
#19
Oct2307, 12:05 AM

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Perspective is a key issue. To any 'fixed' observer, the metric of spacetime appears to be curved. Is that 'reality'? Hard to say. Devising a nonfixed observer is difficult.




#20
Oct2307, 12:40 AM

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#21
Oct2307, 03:09 PM

P: 531

Hi Jorrie,
Good question. To an outside observer who knows that the rocket is the source of acceleration, it seems reasonable to consider this a "real" force. But to an observer who is unaware that she's in a rocket, how does she know whether it's a real or pseudoforce? I guess that the uninformed observer could tell the difference by measuring tidal effects (?) (Can you measure the tidal effect if you're inside the accelerating frame?) As I understand it, an accelerating rocket would not create tidal forces because the acceleration force is completely "uniform", i.e. not a field. Maybe the answer is that things are "real" TO US only if we can observe and identify the underlying cause of movement. By that test, we are currently unable to judge whether gravity is a real or pseudoforce. One can say that we are able to stand outside of the coriolis effect and more or less identify its cause. That is, we can identify its "first order cause" as the rotation of earth's sphere. But below that there remains a "second order cause", gravity, the cause of which we currently are unable to fully comprehend. So one might reluctantly conclude that we can't yet decide whether coriolis is real or pseudo. I think it's going too far to say that if we can't determine whether a particular force is real or pseudo, that we must automatically consider it to be pseudo. In my view, the answer is that "the jury is still out." Another example occurs to me: Is an electromagnetic field a real or pseudoforce? Compared to gravity, we are much more confident about how electromagnetism works (i.e., the force is mediated by exchanges of virtual photons). But there are so many similarities between the fields of electromagnetism and gravity that I would be reluctant to put them in different "reality categories" unless I was absolutely convinced. Jon 



#23
Oct2407, 04:30 AM

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#24
Oct2407, 04:56 AM

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P: 717

Hi Jon.
Jorrie 



#25
Oct2407, 06:28 PM

P: 531

Hi Jorrie and Bjarne,
1. It sounds right to me that a comoving observer could measure tidal effects. 2. Bjarne, I didn't formulate my question clearly enough. I should have asked, "Does an electromagnetic field cause geometric curvature of space with respect to a charged particle moving through the field?" In that respect, I note the following from the Wikipedia article on "Maxwell's equations in curved space:" "In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (or more generally, spacetime with a nonEuclidean metric). They can be viewed as a generalisation of the vacuum Maxwell's equations as they are normally formulated in the local coordinates of flat spacetime, but general relativity dictates that the presence of electromagnetic fields themselves induce curvature in spacetime, so Maxwell's equations in flat spacetime should be viewed as a convenient approximation." It sure is interesting to contemplate the idea that an electromagnetic field actually curves spacetime, but in a way that is "apparent" only to charged particles. If it's true, then it reinforces the question of how "real" the curvature of space by gravity is. Jon 



