Atomic clock behaviour in a gravitational field explained with 1905 Relativity
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From: valls on 24 Jun 2010 06:26 On 23 jun, 17:24, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > <va...(a)icmf.inf.cu> wrote in message > > news:53aa1a16-ebc8-4368-a875-bc542e8b2946(a)d37g2000yqm.googlegroups.com... > On 23 jun, 16:52, "Dono." <sa...(a)comcast.net> wrote: > > > > > > > On Jun 23, 3:59 am, va...(a)icmf.inf.cu wrote: > > > > On 22 jun, 16:53, "Dono." <sa...(a)comcast.net> wrote:> On Jun 22, 2:34 > > > pm, va...(a)icmf.inf.cu wrote: > > > > > > Sure? Is it not sufficient to you the Pound&Rebka experiment and all > > > > > the continuous successful function of today GPS? > > > > > Old fart, > > > > > Pound-Rebka is about chage in FREQUENCY. Has nothing to do with your > > > > idiotic formula about mass change. > > > > The experimental frequency change in P&R is explained by the change of > > > mass predicted by 1905R. > > > ...only in your demented mind. > > I showed you already the relevant formulas in all detail, derived from > the following: > > a) 1905 Einstein Principle of Relativity. > b) Conservation Principle of Energy. > c) Newtonian gravitational formulas. > > Specify what are you rejecting and why. > > RVHG (Rafael Valls Hidalgo-Gato) > ===================================== > What's the formula for > a) 1905 Einstein Principle of Relativity? Hello Androcles. You can read a) in the introduction of the 30jun1905 Einsteins paper: [The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good] In the 1905 context, those laws and the corresponding equations are the Maxwell ones. By the way, I asked you more than one time if you accept a), never obtaining an answer. RVHG (Rafael Valls Hidalgo-Gato)
From: valls on 24 Jun 2010 17:07 On 24 jun, 10:14, harald <h...(a)swissonline.ch> wrote: > On Jun 22, 5:48 pm, va...(a)icmf.inf.cu wrote: > > > > > > > On 22 jun, 07:53, harald <h...(a)swissonline.ch> wrote: > > > > On Jun 22, 1:43 pm, va...(a)icmf.inf.cu wrote: > > > > > 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 Einsteins 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. About > > > > the presence of Potential Energy in 1905 Relativity see the following > > > > link:http://groups.google.com.cu/group/sci.physics.relativity/browse_frm/t... > > > > 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. 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 1905 Relativity (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. The arbitrary additive > > > > constant characteristic of potential energy disappears in 1905R, > > > > appearing 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. > > > > Again, please mention your ad-hoc *assumption* of ceteris paribus: > > > that nothing else changes (in particular dimensions). > > > Hello Harald. Yes, I remember in our past talking in the other thread > > that you say something about dimension. I supposed in that occasion > > that you were referring to the atomic scale (evidently, I missed > > something important). My answer was that Newtonian equations hold good > > following 1905 Einsteins definition of stationary system. > > Not entirely, as 1905 SRT makes at least the following modifications: > Remember that I distinguish between 1905R and the Special Relativity (SR) introduced by 1916 Einstein. In first place, gravity is declared out of the scope of SR, and we are precisely addressing here gravitational effects on rest clocks. Obviously, I am considering included in the Newtonian equations the gravitational ones. Exists here a very important detail that I want now to address. How if by definition the Newtonian equations hold good, can we derive later a modification of them? This is a very profound logic topic close related to the dialectic of the scientific increasing knowledge process. Once new principles or postulates are admitted as the base of a new theory, the consequences cant be known immediately. The experimental evidence plays then a decisive role here and, as the history of science development put out of any doubt, contradictions arise in all the process. Not knowing your philosophical ideas, let us see if we can continue our talking without going any further in this rather difficult topic. > - Contraction of material objects > - slowdown of clocks > - increase of dynamic "mass" > Fortunately, your three modifications are speed dependent and dont apply to rest clocks. By other part, I am especially interested in the speed up of rest clocks when increasing the gravitational potential, owed to the increase in the rest mass. You can see in the following