Gravity. Please knock this down

[studiot]

Mistermac

It is worth noting that the word 'event' is one of those terms which has been given special meaning in relativity.

The trouble is event implies 'something happens', but this is not the case with the special meaning.

An event in spacetime is simple a point in spacetime, whether there is anything there or not.

A a point it takes up no space and lasts for no time, it is just a (set of) coordinate(s).

 

To me. at any rate, an event implies change, as does a flow.

 

Now if there is something that has a value at a bunch of points located together in spacetime, for example a gravitational field, then we can compare the mathematics of the change of the value of this from one event point to another.

We find that mathematics describing this can be very similar to that of fluid flow in ordinary mechanics.

That is where the idea of 'flow of space / spacetime ' arises.

I doesn't mean that property  physically moves from one point to another (although it can do for some flows); it means that a scanner (the moving finger of Omar Khyam if you like) reading out a sequential list of values registers a change.
 

Does this help?

[mistermack]

5 hours ago, Markus Hanke said:

If you think about it carefully, you will realise quickly that spacetime is a completely static construct, in the sense that it is not embedded in any higher-dimensional manifold with additional dimensions of time. Spacetime is hence the totality of all events at all times, and therefore cannot in itself exhibit any dynamics.

Not so. Even if you reject a flow of space time, you still surely have to acknowledge some movement. How else can it curve, as a super massive black hole passes through it or near it? How can gravitational waves be transmitted? I know that's not the same as tranlational movement, but I don't see how you can maintain that it's static. And if you can accept that space time can be re-shaped violently by gravity (or rather, by matter, causing gravity), it's not such a huge step to picture that it can flow.

Studiot, I'm with you on some of that. I'm not picturing space as a fluid like water. It's clearly not. But what is the difference, between a flow of the properties of space time, and a flow of space time? 

Looked at in reverse, what is water, but a collection of properties of space time? But we are content to say that the water flows. It's a bit long winded to say that a river of water is a river of space time properties. 

Edited June 17, 2018 by mistermack

[studiot]

38 minutes ago, mistermack said:

Studiot, I'm with you on some of that. I'm not picturing space as a fluid like water. It's clearly not. But what is the difference, between a flow of the properties of space time, and a flow of space time? 

Looked at in reverse, what is water, but a collection of properties of space time? But we are content to say that the water flows. It's a bit long winded to say that a river of water is a river of space time properties. 

I glad you are at least half listening.

I warned you about specialist technical terminology.

 

Here is an example

https://en.wikipedia.org/wiki/Ricci_flow

 

Note carefully they make a point of saying that the flow may be in time or in something quite different (but static).

 

You need to start by differentiating clearly between the following concepts.

 

Static

Quasi static

Dynamic

Note that Nature ( as so often) thwarts our desire to create a binary (one or the other, A or B) choice.

 

Before the days of computers and finite element  numerical methods much calculation was done by the method of 'conformal mapping' as applied to electrostatics, magnetostatics, fluid flow quasi statics, elastostatics, thermostatics, aerostatics and so on.
Solutions to Laplace's or Poisson's equations abounded.

Most of the work was done in complex analysis format and many famous names were associated with this work.

The point is, as I said, the equations and techniques are similar.

All involve comparing the value of some quantity at some point A with that of other points, B, C, D etc.

As a result a table or map of how the quantity changes from A to B to C to D can be made up.

This quantity may be a dynamic quantity such as fluid velocity or volumetric flow rate.

Or it can be a totally static quantity such as the magnetic field lines of a permanent magnet.

 

I stress that the equations are simialr, not identical.

The mathematical analysis of most situations boils down to identifying the controlling driving forces and contraints and writing equations for them.

The driving forces are often called the equations of constitution

The constraints are often called the equations of compatibility

For each of the situations (applications listed above) there is a unique set of these.

[mistermack]

Even in the wikipedia first page on GR, you get statements that give a very "river-like" picture. 

" Wikipedia said:

Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames. Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry."

So you have a flow of inertial frames at the surface of the Earth, accelerating at 32ft/sec2 relative to me. 

 

 

[Janus]

On 6/15/2018 at 6:27 PM, mistermack said:

Not a rocket with a clock. Maybe an isotope with a known characteristic frequency could be fired downwards and checked for how it compared to a stationary one? ( I'm just speculating ). 

Why two solutions? Well, if a river of space is passing downwards, then a stationary clock on the surface is moving at high speed relative to that space, and should be slowed. Whereas a clock co-moving with that space (ie stationary in that space) should run faster. According to time dilation due to motion through space.  

Whereas if the river model was wrong, then the surface clock is gravitationally slowed ( effectively the same) but the descending clock should be slowed even more, due to it's relative motion.

The "river model" is not an alternate to GR,  It was an something that was come up with to help students visualize what what going on near Black holes.  It has problems, one being that it doesn't work for general solutions, but is restricted to certain solutions for Black holes.   There has been no indication that it could be expanded out to more general solutions.  Even if this were to become possible it would only be because it would produce the same answers as GR gives in those cases.    In other words, a river model for GR that worked for the region near the surface of the Earth would not give any different answer than the one GR presently gives.  

You have read something without fully understanding it and then jumped to the wrong conclusion.

[mistermack]

9 minutes ago, Janus said:

You have read something without fully understanding it and then jumped to the wrong conclusion.

I'm sure the first bit's right, but what wrong conclusion have I jumped to?

[Janus]

1 hour ago, mistermack said:

I'm sure the first bit's right, but what wrong conclusion have I jumped to?