#26
Oct2607, 08:13 PM

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P: 2,341

Shouldn't this thread be in "Astrophysics", or even "Beyond the Standard Model"?
http://relativity.livingreviews.org/...43/index.html I suppose you can say that it is a mystery why the presence of matter (or other massenergy) affects the geometry of spacetime. But is this really more mysterious than saying that the motion of charges in a wire creates something we call a magnetic field? What the heck is a magnetic field "really"? What is "electrical charge"? And why should magnetism care a jot about charge? I dunno, but I know that according to Maxwell's theory, it does, and I know that this has been a highly successful theory which predicts/explains a lot of useful stuff, like radio waves. I dare say that most physicists asked such questions when they were young. But at some point, one learns to focus on questions which can be attacked via the scientific method. Specificially, wolram should be encouraged to try to formulate a theoretical speculation which might someday admit an experimental test. The best short answer to the question "how does gtr treat gravitational interactions?" is that gtr treats "the gravitational field" as (part of) the curvature of spacetime itself, i.e. as a geometrical effect which affects how objects move, how clocks behave, and so on. In addition, energy and momentum act as the "source" of the gravitational field, i.e. when they are present in some region of spacetime, that region is curved in a certain way. This circle of ideas is very well summarized in the famous slogan of John Archibald Wheeler: "[the geometry of] spacetime determines how matter moves, and matter tells spacetime how to curve [which changes its geometry]". However, in some contexts it is convenient to elaborate on this slogan. In gtr, a special case of Wheeler's slogan shows that the world line of a small freelyfalling object in a vacuum region is a timelike geodesic in the Lorentzian manifold which we use to define the geometry of the "setting" for physics, spacetime. But in Newtonian gravitation or rather, the nonrelativistic "Newtonian" field theory in which the Poisson equation plays a role analogous to the EFE in gtr offers a very different description of gravitation in this situation. Namely, the gravitational acceleration of a small object in a vacuum region of space is given by the gradient of the gravitational potential, which is determined by solving the Laplace equation, the analogue in this theory of the vacuum EFE. Now Newtonian gravitation works very well in many situations, so one of the the first tasks facing the physicist who constructed gtr[*] was to verify that in an appropriate limit it gives the same predictions as Newtonian gravitation. To do this, one studies a slow motion weakfield limit and reexpresses the gtr law in an operational but less geometric way (one looks at the connection), and one verifies that in this limit, gtr does indeed give the same predictions as Newtonian gravitation. My point is that you shouldn't be surprised that this "correspondence" between slow motion weakfield gtr and Newtonian gravitation is somewhat roundabout, given that these two theories are based on such different conceptual principles! [*Yes, of course I mean Albert Einstein!] It might also be useful to state that in gtr, there is a very simple and beautiful geometric concept which corresponds quite precisely to acceleration (the kind measured by accelerometers): small objects (or more generally, bits of matter inside big objects) have world lines which are timelike curves. Such curves have path curvatures defined at each event on the curve. The path curvature at any event on the curve is a spacelike vector which is in fact orthogonal to the tangent vector. Its length gives the magnitude of acceleration experienced by the object at this event, and it's direction gives the direction of acceleration. (More precisely, one should smoothly assign a frame field along the curve, and then any vector orthogonal to the tangent vector, which is the timelike unit vector in the frame, is a linear combination of the three spacelike unit vectors in the frame. Thus, it makes sense to regard the path curvature as a three dimensional vector which lives in the "spatial hyperplane element" orthogonal to the curve at a given event.) In contrast, in gtr the gravitational field is treated as (part of) the curvature of spacetime itself. Spacetime curvature is tensorial and the components of the Riemann (or Weyl, or Ricci, or Einstein, or tidal) curvature tensors have the units of reciprocal area. Path curvature is vectorial and its components have the units of reciprocal length. So once you know the math, there is little chance of confusing them! Curious readers may wish to depart the thread at this point and study Box 7.1 and 17.2 in MTW, then related discussion in the textbook by Weinberg. Tidal accelerations are modeled in gtr by the electrogravitic tensor, or tidal tensor, which is one piece of the Bel decomposition of the Riemann tensor, and spinspin accelerations are modeled by the magnetogravitic tensor. The Bel decomposition splits the Riemann tensor into threedimensional tensor fields, wrt some timelike congruence. It is fully analgous to the decomposition of the "EM field tensor" into electric and magnetic fields (vector fields), with respect to some timelike congruence. In this way, when one forms a star by gradually concentrating matter in a compact region, the surrounding vacuum region is slowly curved up. In the end we have a region filled with matter, in which the geometry is dominated by Ricci curvature (in fact, in the simplest model of an isolated object, Schwarzschild's stellar model, the only curvature inside the star is Ricci curvature), surrounded by a vacuum region, in which the geometry is controlled by Weyl curvature. In the case of an isolated object, the curvature in the vacuum region falls off like [itex]O(m/r^3)[/itex], the same way that tidal accelerations of test particles scale in Newtonian gravitation. To forestall possible confusion, I should emphasize that Weyl curvature includes both such "Coulomb curvature" and the curvature typical of gravitational radiation, which typically oscillates in time but which decays with distance much more slowly, like [itex]O(1/r)[/itex]. (The respective buzzwords in the trade are "Petrov type D" and "Petrov type N" Weyl curvature; there is also Petrov type III Weyl curvature which decays like [itex]O(1/r^2)[/itex].) Incidently, it is possible to write down exact solutions of the EFE which represent an EM plane wave accompanied by a comoving gravitational plane wave. This is a very direct way of appreciating what we mean by saying the EM radiation and gravitational radiation propagate at the same speed! 



