I didn't begrudgingly agree to anything, and I'm not, nor have I ever defended the man. I have specifically and explicitly addressed your assertions. Right now I'm disputing what you are attributing to me. My point was that your entire argument rests on a very specific interpretation of Galileo's statement. In the first instance I made the argument that when you examine the context of the original statement your interpretation of Galileo's statement appears to be wrong. In the second instance I made the point that your argument takes the statement outside of the domain within which it is regarded relevant and therefore can not be used to comment on whether or not it is valid. I've given two examples of this: If I examine mammals in one region and state "all mammals in this region are cats", then does finding dogs in another region invalidate my original statement? Of course not. If I make the statement "If A is true, and B is true, then C is also true" and you then prove that "When A is false or B is false, then C is also false" does that disprove my original statement? Of course not.
RJ, this is addressed to you, too, esp. the note below. Nothing personal. I like to play poker just as much as you do. I just called bluffs as I read them. You know, that illustrates relativity all the more. From your POV you are on top of your game. For the rest of us, no, we see the shallow facade. So although I was inclined not to accept that characterization, since challenging your methods does not constitute an ad hom, I think I can understand why you call it that. It's the relativity of ego. Hah! My reaction was to tell you that you started with the Law of Universal Gravitation, then you introduced the Hamiltonian, and then arrived back at the Law of Universal Gravitation. When I pointed that out to you, rather than admit it, you defended it by saying "this is how it is commonly done." But the skilled readers here remember solving these kinds of problems at the very beginning of their academic careers, and thereafter, simply by application of the Law of Universal Gravitation. When I pointed that out to you, you denied it and said that your "method" is found in Wikipedia (a flag goes up when that claim arises) as well as in the textbooks. That sends another flag up, because, although we encountered the Hamiltonian later, it adds nothing to this problem (as you illustrated) therefore the texts don't bother with it for these applications. I asked you for cites and you never provided any. When I pointed out to you that you and RJ were using a non-inertial reference frame, you immediately balked, because I first explained that it's invalid for scenarios in which the g-field is not homogeneous or isotropic. So I offered instead the more tangible characterization, that the frame can not be accelerating, but you balked at that, so I added the even more tangible requirement that an accelerometer placed at the origin must read zero. You seemed to come around, but then began to argue that since you placed your origin at the c.m., you are safe. And, as I pointed out to you, that's a frame which is accelerating, by definition. That is, the origin of the frame accelerates as a function of the acceleration of the falling object. If you hadn't insisted on Wikipedia as the source of technical definitions, if you hadn't called Physics I "Classical Mechanics", if you hadn't fail to notice that your "math" was circular, and if you hadn't chosen a reference frame that accelerates, I don't think I would have thought to challenge you. But on top of this you did say you were an expert, so you did set yourself up for the replies I gave. But none if that exhibits merely a high school level of physics education, although I must admit the high school curricula are quite good, esp. the AP courses, so I would not disparage them by assuming that high school students could explain your errors to you. Well, let me put that to the test: if a person tells you that when you change reference frames you need to carry the forward and inverse transforms to properly compare values between frames, does that sound like the admonishment of a 16 year old? A few 16 year olds no doubt understand this, but you would not for a moment characterize them as having the intellect of 16 year olds. It would be better for you to concede to the facts that are established, especially by use of cites wherever you feel aggrieved. And it would be better for you to figure out that there are only two kinds of inertial frames for this problem: one kind is any Earth-centered frame, and another kind is any falling-object centered