link my arguments supporting the presence of potential energy (including the gravitational one, of course) in 1905 Relativity: Potential energy in Einsteins 1905 Relativity http://groups.google.com.cu/group/sci.physics.relativity/browse_frm/thread/f50627c5376608fa/48260fe6dfdd7b36?tvc=1&hl=es#48260fe6dfdd7b36 > Now, as I emphasized before, Einstein gave in 1905 (but not in 1911) > the good example, when he made a ceteris paribus assumption, that he > indeed made such an assumption. > Good news. My goal is to follow 1905 Einstein in his historic context without introducing any new concept from me. > To elaborate: one should account for all obvious possible effects. > - if you neglect any possible effect of acceleration on clock > frequency either because your theory does not provide for any clue of > what that effect should be, if any, or because you really think that > acceleration has a negligible influence for the considered case, this > should be stated (as Einstein did in 1905, although without > elaboration). > Remember that I have no theory at all, or at least I am trying to no have. As the experimental evidence of today GPS shows, clocks can be moving with any variable velocity, without affecting the application to them of 1905 Relativity results, the old ones (speed dependent) or the new derived by me (gravitational potential dependent) respecting the 1905 historic context. > - similarly, if you neglect any possible effect of gravitation on > clock frequency due to a change of the size of objects, either because > your theory does not provide for any clue of what that effect should > be, if any, or because you think that gravitationally induced size > change has a negligible influence for the considered case, this should > be stated (a point that Einstein also overlooked in 1911 - > seehttp://www.mathpages.com/home/kmath115/kmath115.htm). > Thanks to your recent very valuable contribution giving me access to an English version of the 1911 paper, I am now able to make the following comments about it. I repeat here the first part of paragraph 2: [ 2. On the Gravitation of Energy ONE result yielded by the theory of relativity is that the inertia mass of a body increases with the energy it contains; if the increase of energy amounts to E, the increase in inertial mass is equal to E/ c^2 when c denotes the velocity of light. Now is there an increase of gravitating mass corresponding to this increase of inertia mass? If not, then a body would fall in the same gravitational field with varying acceleration according to the energy it contained. That highly satisfactory result of the theory of relativity by which the law of the conservation of mass is merged in the law of conservation of energy could not be maintained, because it would compel us to abandon the law of the conservation of mass in its old form for inertia mass, and maintain it for gravitating mass. But this must be regarded as very improbable. On the other hand, the usual theory of relativity does not provide us with any argument from which to infer that the weight of a body depends on the energy contained in it. But we shall show that our hypothesis of the equivalence of the systems K and K' gives us gravitation of energy as a necessary consequence. ] The last text is sufficient to convince me that 1911 Einstein do not realize all the consequences of the 27Sep1905 paper where the universal relationship between mass and energy is showed. In this paper the word inertia appears only two times, in the title and in the last line. [Does the inertia of a body depend upon its energy-content?] [If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.] As you see, you can substitute inertia by gravitating mass (or simply mass) without altering at all the essential content of the paper. 1911 Einstein has no right at all to say that 1905 Relativity (1905R) only address inertial mass and not gravitating mass, by the very simple reason that he doesnt say a word (literal) about that in 1905. In my thread Potential energy in 1905 Relativity (I gave you already the link) I put out of any doubt that Potential energy is present in 1905R (and then also the gravitating mass generating the corresponding Potential field). In the paper the word mass appears four times, all in the following text (the more important one): [If a body gives off the energy L in the form of radiation, its mass diminishes by L/c^2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 x 10^22, the energy being measured in ergs, and the mass in grammes. ] As you see, no word at all making different inertial mass from gravitating mass. Both Potential energy