According to 1905 Relativity, a single material point must be always at rest
in [Relativity]
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From: Androcles on 28 May 2010 17:57 "Darwin123" <drosen0000(a)yahoo.com> wrote in message news:8b198c33-a9b6-43ed-aea5-1cecd7fa7158(a)c22g2000vbb.googlegroups.com... I made a mistake. The maximum precession is at the poles, not the equator. So here are my corrected questions. Explain to us, in your words, why a Foucault pendulum has a precessing period between 0 and 24 hours. Explain to us why the precess period at the equator is 0 hours, and at the north or south poles is 24 hours. ============================================== False.
From: valls on 28 May 2010 19:29 On 27 mayo, 12:48, PD <thedraperfam...(a)gmail.com> wrote: > On May 26, 3:49 pm, va...(a)icmf.inf.cu wrote: > > > On 25 mayo, 10:46, PD <thedraperfam...(a)gmail.com> wrote: > > > > On May 25, 10:19 am, va...(a)icmf.inf.cu wrote: > > > > > On 24 mayo, 07:27, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On May 24, 6:13 am, va...(a)icmf.inf.cu wrote: > > > > > > > On 21 mayo, 10:22, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > On May 21, 6:27 am, va...(a)icmf.inf.cu wrote: > > > > > > > > > On 20 mayo, 13:09, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > > > On May 20, 8:19 am, va...(a)icmf.inf.cu wrote: > > > > > > > > > > > In his first Relativity paper (30June1905), after declaring the ether > > > > > > > > > > superfluous, Einstein considers a material point at rest. He uses a > > > > > > > > > > system of Cartesian coordinates in which the equations of Newtonian > > > > > > > > > > mechanics and Euclidean geometry hold good. If the massive body is > > > > > > > > > > alone (and then without a Newtonian gravitational force acting on it), > > > > > > > > > > it must remains forever at rest in its own centre of mass inertial > > > > > > > > > > frame. > > > > > > > > > > Yes. So? > > > > > > > > > > Every object lives in an infinite multitude of frames. The ones that > > > > > > > > > have constant velocity with the frame you just described, plus this > > > > > > > > > frame itself, constitutes the set of inertial frames. > > > > > > > > > If we apply that to the single material point case, the result is an > > > > > > > > infinite number of inertial frames where the single material point can > > > > > > > > be moving with any velocity v. > > > > > > > > Any velocity of magnitude less than c, yes. So? > > > > > > > > > Once the ether is put out by 1905 > > > > > > > > Einstein (and with it the Newtonian absolute space and time), can you > > > > > > > > explain to me with respect to what a single material point can have > > > > > > > > then a velocity different from zero? > > > > > > > > A reference frame does not require a material "anchor" object, for > > > > > > > which that anchor object is at rest in that frame. > > > > > > > What do you say is totally valid in today Special Relativity, but not > > > > > > in 1905 Relativity. See the following references to the 30Jun1905 > > > > > > text. > > > > > > Almost at the end of the Introduction: > > > > > > R1. [The theory to be developed is based like all electrodynamics on > > > > > > the kinematics of the rigid body, since the assertions of any such > > > > > > theory have to do with the relationships between rigid bodies (system > > > > > > of co-ordinates), clocks, and electromagnetic processes.] > > > > > > At the beginning of paragraph 3: > > > > > > R2. [Let us in stationary space take two systems of co-ordinates, > > > > > > i.e. two systems, each of three rigid material lines, perpendicular to > > > > > > one another, and issuing from a point.] > > > > > > In R1 a system of co-ordinates is identified with a rigid body, and in > > > > > > R2 (more detailed) with a system of tree rigid material lines. Even a > > > > > > single material point must have some mass, imagine tree material > > > > > > lines. Do you continue thinking that in 1905 Relativity a reference > > > > > > frame does not require something material to establish the rest? > > > > > > Yes. Just because Einstein uses a material framework to *explain* his > > > > > position does not mean that it is essential to the conceptual > > > > > framework. The idea of reference frames without material anchors > > > > > preceded Einstein by at least a century. > > > > > And what? How many centuries preceded Ptolemaic view the Newtonian > > > > one? > > > > Taking out the ether with its Newtonian absolute space and absolute > > > > time is the essence of the Einsteinian relativistic view. > > > > Yes. > > > > > In it remain > > > > only the material bodies themselves to determine inertial frames. > > > > No. Again, you feel it is essential to anchor a frame to *something* > > > material for some reason. Thus, if the aether is removed, then to you > > > it MUST be material bodies. And if loosed from material bodies, then > > > to you this DEMANDS the aether back again. This is simply wrong. > > > Reference frames do not need material