# Why two mass attracts each other?

Discussion in 'Physics & Math' started by hansda, Mar 19, 2013.

Not open for further replies.
1. ### Markus HankeRegistered Senior Member

Messages:
381
What, by not even knowing which values the indices in the equations take ? By thinking that the Riemann curvature tensor is a force ? By asserting that the metric tensor contains pressure, stress and flux ?
Yeah right !

To acknowledge or reject something mathematically, you first need to understand those maths, which you clearly don't, a fact that you yourself make no secret of. And those who do, like AlphaNumeric, are being told by you that they are "hiding behind the maths". So really, you aren't in a position to either reject or acknowledge what GR says, because you don't know enough about it.

Huh ?!

It traces out (null) geodesics in space-time. Since we only have one time dimension, these geodesics are obviously static. I never said anything else. The Newtonian concept of "motion" just represents cross sections of space-time ( foliations ), but we are nontheless dealing with space-time.

It does not go slower. It traces out a longer world line at constant speed due to intrinsic curvature.

Replace "space" with "space-time", and recognize that the "state" is a geometric property, namely curvature, and you got it.

Can you write them down for us ? And explain once again what they are solved for, and what range the indices run over ?
You do realize that "equation of motion" is a generic term, right.

3. ### Markus HankeRegistered Senior Member

Messages:
381
So your night sky is static ?
You really do live in your own little fantasy world !

Then why are arguing against it so vigorously, refusing to acknowledge that GR is in fact a model of space-time ? Why not just acknowledge our model of curved space-time, since, as you quite rightly say, it works fine and is a good model ?

You are contradicting yourself now. Above you said that space-time works, and that it is a good model. Geodesics are part of that.
The other thing then is that I am pretty sure that you don't even fully understand what a geodesic is, because it has to do with parallel transport and affine connections, which are all concepts you seem to be rejecting, despite the well developed maths.

So what you are saying is that, when a pilot navigates from LA to London Heathrow, he should not be following a circle segment across Canada because it is not actually the shortest way due to being "just" on a map ? And if he does, in what way exactly is the plane "veering" ?

So then tell us, which route should our pilot be taking from LA to London if geodesics ( arc segments, in the case of the Earth ), are somehow wrong according to you ?

5. ### Markus HankeRegistered Senior Member

Messages:
381
I understand what you are saying Undefined, but there is no real way to reach an "agreement" here. What Farsight is asserting is that Einstein in fact modelled a flat space ( not space-time ) on which somehow the speed of light varies ( without giving an explanation of exactly how and why that is, since it contradicts Maxwell's equations ), instead of a space-time with intrinsic curvature. By doing so he rejects all conventional understanding of the mathematics and physics involved in GR; all the various elements of the field equations ( the metric tensor, the curvature tensors etc ) have precise, well defined meanings, which he all rejects and wishes to re-interpret in his own ways. Basically, agreeing to his point of view means rejecting more than a century's worth of established mathematics and physics. Obviously no one will do this just because of some guy popping up on Internet forums.

The only way to bring this to a civilized end would be for Farsight to acknowledge that his ideas are just that - his own ideas. We are all entitled to our own ideas, and we are all entitled to discuss them here. What we are not entitled to is our own facts - we can't go and say "I alone understand what Einstein really meant ! You, and hundreds of thousands of people in the past 100 years ( students, teachers, professors, researchers... ), were all wrong !", especially if we don't fully understand what it actually is that we are rejecting. After all, Farsight has made no secret of the fact that he knows very little about maths, and that he deeply dislikes those who do, probably because they have the ability to expose the fallacies in his ideas. You can't reject or acknowledge something that you don't fully understand, especially not while at the same time implying that you are the only one who is right, and everyone else is wrong.

Farsight bases his personal opinions on bits and pieces of sentences which Einstein has said and written; AlphaNumeric, przyk, myself and others base our understanding on various well established textbooks, which in turn summarize 150 years of understanding and research by a wide variety of scientists who dedicated their entire lives to the study of this subject. These textbooks don't just state things, they define and derive them in mathematically rigorous ways. We base our understanding on the bigger picture, which encompasses not just what Einstein may or may not have said, but the much wider area of differential geometry as a whole, which predates Einstein by a century. The notions of differentiable manifolds, metrics, tensors and curvature were well understood and rigorously defined long before Einstein was even born. He merely made use of a language which was already in existence when he developed GR. Going back now and saying "That is not what Einstein meant, there is no curvature in GR, only a varying speed of light !" is simply laughable. Einstein didn't go and redefine all those concepts of differential geometry, he quite simply made use of them as they were. Not surprising, since he was not a mathematician, and by his own admission found tensor calculus very hard. Look at the link I gave in post #353 - that is the actual document in which Einstein published his field equations for the first time. You'll notice he talks a lot about space-time coordinates and Riemann manifolds there, but does not say a single word about light, or varying speeds thereof. Don't you think he would have given it some discussion if it really were of such central importance ? Do you think he would have chosen to use Riemann manifolds and curvature tensors, if all GR was is just variances in the speed of light ?

