Dear Sergey,
Thanks for your interest in my essay. I did not understand the points you are trying to make. You say: ''I think if the equation of physics are written with the help of vectors and tensors they can be truly for absolute reference frame.''
The whole business of using tensors suggest background independence because tensors have an existence independent of any basis in which their components may be written. I don´t understand what you mean.
Hi Daniel,
The weak field approximation I use is derived in Hobson, Efstathiou and Lasenby's book, "General Relativity, An Introduction for Physicists" page 491. Another treatment begins on page 313 in Moller's "The Theory of Relativity".
I do not, as a matter of first choice, think in terms of diffeomorphisms, and, with all of the questioning in current essays of the interpretation of General Relativity and its relation to Quantum Mechanics, I don't plan to focus on diffeomorphism invariance. Upon reading your essay it appeared to me that it bore some relation to mine, but it looks as if this relation will die from the lack of a common vocabulary and common expertise. Thanks again for your efforts, and good luck in the contest.
Edwin Eugene Klingman
Edwin,
I don´t think any lack of expertise of my own should be a problem because my question is very simple. Unfortunately I could not find your references.
Let me put it in this way: The C-field is not a 4-vector (certainly because the curl operator is defined only for 3 dimensions). I´m just asking you to provide the tensorial version, i.e. the covariant version of the C-field equation.
Then I´m sure we can have a good talk.
Best regards
Daniel,
Due to the high degree of non-linearity in the field equations a general solution for arbitrary matter distributions is "analytically intractable". One approach to this is to linearize general relativity, and an excellent treatment of this is provided beginning on page 467 of the Doran reference given above and continuing to page 497. [An equivalent treatment begins on page 313 in Moller, as noted.] The key equation is probably the metric equation (17-4) on page 469, based on infinitesimal transformations (of the form given in equation 17-2) that apply to changes in scalar, vector, and tensor fields, but the claim is that these can be ignored in all quantities except the metric, "where tiny deviations from eta-sub-mu-nu contain all the information about gravity. Equation (17-4) is considered as analogous to a gauge transformation in electromagnetism, and hence has the form of the tensor F-sub-mu-nu given on page 4 in my previous essay, that I already referenced above.
I'm sure that you are quite competent, but if the linearized form of General Relativity is unfamiliar to you, I doubt that a comments blog is the place to remedy this. And, as I noted above, I don't wish to invest more effort into GR field equations, since I have doubts about the ultimate interpretation of GR and I currently find the Maxwell form of the equations much more useful for analogies with electro-magnetism, which I believe most applicable to the quantum approach I am currently interested in. Thanks yet again for your efforts.
Edwin Eugene Klingman
Dear Daniel,
The background of it as follows: The conceptual meaning of force ist that it is the cause of change. That means the function f(ik), whose form enters into the solution as a system parameter, is proportional to the time deritative of a state variable. It is thus already assumed how the force will depend on the state, and this force then determines the change of the state in time.
In brief, one understands f(ik) not as one cause among others but as the cause of the change of state. Mathematically it is due to the differential equation being of second order. The state variable x(ik) alone does not determine its own subsequent development, but does so only in conjunction with its time deritative v(ik) as an arbitrary initial condition. In particular, setting the force, which is assumed to be the cause of the change of state, equal to zero, there are still solutions with constant velocity:
x(ik) = a(ik)t + b(ik)
v(ik) = a(ik)
A body with no motive force acting upon it moves with constant velocity.
The physical background of v. Weizsäcker's argument is: Two bodies with the same velocity but at different locations are in different states, if correctly put by the modern description in phase space; and during inertial motion the point in phase space varies. V. Weizsäcker proposes: If one wants to think causally in a consistent way, one must radicalize Machs ideas and interpret the inertial motion as being caused by the universe (i.e. the distant masses).
Hope it helps to understand the point..
Best wishes
Helmut
Edwin
I found a good reference (Carrol´s book) and I now understand the C-field is a 3 vector formed upon the (0i) components of the pertubation of the metric huv in the linearized approach.
The C-field has an existence relative to any inertial frame, but just as the eletric and magnetic field are part of a basis independent tensor Fuv, the basis independent object from which C-field is derived is huv.
NASA´s probe b may have measured the C-field, but we should not forget that that was made in a particular reference frame. In a different frame, the result would be different (just as in electromagnetic measurements of the E and B fields).