anchors, period. And they did > > > not, for a long time preceding Einstein. Newtonian mechanics easily > > > considered motion in frames in which there was no material object, > > > including any supposed ether, at rest. > > > The fact is that all Newtonian mechanics is based in its absolute > > space and time, the unique privileged inertial frame considered real > > and true. > > I disagree. Newton did believe in absolute space and absolute time. > However, in terms of the laws of physics, it was in no way a > privileged inertial frame. Indeed, he took the same position (and > developed it further) that Galileo had: that the laws of physics are > identical regardless of inertial reference frame. Calling out one of > those frames as being somehow preferred even though the laws of > physics are unchanged in it, is a rather empty statement. And in fact, > when the ether was supposed, in order to support electrodynamics, the > immediate implication was that the laws of electrodynamics had to be > different in this frame than in any other frame. > In his 1684 Principia , long before the development of electromagnetism, Newton starts conceiving the absolute space and the absolute time as a privileged and unique real and true inertial frame. The movement of any body in that frame is considered the unique real, absolute and true one. Any other movement with respect to some other thing is considered apparent, relative and false (all this can be read without any ambiguity in the 1684 text). The privileged absolute frame is absolutely necessary to support the first law of inertia, because a material point can be free only being the unique one in the absolute space and time (without gravity or any other kind of force). BTW, this is why in 1905R (without that absolute space and time) a single material point must be always at rest (having nothing more to move with respect to it). You are accusing then 1684 Newton to make a rather empty statement (without any valid argument to support it). The concept of the non- existence of a privileged frame is developed precisely by 1905 Einstein, and the translation of something to the past of its developing epoch is the more dangerous mistake that can be done when analysing an old text (but unfortunately a very common one, because it is not an easy task at all to consider out of our mind what it is already there when reading the old text, and the greater the knowledge, the greater the possibility to fall in mistake). > > You are right saying that in it is very easy to consider > > motion in frames without a material object, because an empty frame > > moving with ANY uniform velocity v with respect to the privileged one > > is also an inertial frame (even if considered apparent and false). > > Then, we have in Newtonian mechanics ALL possible inertial frames, and > > ALL of them without the need of a single material body. > > Yes. And that "ALL of them" *includes* the absolute frame. > Total agreement in this point. How can we consider out precisely the privileged absolute frame from which all the others are derived? If you take out the first floor from a building, all the rest of them crash down. But dont forget that we are referring here to the infinite empty inertial frames of the Newtonian view, not to the 1905R view where all that empty frames are absent. > > The situation is totally different in 1905 Relativity. Once the > > privileged frame with absolute space and time is declared superfluous, > > ALL the others empty frames moving with respect to it with any uniform > > velocity v result also superfluous. > > Nonsense. All you've just said is that the inertial frames without a > single material body owe their existence to being referred by a > relative velocity v to a frame with some material body anchor. Thus, > it is "anchoring by association" to a frame with a material body at > rest. Nothing could be further from the truth. What you said earlier > is correct. ALL inertial frames are perfectly well defined without > anchoring to any material body at rest. That "ALL" is comprehensively > inclusive. >Nonsense. If you conceive an imaginary empty frame moving with respect to a real one, the CM of the two frames continue being the same because the empty frame contribute with nothing to the position of it. But that doesnt provide you with a new inertial frame (where the Newtons law hold good), because you never can have an imaginary entity at rest with material bodies moving with respect to it (that is only possible in the Newtonian view where an initial imaginary frame is conceived as the unique real one). Perhaps you will understand this better if we suppose not an empty, but an almost empty frame with a very small mass relative to the mass of the original real frame. Suppose that the original frame is the Sun and the one with small mass is the Earth. Which is moving, the Earth of the Sun? Both are moving with respect to the common CM inertial frame, but Earth is moving faster and the Sun is practically at rest (following Newtons laws). You