#27
Oct2607, 10:20 PM

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#28
Oct2707, 04:37 AM

P: 344

Chris Hillman
The question of this tread is: Why is the origin of gravity so elusive? No doubt that the origin of gravity is elusive,  we even don’t know if gravity is caused by a force or not. Imaging a football flying through the air side by side with a canon ball, (with same speed) Some kind of a FORCE pulls the canon ball faster down to the earth like it pull down a football. If gravity only was a property of space, the canon ball would fly the same distance like the football,  right? So is gravity caused by a FORCE?  Or caused by curvature of space? – Or both? Was Einstein right or do we (still) have more or some faith to Newton,  or was both right? Are these confusions not elusive? It is inevitable;  we are force to ask the question: Is gravity in reality a force that not only pulls down the canon ball, but that also pulls space until it curves. – And yes immediate we are forced into philosophy behinds gravity, and still ‘on the thinner ice’ we do not find a coherent answer,  to why is the origin of gravity so elusive. I am not highly educated,  but it would surprise me a lot if space not should curves proportional with the acceleration of gravity. I weak remember a quotation of Einstein,  he was wondering what space really was. But I can’t find that piece of text again, maybe someone have seen it and remember it. Bjarne Lorenzen 



#29
Oct2707, 04:04 PM

P: 531

However, before they can fall, they each must be projected upwards, against gravity, by the application of force. More force is required to raise the heavier object to the highest point in its arc than to raise the lighter object to the same height. More force is also required to impart any given horizontal speed to the heavier object. The difference in the two objects' total flight time depends on how high the highest point in their respective flight arcs are, not on their respective masses. Air friction and wind introduce additional forces that can cause variations in the outcome, of course. Jon 



#30
Oct2807, 02:06 AM

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PF Gold
P: 9,185

There is no harm in conceding you might be in over your head, Jon. Chris is a world class phycisist who donates his time here to explain the difference between science and superstition.




#31
Oct2807, 05:22 AM

P: 344

Joinmtkisco
Right.  Bodies accelerate and fall towards a gravity field (vacuum) with the same speed.. This happens even though the pull of gravity affects the canon ball with much greater attraction than it effect the football. The cause of this factum is it self really a mystery,  we have no idea of why this is so. Intuitive we would expect that the canon ball would fall faster,  but it’s not what happens. Imaging a football and a canon ball falling down to earth from let say only 1 meters height. Its not “space enough” for believing that the cause of these bodies both fall with the same speed, (on that short distance) is due to curvature of space. Both bodies follow a straight line and are not affected of the curvature of space. – So how can the curvature of space in this particular example be the cause of gravity?  It’s simple make no sense. What we do know is that it requires more force to lift a canon ball to 1 meter height as it require to lift a football to same height. The canon ball will in this position have greater potential energy. If we accelerate the football and the canon ball up to both 100 MPH (1 meter above the surface of earth) the canon ball still will have greater potential energy. Let’s say that that the size of the canon ball and the football is the same, wind resistance is therefore also the same. If we should be able to explain gravity based on curvature of space,  the football as well as the canon ball (moving with 100 MPH) would hit the earth’s surface simultaneously,  but this is not what happens. The explanation is of course,  the canon balls have greater potential energy proportion to the earth. – It is this FORCE involved that pull down the canon ball first. So based on simple everyday’s observation gravity seems to be a FORCE. – On the other hand we can not close our eyes for the fact that the curvature of space ALSO seems parts of the gravity phenomena. But attempt to implement this aspect in a complete and coherent way is: 'the end of the known road';  from here we are forced into philosophically considerations. So far we have not been able to archive any kind of coherent understanding to why we can say we have two independent (and both pretty good) theories for the same gravity phenomena. Common for these 2 theories is that we do not understand on the one hand why space curves, and on the other hand from where does the 'well known' FORCE come from, and how does it occour. Well,  it seems to be a broad hint build in,  matter must be responsible / the origin for this force,  Could this force also be responsible for space to curve? – Or why do space curve?  What does 'curvature of space' really mean?  I mean think about a gameroulet,  it is something physical we know  but this is not the way space is?  What is space?  What's its nature? Bjarne 



#32
Oct2807, 08:21 AM

P: 48

Although the search for gravity began before 500 years but we don't yet have a complete picture about how gravity works. So we come across this sort of many times. What you have to note is "what we see and feel in everyday life in not nature"So spacetime curvature can't be felt in everyday life.To feel it you have to go extreme.
<< post edited by PF Mentor berkeman >> 



#33
Oct2807, 09:12 AM

P: 344

We do not need to involve time, even though its ‘deformation’ together with space is a consequence. It will only contribute to unnecessary confusion. We can feel and measure gravity. The force is a reality.




#34
Oct2807, 12:30 PM

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P: 2,341

(Before anyone cites Jn8:7, I am aware that in the past I have myself sometimes expressed frustration stemming from the apparent obtuseness of some PF poster.) 



#35
Oct2807, 12:37 PM

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P: 2,341

Hi, Chronos,



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