But again, Farsight is entitled to his personal opinions, just like all of us. What elicits strong responses is trying to sell these personal opinions as some kind of "superior understanding" that no one else has, because they are clearly not. And make no mistake about it, Farsight's ideas are not to be found in any textbook on the subject of geometrodynamics. So the question is really - are we going to believe some guy on the Internet, or are we going to believe the accumulated knowledge and understanding of a large number of scientists and researchers over the past 100-150 years, which culminated in established textbooks like Gravitation by Thorne/Misner/Wheeler, for example ? In all those textbooks GR deals with curved space-time, not "inhomogenous space" with a varying speed of light, and that curved space-time is derived and treated in a mathematically rigorous way.

Note that on this thread, Farsight has already explicitly rejected the above mentioned textbook. I bet he hasn't even read it.

You take your pick - choose wisely, and remember that in the day and age of easy access to information and learning, ignorance is a choice, not a given.

Last edited: May 11, 2013

7. ### Markus HankeRegistered Senior Member

Messages:
381
So let us go on, Farsight. In post #414 you have wisely and correctly agreed to the fact that the indices on the metric tensor run over a range of four values ( which you are free to choose if you so wish ). Now I have two more simple questions for you :

1. Do you agree that two vectors can be multiplied in such a way that the operation yields a scalar ? In 3-dimensional Euclidean space this is called "dot product", more generally this is the "inner product".
2. Do you agree that, if an inner product between two vectors is formed on a Euclidean space, and then again on a sphere ( i.e. in spherical coordinates ), you get a different result in general ?

8. ### przyksquishyValued Senior Member

Messages:
3,203
I'm not sure I see what the confusion is. Spacetime refers to a view where we look at ordinary three dimensional space and time together as a combined four dimensional space, and we emphasise their similarities as much as possible for the purpose of modelling in physics.

Space, depending on context, could refer to the three dimensional space we live in, or spacetime, or any abstract n dimensional parameter space. Using the same word "space" for all of these does not imply we think they are all the same thing, which makes paying particular attention to context important. But to be clear, the three dimensional space we live in is not the same thing as spacetime.

As far as reality is concerned (does "spacetime" exist or is it just an abstract idea?), that's a question that's only inevitably going to lead to a pointless and ill-defined discussion about existence, and most sane physicists would steer clear of this.

That said, relativity blurs the distinction between space and time, at least from an experimental point of view. If you depict space and time together on a Minkowski diagram, then you can identify space, at a given time, as a particular slice in spacetime, for example the red line depicted below:

The problem is, according to relativity you could alternatively identify space as the slanted red line depicted in this diagram:

According to relativity, there is no experiment you can perform or observation you can make that will tell you that one slice is a better identification of space than the other. Consequently, any view or interpretation in which you think of space and time as being of completely different natures would normally be regarded as contrary to the spirit of relativity.

9. ### OnlyMeValued Senior Member

Messages:
3,914
Marcus, I don't think the situation is as simple as you describe above. I always try to understand from where someone is approaching an issue, not always successfully. In this case I went back to a paper describing the process that Einstein went through in developing GR. There is reference to much of what Farsight has been encorporating in his "understanding", though I believe he is stuck trying to understand all of GR from the context of that developmental period alone. He just doesn't seem to be able to get past some of those early developmental aspects.

Below is a quote from, "Foundation in Disarray: Essays on Einstein's Science and Politics in the Berlin Years" (1997 Max Planc Institute). The second essay of three, "The Rediscovery of General Relativity in Berlin" by Jürgen Renn and Tilman Sauer.

The "he" referenced below is Einstein. This is only one of several quotes on the subject.

As early as 1907 he also considered possible physical con-sequences of the Equivalence Principle, in particular the gravitational red-shift and the bending of light in a gravitational field. He inferred from the Equivalence Principle that the speed of light must be variable, in contrast to one of the fundamental principles of the special theory of relativity of 1905.