That there would be two solutions to your scenario.  Even if we apply the river model to the region in which it works (black Holes) is doesn't produce any different solution than any other way of looking at GR.

[mistermack]

33 minutes ago, Janus said:

That there would be two solutions to your scenario.  Even if we apply the river model to the region in which it works (black Holes) is doesn't produce any different solution than any other way of looking at GR.

I haven't concluded that. Although I can see how you could jump to that conclusion.  

I'm wary of concluding anything at all in physics, or indeed any other science. Exploring the concepts, and making theoretical arguments is something I enjoy. I certainly don't nail my colours to a mast, just because I'm currently exploring in the same direction. 

If the river model brought up any contradiction to GR, I would of course view it as faulty. To me, at the moment, it's a different way of viewing the same thing. Instead of curved space-time, it's a picture of a flow of inertial frames. 

I haven't come across any work that declares that it doesn't work for bodies other than black holes, as you have asserted, so I would appreciate any link.

[Mordred]

the river model would be pointless to describe any scalar field as a scalar field doesn't flow. ie it cannot describe the universe as a whole as the universe metric of LCDM is a homogeneous and isotropic field. (no net directional components). This also applies to the vacuum solutions of GR. The River model requires a gradient of a field to flow in either a convergent or divergent manner.

[Markus Hanke]

18 hours ago, mistermack said:

How else can it curve, as a super massive black hole passes through it or near it? How can gravitational waves be transmitted? I know that's not the same as tranlational movement, but I don't see how you can maintain that it's static.

It’s like one of those old style film projectors - you project a rapid succession of frames onto a screen, and as a result you get the illusion of motion. But in reality, there is no motion, because the reel of film itself is a completely static construct. All frames are there already, eternalised on the reel, and never change; in fact, the very notion of “change” is meaningless here, except as a relationship between static frames. But neither the frames themselves, nor the collection of all frames (the film reel) ever changes in any way.

In the context of GR, there is also not really any such thing as motion, or the passage of time; those are only auxiliary concepts that are “left-overs” (so to speak) from the old Newtonian paradigm. For example, we usually think of the moon revolving around Earth - a dynamic process, described by an elliptic orbit in space, that repeats in time. But in GR, we no longer separate space and time, so the moon becomes a bundle of world lines in spacetime, that looks like a helix winding around another bundle of world lines that is the Earth. This geometric structure encompasses both space and time, and is itself completely static (just like the film reel), because it encompasses all locations in space of these objects at all instances in time throughout their history. Any notion of “past”, “present”, “future” and “motion” is now completely arbitrary, and not fundamental to the universe. Everything that was, is and will be, is there - and that collection of all points in space at all instances in time is not embedded in anything else, and hence the notion of “change” is meaningless if applied to it. As such, GR is a completely deterministic view of the world (ref “block universe”).

The same is true for the spacetime geometry that accompanies the world lines (or for gravitational waves) - they are just continuous deformations at all points in space and all instances in time, and themselves completely static. 

But of course, one can always recover the notion of dynamics, by “slicing up” spacetime into hypersurfaces of simultaneity. You then have slices of 3D space, which are ordered in an oriented way (i.e. from past to future), and which are causally linked to each other by dynamic laws. This is called the “ADM formalism”, and is analogous to the film reel being projected onto a screen. However, such a “slicing-up” of spacetime into hypersurfaces is a completely arbitrary procedure, and not in any way fundamental to nature.

One must remember that - in the context of GR - the passage of time is merely an artefact of human perception of consciousness. There is no fundamental mechanism that picks out a particular hypersurface of simultaneity, and gives it any kind of physical property that somehow distinguishes it from any other hypersurface (“the present” as opposed to past and future), or “advances” that hypersurface selection in a linear manner. GR simply treats all points in space and all instances in time in the exact same way. One can impose other structures on top of that, but those will always be arbitrary, and have no real physical significance.

 

To give a very practical example - the process of free fall is not described as a dynamic process. Instead, it becomes a purely geometric problem - we find that world line between two given events on a static manifold, which forms a geodesic of that manifold, given a connection and a metric. Mathematically this is done by finding that world line, which parallel-transports its own tangent vector at all points; so the “process” of free fall becomes a simple concept in static geometry. If you write this statement down in mathematical form, you end up with the geodesic equation. That’s all there is to it.  

13 hours ago, mistermack said:

If the river model brought up any contradiction to GR, I would of course view it as faulty.

As mentioned before, it can be a useful analogy to explain certain situations in a visually appealing manner. But that’s all it is - an analogy.

[mistermack]

Thanks Marcus, that's an interesting post. The problem I have with it is that if everything is as you describe, then all of the past and future must be sitting there available to be re-run, like your film in the projector. It's a gigantic expansion of the notion of the universe, if every incident that ever happened or ever will happen is lying around somewhere. 

You also have the problem of random uncertainty. You have to have every possible incident lying about, not just the actual ones. That makes for a gigantic expansion of a gigantic expansion, of something that was unbelievably gigantic to start with. 

[studiot]

1 hour ago, Markus Hanke said:

It’s like one of those old style film projectors - you project a rapid succession of frames onto a screen, and as a result you get the illusion of motion. But in reality, there is no motion, because the reel of film itself is a completely static construct. All frames are there already, eternalised on the reel, and never change; in fact, the very notion of “change” is meaningless here, except as a relationship between static frames. But neither the frames themselves, nor the collection of all frames (the film reel) ever changes in any way.

Like it, must remember that one it's much earthier than comapring properties at points in Hilbert Space.  +1