frame. Both of those frames produce identical results. But when you step out into the non-inertial frames and try to calculate the vector math, you get the wrong answers. And that's because you haven't applied the coordinate transforms needed to correct for the warped perspective of those non-inertial frames. I do hope this has been a teaching moment. Don't go away mad, just embrace the knowledge and move ahead. Any Earth-centered frame must be inertial, since the accelerometer placed at the origin of any such frame reads zero. [/quote] Can someone else chime in and confirm for me that this statement is wrong? Because I'm pretty sure gravity is only part of the definition of "inertial" in relativity. [/quote] No, they can't, because that's not right. It's a question of acceleration . You set up your frame to accelerate. By all means, prove me wrong. But the easiest thing would be to Google it. And I would avoid Wikipedia since it's easily corrupted. Better is to refer to university and science academy sites. For example: Galilei's law of inertia and Newton's First Law are valid only in inertial reference frames, those are reference frames which are not accelerating. http://videolectures.net/mit801f99_lewin_lec06/ All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating (in the sense of proper acceleration that would be detected by an accelerometer). http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Inertial_frame_of_reference.htm
Can someone else chime in and confirm for me that this statement is wrong? Because I'm pretty sure gravity is only part of the definition of "inertial" in relativity. [/quote] No, they can't, because that's not right. It's a question of acceleration . You set up your frame to accelerate. By all means, prove me wrong. But the easiest thing would be to Google it. And I would avoid Wikipedia since it's easily corrupted. Better is to refer to university and science academy sites. For example: Galilei's law of inertia and Newton's First Law are valid only in inertial reference frames, those are reference frames which are not accelerating. http://videolectures.net/mit801f99_lewin_lec06/ All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating (in the sense of proper acceleration that would be detected by an accelerometer). http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Inertial_frame_of_reference.htm [/QUOTE] That pretty much sums it up. Fednis48 doesn't know much about gravitational physics. Not even Newtons model. Not even the consequences of Newtons First Law Of Motion. Pretty much nothing. I think you've ferreted out another crank. His attempt to talk down to you is pathetic nonsense.
I have a half hearted, half assed derivation at home that I had been working on, which I am half debating the merits and flaws of completing and posting when I get home.
tashja, what you just posted, Prof. Holz's responses, is largely consistent with what I have been attempting to say, but far clearer and more direct, than any of my rambling. While I will admit that theoretically even a pea dropped toward the earth would cause some theoretical acceleration of the earth, toward the pea, the earth's acceleration for even bowling balls and such, is so far into the realm of unmeasurable that it becomes the domain of theoretical technicality. We do not now nor will we likely ever have the ability to measure any acceleration the earth undergoes in those circumstances, thus they remain theoretical. If one were to project the same sort of reasoning to theoretical physics in general, beginning with an admission that, by this argument, Galileo was technically wrong, you would also have to say that Newton was technically wrong, that SR is technically wrong and even that GR itself is technically wrong, because in each case they all at some point, run into situations that they cannot explain or may be explained better by other methods.
I'm inclined to link him to the Sock Puppet Army of Zealots (SPAZ) attackers, but that's inferred by a a dozen or so things he posted. It was strange that RJBerry summoned hum like a genie from a lamp, then he came in quick to denounce the science, by putting up some rather moronic math which vaguely reminded me of some of the cranks you & I have taken to task before. And he was quick to heap lavish praises on the hearsay evidence that tashja kept offering in the other thread. I think it was Declan Lunny who posted the remark that grabbed me--that the good professor had referred to Sgt A* as a "massive star", as if tashja (or whoever fabricated the email) was assuming that Sagittarius A-star is actually a star! The