can never have the Earth at rest with the Sun moving without a violation of Newtons laws. This is why the adding of imaginary empty frames moving with respect to real ones is totally useless and without any sense. I repeat then your nonsense. > > Velocity with respect to nothing > > simply cant exist in 1905 Relativity. > > It's not nothing. A reference frame is not nothing. You have in your > head that the only "somethings" that velocity can be in reference to > are material objects. This is not the case. > See my previous comment. > > From where do you take a > > reference frame without material bodies? It is moving or at rest? If > > moving, with respect to what? > > It is moving with respect to one (set of) inertial reference frame(s), > and it is in motion with respect to other inertial reference frames. > And what is the sense to have imaginary moving inertial frames that cant be never at rest describing the trajectory of real bodies with respect to them? > > And if at rest, with respect to what? > > And if you say that it is at rest with respect to itself, > > I didn't say with respect to itself. It is at rest with a particular > reference frame. That reference does not have to be with respect to a > material object. > An imaginary frame at rest with respect to other imaginary frame implies that the two frames are the same, and if they were different it continue being only a nonsense. > > you are > > simply repeating Newtons primary absolute frame already put out by > > 1905 Einstein. > > In any case, in this thread we are considering only 1905 Relativity, > > where a system of coordinates is identified with tree rigid material > > lines, as the 1905 Einstein text put out of any doubt. > > No, he did not make that identification. A reference frame CAN BE but > NEED NOT BE represented with three rigid material lines. You confuse a > representation with the thing itself. > 1905 Einstein rigid material lines is NOT a representation. Material implies mass, a real body. 1905 Einstein knows that without the imaginary absolute frame he needs something to substitute it, and the unique available are the material bodies themselves. See how the material, fluid and massive real rotating Earth determines a real inertial frame. See how a space is derived from the material Earths parts rotating with different linear velocities. See how the first material line emerges, the rotating axis. Add two other axis perpendicular to it in the unique determined centre of mass and you have already an idea about how ANY material body set composed by interacting bodies determine a UNIQUE space with all its points at rest. The rest emerging from the relative movements among the interacting bodies. A little more difficult is to see how emerges the UNIQUE time. In the rotating Earth case it is related to the determined angular velocity. Space and Time emerging from the Mass and Newtons laws. But what bodies trajectories can be determined in the emerging UNIQUE inertial frame? ONLY the ones belonging to the same bodies that determine the frame. If you take out or take in a single body, we have a new inertial frame with a new space and time. > > And you have no > > right at all to put in 1905 Relativity what you want without the > > support of a 1905 text. > > Reading things in isolation is dangerous. Einstein was not ignorant of > the use of reference frames unlocked from material objects, as had > been understood for at least a hundred years prior, nor did he propose > to replace that concept with one solely identified with a material > object. > The absolute frame without material bodies is the first thing put out by 1905 Einstein. We are in agreement about not reading a thing in isolation. The unique right way to interpret and old text is precisely taking into account all its future and all its past. The past to be used in the interpretation, and the future to NOT be used in the interpretation. The last part is the more difficult task. > > > > > > You are free to support the old Newtonian view if you want, but that > > > > doesnt give you the right to say that in 1905 Relativity a reference > > > > frame does not require something material. You cant change what 1905 > > > > Einstein writes, even thinking you that it is something wrong. > > > > > > > > If that were the case, then for two reference frames to even exist, > > > > > > > you'd need two objects. For three, you'd need three objects. > > > > > > > Exactly. See in the previous reference R2 a different material object > > > > > > for each one of the two different reference systems introduced.