Why two mass attracts each other?

Hansda, based on past discussion I believe what you are confusing is "frame dragging" and "spacetime".

Frame dragging can be described or modeled within the context of GR and thus spacetime, but is represents a predicted interaction between the motion of a gravitationally significant mass and "space". This is another one of those points of confusion when discussing GR. "Space" and "spacetime" are not the same thing. Space is one of the dynamic components described or modeled within the context of GR and spacetime.

Spacetime is, as Dinosaur describes, a mathematical model that describes the interaction of "objects" with "objects" and "space". One of the clasic confusions is that we have no good description of space as a "substance" and our everyday classical experience suggests that for things to be dynamic or interact they must have some independently defined "substance". (This lack of a diffinitive definition often becomes the basis of the space is ether distractions.) Some of the work on quantum gravity tries to answer this question and bridge the gap, but we really don't at this time have any conclusive answer. All we can do is continue to "describe" the interactions.

It is a difficult task, but something to try and keep in mind while exploring GR and the spacetime model, is that what you are dealing with is a description of what is happening, not why or how it happens. This thread has gone on as long as it has because no one has the answer to the question in the thread title. We have a lot of information about what is happening, but not much about why it happens.

 

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Dont mix-up the threads. Newton's Cradle is not being discussed here.

 

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Hansda, is struggling with trying to understand the distinction between space and spacetime, which is very difficult to explain in a satisfying lay oriented manner. Frame dragging, which he returns to very often only complicates things. These are very difficult concepts to address, solely within the context of lay oriented discussion and language.

 

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Well, in "frame-dragging" also space becomes dynamic. I was exploring "why" time merges with space in "relativistic contexts" but time does not merge with space in "non-relativistic classical mechanics".

I was trying to explore this "why".

 

Time is really the same in both cases. What it seems your are trying to compare is in essence the coordinate systems used to describe things.

Spacetime is just like the two dimensional graph you use with an x and y axis, where you can either describe a line at one instant in time or the coordinates of a point, as it changes over time. In both case the time component is implied time, as ether fixed and unchanging inthe case of the line or changing in the case of a point. That makes the piece of graph paper in practice a three dimensional representation of two spacial coordinates and one for time. When you add the z axis to the space coordinates, and plot two or more points you are again either describing a line by two points on the line at an instant in time or assumming again, an implied chnaging time element and following an object as it's coordinate location changes over time. That winds up being a 3D+1 coordinate framework, which is the same thing as spacetime.., as a coordinate system.

Spacetime can be described either with 3D+1 coordinates or as 4D. The difference is really just mathematical convention. They both say the same thing. It is just more convenient to use one for some discussions or descriptions and the other in other circumstances. I believe przyk, did a good job of explaining this in another thread. But you can also read some of the papers published, which explore the process of how Einstein developed GR.

You are not alone in that. There are a lot of working physisicts exploring the same issues. There have been many suggested answers and so far none that really fits all of the experimental evidence we have today.

 

Apologies for being tardy, all.

It wasn't an analogy, OnlyMe. Einstein referred to the state of space defined by the ten functions which include energy density, pressure, flux, and shear stess. He didn't actually say curved spacetime. See his 1929 field theory presentation and note "It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds".

I'm afraid it isn't an analogy. Have a read of this essay by Pete Brown: http://arxiv.org/abs/physics/0204044 . The last line of the abstract sounds a bit outrageous doesn't it? But try and find Einstein saying "curved spacetime". I can't.

It's changed. That's the underlying issue here. Einstein talked about the state of space and the variable speed of light, but modern relativity doesn't. And when you look hard at what clocks do and those NIST optical clocks and the parallel-mirror gif, you appreciate that Einstein was right.

 

That's true, and also coupled with the fact that hansda is extremely muddle-headed.


His comment below demonstrates just that.

 

Seriously, what???!

The ten functions that Einstein refers to in your favourite passage from the Leyden address are the metric components \(g_{\mu\nu}\). These are not the same thing as the components of the stress energy tensor, which are often noted \(T_{\mu\nu}\). They are two entirely different tensors that are defined and used in different ways.