SPAZ attackers are keenly interested in sowing seeds of doubt and dissention among the purveyors of science, as a scheme to shore up creationism; as if to say 'Look we can't rely on radioactive dating since there is this other theory we call the coordinate speed of light and then there is serious doubt about the Big Bang since it's tied to the Big Crunch which is tied to black holes -- and now we see reason to even doubt the existence of black holes. . . ' (etc.) I know you know all of this but I'm mentioning it again for the other readers who may be undecided or unaware about the extent of SPAZmodics. I haven't been keeping up with the posts here in general -- just responding to replies I get -- so I'm not aware of the consensus of the good readers here who have been immunized against SPAZms of their own by working to develop their skills. So I hope I'm not repeating anything already posted when I post the following analysis but it might interest you. Let me begin by noting that the Earth is not exactly inertial, since the centripetal accelerations due to diurnal rotation and annual orbits contribute a little. But it's around 0.3 % the magnitude of acceleration due to gravity, so no one usually cares. We ignore it as negligible, and we usually treat the Earth as an inertial reference frame for all applications like this. This thread purports to present an issue in gravity, but it's actually an issue in Galilean relativity. Let me establish what that means: 1. The Earth-centered observer sees \(\\ F\quad =\quad \frac { G{ m }_{ ⊕ }{ m }_{ 0 } }{ { \left\| r \right\| }^{ 2 } } (-\hat { r } )\quad =\quad { m }_{ 0 }g\quad ,\quad g\quad =\quad \frac { G{ m }_{ ⊕ } }{ { \left\| r \right\| }^{ 2 } } (-\hat { r } )\\ \\ h\quad =\quad \frac { 1 }{ 2 } \left\| g \right\| { t }_{ 0 }^{ 2 }\quad ,\quad \quad { t }_{ 0 }\quad =\quad \left| \sqrt { \frac { 2h }{ \left\| g \right\| } } \right| \\ \) And all is good and well. In a nutshell, this is not simply a problem in mechanics, but in vector mechanics. Those vectors are not portable across a change of reference frame without the required forward and inverse transformations. 2. A faerie riding on the falling object sees exactly the same thing, in reverse. As far as she knows, the Earth is falling on her, and the impact is also at \({ t }_{ 0 }\). 3. At the OP you pick a third arbitrary reference frame. You liked this idea because you noticed that from this POV you can detect motion in both the Earth and the object. Without asking for help from the skilled readers, you quickly concluded the following: both objects are in motion, therefore the impact will be sooner than Newton says, therefore Galileo must be wrong. And of course by this you really mean Newton must be wrong. 4. A flurry of objections were raised. At some point I suggested that you need to choose a reference frame. You chose the center of mass. What does that mean? It means we want to know the radial coordinate -- on the radial extending from the center of the Earth out to the object as it falls -- satisfying the following: \( { r }_{ c.m. }\quad =\quad \frac { \sum _{ i=1 }^{ N }{ { r }_{ i }{ m }_{ i } } }{ { m }_{ \oplus }+{ m }_{ 0 } } \) where N = number of particles in the earth + object system, and \({ m }_{ i }\) is the mass of the ith particle, including all the particles in the falling object. This is no simple task for you to figure out. And BTW it's very near the center of the Earth -- dead on the c.m. of the Earth when the falling object lands. 5. After the formula is in place which describes the origin of the coordinate system as a function of time, you need to construct the transformation that maps values in your system to values in Galileo's frame. Galileo's r maps to RJ-space according to the transformation r' = T[r(t)]. This is going to be messy, and it requires experience in calculus which as far as I can tell is not your forte. 6. Once you define T[∙], you will discover [or you will have to be led to that trough to drink -- whether you do is highly dubious] -- that T[∙] ≠ I. Once that dawns on you -- if that is achievable in the near future -- you would have to admit that you were mistaken. You didn't understand that you needed to compute the time of impact using r' = T[r] and g' = T[g]. Once you do this, you will get the exact same results as Galileo did, and as the faerie did. But I doubt that you can pull that off, and I doubt you will want to attempt it since it will prove you wrong. But this is your chance to come clean if you're not actually part of the SPAZ attack, or harboring some unrelated reason for attacking science.