Given the background independent nature of GR, 2 configurations of the universe related by a diffeomorphism (like moving the whole universe to the left) are not physically distinct, and also the huv before and after a diffeomorphism are not physical distict (even though the C-field might be, but that is analogous to the transformation of eletric field to magnetic field in different frames). So, just like anyother relativistic field, the huv has a background independent character and the C-field derived from it is meaningful only in a particular basis. There is no room for absolutness.
Dear Helmut,
Thanks for the reply.
First notice that the concept of velocity is not unique, as an objects velocity varies within different inertial frames. Since classical mechanics is galilean invariant, absolute velocity has no importance at all.
Also, the fact that ''A body with no motive force acting upon it moves with constant velocity'' is not strange or undesirable! It seems you feel unconfortable with the fact that the lack of force (F=0) implies a change of state. It may be easier to see that there is no problem by remembering that F is just -(grad V) which may be 0 even when V is different to 0.
Daniel,
I'm glad you found a reference. And I agree with you that if it "is analogous to the transformation of electric field to magnetic field in different frames" then "like any other relativistic field, the huv has a background independent character and the C-field derived from it is meaningful only in a particular basis. There is no room for absolutness."
I am not certain that the analogy holds, due to some features of Martin Tajmar's measurements of the C-field and due to my own interpretation, but it is likely that it actually is analogous, in which case I fully agree with you.
I still recommend Daryl Janzen's essay and Israel Perez's essay as potentially related to yours. I think you will enjoy fruitful discussions with both of these authors.
I very much appreciate the effort you have made to understand the C-field and relate it to your own essay, and wish you the best in this contest and in your career.
Sincerely,
Edwin Eugene Klingman
Dear Daniel,
you avoid the problem connected with it: Neither Galilean nor Special Relativity is able to justify the privileged role of inertial frames of reference. Newton's law is epistemologically circular. Today this problem is only solved by means of an incomplete induction. Einstein was aware of this problem, which he tried to eliminate it by introducing Mach's principle into his general theory of relativity. But he failed. Even in his last lecture, given at the Palmer Physical Laboratory in April 14, 1954, he struggled with this problem. He compared the inertial frame with God Almighty. Like him it would be unaffected by anything else.In this lecture he also explained why the implementation of Machs principle into his GTR failed. --If you give up space, you have an enormous number of distances, and unhandy consistency relations.-- (Einstein, 1954)
Hence, I resist: THERE IS A PROBLEM and its solution determines essentially how we understand MOTION.
Kind Regards
Helmut
Dear Daniel (part 1)
I enjoyed reading your clear and well written essay. I would like to make some comments so you can understand some nuances in how we should understand absolute motion. As I argued in my reply to you in my entry, I hold that space is some sort of aether which for modern convenience we can call it quantum vacuum or better the zero-point field (ZPF) and therefore it can be considered as the PSR. Because relative to this ZPF all objects move (including light). If we have an object at rest this object is absolutely at rest otherwise it is in absolute motion. So, as you can see I am being truly relational, unless you disagree. I am going to quote one of the arguments that Newton gave in his famous scholim when he was arguing in favor of the existence of absolute motion (which is basically the same idea I am stating):
"But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their instead we use sensible measures of them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred.
But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but IMPOSSIBLE TO KNOW, from the position of bodies to one another in our regions whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions.
As you can see Newton was also truly relational in contrast to what most people believe about him, the problem is that Newton's space was envisaged as total emptiness and relating the motion to nothingness is meaningless. He also knew that it may not be possible to detect absolute motion but despite this when something moves it really moves not only relative to a reference object but, within the modern context, relative to the ZPF. This field pervades the whole universe and interconnects all physical objects (particles). Therefore, the water of the famous bucket experiment, moves relative to the ZPF which in Newton words would be "absolute space" and in Einstein words would be "the gravitational potential or the metric tensor". The problem with the metric tensor is that it is nothing but a mathematical object, pure geometry.
On the other hand, the programme your are endeavoring is not knew for me. I have tried in the past to reformulate mechanics getting rid of time and space. This would lead to a thermodynamic-like formulation of mechanics, but I found it fruitless basically because one cannot avoid the involvement of time-like parameter in the formulation. As I could see in your essay the parameter gamma plays the role of t, which appears to be redundant if one tries to get rid of one parameter and introduce another. My question here is, how is this parameter gamma going to be measured? With a clock?