This particular paper, covers only the developmental time period leading up to his publication of GR and not any changes of concept or ideology that occurred after that.

Einstein did base the developement of GR at least in part in the idea that within the context of GR $c[/tec] was not invariant. I am unsure that Farsight understands that in the context Einstein intended, but I also do not believe that within the context of GR a variable [tex]c[/tec] is a problem. Most of the time how that is understood depends upon the model within which one views it. Do not take any of this as support for Farsight's interpretaions. I interpret most of those historical references differently than he does. But I do see the seeds of where he is, in some literal interpretations of historical record and analysis.$

10. ### hansdaValued Senior Member

Messages:
2,424
NOT all physics are "models". For example, mass is not model. Energy is not model. Space is not model. "Time" as indicated by a clock may be model because it is basically motion of a clock.

11. ### UndefinedBannedBanned

Messages:
1,695
My naive understandings go behind "beliefs" or "some guy on the internet" as you say it. I ask naive questions when my naive understandings need to cut through jargon and abstract interpretations or modeling which sometimes seem to confuse mathematics with what is happening physically irrespective of abstract or mathematical modeling and interpretations. Your opinion about Farsight does not interest me one way or the other because I don't go by "opinions". I ask naive questions and make naive sense of the answers I get if possible.

Thank you and Farsight and przyk for posting answers to my naive questions, it helps me improve my naive understandings behind all that emotional and abstract theory "interpretations" from all who have an opinion on them at this stage in development of theories involved. Sometimes theories evolve from simple beginnings, but just because it evolves it doesn't guarantee it brings closure or the final say. If theory was no longer developing then my questions wouldn't be asked because the confusion and opinions and abstractions would end in favor of the ultimate naive physical understanding of it all.

I am left with one naive understanding about that section of your comments I put in bold:
My naive understanding of what you and Farsight are both saying is the same effectively, only he is using real physical observables and you are using abstract mathematical labels for those same things? What I mean is that in Farsight's case the observables are 3D-space and light's MOTION in that space to "parametrize" it according to some "distance and timing" values for convenience. On the other hand you go abstractly to 3D-space and TIME directly without going through the "original observables" basis of "motion in space" which "TIME" label comes from and made a "mathematical shortcut terms for convenience to "summarize" the "motion in 3D-space" original observable physics?

I naively see that Farsight is pointing to the primitive physical origins and you are pointing to the evolved mathematical abstractions of effectively the same things! but used for different purposes and contexts like you say! The primitive origins version for naively understanding physics directly, the evolved abstracted version for 'modeling' the mathematical relationships in that primitive physics, yes?

That is why I was initially confused what the issue was that leads to such emotional arguments and "apples and oranges" type frustrations which could be cleared up quickly if my naive understandings of it now reveals to my mind is happening between the arguers on this "issue". Which is that you are both talking of the same things at different stages of evolution and purpose, uses, contexts: from "original physics observables" stage to "abstract analytics terms" stage?

Last edited: May 11, 2013
12. ### UndefinedBannedBanned

Messages:
1,695
Thankyou przyk for basically confirming my naive understanding of the difference between 3-D space and Motion, and 3-D space and Time. The first "version" is the "physical observable space and motion" convenience, the second version is the mathematical "abstraction Higher-D or topological spaces" convenience. Different purposes and versions of the same things when boiled down and constrained to "observable only" case of 3 spatial dimensions plus a motion(timing) referent in that space?

I recognize that "according to relativity" qualifier you used. The other "qualifier" would be "according to observables", wouldn't it? That second qualifier is where Farsight is coming from as far as my naive understandings of your discussion reveals to me so far about Physical Observable self-consistency and Theoretical Interpretation self-consistency. You two are arguing across each other because the first does not equal the second unless all "abstractions" are eventually removed from "theoretical" version so the "understanding" of everything is naively as possible without having "interpreters" to get in the way?

13. ### Markus HankeRegistered Senior Member

Messages:
381

Last edited: May 12, 2013
14. ### ash64449Registered Senior Member

Messages:
795
i have somewhere heard that Einstein didn't know what mathematical principle GR follows. So he sent a message to his friend(don't remember which) to help him out.when they searched a library,they found out a lecture of reinmann in 1854. They were surprised because,what reinmann proposed was exactly mathematical principle of GR!! So Einstein didn't found the mathematical principle.