> This however, is not the case. A reference frame has a perfectly well- > > > > > > > defined meaning with or without a material anchor in it. > > > > > > > A valid assertion in today Special Relativity, but a totally invalid > > > > > > one in 1905 Relativity. In this thread we are addressing only 1905 > > > > > > Relativity (see the title). > > > > > > This, in my opinion, is a boondoggle. > > > > > I don't see the point of it at all. > > > > > Relativity is relativity. It is not a *creation*, it is a discovery. > > > > > When the first sailors navigated to the New World, they drew maps that > > > > > represented their view of their discovery. Of course, those maps did > > > > > not at all accurately represent the shape of the Americas. It does > > > > > absolutely no good to take one of those maps and say, "But this is the > > > > > America of 1500." It is not. The shape of the continent has not > > > > > substantively changed since 1500. The America of 1500 is the same as > > > > > the America of 2010. It's just that how people have described it is a > > > > > little different from 1500 to 2010. > > > > > If I am interpreting well, you are suggesting that 1905 Relativity > > > > contains errors (first sailors making bad America maps) that were > > > > already corrected in today Special Relativity. And surely you think > > > > that the need to have material bodies to determine an inertial frame > > > > is one of these errors. > > > > Not errors per se. Just not completely worked out, and so there is an > > > incomplete presentation of the model. > > > > A map of the eastern seaboard of the Americas is not inaccurate, but > > > it is not a good map of the Americas, either, because it is not > > > completely articulated. > > > That you consider 1905 Relativity incomplete dont give you the right > > to complete it in the way you want. You (or anyone) can modify it in > > any way, but not with the right to continue naming it 1905R. We cant > > change history, and I have powerful reasons to consider 1905R as it > > is. You will know about them in my next comment in this same post. > > Again, I want to point out that historical representations are > important when you are talking about a *creation*, but relativity is > not a *created* thing, it is a DISCOVERED thing. > All science is not a creation, but a discovered about how Nature is. We are in agreement about that. I dont know about creation, but I consider History a very useful scientific resource. The knowledge of Nature by men is an endless process where the historic order is important. > When fossils of dinosaurs were first found, paleontologists > inappropriately connected the leg bone fossils, giving the assemblies > the postures of lizards, from which they concluded that the animals > were cold-blooded and covered in scales. This, of course, has little > to do with what dinosaurs REALLY were. So the initial *representation* > of dinosaurs may have been one thing, but the intent was to represent > something actual, and that representation was not complete. > > PD RVHG (Rafael Valls Hidalgo-Gato)
From: valls on 28 May 2010 19:42 On 27 mayo, 12:55, PD <thedraperfam...(a)gmail.com> wrote: > On May 26, 3:49 pm, va...(a)icmf.inf.cu wrote: > > > > > > > > > Suppose now that somebody finds the way to explain GR effects (like > > > > the ones necessary to adjust GPS clocks in the Earths gravitational > > > > field), but using only 1905 Relativity (Newtonian mechanics, Euclidean > > > > geometry). Would you consider that a boondoggle? (English is not my > > > > mother language, and I dont know the meaning of that word). > > > > By my guest. Would love to see it. > > > Let be two material points M and m (one with a great mass M, and the > > other with a small mass m<<M). We can consider then M practically the > > Centre of Mass (CM) of the 2-point system (for example, M and m can > > model Earth and an electron). In the corresponding CM inertial system, > > let be r the distance between M and m. > > From the 27Sep1905 paper we know that The mass of a body is a measure > > of its energy-content. In 1905, a body Total Energy E=K+U, where K is > > the Kinetic Energy and U the Potential Energy. > > This is incorrect. What was proposed, in fact, was that the total > energy of a body was > E = mc^2 + K + U. > You have misidentified mc^2 as being part of U, when it is not. What you say is absolutely impossible. Strange at it can seem, an expression as mc^2 doesnt appear at all in the only 3 short pages paper. That makes me to think that you are repeating what others say about the 27Sep1905 Einsteins paper, without reading by yourself the original one (I apologize you in advance if am wrong about that, but that is what you write suggest me). Whatever the case, the paper can be obtained at http://www.fourmilab.ch I encourage you to read or re-read it. We need here a very careful historic interpretation of the text. I start doing it for you. The more relevant part of the text (between [ ], page 2 of 3) is the following (I made some minor non-essential changes with comments between { } that identify the frames): [ H and E are energy values of the same body referred to two systems of co-ordinates which are in motion relative to each other, the body being at rest in one of the two systems {body with total energy E}. Thus it is clear that the difference H E can differ from the kinetic energy K of the body, with respect to the other system {body with total energy H}, only by an additive