You have not understood any account of general relativity.

 

Tell me about it, Guest. Sorry to be tardy.

Sounds interesting!

Tricky. I have a memory like an elephant, but no way could I pour out The Foundation of the General Theory of Relativity. I could do SR fairly easily from scratch, but not GR. Sure I could retell post #158 with a stick in the sand. And I could write out \(R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\). Given enough time I could dredge up more, but I'd be struggling. And probably struggling to eat too, with more pressing concerns.

This sounds like A Canticle for Leibowitz only worse, because I don't even have any books. And doubtless no laptop or memory stick either. Tricky.

Ooh, Guest, are you suggesting I'm over confident? Why, Guest, all I can say to that is this: all the professionals you know could pour it out. But I understand it. LOL!

I'm sure he could have reproduced a good amount of it from the ground up too. But honestly Guest, I don't think he understood it. I've always thought well of Dirac, but after reading up on the history, I have to say I think he was lucky to get the Nobel for predicting the positron. It's like he shifted his position as the experimental results came in. If he'd focussed on Maxwell's vortices he would have understood from the off that positrons had the opposite chirality, and weren't "holes" at all.

Why thank you Guest. Always a pleasure. And if there's anything you'd like to understand about gravity or electromagnetism, just say the word!

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What are you referring to - the metric tensor, or the SEM tensor ? They are not the same thing. The latter describes density, pressure, flux and stress. The former doesn't. This has already been explained to you multiple times.

Indeed.

That is because you don't want to find it. Have you looked at the reference I have given in post 353 ? Look at the entire original publication of the GR field equations, and then answer my question with regards to the indices in the field equations.

 

It seems obvious now that Farsight has no intention of addressing, or even acknowledging, his misconceptions with regards to GR.

I repeat : Tell us, in the GR field equations what range of values do the greek indices cover ? What does that range of values represent ? Do you know the difference between the use of greek and latin letters in a tensor equation ? Do you agree that these are Einstein' equations ?

 

Sorry przyk, slip of the tongue, my mistake. I was getting my cause and effect mixed up.

What I find funny is your inability to say "Sorry, my mistake, slip of the tongue".

It isn't. It's wrong.

No, I should have said relates instead of equate. Sorry, my mistake, slip of the tongue.

That's a no then. Bah, you refuse to address it because you know it's a fair description that gets to the heart of the matter. And that when you can't find fault with it, you will have to concede.

Why Alphanumeric, I do declare you're flaming me.

The whole problem is that GR then is not the same as GR now.

You're attempting to give a display of mathematical prowess to conceal your refusal to address post #158. It reminds me of the guy in black with the sword in Raiders of the Lost Ark. You know, swish slash pirouette. But Indiana Jones pulls out his Webley and BOOM! Just address post #158. Go through it, paragraph by paragraph, point out where it's wrong. Shouldn't be such a problem now should it? Try not to hide behind smoke and mirrors, there's a good lad.

 

One thru four, time and space dimensions in the metric tensor. Yes. Yes. Yes. But I'm not fond of kappa. Now you go and address my post #158. Stop ducking it, and don't try to digress.

Address post 158 first.

Oh and Markus, pay attention to this guy:

He's not naïve.

 

Your beef with me revolves around the map is not the territory. I'm not some crank who goes round saying GR is wrong, I acknowledge what GR is mathematically, I don't go round saying it's BS. And I also acknowledge what Einstein said, and what those optical clocks are telling us. And that spacetime is a static all-times at once block-universe mathematical model in which motion doesn't occur. You think of it as space. You confuse the model with reality. Let's see if I can demonstrate:

That's in the model. In reality the rock tends to fall straight down, and the ground stops it doing so.

It doesn't actually accelerate upwards, but I'll put that down to a bad choice of words.

OK, the principle of equivalence and all that. No problem.

Its worldline is vertical. And the rock isn't actually moving up it like Alphanumeric thinks. It's like you film the rock sitting there, then develop the film and cut it up into individual frames, then stack them into a block. The worldine of the stationary rock is a grey smear running up vertically through the block.

