to justify why it's really really necessary.
@heather when I delete a pseudo-answer, in a way, that is exactly I am doing. It says "that's not the right way to post an answer, please try again in the proper box this time". This not only forces that one pseudo-answer to be entered in properly, but it (hopefully) does the same for any future posts by the same user.
@JohnRennie 4-velocity is $U^{\alpha}=\frac{dx^{\alpha}}{d\tau}$ and the spatial components are the velocity (corrected by relativistic fators such as $\gamma$, since the 4-momentum is $mU^{\alpha}$ and the spatial components will then be the momentum of the object) of the object while the time component is just c. 4-acceleration is $\frac{d^2x^{\alpha}}{d\tau^2}$, thus the spatial components thus will be describing the acceleration of the object (?). But in both case it is not very clear what's the physical meaning of the time component
@lucas The point is that that post actually answers the question. It is short, sweet and concise, and it does a wonderful job at defusing the misconceptions at play.
Ah I see. Ok, so if my deduction right before the (?) (i.e. my claim that "the spatial components thus will be describing the acceleration of the object")is correct, then $a^{0}$ describe the rate the time dilation changes as viewed in the rest frame?
If (?) is wrong, then I am not sure if $a^{0}$ has easily interpretable physical meaning
@Secret I suppose $A^0$ would be the rate of change of the time dilation (with proper time). But I think that trying to attach physical significance to any other than locally measured properties is something of a wild goose chase.
@DavidZ, and that way would be to delete every pseudo-answer, whether good or bad? In my mind it sounds extreme...While I understand your point of view and think it a better solution than I originally thought it I think my solution completely solves the problem, as I don't think some of these pseudo-answers sill make it to full answer form if we just flag/delete them.
@EmilioPisanty, I see...I do think it would be necessary for it to be a non-moderator queue, but I think it's important. What we could do is ask for an all-purpose comment queue for non-moderators for all flags...then that accomplishes both the new purpose and relieves some of the moderator work load, right?
A stopping vehicle (say a car) has an apparent retardation (which may/may not be constant in magnitude) when force via brakes is applied.
I travel by subway trains, and I noticed an odd phenomenon. The thing about such trains (might be irrelevant) is that, being light-weight, their motion somew...
What is entropy really?
I want to answer(!) this question from a different point of view.
First off, I focus on your title and the phrase “really”. We don’t know what entropy is really. We don’t know what energy is really also, and any thing or concept else too. Entropy, like all other conc...
By definition of spin $S$ it is a positive integer number or zero. Not to confuse with the spin projection possible values $S_z$, which may run from $-S$ to $S$.
