Why two mass attracts each other?

[OnlyMe]

He is also saying that space-time is a "model" and not "real".

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.

 

[hansda]

Don't mind hansda, he's got some sort of memory loss.

In one thread on Newton's Cradle, I would answer his question, then he would ask the exact same question five posts later.

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

 

[OnlyMe]

Don't mind hansda, he's got some sort of memory loss.

In one thread on Newton's Cradle, I would answer his question, then he would ask the exact same question five posts later.

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.

 

[hansda]

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

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".

We have a lot of information about what is happening, but not much about why it happens.

I was trying to explore this "why".

 

[OnlyMe]

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".

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.

I was trying to explore this "why".

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.

 

[Farsight]

Apologies for being tardy, all.

Farsight.., Einstein was presenting an analogy in that instance. He did not presenting a definitive definition. He was speaking in analogy when he said, spacetime is the ether of GR.., as within the context of GR light propagates through spacetime. Once again and as przyk has pointed out at least indirectly, the Leyden address and his initial presentation in 1916.., to his peers, were directed toward different audiences.

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".

Generally speaking his audience at Leyden were for all intents and purposes, rooted in having been thought physics from the perspective of the existence of the aether and Newton's mechanics. These were students and some of the staff (not all of which had strong backgrounds in cutting edge physics). His references of analogy were intended to bridge the gap between their earlier education and understanding of the world and a model relatively new to the achedemic setting they were in.

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.

You have to at least try to understand the context within which anyone makes any statement. That becomes even a greater issue when dealing with historical accounts were not only the culture of science was different, but the shear weight of experimental evidence has changed. Einstein set the stage for and ushered in a sea change in how the scientific community has come to understand the world, but lacking knowledge only available after the fact, he is not the foremost authority on GR. The child of his imagination and insight has grown far beyond his dreams.

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.

 

[eram]

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.

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


His comment below demonstrates just that.

Don't mind hansda, he's got some sort of memory loss.

In one thread on Newton's Cradle, I would answer his question, then he would ask the exact same question five posts later.

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

 

[przyk]

Einstein referred to the state of space defined by the ten functions which include energy density, pressure, flux, and shear stess.

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.

 

[Farsight]

Apologies for such a late response Farsight, very busy week!

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

I think I might have a way to get to the bottom of this. I think your continued run-ins with people on this forum stem from your notion of "understanding" a scientific theory and other people's notion of "understanding" a scientific theory. I think the following might help.

Sounds interesting!

Let's pretend that (heaven forbid) the entire population of the planet was wiped out tomorrow, apart from you and a collection of 10 intelligent but scientifically uneducated adults (e.g. they've not heard of Einstien). In addition, let's assume that all literature was wiped out, so there's no books, papers, articles to which you can refer. How would you pass on Einstein's legacy?

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.

You can no longer answer questions with "because Einstein said", or do a quick google and point people to Wikipedia. If you claim that the Riemann curvature tensor has something to do with tidal forces, you'll have to explain to these people what on earth the "Riemann curvature tensor" is and demonstrate its relationship to tidal forces. If you want to talk about about specific solutions to the Einstein equations, e.g. Schwarzschild, you'll have to convince everyone why they're solutions (not to mention the fact you'd have to explain what the field equations are where they come from).

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.

All the professionals I know of could do these things, and they don't have anywhere near your level of confidence.

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 guess I could make a similar post with electromagnetism in place of general relativity, since you've told us you understand (your usage of the word) electromagnetism better than Dirac. I'm positive Dirac could have reproduced a good amount of it from the ground up, because he understood (my usage of the word) the theory.

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.

Genuinely interested in your response - I've said this before, but I think you're a fantastically interesting character!

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!

 

[Markus Hanke]

Einstein referred to the state of space defined by the ten functions which include energy density, pressure, flux, and shear stess. .

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.

You have not understood any account of general relativity.

Indeed.

But try and find Einstein saying "curved spacetime". I can't.

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.