RJBEERY IS TECHNICALLY RIGHT !! HE HAS PROVED THAT NEWTON's THIRD LAW IS ALSO WRONG !! Proof (All variables and constants taken from OP, not mine, not verified) Force on golf ball (Action) = m*g = 0.5 * 9.82 = 0.491 N Force on Earth (Reaction)= M * a_e.gb = 5.972E24 kg * 0.00008029 = 4.79 * 10^20 N So, Action NE Reaction.....Newton Can go to hell... The point is both RJbeery and other Mr 48, could not figure out this apparent mistake in this calculation, when pointed out, they wanted to know where is the mistake ?? When they can't figure out any WRONG in their calculations which is visible apparent and of the order of 10^20, then how could they find out mistake in Galileo observation which is of the order of 10^-20 (if at all)?? I am still sticking with my solution : the acceleration of ball will be g-gm/M, with due respect to professors, I cannot figure out, how Ball is not effected by the acceleration of Earth, however it may have been caused..
Wow. And I thought Aqueous Id said it so well. With due respect to professors, of course. Please Register or Log in to view the hidden image!
I have a simple question, if any one can answer.. 1. There is no doubt that an upward force (in the direction of ball) will be felt by the Earth, this will cause a very small upward acceleration on the Earth and there would be some travel of Earth in upward direction. Now, please consider two birds, one (B1) near the original position of ball, and another (B2) at a point which is diametrically opposite (other side of Globe). So if we whatever RJB and his followers are saying, and even those who are saying, that Earth would move up but by an insignificant amount, then the separation between Earth and B1 will reduce, and separation between earth and B2 will increase ? Is it so ??
Bingo!!! Fair dinkum, after a beautiful long holiday weekend in Sydney town, BBQ's to attend, a 2 mtr swell rolling at Maroubra yesterday, and the NRL, Rugby League Grand Finals last night, I was about to say something quite similar, probably not as lengthy, but certainly more to the point[ calling a spade a shovel] but AId has beaten me to it! And the proof is in the other thread started around the same time, with a similar anti science theme on the "QM + GR= BH's do not exist" That was shown to be a furphy also. Once again though, we [us science cheer leaders Please Register or Log in to view the hidden image! ] need to realise that forums such as this are the only outlet these people have..... What they hope to achieve is beyond me, as any change, alteration or tinkering to any of the main physical/cosmological theories will not be coming from these people...You can bet your short n curlies on that! It will be from mainstream scientists themselves.
It should be enough for RJ to understand that he can not import vectors from another system without reorienting them according to his proprietary system, via the correct transformation. But that requires him to understand the basics of vector math, which Fednis tried to trump (quite sneakily I thought) by introducing relative quantities, and jumping on the idea that the c.m.-centered frame is at least parallel to Galileo's. Another simple way for RJ to think about this is that in his system the origin is moving with respect to the bodies, therefore it's false to claim they undergo 9.8 m/s² acceleration in his system. The c.m. moves away from the object as it falls and toward the center of the earth -- therefore those transforms have to be applied to g for each case or else he is introducing the error, not Galileo.
Noted. Glad to hear you partied hardy down yonder. Would that we could on occasion put the offending short curlies to the embers of the BBQ, at least in virtual terms, there might be less melodrama and a little more chance to just dabble in . . . I don't know . . . interesting facts of science maybe?
Indeed I would like to know the end of that story. Did tashja really fabricate those emails? Something stinks in Denmark and it's certainly not the profs, who I think don't even sweat any more.
Man, now I'm almost too scared to post my half assed half finished all classical analysis. Well, equal parts scared and curious.
Forgot to add.... RJ Beery's scale of operation in long mathematical desertion in the OP is mind boggling. In one shot he could find "WRONG" at less than electron level (10^-20) to around cosmological level (10^20). Mind boggling span...
The significance of this question is lost in the din, and I must admit, this is very crucial even to my solo stand on the issue that ball will also accelerate upwards... (We restrict ourselves to parts of Earth, which are contributing to Earth's Gravity [no moon, no asteroid no BH]). The question is, when do we consider an object as part of Earth in a sense when do we treat them co-moving ? When they are on the hard surface ? When they are on (or inside) water ? When they are in air like that ball or a bird or an aircraft ?
Awesome replies, yeah? Like collimated beams they are. Yes, I agree one can get overly fastidious, but wasn't that whole point of the topic? Please Register or Log in to view the hidden image!