To be continued...
Israel
Part 2
You also discuss the nature of time and take as a departure for your argumentation Newton's absolute notion. Indeed Newton's time appears to be unaffected by the motion of objects, it is a continuous flow that never stops, nor accelerates. I agree with you that the precursor of time is change/motion (CM) of things, this is what makes us feel the passage of time. I think that something that appears to be certain is that CM of things is seen everywhere in nature, I mean, there are things in the universe (motion of planets, etc.) constantly occurring following some physical laws, and in this sense the continuous occurrence of events can be thought of as a flow of CM and therefore this resembles a flow of time in the Newtonian sense. The inference we grasp from the previous reflexion is that to say that there is a flow of changes is equivalent to say that there is a flow of time. In physical terms this flow is measured with a clock (that is a material body that moves or changes) and is mathematically represented in physics as an "independent" variable. Certainly, it has to be independent because it seems that CM is an intrinsic aspect of the universe. According to the theoretical framework under consideration this variable is considered as a parameter (e.g. classical mechanics) or as a coordinate (relativity). Now, whatever the physical meaning of the variable is, I also hold that this CM has to be related to a reference CM. And since I am assuming a PSR I also hold that there is a preferred clock (time) and again if this clock is at rest in the ZPF one has a universal (absolute) time for all observers (see also the essay of Daryl Janzen). If a clock moves relative to the PSR it dilates as function of the speed (imagine again the light beam clock in which the mirror is held by a metallic bar that delimits the distance L).
The dilation effect is caused basically by the fact that the light beam --traveling through the ZPF-- will traverse an optical path length much larger than when the clock is at rest. If our light beam clock is placed perpendicular to the motion of the clock, the light beam will follow a diagonal trajectory in the forward and backward journeys. In this case there is no Lorentz-FitzGerald contraction of the clock bar and we can calculate the amount of dilatation by using the Pythagoras theorem. But if we place the clock in a horizontal position the bar will undergo Lorentz-FitzGerald contraction by the factor gamma and we have to consider this effect in our calculations. Hence, no matter the orientation of the clock with respect to the motion, the dilatation will be in the same amount.
The Lorentz-FitzGerald contraction is a consequence of the fact that the bar of the clock is made up of atoms (particles) glued by electromagnetic fields. Thus, to set the clock into motion from absolute rest we have to apply a force, this force will cause a reconfiguration of the atoms in the direction in which the force is applied manifesting itself as a contraction of the length.
Special relativity gives a geometrical explanation of these effects based on the two postulates (which as I argued in my essay is only one). In a certain sense we can say that relativity makes a mathematical abstraction of the physical properties (such as length) of real objects (please read Einstein's essay: Geometry and experience). The abstraction of extension of a material object is mathematically represented by a three dimensional manifold. There is a caveat to make here, one should distinguish between physical space (ZPF, vacuum and aether) and the mathematical representation of physical space. Newtonian space was envisaged as nothingness, total emptyness and its mathematical counterpart is Euclidean geometry. Recall that in special relativity space is also totally empty as in the Newtonian case and its abstraction is the Minkowskian space-time, which is a psedo-Euclidean space (due to the minus sign in the metric). General relativity does the same thing, from this perspective space is epitomized as non-Euclidean which warps according to the energy-momentum tensor, but again, it is just a geometrical abstraction.
Best wishes
Israel
PS. I have replied to your last post in my entry.
Dear Israel
Thank you very much for taking your time to read my essay and my arguments on your own essay. I am a little bit busy with my university now so I may take a few days to reply your posts. Come back here until thursday and I will analyze your arguements carefully, both here and on your essay´s thread.
Once again thanks for an awesome discussion.
Daniel
Dear Daniel,
I supposed that in the beginning we have only one frame which is absolute reference frame. Then we discover vectors and tensors in this frame. After it we discover such transformation of coordinates and time that we can study phenomena in relative reference frames using the same vectors and tensors but with relative coordinates and time.
dear Daniel
I will post this also in reply to your post concerning my essay.
Thanks for suggesting I should read your essay.
I enjoyed it very much.
Of course we are pursuing different objectives, but there is a common drive toward seeking the building blocks of space-time notions in your essay and mine.