constant C, which depends on the choice of the arbitrary additive constants of the energies H and E. Thus we may place H E = K + C ] Let us put for a future reference the formula as: H = K + (E + C) Even if in the text the phrase potential energy doesnt appear, the management of the arbitrary additive constants energies put out of any doubt that potential energy is present (in 1905, and perhaps also today, the unique kind of energy in Physics with arbitrary additive constants is the potential one). Another strong argument is that in 1905 the conservation Principle of Energy (considered valid by 1905 Einstein in the two frames according to his Principle of Relativity) is expressed as Total energy = Kinetic energy + Potential energy What coincides exactly with its formula H = K + (E + C) Where E is the Potential energy with its characteristic arbitrary additive constant C. In the frame the body is at rest, its Total energy coincides with its Potential energy (Kinetic energy=0), the unique kind of energy a rest body can has in 1905 to add it with its Kinetic energy to obtain its Total energy. The today rest energy concept with no relation at all with Potential and Kinetic energies doesnt exist yet when 1905 Einstein is writing his paper. We cant use it then to interpret the paper content, and to say that in the paper is proposed that Total energy = Rest energy(mc^2) + Kinetic energy + Potential energy is only a complete falsehood that you can verify by yourself. The true is that in the text the Conservation Principle of Energy is taken for granted and used as a starting point in the unique possible way compatible with the historic context: Total energy=Kinetic energy + Potential energy > And in fact, you should review what the allowed contributions of U > are, from classical mechanics. 1905 Einstein derivation is totally a universal one, doesnt put any restriction at all on kind of potential energies. All of them are included, known or for known (nuclear potential energy is not known in1905) > It simply isn't true that just any old thing that is not associated > with K are then U. In the text exist no reference at all about a thing not associated with K being potential energy. Why do you say that it is not true? Who is saying that it is true? What the text implies is that rest energy and potential energy is one and the same thing, what simply coincides with the classical concept that the energy a rest body has is denoted potential energy. The E is declared from the beginning the energy of the body at rest, I dont find any other alternative different from to interpret E as what today is denoted rest energy. And the E is in the place corresponding to the potential energy on the classical expression for the Conservation Principle of Energy, including its characteristic arbitrary additive constant energy C. Revise the conclusion of the paper: The mass of a body is a measure of its energy-content. And if the body is at rest The (rest) mass of a body is a measure of its (potential) energy-content, because that conclusion is derived using precisely the conservation Principle of Energy as Total energy=Kinetic energy + Potential energy. > A potential energy requires a connection with a *conservative force*, > and one that can generate recoverable work. Of course, that is only classical mechanics (Newtonian), the one that hold true (by definition) in all 1905R stationary systems. > The term you've suggested -- m(r)c^2 -- does not meet those criteria. > I have suggested nothing, that mass measures energy (multiplying it by c^2) is the principal conclusion in the 1905 Einsteins paper. I am also not the one saying that rest mass measures potential energy, you can see the derivation in the paper. If you claim some error in the paper (respecting the historical context, of course), point which is it. If you cant do it, then wait for the consequences that real experiments can support or not. Consider the conversion of a pair electron-positron (starting at rest, with infinite distance between them) in 2 photons. Experiments show that the rest energy of both particles is equal to the energy of the resulting photons. At the beginning we have an electric field that disappears completely when the two photos are formed. How can explain you that flagrant violation of the Conservation Principle of Energy? (the electrostatic energy of the original field, simply disappears converting in nothing?) > The rest of this paragraph then falls. > You are not interested in the consequences of rest mass measuring potential energy? If 1905 Einstein derivation is wrong, more probably its consequences cant match with the real world. But what can you say is the match is obtained? > > > > If the body is at rest, > > K=0, being then U measured by the rest mass. In the case we are > > addressing, for the body m we have then U(r)=m_0(r) c^2, where m_0(r) > > is the body m rest mass and c the constant vacuum light speed. We know > > that the gravitational potential energy increases when r increases. > > Its limit