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Warping Of Space


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I would like to know if the warping of space assumes that massive objects are "on" space instead of "in" space, if that makes any sense. If space is all around the matter, enveloping objects from all sides, how could it warp in only one direction, as depicted in most diagrams making the rounds on the web?

 

Google images

 

 

Shouldn't there be an "indentation" or a "dent" in all directions and not just at one pole?

 

And if space is indeed warped in all directions depending upon how heavy the object is, how exactly are the smaller objects "gravitationally attracted" to the bigger objects and vice versa? In other words, how exactly are they pulling/pushing one another via these "dents"?

 

Thanks,

 

K

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i think the "warp" you are referring to deals with gravity, am i correct

 

i think if you look at it in a new perspective the concept becomes a little bit different, and a little bit clearer

 

think of 3 ways something can affect the universe

 

 

Gravity

 

magnetism

 

spacetime-bend

 

1-gravity

observed effects, pulling matter together, the increased density of the matter increases the amount of matter

the field of this always points to the center of the mass in question

 

2- magnetism

observed effects, pulling other magnetic objects towards eachother, repelling other magnetic objects from another

measureable magnetic filed lines (the donut)

causes electron flow when moved across a conductor

 

3-space-time bend

observed effects, mushroom like appearance of specifically dense celestial objects, apparent time-dialation vs C (speed of light)

if

a pulsar can bend space-time by both expanding and contracting space

then

at the "stem" of the mushroom where space contracts, the light that is ejected out of the "tunnel" or new vector, is in the x-ray spectrum , where it is similar to a redshift

at the "cap" of the mushroom where space expands, even slight vector difference translates to exagerated dispersal of matter from the center point

 

so this specific type of space bend's representation should be a mushroom instead of a indention (see crab nebula)

 

questions, gravity affects matter, but does it affect space or time?

magnetism affect other magnetic objects and conductors, but does it affect space or time?

a bend in space time of this calibre, may affect space, but does it affect matter?

 

 

if, gravity is powered by time throught impetali

and if, time flows constant in this specific type of wormhole

 

then gravity and matter reamain unaffected by the bend in space time, similar to a non-magnetic, non conductive object not being affected by a magnet

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...[word salad]...

No. If you take a moment to try to gather support for your ideas, you may find that you are less likely to post fantasy disguised as information.

 

 

K.C- your question is an important one and is evidence that you are thinking critically about common explanations. The images you linked to do indeed represent all three spatial dimensions and the temporal dimension as a two-dimensional "fabric" that is warped by mass. It is a graphic representation, not a true model, so it has limitations as do all analogies (specifically, it represents four dimensions as two). If you know someone with a trampoline, try placing two relatively free moving objects of different weight near one another. As long as one object isn't tremendously more massive than the other, you will notice that they come to rest at a point in between the two objects.

 

A similar example of the analogy's inadequecy can be observed when you look at a two dimensional representation (map) of the Earth's three dimensional curved surface. If you plot the motion of an airplane flying in a straight line between two sufficiently distant points, the plot on the map is a curve, even though the plane travels in a straight line over the ground.

 

Similarly, light and objects traveling in a straight line through space-time, in close proximity to a massive body, follow a curved path. This is a prediction made by general relativity because of the equivalence principle.

 

Please read this excellent description of how objects follow geodesic paths through "warped" space-time.

http://www.astronomynotes.com/relativity/s3.htm

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Thank you both for your responses.

 

I am not sure I understand the "curvature of space-time" concept at all. Does the testability of this concept necessarily involve expensive, time consuming, experimentation such as Gravity Probe B? Could we perhaps do something simpler, something as suggested by JMJ, only to understand the principle behind the concept (at the risk of over-simplifying, placing objects such as marbles/baseballs etc with different weights on a trampoline like material and observing the effects of curvatures by way of a simple gyroscope and extrapolating the results to ... the entire Universe?! Isn't that extreme generalization?)

 

More questions:

 

What is space curving into? More space?

 

How much matter does it take to introduce a curvature to space (I am not sure why I should consider a time dimension when understanding warped space but I will leave that discussion to another time)?

 

Presuming dark matter also affects the curvature of space (please correct me if I am wrong here), and assuming it exists everywhere including in our own solar system, how do we explain the orbital planes of the planets and the Sun (and other objects such as moons, asteroids etc) in terms of the curvature of space caused by matter in our solar system + dark matter in our solar system? Is there a good explanation as to why they are all not crashing into one another more often?

 

Can a subatomic particle introduce a curvature in space? Positing that the macroscopic world emerges from the microscopic world, how does curvature manifest from the smallest of scales (quarks) to the largest of scales (galaxy filaments)?