15. ### Markus HankeRegistered Senior Member

Messages:
381
I'm afraid it is not quite that simple. You need to consider this not only within the confines of GR itself, but in the context of all the rest of physics as well; a curved 4-dimensional space-time is not physically equivalent to flat space with a varying speed of light. I give you two examples on where they would differ, just to illustrate the point :

1. Electrodynamics. The speed of light in vacuum is not an independent quantity, but actually the result of vacuum permittivity and vaccum permeability. These are fundamental physical constants, and our model of electrodynamics, Maxwell's equations, relies explicitly on the fact that they are in fact constant. If we allow them to vary, as would need to be the case to get a variable speed of light, we will get a situation where different observers at points of differing gravitational potentials see different laws of electrodynamics. The most striking result is that total energy in an electromagnetic field within the influence of non-uniform gravity would not be conserved, since energy density in such a scenario explicitly depends on vacuum permittivity. This violates the so-called continuity equation, both in its classical and in its relativistic form. In more formal terms, allowing permittivity and permeability to vary will introduce additional degrees of freedom, which are simply not accounted for or observed. Also, why would acceleration lead to changes in vacuum permittivity or permeability within the accelerated object only ? What is the mechanism ?
2. Time dilation. Consider an elementary ( not composite ) particle with finite life span, say for example the Z boson. For a stationary Z boson its lifespan is an intrinsic property, and depends only on its rest mass, not the speed of light or permittivity/permeability of vacuum. In Farsight's model there is no curvature of space-time, so all time dilation effects are results of a varying speed of light, hence his constant mention of light clocks. Consequently, we would not expect the lifetime of an elementary particle to change under the influence of gravity, since that lifetime does not depend on the speed of light ( it is an elementary particle, so there are no "internal dynamics" or any such thing ). However, we do in fact observe particles to "live longer" under the influence of gravity. In GR this is naturally explained by space-time curvature without any further ado ( not just for elementary, but for all particles ), but Farsight's model has no such explanation. I brought this up with him before, and he talked about "internal dynamics", but then elementary particles do not have any such "internal dynamics" since they are not composite systems. Even if they did - how come their lifespans are affected, but not their electromagnetic fields, if permittivity and permeability changes for them ?

This is just to show that the two models are not physically equivalent. GR, understood as a model of curved space-time, does not deal with electromagnetism. Nowhere in the field equations will you find permittivity or permeability, or any relation on how exactly they would vary. In fact ( see post #353 ) Einstein himself explicitly says that GR makes not predictions of natural processes other than gravity.

Talking about real physical observables ( I presume you mean actual measurements ) - no one has ever measured the speed of light to be anything else than exactly c in vacuum. Likewise, no one has ever measured vacuum permittivity and permeability to vary with gravitational potential; this would have consequences far more wide-ranging than just light deflection.

Last edited: May 12, 2013
16. ### Markus HankeRegistered Senior Member

Messages:
381
By "model" I mean things like GR, electromagnetism, QED, QCD, thermodynamics...

That makes no sense. You need a clock to measure time. Likewise, you need a ruler to measure space. Why is one of them not a "model", but the other is, according to you ?

17. ### Markus HankeRegistered Senior Member

Messages:
381
Yes, Riemann geometry was fully developed long before Einstein started to work on GR. He merely used its mathematical principles, he didn't develop them himself.

18. ### OnlyMeValued Senior Member

Messages:
3,914
The link below will take you to the paper I was referring to earlier. It mentions some of what you refrence above... Just remember it is a historical interpretation. It describes what has been reconstructed as a series of false starts and the process that Einstein seems to have gone through on his way to GR.

http://www.mpiwg-berlin.mpg.de/Preprints/P63.PDF

19. ### hansdaValued Senior Member

Messages:
2,424
What is measurement? It is basically comparison, where one well defined standard unit is compared with the 'variable to be measured'. The measurement becomes in the multiple of the standard unit.

In the case of "space", 'ruler' is well defined fixed "distance". With this 'defined distance' all other distances are being compared to make a measurement of distance.

In the case of 'time measurement', the clock's speed is fixed. With this 'fixed speed' all other speeds are compared to measure "time". Here time is not directly measured like the distance. So, case of "time" is different from the case of "distance".

20. ### UndefinedBannedBanned

Messages:
1,695
The "ruler" is "mapped directly" over a surface or area or volume or lines or distance directly. The "clock" is a mathematical relationship based on comparative motions where one is "standard" motion increments used for "timing" and the other is the motion under study using that standard "timing" as a logical relationship, not a direct physical mapping as a "ruler" operates. That is a qualitative difference that is very important to remember, yes? That is why "motion" in space is an physical observable "action" irrespective of any "measurement" of it by a ruler to exact values. Where "time" on the other hand is not a physical observable action, but a "logical comparison" of one observable (object motion) with another (cyclic or "clock standard" motions or changes used to "time" the object of interest's motion)? That is as naively as I can tell the difference between "rulers" and "clocks". One is direct observable based, the other is logic comparison based?