maximal value when r tends to infinite is then m_0m c^2, > > where m_0m is the corresponding limit maximal value of the rest mass > > m_0. We have then > > U(r)= m_0(r) c^2=m_0m c^2 (GM/r)m_0(r) > > Here G is the Newtonian gravitational constant, > > and (GM/r) is the gravitational potential owed to M with a supposed > > arbitrary value 0 at r infinite. As you can see, U(r) takes the very > > definite maximal value m_0m c^2 at r infinite. With some simple > > algebraic handling we obtain > > m_0(r)=m_0m/(1+GM/rc^2) > > We have then derived from 1905R how the rest mass of a small body > > changes as a function of its position r in the central gravitational > > field of a great mass M body. Note the absent of any constant > > arbitrary potential energy and the presence of an ABSOLUTE zero > > potential energy point at r=0. If M and m are the Earth and an > > electron, m_0m is the ordinary rest mass of a free electron (its > > maximal value at r infinite). The frequency emitted by an atomic clock > > is proportional to the rest mass of the electron involved in the > > change of state. In GR the rest mass is supposed a constant an > > intrinsic electron attribute, justifying the change in frequency with > > the warp of the space-time provoked by M. As you see, the things in > > 1905R are very much simple. > > I left to you the verification that the change of frequency predicted > > by 1905R coincides with the GR one in all the range of practical r > > values in real experiments like the Pound&Rebka one. By the way, the > > 1905R formula applies for ALL values of r from 0 to infinite, while > > the GR one has a limited range of application owed to the presence in > > it of a singularity that is absent in the 1905R one. RVHG (Rafael Valls Hidalgo-Gato)
From: Sue... on 28 May 2010 20:38 On May 28, 7:29 pm, va...(a)icmf.inf.cu wrote: [...] =================== > > In his 1684 "Principia...", long before the development of > electromagnetism, Newton starts conceiving the absolute space and the > absolute time as a privileged and unique real and true inertial frame. > The movement of any body in that frame is considered the unique real, > absolute and true one. Any other movement with respect to some other > thing is considered apparent, relative and false (all this can be read > without any ambiguity in the 1684 text). The privileged absolute frame > is absolutely necessary to support the first law of inertia, because a > material point can be free only being the unique one in the absolute > space and time (without gravity or any other kind of force). You can cherry-pick the story as you please but Einstein seems to have given Newton more credit for critical thinking than you do. <<Already Newton recognized that the law of inertia is unsatisfactory in a context so far unmentioned in this exposition, namely that it gives no real cause for the special physical position of the states of motion of the inertial frames relative to all other states of motion. It makes the observable material bodies responsible for the gravitational behaviour of a material point, yet indicates no material cause for the inertial behaviour of the material point but devises the cause for it (absolute space or inertial ether). This is not logically inadmissible although it is unsatisfactory. For this reason E. Mach demanded a modification of the law of inertia in the sense that the inertia should be interpreted as an acceleration resistance of the bodies against one another and not against "space". This interpretation governs the expecta- tion that accelerated bodies have concordant accelerating action in the same sense on other bodies (acceleration induction). This interpretation is even more plausible according to general relativity which eliminates the distinction between inertial and gravitational effects. It amounts to stipulating that, apart from the arbitrariness governed by the free choice of coordinates, the g ì v -field shall be completely determined by the matter. Mach's stipulation is favoured in general relativity by the circumstance that acceleration induction in accordance with the gravitational field equations really exists, although of such slight intensity that direct detection by mechanical experiments is out of the question. <1> Mach's stipulation can be accounted for in the general theory of relativity by regarding the world in spatial terms as finite and self-contained. This hypothesis also makes it possible to assume the mean density of matter in the world as finite, whereas in a spatially infinite (quasi-Euclidian) world it should disappear. It cannot, however, be concealed that to satisfy Mach's postulate in the manner referred to a term with no experimental basis whatsoever must be introduced into the field equations, which term logically is in no way determined by the other terms in the equations. For this reason this solution of the "cosmological problem" will not be completely satisfactory for the time being. >> http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.html Sue...