 

Is curvature an indicator for the "thickness" of space?

 

Considering matter is "unevenly" distributed in all possible directions in our 3 dimensional space, the straight forward implication there being there's no one layer of space where the orbits of all objects line up, rather objects are completely enveloped by space, inside and out, how does the curvature of space affect "free falling" objects in space?

 

Thanks again!

 

K

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Your questions betray the questionable utility of the "warping of the fabric of space-time" analogy. Space-time does not curve into anything any more than the surface of the Earth curves into anything, it is just curved. It is common to think solely in Euclidean geometry, but many things are not Euclidean. For example, you may remember that the three angles of a triangle add up to 180 degrees. However, if you draw a sufficiently large triangle on the surface of the Earth, its angles will add up to more than 180 degrees. If you draw a triangle on the surface of a horse saddle, its angles will add up to less than 180 degrees.

 

Let's agree to limit the analogy to be only a simple representation of how general relativity explains gravity as a consequence of the shape of space-time rather than the Newtonian view of gravity being a force between massive objects.

 

General relativity can and has been tested using somewhat primitive methods, see this wikipedia article on classical tests of GR.

 

Everything with mass curves space-time, but if the object has very low mass, the curvature is so small that it can't be measured. There has not yet been a successful way to tie GR's concept of gravity in with what we know about forces dominant at the atomic scale, though many physicists are working on a workable model of quantum gravity

 

Presuming dark matter also affects the curvature of space (please correct me if I am wrong here), and assuming it exists everywhere including in our own solar system, how do we explain the orbital planes of the planets and the Sun (and other objects such as moons, asteroids etc) in terms of the curvature of space caused by matter in our solar system + dark matter in our solar system? Is there a good explanation as to why they are all not crashing into one another more often?

I'm not exactly sure what you're asking here, and to be frank, not entirely sure I could answer to your satisfaction. Dark matter may be an unnecessary complication in the conversation at this point. Here is a wikipedia article explaining how the solar system developed from the accretion disk around our sun.

 

Considering matter is "unevenly" distributed in all possible directions in our 3 dimensional space, the straight forward implication there being there's no one layer of space where the orbits of all objects line up, rather objects are completely enveloped by space, inside and out, how does the curvature of space affect "free falling" objects in space?

I think this question arises from trying to rely too heavily on the flawed "fabric of space-time" analogy. A free-falling object follows a geodesic rather than a Euclidean straight line through space-time. Massive objects distort space-time so that the geodesic, even though it is the shortest distance between two points, may not be "straight" to an outside observer. Space-time is not a sheet though, and one should not expect all orbits to exist in the same plane, as they don't.

 

NOTE: I have repeatedly used "space-time" (others may prefer "spacetime") because time is intrinsically linked to space in how it is distorted by massive objects.

 

I don't know if any of this really answers your questions. General relativity is not at all intuitive until you are accustomed to thinking differently. My basic and relatively uneducated understanding is this: Galilean relativity is intuitive, it is a way to translate measurements between different inertial frames, or coordinate systems. If I am on a bicycle traveling 15 mph and throw a ball at 60 mph relative to me, a stationary observer would measure the ball to be traveling at 15+60=75 mph. Special relativity arises from the fact that photons do not obey this intuitive Galilean relativity. If I am in a rocket traveling 3000 kilometers per second and fire a laser beam at 300,000 km/s, a stationary observer still measures the photon to be traveling at 300,000 km/s. General relativity applies the equivalence principle to this, in that there is no difference between inertial acceleration (stepping on the accelerator pedal in a car) and acceleration due to gravity. Warping of space-time is the way that general relativity explains gravity, but it does not posit that space-time is a sheet with indentations in it. That idea is just a function of the inadequate analogy of the "fabric" of space-time.

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I don't know if any of this really answers your questions.

 

It does, at least a couple of them. For one thing, the "fabric of space-time" analogy is not a good aid in understanding space-time curvature. Wonder who came up with that?! In all the videos that I have seen and all the articles that I have read space-time is consistently referred to as a fabric.

 

I would rather visualize space-time as pixels (thus making it discrete). To the extent that all matter and forces are either fermions or bosons at the fundamental level, I am postulating, for visualization purposes, that space too has a fundamental particle as its building block. Could it be a graviton?

 

I understand that the macro world is still not reconciled with the micro world ergo GR with QM. My interest lies in such a reconciliation and hence all these questions.