and Kinetic energy have mass measuring it, and a body in free fall maintains constant its total energy (and then also its total mass) according to the Conservation Principle of Energy. The increase in dynamic mass is compensated by the decrease in rest mass and vice versa (at least for a bound body, like Mercury orbiting the Sun, or an electron orbiting a nucleus (before QM epoch). It is ridiculous 1911 Einstein saying that the usual theory of relativity does not provide us with any argument from which to infer that the weight of a body depends on the energy contained in it. I dont want now to address 1915-1916 Einstein Principle of Equivalence in GR. For the moment, gravitation of energy doesnt need it. > Regards, > Harald > Very happy for your continued and high quality contribution to the topic, RVHG (Rafael Valls Hidalgo-Gato)
From: Mathal on 26 Jun 2010 02:57 On Jun 25, 5:46 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > Let's just keep it simple, motion is mv = m.x/t where m is the mass > of the apple. What is *relative* motion? mv is momentum in a classical pre-20th century perspective (minus 10 to 20 years) . Your question is 'what is *relative* momentum?', if you really want to be understood. 'motion' is a nebulous term that diverts rather than focuses one's attention on what you are asking. motion usually refers nebulously to velocity but you couldn't be asking about *relative* velocity?. no, of course not. because if you were you could use the lorenz transform(ula) to determine the *relative* momentum. Mathal
From: blackhead on 26 Jun 2010 08:02 On 26 June, 01:46, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > "blackhead" <larryhar...(a)softhome.net> wrote in message > > news:d7366fa1-8130-46c8-9646-6a027f0cc210(a)j8g2000yqd.googlegroups.com... > On 25 June, 00:58, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > > > > > > > "blackhead" <larryhar...(a)softhome.net> wrote in message [snipped] > > | > > | Examples in electrodynamics where the effects depend only on relative > > | motion. The current induced in a coil by a magnet depends only upon > > | their relative motion and not on which is stationary and which is > > | moving, for example. > > > Well done. Very good, an intelligent reply. > > So the Principle of Relativity is... > > (trumpet fanfare, drum roll...TA..DAAAaaa...) > > ... relative motion. > >http://www.androcles01.pwp.blueyonder.co.uk/1st/1stPostulate.gif > > > Why doesn't genius Einstein say what relative motion is instead of > > giving one lousy example? Naturally we are supposed to know what > > relative motion is because he hasn't told us. It's an axiom. > > > Describing an axiom is like describing a colour. I can't tell you what > > red is, I can only point to a rose and say red is like that flower. Green > > is like the grass. Blue is like the sky. I'm giving examples, you have > > to KNOW what red is, what green is, what blue is. Yes, I know there > > are yellow roses (of Texas, the only girl for me) and white roses > > and pink roses, but the rose I'm pointing to is RED and I'm not going > > to get sidetracked about flowers when I'm talking about colours. > > > Have a go, do it for him. See if you can describe relative motion > > with a simple equation, without all the flowery mumbo jumbo about > > some vague laws of physics being the same in all references of > > non-existent absolutely relative frames of coordinate systems inert. > > > It isn't easy to find the right words, so look it up in a dictionary. > > I have a suggestion. "If A meets B then B meets A simultaneously" > > is a corollary of relative motion. It sound obvious, but stating the > > obvious is the skill of the mathematician. Rene DesCartes was a > > mathematician. He said "I think, therefore I am". It is UNDENIABLE. > > When you have an axiom you have a primitive statement that is > > not provable yet is undeniable. If it can be tested, if it can be denied, > > it is NOT an axiom (or postulate). It is at best an hypothesis, and > > all that is constructed from it is just so much verbal diarrhea. > > Einstein's second postulate isn't a postulate, it is an assertion. > > Einstein's THIRD postulate, that he calls a definition, is along > > the same lines as "all roses are red". > > > The Principle of Relativity is an axiom. Say what relative motion is > > with an equation for me. You can jump ahead 15 years and look here: > >http://www.bartleby.com/173/5.html > > Let A, B be 2 identical coordinate systems, with A_ and B_ labels for > their respective measurements there. If a(A_x, A_y, A_z, A_t) is the > equation of motion of a point in A, we say its