From: PD on 29 May 2010 09:56
On May 28, 6:42 pm, va...(a)icmf.inf.cu wrote: > On 27 mayo, 12:55, PD <thedraperfam...(a)gmail.com> wrote: > > > On May 26, 3:49 pm, va...(a)icmf.inf.cu wrote: > > > > > > Suppose now that somebody finds the way to explain GR effects (like > > > > > the ones necessary to adjust GPS clocks in the Earths gravitational > > > > > field), but using only 1905 Relativity (Newtonian mechanics, Euclidean > > > > > geometry). Would you consider that a boondoggle? (English is not my > > > > > mother language, and I dont know the meaning of that word). > > > > > By my guest. Would love to see it. > > > > Let be two material points M and m (one with a great mass M, and the > > > other with a small mass m<<M). We can consider then M practically the > > > Centre of Mass (CM) of the 2-point system (for example, M and m can > > > model Earth and an electron). In the corresponding CM inertial system, > > > let be r the distance between M and m. > > > From the 27Sep1905 paper we know that The mass of a body is a measure > > > of its energy-content. In 1905, a body Total Energy E=K+U, where K is > > > the Kinetic Energy and U the Potential Energy. > > > This is incorrect. What was proposed, in fact, was that the total > > energy of a body was > > E = mc^2 + K + U. > > You have misidentified mc^2 as being part of U, when it is not. > > What you say is absolutely impossible. I'm sorry, but once again, you are a victim of reading papers in isolation, without the associated context. Moreover, you accuse me of reading something into a paper that is not there, and then you excuse yourself for reading potential energy into a paper where it is not mentioned at all. The lesson here is acquiring the proper context, so that you can *correctly* read things into papers that are not said. You could use some improvement on this front. > Strange at it can seem, an > expression as mc^2 doesnt appear at all in the only 3 short pages > paper. That makes me to think that you are repeating what others say > about the 27Sep1905 Einsteins paper, without reading by yourself the > original one (I apologize you in advance if am wrong about that, but > that is what you write suggest me). Whatever the case, the paper can > be obtained athttp://www.fourmilab.ch > I encourage you to read or re-read it. We need here a very careful > historic interpretation of the text. I start doing it for you. > The more relevant part of the text (between [ ], page 2 of 3) is the > following (I made some minor non-essential changes with comments > between { } that identify the frames): > > [ H and E are energy values of the same body referred to two systems > of co-ordinates which are in motion relative to each other, the body > being at rest in one of the two systems {body with total energy E}. > Thus it is clear that the difference H E can differ from the > kinetic energy K of the body, with respect to the other system {body > with total energy H}, only by an additive constant C, which depends on > the choice of the arbitrary additive constants of the energies H and > E. Thus we may place H E = K + C ] > > Let us put for a future reference the formula as: H = K + (E + C) > > Even if in the text the phrase potential energy doesnt appear, the > management of the arbitrary additive constants energies put out of any > doubt that potential energy is present (in 1905, and perhaps also > today, the unique kind of energy in Physics with arbitrary additive > constants is the potential one). Another strong argument is that in > 1905 the conservation Principle of Energy (considered valid by 1905 > Einstein in the two frames according to his Principle of Relativity) > is expressed as > > Total energy = Kinetic energy + Potential energy > > What coincides exactly with its formula > > H = K + (E + C) > > Where E is the Potential energy with its characteristic arbitrary > additive constant C. In > the frame the body is at rest, its Total energy coincides with its > Potential energy (Kinetic energy=0), the unique kind of energy a rest > body can has in 1905 to add it with its Kinetic energy to obtain its > Total energy. > > The today rest energy concept with no relation at all with Potential > and Kinetic energies doesnt exist yet when 1905 Einstein is writing > his paper. We cant use it then to interpret the paper content, and to > say that in the paper is proposed that Total energy = Rest > energy(mc^2) + Kinetic energy + Potential energy is only a complete > falsehood that you can verify by yourself. The true is that in the > text the Conservation Principle of Energy is taken for granted and > used as a starting point in the unique possible way compatible with > the historic context: > Total energy=Kinetic energy + Potential energy > > > And in fact, you should review what the allowed contributions of U > > are, from classical mechanics. > > 1905 Einstein derivation is totally a universal one, doesnt put any > restriction at all on kind of potential energies. All of them are > included, known