I am trying to take a certain leap in the (conceptually) unknown: doing physics without space, time, motion,,,,only particle detections and relationships among detectors,,,,this is after all what we really do operatively and I am intrigued by the possibility that if we stick to this minimalistic description, if we get read of the extra luggage of space-time inferences, perhaps we might travel more comfortably toward addressing some of the foundational issues we are facing
and by the way to me a clock is a box Alice gives to Bob: when the box is materially connected, in appropriate ways, to Bob's ``particle-detector box" the combination of the two boxes produces readouts which assign a certain number, "time", to each particle detection,,,,,it seems to me this is what is actually done by the objects we call clocks,,,
if we found a steady source of particles in nature, let me call them particles of type A, it could be all in one box: detector distinguishes two types of particles and uses number of particles detected of type A as time whereas it handles number of particles detected of type B as its actual detections, so it times the detections by producing readouts of pairs of numbers, correlations n_A,n_B (had value of the counter B equal to n_B in correspondence of the value of the counter A equal to n_A)
best wishes for the competition
Giovanni
Dear Helmut
The role of inertial frames was made clearer in the 19th century by the works of Lange and Tait. They showed how to define an inertial frame of reference operationally. But it is possible to recover all results from classical mechanics without using absolute spatial frame (associated with inertial frames). This is exactly Julian Barbour´s relational particle mechanics, implemented via his method of best matching. It recovers the notion of an inertial frame by an average procedure on all the masses of the universe, thus giving life to machian philosophy.
Dear Sergey
Mach once pointed out: ''what would be of our law of inertia in the middle of an earthquake?''
Due to the fact that we are used to live in a relatively stable enviroment, it is very natural to introduce an absolute frame. But when we find out that the whole background is not so stable (the earth moves, the sun moves, the galaxy moves) it really becomes compelling to look for background independent or backgroundless formulations for physics. We have almost a ''historical reason'' to look for such theories: newton´s absolute physics could well be an accidental mistake due to our stable enviroment.
(Part1) Dear Israel
You state that: ''Because relative to this ZPF all objects move (including light). If we have an object at rest this object is absolutely at rest otherwise it is in absolute motion''
That seems true, but it is not! That is because you cannot indentify space points with field values. I have argued for this before, but I will try to be clearer now. Suppose we have a snapshot of your ZPF. Then we have a spatial frame in which we can do physics: lets suppose that, by some procedure, it is possible to measure positions against this quantum vaccum field. After a small amount of time has elapsed can we calculate the displacement of a macroscopic object? Your anwser would be: YES! Just look at the quantum vaccum background.
But actually it is not so simple: how do you identify a point in one of your ''quantum background'' with a point an amount of time later? We need an equilocality relation for that. Please see the attachment, I took from Barbour´s book ''The Discovery of Dynamics''. The snapshot argument I have mentioned before holds both with ''point particles'' and 'fields''.
''The argument goes like this(again, taken from barbour´s book):
(...) let us consider the situation in field theories. In field theory the dynamical problem can be posed typically as follows. Imagine a pattern of intensities in two dimensions (supressing again the third dimension of space for better visualization) and once again suppose a snapshot taken of the intensities. A little pattern of intensities has changed everywhere by a certain amount. We take a second snapshot. No the aim of a dynamical field theory, expressed in these terms, is to formulate laws which say how the intensity at each point of space changes with the passage of time. But again, we confront the invisibility of space. Given our two snapshots, the only way we can determine how much the intensity has changed is by comparing the one pattern of intensities with the other. But how is the second snapshot to be placed with respect to the first? We lack all objective criteria for making any definite placing of one snapshot relative to the other but for every particular placing we choose we obtain in principle different changes in intensities. No less than in the case of material particles, the universal change that takes place between the two snapshots simultaneously severs all connections between the two time slices.''
(Julian Barbour, The Discovery of Dynamics)Attachment #1: barbours_arrow.png
Part 2
You´ve written: ''But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but IMPOSSIBLE TO KNOW, from the position of bodies to one another in our regions whether any of these do keep the same position to that remote body''
Perfectly. As I have stated in my essay, inertial frames of reference were defined operationally in the 19th century. You may introduce absolute space, but there is no way to operationally define absolute velocity and absolute position! These are, as you put, impossible to know. No problem with this, as long as absolute space is useful. However, if we can do mechanics without invisible concepts, why not do it? Relational particle dynamics is superior to Newton´s theory: it recovers the concepts of inertial frame and duration solely from observable data. Furthermore, there are very objective advantages, such as relational particle dynamics reducing the number of initial conditions needed to solve the equations for motion: it has a bigger predictivity. Less data is needed.