 

I take an inside-out approach starting with understanding the elementary particles and "progressing" to the largest structures in the universe, but somehow the curvature of space at the micro level is not at all intuitive. I can't imagine particles with negligible mass (stuff like neutrinos?) "bending" space. If there is a one-to-one interaction between an elementary particle with mass (however negligible) and a space "pixel", how does that work? And if there is no such interaction, then on the larger scales, with heavy objects, how does curvature become evident to an observer? What about particles with negative mass (exotic matter)? How do they affect the curvature of space (or space-time if you prefer) if at all they exist in nature?

 

Too many questions, I am afraid.

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Bah, no such thing as too many questions, though we have arrived at the point where someone else will need to step in and answer your questions :)

 

I've found a few common analogies used to talk about features of the world around us that are really only good if you already understand the concept that you're trying to explain. The balloon analogy used to describe expansion of the universe is another example. If the analogy takes more explanation to correct its inadequacies than the concept itself, it isn't very useful as a teaching aid. But, they persist.

 

The fabric analogy is useful as long as you realize that it contains condensed dimensions. 4d is represented as a 2d sheet. We do this in graphs as well, where three dimensions are condensed down to one axis and time is the other axis. The key is to stick to the constraints of the analogy. It is far more difficult to accurately represent some situations without this condensing. Similarly, a map is useful, but not truly "accurate" and a truly accurate representation would be indistinguishable from the thing you are trying to represent. Remember, the map is not the territory

 

If you're more of a visual learner, as I am, you may find these youtube videos useful.

 

3D representation of the curvature of space-time.

 

Why do we think of space-time curvature?

http://www.youtube.com/watch?v=8cOaagyEWVI&feature=related

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  • 2 weeks later...

It's not possible to warp space. Space is uniform everywhere. See my post in the physics section on how to create an infinite space within a finite sphere.

 

Following on from that, the spacebubble trapped within this sphere is the equivalent of an atom of matter, which is to say it is a unity of space. As an atom of matter is actually a unity of matter (or a matterbubble, as we like to call it), it cannot be warped at all. If it could be warped, then the matterbubble would collapse or, to put it another way, it would be destroyed. This is why matter itself cannot be warped, because if it could then matter could be destroyed. You guys now have an explanation for why matter cannot be destroyed.

 

To put this mathematically, unity cannot be divided in any way at all.

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Following on from that, the spacebubble trapped within this sphere is the equivalent of an atom of matter, which is to say it is a unity of space.

 

Why/how is space a bubble?

 

How is it "equivalent" to an "atom of matter"?!

 

What does "unity of space" mean?!

 

As an atom of matter is actually a unity of matter

 

??? I have no idea what this means!

 

(or a matterbubble),

 

matter bubble?!

 

as we like to call it),

 

We who?

 

it cannot be warped at all. If it could be warped, then the matterbubble would collapse or, to put it another way, it would be destroyed. This is why matter itself cannot be warped, because if it could then matter could be destroyed. You guys now have an explanation for why matter cannot be destroyed.

 

OK, seriously, you are trying to yank our chains here.

 

To put this mathematically, unity cannot be divided in any way at all.

 

How is the above considered as putting it mathematically?! Where is the math?!

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  • 2 weeks later...

Let's start with this one:

What is space curving into? More space?
An important thing to note is that what counts for modelling gravitation is intrinsic curvature, which can be defined according to differential geometry (which is based on the formalism of tensor calculus). To see it simply, imagine you take a sheet of paper and roll it up... Oddly enough, its intrinsic curvature hasn't changed! It remains zero, as quantified by the Ricci scalar. The surface of a sphere does have nonzero, positive intrinsic curvature and, if you make paper onto it, remove a piece and bend it around, it doesn't change either. Technically, we say that intrinsic curvature doesn't depend on how one embeds the manifold in question into one with more dimensions, hence it is defined regardless.

 

The intrinsic curvature changes when there is stretching or contracting which isn't uniform throughout. Those trampolines that you see in some of those illustrations assume a negative value of it in the area around the object that is pressing into them. Quiz: In the case of gravity, with a ball of mass and vacuum outside it, what is the intrinsic curvature of the space outside the ball? Don't jump to hasty conclusions, mind!

 

As Jones said, GR isn't so intuitive and those illustrations need to be taken as more or less vague analogies, only the formalism can tell you things for sure.

 

I'll add another thing, but it's a secret. The equivalence principle makes geometry a very useful mathematical tool for describing gravitation and many folks (including Einstein) view curvature as an "actual fact", assuming it is so in an ontological sense. Few people (including this dumb *** and also, ehem... Steven Weinberg in his classic textbook) don't take it for granted as a "fact of reality" until some hardly feasible observations might eventually actually distinguish the matter. It would remain a quite subtle case even with observations quite near the event horizon of a black hole.

Edited by Qfwfq
clarity
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