or for known (nuclear potential energy is not known > in1905)> It simply isn't true that just any old thing that is not associated > > with K are then U. > > In the text exist no reference at all about a thing not associated > with K being potential energy. Why do you say that it is not true? Who > is saying that it is true? What the text implies is that rest energy > and potential energy is one and the same thing, what simply coincides > with the classical concept that the energy a rest body has is denoted > potential energy. The E is declared from the beginning the energy of > the body at rest, I dont find any other alternative different from to > interpret E as what today is denoted rest energy. And the E is in the > place corresponding to the potential energy on the classical > expression for the Conservation Principle of Energy, including its > characteristic arbitrary additive constant energy C. Revise the > conclusion of the paper: The mass of a body is a measure of its > energy-content. And if the body is at rest The (rest) mass of a body > is a measure of its (potential) energy-content, because that > conclusion is derived using precisely the conservation Principle of > Energy as Total energy=Kinetic energy + Potential energy.> A potential energy requires a connection with a *conservative force*, > > and one that can generate recoverable work. > > Of course, that is only classical mechanics (Newtonian), the one that > hold true (by definition) in all 1905R stationary systems.> The term you've suggested -- m(r)c^2 -- does not meet those criteria. > > I have suggested nothing, that mass measures energy (multiplying it by > c^2) is the principal conclusion in the 1905 Einsteins paper. I am > also not the one saying that rest mass measures potential energy, you > can see the derivation in the paper. If you claim some error in the > paper (respecting the historical context, of course), point which is > it. If you cant do it, then wait for the consequences that real > experiments can support or not. > Consider the conversion of a pair electron-positron (starting at rest, > with infinite distance between them) in 2 photons. Experiments show > that the rest energy of both particles is equal to the energy of the > resulting photons. At the beginning we have an electric field that > disappears completely when the two photos are formed. How can explain > you that flagrant violation of the Conservation Principle of Energy? > (the electrostatic energy of the original field, simply disappears > converting in nothing?) > > > The rest of this paragraph then falls. > > You are not interested in the consequences of rest mass measuring > potential energy? If 1905 Einstein derivation is wrong, more probably > its consequences cant match with the real world. But what can you say > is the match is obtained? > > > > > > > > If the body is at rest, > > > K=0, being then U measured by the rest mass. In the case we are > > > addressing, for the body m we have then U(r)=m_0(r) c^2, where m_0(r) > > > is the body m rest mass and c the constant vacuum light speed. We know > > > that the gravitational potential energy increases when r increases. > > > Its limit maximal value when r tends to infinite is then m_0m c^2, > > > where m_0m is the corresponding limit maximal value of the rest mass > > > m_0. We have then > > > U(r)= m_0(r) c^2=m_0m c^2 (GM/r)m_0(r) > > > Here G is the Newtonian gravitational constant, > > > and (GM/r) is the gravitational potential owed to M with a supposed > > > arbitrary value 0 at r infinite. As you can see, U(r) takes the very > > > definite maximal value m_0m c^2 at r infinite. With some simple > > > algebraic handling we obtain > > > m_0(r)=m_0m/(1+GM/rc^2) > > > We have then derived from 1905R how the rest mass of a small body > > > changes as a function of its position r in the central gravitational > > > field of a great mass M body. Note the absent of any constant > > > arbitrary potential energy and the presence of an ABSOLUTE zero > > > potential energy point at r=0. If M and m are the Earth and an > > > electron, m_0m is the ordinary rest mass of a free electron (its > > > maximal value at r infinite). The frequency emitted by an atomic clock > > > is proportional to the rest mass of the electron involved in the > > > change of state. In GR the rest mass is supposed a constant an > > > intrinsic electron attribute, justifying the change in frequency with > > > the warp of the space-time provoked by M. As you see, the things in > > > 1905R are very much simple. > > > I left to you the verification that the change of frequency predicted > > > by 1905R coincides with the GR one in all the range of practical r > > > values in real experiments like the Pound&Rebka one. By the way, the > > > 1905R formula applies for ALL values of r from 0 to infinite, while > > > the GR one has a limited range of application owed to the presence in > > > it of a singularity that is absent in the 1905R one. > > RVHG (Rafael Valls Hidalgo-Gato) |