That's back to front. Really. You can plot gravitational time dilation using those parallel-mirror light clocks in post 158. But what you're actually doing is plotting how fast light moves back and forth between a couple of mirrors. There isn't any time flowing between those mirrors. There is no actual time being dilated. But you do plot a curve. You'd prefer to call it a curve in your plot of the coordinate speed of light, which varies in a non-inertial reference frame. But it isn't. It's a curve in your plot of the speed of light. And because that isn't constant, light curves and rocks fall down. Light doesn't curve because your plot is curved. Or because your model is curved.

Replace your observer up in space with two parallel-mirror light clocks. And look at the gif: View attachment 6266 . Put a whole string of light clocks between those two, and plot the cumulative readings. Plot your measurements. On a "metric". Now look at your plot. It's curved. Got it yet?

I take back what I said above. You've got it Markus! Light doesn't move through it! It moves through space. And when it goes slower, it does so because the space it moves through has had its state altered by a concentration of energy tied up as matter in a massive body like the Sun. And because there's a gradient in that state, light curves. Not because it "follows a null geodesic in spacetime". That's just a line on a map. And the map is not the territory.

I can answer that. In the real world, there is space, and motion through it, from which the time dimension is derived. It is a dimension in the sense of measure, but it is not a dimension like the space dimensions that offer freedom of motion. I can hop back a metre, you can't hop back a second. I can show you the space between my hands and I can waggle my hands to show you motion. You can't show me proper time. Point to a clock, and I open it up and show you the cogs whirring round. I show you motion. Through space. And that's what it all comes down to. That's why Einstein gave the equations of motion.

 

It's not outrage przyk, it's just a quote from Avatar.

No. I said there is an issue with general relativity if you don't appreciate that spacetime isn't the same thing as space. The problem is in the way GR is taught. Guys like Markus and Alphanumeric end up confusing the model with reality. Then they get all convictional and dismissive and blind to patent evidence and get the cause and effect wrong, and it's all downhill from there, der da der da. Relativity ends up being the Cinderella of modern physics. And she has some ugly sisters.

This discussion is all about me teaching you how to distinguish abstraction from reality. Now listen carefully.

Q: Does light move through spacetime?
A: No.
Q: In a more abstract sense commonly used in the Minkowski spacetime view, does light move through spacetime?
A: No.
Q: Is there any sense in which light can be said to move through spacetime?
A: No.

No. It's supposed to remind you that when you look up at that clear night sky, you look at space. Not spacetime. And when you see that shooting star moving, and recall that there is no motion in spacetime, it reminds you again that that blackness between the stars is space not spacetime.

Space isn't like North. North is just a direction, one that depends on where you're standing. We can be pointing in different directions and we can all be pointing North. I can point in the same direction as you, and I can be pointing North whilst you're pointing South. Because the North Pole is between us.

Like I've said already, there's nothing wrong with the spacetime view so long as you remember that space and spacetime aren't the same thing. Spacetime works. It's a good model. But a model is what it is.

Oh it's not just figurative, it's just wrong.

Well, they don't follow geodesic worldlines in spacetime. So that "mainstream" understanding of general relativity is wrong. You and me are in a car. You're driving. Across the Great Salt Lake Desert. "Hey przyk", I say. "You're following a line on my map". You shoot me a look. "No I'm not. I'm just driving across this desert". Map=spacetime, space=desert.

It's still wrong. When your leftside wheels encounter wet salt you veer. You don't veer because my map's got a curved line on it. You aren't following the line on my map. You haven't even looked at it.

Gotta go.

 

Mathematical prowess? You just posted the Einstein field equations to Guest. Now if you really understand said equations you'd understand my post. You'd also know that the equations I gave are very very basic. I'm pointing out the link you provide gets the definition of the line element wrong. It literally gets the definition for the metric wrong! This isn't some highly complicated niche corner of GR, the definition of the most central object in all of relativity is wrong in the link.