21. ### arfa branecall me arfValued Senior Member

Messages:
7,652
I disagree. That you can "map" a fixed length ruler to some arbitrary distance is no different to a "map" from a fixed "length" of time to an arbitrary time interval.
This argument does not relegate time to some kind of non-physical status.
All you seem to be saying is that clocks and rulers are needed because time is measured differently to distance. Logically and mathematically both time and distance are equivalent, corresponding to "separation" between events.

22. ### UndefinedBannedBanned

Messages:
1,695
Thankyou Markus Hanke for responding again to my naive questions.

I was not clear? Sorry. I do not mean "measurement" as such, just directly perceivable to exist or happen physically. An observable can exist and be recognized without necessarily depending on "quantification" of its effects. It does not have to be precisely measured to be happening, even without human presence to observe. That "measurement" of "c" in any frame involves using clock timings as well as ruler distances affected by that frame's motion. Light is also dependent on its speed and motion on the vacuum permeability and permittivity in different regions affected by gravitational or other energy "flux" present from region to region, yes? The measuring of those things in gravity wells is maybe self-correcting to give "null difference" results maybe because the "timing" used is the light itself? If the light is used to attempt to measure permittivity and permeability then the gravity effect on lightspeed also affects "timings" used to arrive at "c" and at "null result" for changes in permittivity and permeability and some other things too?

It isn't if you put it like that. But that is not exactly what I meant. I naively put it like this: it is equivalent to flat space which is not so flat where gravity and energy fluxes are present which affect the motion of light and matter which in turn demonstrate variations in both space dimensions and any "clock based timings and calculated measurements" of the motions of light and matter in those space dimensions??

I already agree it is dependent. But like you said in other posts, the space in a gravity well space environment is different from flat space environment, which is what your theoretical model interpretation of "greater distance travelled by that "trapped photon" was all about, yes? So if the vacuum there is different from the vacuum in flat space, the different effects on light would be masked by the use of light itself to make calculations which you and some others call "measurements" but are just calculations using the light effects in vacuum situations affected by gravity which may self-correct those calculations to give the usual "c" and other "constants". I agree they are constants, but they are calculated constants, yes? Have any direct measurements (based on some "ruler" not some "clock timings" based on the gravity affected light itself) been done? I mean without the use of the very lightspeeds which are affected as you explained in your "greater distance travelled" interpretation of what the photon does in a gravity well "distances"?

Implications between theory "domains" are a natural consequence of the unity of nature irrespective of theories about its many "parts", yes? Whether Farsight is correct or not in connecting implications as he does is something that must be tested without just theoretical domain arguments based on the speed of light being used to calculate the speed of light, especially when that speed of light may be interpreted in different ways depending on theory 'models' like your "greater distances traveled by photon" in your previous explanation to me about the "bh horizon 'trapped photon' example I mentioned?

The speed of light is vacuum dependent, yes? The vacuum is affected by energy fluxes from electromagnetic and gravitational energy environment differences across space regions, yes? That is why I still have to try and naively understand where you and Farsight might be coming from that is different and that is the same. Only further thinking about it will help me to naively understand the real issue hidden behind the usual emotional and theoretical approaches I listen to. Thankyou and Farsight for your discussions so far, it is helping me to sift out the similarities and the differences which are underneath.

23. ### UndefinedBannedBanned

Messages:
1,695
Sorry, Markus Hanke (and przyk too if I remember back correctly), but I don't understand why you misinterpret what Farsight actually said and meant there? To my naive mind he said nothing about the night sky being static. He specifically said observing a shooting star moving across the night sky. So how do you misunderstand that as "static night sky" claim? I take the context of his previous distinction made between an "physical observable" active space with motion in it, and an "modeled theoretical" static space-time abstraction used for calculations and predictions of what is going on in the active space and motion dynamic system which we see when we look at the night sky and its shooting stars and such. If it is a misunderstanding I really think it should be put right immediately before more emotional and frustrating arguments based on it break out again, yes? It will help me to concentrate on the real issues in your discussion, which I am following intently for my own naive understandings to improve, so this is an important thing for me if you can clear it up quickly between you? Thankyou.