 

[Markus Hanke]

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 ?

 

[Farsight]

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

Alphanumeric said something moves through space-time along some worldline. You know that's wrong. And Alphanumeric knows that It is very important to be precise about these things.

I find it funny that suddenly you care about details when you repeatedly make the same laughable qualitative mistakes...

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

...For particles moving along a time-like curve... ...then saying a particle moves through space-time along a world line is an entirely sound thing to say.

It isn't. It's wrong.

You said equates to it. Equating two things is to say they are equal. What you should have said is that the Riemann curvature tensor allows you to construct the tidal tensor...

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

Would you care to address my post #158 instead of boring us all with your customary carping whining ad-hominems?

Your post 158 is just rehashing things I've already discussed with you.

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.

And there's your usual excuse. Am I cutting a little too close to the bone for your liking? Couldn't you think of a retort to my querying why anyone should take you seriously when you don't know the quantitative stuff at all and you have dubious grasp of even qualitative stuff? It's the excuse you always use; I give valid reasons to question your self assuredness and you fail to retort them, complaining I'm just ad hom'ing. It isn't an ad hom to point out you have, for all intents and purposes in regards to any of this material, zero mathematical knowledge, it is a statement of fact. It isn't an ad hom to point out you have zero experience with actual data in regards to this material. It isn't an ad hom to point out your flawed understanding of such things as the applicability of the FRW metric. It isn't an ad hom to point out the Riemann curvature tensor cannot equate to the tidal tensor, rather the former is used to construct the latter. It isn't an ad hom to point out your work has zero quantitative structure. It isn't an ad hom to point out that it is hypocritical of you to criticise string theory for, in your view, having no real world applicability/validation while your work has less than string theory. It isn't an ad hom to point out the one and only time, over more than 5 years, you've ever given a direct response to my request you provide a quantitative model derived from your work it was someone else's result and it was pure numerology of a kind secondary school children can spot the flaw in but which you called (something like) 'astounding'. It isn't an ad hom to point out your reliance on metaphor and analogy is never going to amount to anything even remotely resembling viable physics. It isn't an ad hom to point out that your work was rejected from every single journal you submitted it to...

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

All sorts of problems there due to poor explanation. Having looked at the link you used I can see why you're getting confused, since the paper was written a long time ago and thus fails to use definitions and terminology in the same way as present..

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

The issue is the difference between a Riemannian space and a pseudo-Riemannian space. A Riemannian space is one where the metric is positive-definite, ie for all possible vectors X, g(X,X)>0. A pseudo-Riemannian space need not satisfy this, there can be X such that g(X,X)<0 and now the condition is that g is non-singular. The Euclidean metric is Riemannian, it is a diagonal matrix with all +1's down the diagonal, g = diag(+1,+1,+1,...) so g(X,X)>0 for all non-zero X. The Minkowski metric of special relativity is pseudo-Riemannian, since it has (up to arbitrary signature notational choices) the form g = diag(-1,+1,+1,....). Both of these kinds of metric are flat in the Riemann curvature sense, $$R^{a}_{bcd} = 0$$, (the other notion of 'flat' is defined as metrics like the FRW have R = 0 but $$R^{a}_{bcd}\neq 0$$ or the Schwarzchild metric being Ricci flat, $$R_{ab} = R^{c}_{acb} = 0$$, which are weaker conditions than $$R^{a}_{bcd}=0). For metrics in general relativity they have to solve the field equations and can have elaborate forms but thanks to the definition of smooth manifolds meaning that they look flat up close we can use "normal coordinates" to show that any GR metric is also pseudo-Riemannian, as they locally become the Minkowski metric in normal coordinates. A space-like slice of the kinds of pseudo-Riemannian metrics seen in general relativity will give rise to Riemannian metrics on the resultant sub-manifold, as seen in such things as the first and second fundamental forms, which are ways of quantifying curvature on such slices, as well as metric pull backs. But the link doesn't make this restriction, it doesn't mention pseudo-Riemannian anywhere.