As expected you cannot retort what I said and so make excuses. If you understand the equations you post then what I posted should be trivial for you to grasp. You show how dishonest you are. And that isn't flaming, it's a statement of fact, a fact you don't want to hear. And you provide nothing new in 158, all of them are points you and I have rehashed many times. Besides, you have just shown that when I do give a precise, detailed breakdown of how something is wrong you don't respond. I've already gone into detail about how your comments involving how the 10 degrees of freedom via \(g_{ab}\) necessarily imply inhomogeneity and anisotropic are wrong. The use of the metric allows for the description of inhomogeneous and anisotropic space-time but that doesn't mean the use of the metric implies those two.

I'm sorry you don't understand the mathematics I used, that you think what I posted was complicated, that you feel the need to pretend you understand mathematics you do not, but that isn't my problem. It's yours. It's always been a problem of yours. You cannot simultaneously ignore when I provide details and demand I provide details. The details I went into were exactly of the level of a post you provided. Why is it okay for you to post a link with maths in but when someone responds in kind, using precisely the same mathematics, that isn't allowed and you're allowed to ignore it? The answer is you aren't. That is hypocrisy. Saying so isn't an ad hom, it is pointing out that you doing one thing then saying others cannot is the definition of hypocrisy.

If you do it again you're getting another holiday because it is pure trolling. Demanding discussion and then refusing to engage in it when people go into details is trolling and dishonest. By doing this constantly, always making an excuse why you won't reply to my lengthy detailed posts, you prove you are not worth having as a member here or anywhere else.

 

You've given me no reason to believe anyone requires this teaching. You keep "refuting" things that everyone already knows and nobody actually disputes. I mean, look at something AlphaNumeric posted a bit earlier:

So you don't need to explain that to him, and AlphaNumeric should not be required to include this disclaimer in every post he makes. But he says "space". Is he now confusing space with spacetime? No:

so he doesn't need that explained to him either. What about "motion through spacetime"? He starts explaining what he means by that in the rest of the paragraph:

Well I can think of one.

More specifically, there is a sense in which massive test particles can be said to "move" through spacetime. (Note that AlphaNumeric wasn't specifically talking about light [POST=3067416]in this post[/POST].) That sense is that we can parameterise a worldline in terms of a single affine parameter, usually proper time. We write a trajectory as \(x^{\mu}(\tau)\) where \(x^{0}\) is the time coordinate in some given reference frame and \(x^{i}\) are the spatial coordinates, and all four are written in terms of the accumulated proper time \(\tau\). In this abstraction, the "velocity through time", \(u^{0} \,=\, \frac{\mathrm{d}x^{0}}{\mathrm{d}\tau}\), is just the time dilation factor. For light it's more complicated since light has no proper time associated with it, but there are other affine parameters one can use.

This abstraction isn't complicated. It's just the idea that if you draw a worldline on a piece of paper and trace your finger along it, your finger is "moving" through (a depiction of) time as well as space.

Do you like that abstraction and the language and mathematics that goes along with it? You don't have to, and nobody is forcing you to use it. (Though in fairness you should at least try to appreciate why it has become so popular. It's not for nothing.) But either way this doesn't represent a confusion on anyone's part and there is simply no good reason to keep pounding on this unless your goal is specifically to derail the thread.

While this is true, something you need to understand is that the separate space + time view is also an abstract model.

You don't directly see space. What actually happens is simply that your eyes get stimulated in a certain way and that information gets interpreted by your brain. You could be a brain in a vat for all you know. You have no sixth sense about space. The reason you don't normally think of this as an abstraction is that your brain is hardwired to construct the space model from your senses for you, without you even being consciously aware of it. It's far easier to process than a raw stream of information about how stimulated all your rod and cone cells are. But an abstraction it is, however natural it may feel to you.

The spacetime view is an abstraction that is completely divorced from the way we physiologically experience space and time, but that alone says nothing about its merits or lack thereof.