motion is relative to > A. Its relative motion wrt to B is b(B_x, B_y, B_z, B_t). > ============================================== > That's a start. You've labelled two coordinate systems, although why you > left > out A_apple and B_apple and put in A_t and B_t has me somewhat bemused. > I believe "motion" can be described as displacement as function of time, > can't it? Something to do with > v = x/t or > v = sqrt(x^2 + y^2)/t or > v = sqrt( x^2/t^2 + y^2/t^2) perhaps? > Or even > v = sqrt( x^2/t^2 + y^2/t^2 + z^2/t^2) perhaps? > Let's just keep it simple, motion is mv = m.x/t where m is the mass > of the apple. What is *relative* motion? You have defined motion to be momentum and therefore asking what is relative momentum. You can define it however you want, bearing in mind that it's already been done by other physicists who generally agree on this definition. You would need to define what it's relative to, and in what coordinate system the measurement is going to take place. So if you have particles p1, p2 with momentum m1v1 m2v2 respectively in a coordinate system, you could define the relative momentum of p1 wrt p2 as m1v1 - m2v2 using the same coordinate system, or as being the momentum of particle 1 in a coordinate system where the momentum of particle 2 is zero. I think the last definition is the one commonly used. [snipped]
From: Androcles on 26 Jun 2010 12:24
"blackhead" <larryharson(a)softhome.net> wrote in message news:6399f79b-2754-43b8-8403-7e5ce8f15426(a)j4g2000yqh.googlegroups.com... On 26 June, 01:46, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > "blackhead" <larryhar...(a)softhome.net> wrote in message > > news:d7366fa1-8130-46c8-9646-6a027f0cc210(a)j8g2000yqd.googlegroups.com... > On 25 June, 00:58, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > > > > > > > "blackhead" <larryhar...(a)softhome.net> wrote in message [snipped] > > | > > | Examples in electrodynamics where the effects depend only on relative > > | motion. The current induced in a coil by a magnet depends only upon > > | their relative motion and not on which is stationary and which is > > | moving, for example. > > > Well done. Very good, an intelligent reply. > > So the Principle of Relativity is... > > (trumpet fanfare, drum roll...TA..DAAAaaa...) > > ... relative motion. > >http://www.androcles01.pwp.blueyonder.co.uk/1st/1stPostulate.gif > > > Why doesn't genius Einstein say what relative motion is instead of > > giving one lousy example? Naturally we are supposed to know what > > relative motion is because he hasn't told us. It's an axiom. > > > Describing an axiom is like describing a colour. I can't tell you what > > red is, I can only point to a rose and say red is like that flower. > > Green > > is like the grass. Blue is like the sky. I'm giving examples, you have > > to KNOW what red is, what green is, what blue is. Yes, I know there > > are yellow roses (of Texas, the only girl for me) and white roses > > and pink roses, but the rose I'm pointing to is RED and I'm not going > > to get sidetracked about flowers when I'm talking about colours. > > > Have a go, do it for him. See if you can describe relative motion > > with a simple equation, without all the flowery mumbo jumbo about > > some vague laws of physics being the same in all references of > > non-existent absolutely relative frames of coordinate systems inert. > > > It isn't easy to find the right words, so look it up in a dictionary. > > I have a suggestion. "If A meets B then B meets A simultaneously" > > is a corollary of relative motion. It sound obvious, but stating the > > obvious is the skill of the mathematician. Rene DesCartes was a > > mathematician. He said "I think, therefore I am". It is UNDENIABLE. > > When you have an axiom you have a primitive statement that is > > not provable yet is undeniable. If it can be tested, if it can be > > denied, > > it is NOT an axiom (or postulate). It is at best an hypothesis, and > > all that is constructed from it is just so much verbal diarrhea. > > Einstein's second postulate isn't a postulate, it is an assertion. > > Einstein's THIRD postulate, that he calls a definition, is along > > the same lines as "all roses are red". > > > The Principle of Relativity is an axiom. Say what relative motion is > > with an equation for me. You can jump ahead 15 years and look here: > >http://www.bartleby.com/173/5.html > > Let A, B be 2 identical coordinate systems, with A_ and B_ labels for > their respective measurements there. If a(A_x, A_y, A_z, A_t) is the > equation of motion of a point in A, we say its motion is relative to > A. Its relative motion wrt to B is