Sorry, am I getting a bit too technical for you? None of this is particularly advanced, it's undergrad stuff and since these are just the specifics of things your link brought up there shouldn't be anything wrong with raising the discussion a little, right? After all, you do claim to understand quantum field theory better than Dirac and have done multi-Nobel prize worthy work, a little undergrad stuff which formalised notions of curvature, which you have been 'explaining' to everyone (for years!) shouldn't be an issue, right? Anyway...

As a result of all of this there's numerous mistakes and failures to be precise in that link. It says $$ds^{2} = g_{11}dx^{2} + 2 g_{11}g_{22}dx dy + g_{22} dy^{2}$$ is a Riemannian metric. No, it isn't and for a number of reasons. I'd ask you to give them but I know you'll ignore such a challenge. Firstly we note that the right hand side can be written as $$(g_{11}dx + g_{22} dy)^{2}$$, implying $$ds = g_{11}dx + g_{22}dy$$. Utterly wrong. Utterly. Clearly the person doesn't even know how to use a metric. A metric defines a line element ds by $$ds^{2} = \sum_{a,b}g_{ab}dx^{a}dx^{b}$$. In this case a,b take values 1,2 and we get $$ds^{2} = g_{11}dx^{2} + g_{12}dxdy + g_{21}dydx + g_{22}dy^{2}$$. Since dxdy = dydx and metrics are symmetric so $$g_{12} = g_{21}$$ we get $$ds^{2} = g_{11}dx^{2} + 2g_{12}dxdy + g_{22}dy^{2}$$. Notice the difference? This isn't a perfect square, unlike the link. It involves the off diagonal terms $$g_{12} = g_{21}$$, unlike the link. The link then asserts this is a Riemannian metric, just because he's slapped some arbitrary coefficients in the expression. As I've already explained a Riemannian metric is one which is positive definite, g(X,X)>0 for all X, which amounts to $$g(X,X) = \sum_{a,b}g_{ab}X^{a}X^{b} = g_{11}(X^{1})^{2} + 2g_{12}X^{1}X^{2} + g_{22}(X^{2})^{2} > 0$$. Yes, the expression given in the link is manifestly non-negative since it is, as I just explained, mistakenly a perfect square but that isn't the reason the link asserts the expression is a Riemannian metric....$$

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

 

[Farsight]

Farsight, you have not answered any of the points in post #353. Specifically you need to answer this : in the GR field equations

$$\displaystyle{G_{\mu \nu }=\kappa T_{\mu \nu }}$$

what range of values do the greek indices $$\displaystyle{\mu, \nu}$$ 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 ?

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.

We'll take things slowly from there, then.

Address post 158 first.

Oh and Markus, pay attention to this guy:

Light cones are just representations and recognition that light and its information or exchange has a limited speed, right? So that is just a reflection of what happens in space across distances which may or may not be within reach of a particular light signal. It doesn't actually "cause" anything in "time". It just makes motion of light across space the "determinant" of any "time" interval between any two spatially separated objects or locations, yes? These "cones" don't exist except as models. The final determinant is the light travel in space which "results" in such limitations across space which our "spacetime cones" only model but not actually create? That is my naive understanding of all that "theoretical construction" of the "light-motion-across-space" effects on physical objects and event timings and such?

He's not naïve.

 

[Farsight]

My beef with Farsight is not about the validity of GR as a model of reality, it is about his failure to acknowledge GR for what it is mathematically, which is a model formulated on (3+1) dimensional space-time.

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:

Basically, the rock tends to describe a curved world line in a curved space-time, as before;

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

however, the interaction with the surface of the earth counteracts the free fall, accelerating the body upwards.

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

That is why an observer on the rock measures a gravitational field ( which is equivalent to local acceleration, as you probably remember ), and the body does not move.

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

Because it doesn't move, the world line ( not space-time ) of the rock has no components in the spatial directions ( in other words - it remains stationary in one spot, which we can choose to consider the origin of our coordinates ), but it still has components and curvature in along the time axis

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.