The space + time and spacetime views are observationally indistinguishable because they always describe the same thing, even if in very different language, down to the very level of your thoughts and experiences. What happens when you stand in your garden and look at the stars? As far as physics is concerned, you are an organic physical system with a piece of meat between your ears that is being stimulated a certain way. The space + time and spacetime models would always end up describing you, using different language, as ultimately the same being with the same brain being stimulated the same way, experiencing the same experiences and thinking the same thoughts.

Well, take that up with Einstein.

 

Guys, I am trying to naively follow and understand what is the "space" versus "space-time" issue in this discussion, so please bear with me for asking some naive questions based on the above explanation of "manifold" I got from Wiki in "mathematics"?

pryzyk, my naive understanding from those discussion posts is that AlphaNumeric means "generalized mathematical spaces" of "n-dimensions", not just the physical "3-d space" which does not depend on mathematics to observe and measure and move in, yes? The "topological etc spaces" can be of any dimensional number in mathematics, but in physics we have only 3-d space to use and observe, yes? We add "time" conception as another "mathematical dimension", but not actually add another "topological space" or "physical space" dimension, just a "timing" convention, yes? So when Farsight says "space" he is referring to 3-d space only, plus any time dimension added for mathematical purposes in relativity "space-time" construction modeling?

They are two mutually exclusive "spaces", aren't they, "spacetime" and "space" as is being meant in this discussion? One is a mathematical "topological space" of any hypothetical dimension, and such mathematical modeling only "represents" the observable "space" when that mathematical topological space "dimensions number n" are constrained to the 3-dimensions which all observables are moving and interacting in, yes?

And again I naively understand that two people are talking of completely different "spaces" both in conception and in "physics" unless the "general" n-dimensional mathematical modeling is constrained to the 3-d only "space" we know and observe things moving and changing and exchanging properties and other factors in?


So why can't this issue be settled between both sides of this discussion by saying clearly that the "spaces of mathematics" are abstracted and unconstrained in dimensionality unless that model tries to involve just the 3-d space which we know exists for a fact because things move through it and we observe them doing it using timings and measurements which we can use to "parametrize" that space. Whether one can "physically" rather than "purely mathematically" parametrize those other purely mathematical spaces of "higher dimensionality" is just a matter of axioms and assumptions from mathematics about hypothetical "toplogical spaces" of "higher abstract dimensionality topological constructions" which may or may not be possible for real physical existence, yes?

In my naive thinking I see that as the only way to reach an unconfusing agreement that will not leave my naive mind spinning like it has been so far listening to this discussion without end but plenty of personal emotions being worked out in public?

 

...being your complete ignorance of GR, electromagnetism and pretty much all the rest of physics. As repeatedly demonstrated.

Post #158, which you so fondly keep mentioning, demonstrates nothing but your wrong assertion that the speed of light varies. In actual fact though it doesn't, so the post is entirely without meaning.

Yet it was yourself who got a 1 day timeout for flaming...

Wrong. The problem is merely that you don't have the first clue what you are talking about. You simply don't understand GR. GR "then" is exactly the same as GR "now" - a model of a space-time manifold with non-trivial geometry.

All he displays is a thorough understanding of the principles involved in GR. He addresses some of the points raised in a scientifically acurate manner, which is something you are clearly incapable of.

 

The greek indices do not run 1...4, they run 0...3.
Of course that is just convention, but it is also yet another embarassing display of the fact that you don't even know the basics of what you are arguing against.

Anyway, the point is that the indices in the field equations cover all four dimensions, to which you have just agreed. Thus we are dealing with physics in space-time. The equations are not separated into "time" and "space" parts. Also, this system of equations is obviously not linear ( probably not obvious to you, since you don't understand them ), since the coordinate representations of the tensors each depend on all coordinates, in all index values, in non-linear ways.

It is a tensor equation in space-time, not space.

Would you like a demonstration how to derive a simple solution to the equations, say for example the exterior Schwarzschild metric ? It shows very nicely how all terms depend on all coordinates, and thus that we are very clearly and obviously dealing with space-time. But of you are not interested or not able to understand it, I won't bother, because there is a lot of typing LaTeX involved, which is tedious.