b(B_x, B_y, B_z, B_t). > ============================================== > That's a start. You've labelled two coordinate systems, although why you > left > out A_apple and B_apple and put in A_t and B_t has me somewhat bemused. > I believe "motion" can be described as displacement as function of time, > can't it? Something to do with > v = x/t or > v = sqrt(x^2 + y^2)/t or > v = sqrt( x^2/t^2 + y^2/t^2) perhaps? > Or even > v = sqrt( x^2/t^2 + y^2/t^2 + z^2/t^2) perhaps? > Let's just keep it simple, motion is mv = m.x/t where m is the mass > of the apple. What is *relative* motion? You have defined motion to be momentum and therefore asking what is relative momentum. ============================================== Yes indeed. DEFINITION I. The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. THUS air of double density, in a double space, is quadruple in quantity; in a triple space, sextuple in quantity. The same thing is to be understood of snow, and fine dust or powders, that are condensed by compression or liquefaction; and of all bodies that are by any caused whatever differently condensed. I have no regard in this place to a medium, if any such there is, that freely pervades the interstices between the parts of bodies. It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to the weight, as I have found by experiments on pendulums, very accurately made, which shall be shewn hereafter. DEFINITION II. The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly. The motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple. -- "Principia Mathematica" - Sir Isaac Newton. =================================================== You can define it however you want, bearing in mind that it's already been done by other physicists who generally agree on this definition. =================================================== Motion was defined by Newton. I'm not changing the definition. =================================================== You would need to define what it's relative to, and in what coordinate system the measurement is going to take place. =================================================== Very good. =================================================== So if you have particles p1, p2 with momentum m1v1 m2v2 respectively in a coordinate system, you could define the relative momentum of p1 wrt p2 as m1v1 - m2v2 using the same coordinate system, or as being the momentum of particle 1 in a coordinate system where the momentum of particle 2 is zero. I think the last definition is the one commonly used. =================================================== Very good. But you now have two motions measured in one coordinate system which has no mass or velocity of its own, and originally you stated "If a(A_x, A_y, A_z, A_t) is the equation of motion of a point in A, we say its motion is relative to A. Its relative motion wrt to B is b(B_x, B_y, B_z, B_t). " How about: If b(A_x, A_y, A_z, A_t) is the equation of motion of a point in B then a(B_x, B_y, B_z, B_t) is the equation of motion of a point in A? Now you can put in your m1v1 - m2v2 definition and say difficult words like "symmetry". That way we eliminate the third universal absolute at rest empty space coordinate system inertial frame of reference, yes? Or we can put it back in... II. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is vulgarly taken for immovable space; such is the dimension of a subterraneaneous, an �real, or celestial space, determined by its position in respect of the earth. Absolute and relative space, are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be perpetually mutable. So you see, I have a problem that I want your help with. It is this: Uncle Bonehead Green Ph.D. (look him up in American Men of Science) tells me I don't know the difference between a closing velocity and a relative velocity, and he's right, I don't; but the old meanie won't tell me what it is. Which pair or pairs of inertial frames of reference systems of coordinates have the closing velocity, which have the relative velocity, and which is the one at rest? http://www.androcles01.pwp.blueyonder.co.uk/closing.gif We have to pin this down, because "light is always propagated in empty space (aka universal absolute at rest coordinate system inertial frame of reference that doesn't exist) with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The introduction of a ``luminiferous ether'' will prove to be superfluous inasmuch as the view here to be developed will not require an ``absolutely stationary space'' provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place" and we do want a simple and consistent theory, don't we? |