The only way out is if, by some procedure upon the quantum vacuum you propose, it could be possible to have distinguised positions! I have big doubts on that however, because GR is background independent!
In the end, if the absolute background hypothesis you advocate proves to be useful, I will always agree that theories should be built with it. But, I tried to make clear that it must be REALLY useful, because it is not simpler then stating that there is no background.
Actually my essay was not strictly about the relational formulation for mechanics. I try to argue that there are more ways one can conceive motion other than absolutely or relationally. You should discuss these points more thoroughly with Julian Barbour, he´s the author of Shape Dynamics and strongly advocates Machian philosophy.
Best Regards,
Daniel
Dear Giovani
Thank you very much for your interest and comments in my essay! I feel that if one focus to build physics on operational procedures, he would inevitably arrive at something close to mach´s philosophy. For instance, positions are usually defined in relation to absolute space, but we operationally always measure it against some objetc (we don´t use an invisible frame to define positions because we can´t see it!). How is the relation of your proposal with this?
Also, I see a problem with your clock definition: it must rely, as you put, on a steady source of particles in nature. How can we characterize if the source is steady if we don´t have a clock?
Best regards,
Daniel
Dear Daniel
You seem to overlook Newton's words, I quote them again to remark their deep meaning. "And so, instead of absolute places and motions, we use relative ones". Notice how he was aware that for practical matters we use relative places and motions. Notice also how he was relating motion not only to reference bodies but also to space. I agree with you that is difficult (or may be impossible) to put a material object at rest relative to the ZPF, but despite that one cannot reject its existence. In my entry I replied to you and discussed how the principle of relativity should be understood. I would be glad if you take a look at it and answer the questions I raised there in relation to the rejection of the PSR.
As far as I can see you do not get the usefulness as I do, and so you conclude that, as absolute newtonian space, my arguments are devoid of utility. This is not the case. In my last replied to you I provided a counter example in allusion to the measurement of the one-way speed of light. So far, no experiment has ever measured it, but despite this, as we all have witnessed, the special relativity has been quite successful for physics. The case is similar with the ZPF, despite that the absolute position of an object relative to ZPF could not be determined I find the assumption elucidating and helpful for the construction of a strong and coherent theory. Just because fields (gravitational, electromagnetic) cannot be seen by the senses, this does not mean that they do not exist. Similarly occurs with the ZPF. Despite that it cannot be perceived by the senses we know it is there (do you deny this?), just recall the Casimir effect. So, I can assume it as a continuous fluid because this will help me to explain the body of observations. Moreover, the existence of this omnipresent field allows us to assume the PSR, again, despite the fact that (as Newton argued) we only had access to relative measurements. The ZPF and the PSR has to be considered, above all, because light, seen as a wave, demands it (as a photon the explanation becomes faint). Because its speed is defined relative to the ZPF, not relative to the source or any other material body. Light does not travel relative to the empty space as Newton contended, but relative to the ZPF. If you have understood this, I ask you to provide any objection to the motion of light. According to you, with respect to what physical entity do light move? What physical entity defines the speed of light waves?
In addition to these arguments, I pointed out another paradox in relation to the isotropy of the speed of light (see my reply to you in my entry). To avoid the paradox, it is necessary to assume the PSR. You say: if we can do mechanics without invisible concepts, why not do it? Because if do not introduce the PSR we arrive at several paradoxes. Furthermore, if a theory A assuming a PSR explains the same amount of observations as another theory B in which there is no PSR, I would chose theory A, because theory A would be free from paradoxes.
You: You should discuss these points more thoroughly with Julian Barbour, he´s the author of Shape Dynamics and strongly advocates Machian philosophy.
As I explained, Newton was also relational contrary to the customary view. The material objects we used as reference systems are in space, but one has be careful in how we conceive space. From my perspective, Mach misconceived the deep meaning of Newton conceptions because Mach thought of space as an empty vessel not as a massive fluid, this is why he claimed that the stars, and not space, were playing the major role in defining inertia and centrifugal forces.
Best Regards
Israel