Physically this is what gives you gravitational time dilation.

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.

To be honest this is a scenario which, though very basic, is actually really hard to visualise, so I appreciate the difficulties one may have with this. However, it is of course possible to do the maths here, and you will find that it yields just what one observes - a stationary rock on the earth's surface, which, as compared to some far away observer, experiences a well defined amount of gravitational time dilation.

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?

Sorry, I am not entirely certain what you mean to ask here. You are correct in that our Riemann manifold combines space and time into just one construct; therefore you don't get "just motion" as we experience it in our daily lives, but rather static 4-dimensional world-lines, which represents objects at all times of their existence. A 4-dimensional space-time encompasses not just all points in space at a given time, but all points in space at all times, in just one manifold.

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.

One question I can not answer for you is why we as human beings perceive only "slices" of that space-time, i.e. why we only perceive three dimensions out of the four. For us it appears as if we see a rapid succession of "slices" out of that space-time, i.e. we can only perceive one moment in time, the "now", like in a film projector. This still gives us a total of four dimensions ( since it is just a so-called "foliation" of hypersurfaces parametrized by the time coordinate, which is mathematically equivalent to 4-manifold ), but we perceive only three of them at a time. The easy answer is probably that our sensory apparatus is simply incapable of perceiving anything more than three dimensions, so our mind cannot visualise a 4-dimensional manifold for lack of a suitable model.

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.

 

[Farsight]

Getting outraged by a certain use of language, without considering what it refers to, is not educating anyone.

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

The difference is obvious and not an issue to anyone's understanding. I mean, what's your story here? You think the average physics undergraduate can learn calculus, differential equations, linear algebra, group theory, matrix Lie algebras, and more, but can't count to four? Is that really what you believe?

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.

In a literal sense, no. In a more abstract sense commonly used in the Minkowski spacetime view, where worldlines are parameterised in terms of an affine parameter and we define things like the four velocity and four acceleration, it does.

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.

Er, yes? And...? Is this supposed to be surprising or profound?

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.

Yes, you look at space and you see space. Just like if you look north you'll see what lies north and you won't see south.

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.

Because that's what you asked for by definition. The spacetime view doesn't change that and doesn't imply otherwise.

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.

As I've tried to explain, what they actually think is more nuanced than that and some of the language (e.g. stuff moving "through spacetime") is meant figuratively and is not intended as a reference to the literal (v = dx/dt) Newtonian definition of motion.

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

That is not an accurate restatement of how it works in general relativity. In the mainstream understanding of general relativity, light and other test particles follow geodesic worldlines in spacetime.

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.

Geodesics are the closest equivalent to straight lines on a curved Riemannian manifold and to say that light and other test particles follow geodesics is to say that they are behaving in the simplest way they possibly can behave.

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.

 

[AlphaNumeric]

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.

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.

 

[przyk]

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

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:

The world line is not time dependent, it is a fixed curve through a 4 dimensional space

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:

(where 'space' is now being used in the general manifold sense).

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:

However, the line is parametrisable (as all continuous paths in any hypothetical suitable construct are) by a single variable. [...]

Q: In a more abstract sense commonly used in the Minkowski spacetime view, does light move through spacetime?
A: No.

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.

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.

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, they don't follow geodesic worldlines in spacetime.

Well, take that up with Einstein.

 

[Undefined]

In mathematics, a manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot.

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"?

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

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:

The world line is not time dependent, it is a fixed curve through a 4 dimensional space

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:

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?

(where 'space' is now being used in the general manifold sense).

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:

However, the line is parametrisable (as all continuous paths in any hypothetical suitable construct are) by a single variable. [...]

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?

 

[Markus Hanke]

it's a fair description that gets to the heart of the matter

...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.

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

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

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

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.

You're attempting to give a display of mathematical prowess to conceal your refusal to address post #158.

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.

 

[Markus Hanke]

One thru four, time and space dimensions in the metric tensor

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.