Does the curvature of space-time create the illusion of distance shrinking?

  • Context: Graduate 
  • Thread starter Thread starter mdl
  • Start date Start date
  • Tags Tags
    Bending Spacetime
Click For Summary

Discussion Overview

The discussion revolves around the concept of space-time curvature and its implications for the perception of distance. Participants explore whether the bending of space-time, as described in general relativity, creates an illusion of distance shrinking or if it fundamentally alters the nature of distance itself. The conversation includes theoretical considerations, analogies, and challenges to various viewpoints.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants argue that bending space-time does not change the physical properties of the space itself, suggesting that it is merely a conceptual shift in understanding.
  • Others counter that curving a surface, such as a sheet of paper, alters the relationships between points on that surface, which could analogously apply to space-time.
  • A participant mentions the Einstein Equivalence Principle, stating that locally, one cannot detect curvature, but globally, paths can converge or diverge based on curvature.
  • There is a discussion about measuring distance, with some asserting that distance cannot simply be counted in terms of molecules or points, while others suggest that the proper distance changes as paths converge.
  • One participant introduces the distinction between intrinsic and extrinsic curvature, emphasizing that general relativity focuses on intrinsic curvature relevant to gravity.
  • Another participant raises concerns about discrete space-time theories and their implications for established principles like Lorentz Invariance.

Areas of Agreement / Disagreement

Participants express differing views on the nature of distance and the implications of space-time curvature. There is no consensus on whether the bending of space-time creates an illusion of distance shrinking or if it fundamentally alters distance itself.

Contextual Notes

The discussion includes various assumptions about the nature of space, distance, and curvature, with some participants referencing mathematical concepts and principles without resolving the underlying complexities.

mdl
Messages
18
Reaction score
0
If I bend a paper, it doesn't change the things written on it.

If gravity is bent space(time), we shouldn't be able to detect it. (e.g. things shouldn't be dragged by it)


So why are we talking about bending space, if it's not the space itself that is bending?
it's only our mental concept of how things will be that is "bending".
 
Physics news on Phys.org
What? If I curve a sheet of paper, of course what's written on it will change...I don't understand your argument.

Draw a straight line on a piece of paper, and then curve that piece of paper into a cylinder, now your straight line turned into a circle...
 
Matterwave said:
What? If I curve a sheet of paper, of course what's written on it will change...I don't understand your argument.

Draw a straight line on a piece of paper, and then curve that piece of paper into a cylinder, now your straight line turned into a circle...

If you are created by the molecules of paper, you can't tell if it's curved, or strechted.

Do we exist beyond spacetime?
 
If I lived on the paper, I can't tell the paper is curved locally - this is a statement of the Einstein Equivalence principle. But globally, I can tell if the paper is curved. If me and my friend started on parallel paths, we find that eventually our paths either converge or diverge, depending on the curvature. This is the so-called "geodesic deviation".
 
Matterwave said:
If me and my friend started on parallel paths, we find that eventually our paths either converge or diverge, depending on the curvature. This is the so-called "geodesic deviation".

You could only measure the distance between paths with counting molecules.
The number of molecules is not changing, so the distance would be the same.

It only works if bending means creating or removing space.
 
I don't necessarily need to measure distance by "counting molecules". The proper distance between me and my friend changes. A light pulse will take shorter and shorter time to bounce from me to my friend and back as I move along this piece of paper assuming our geodesics are converging.

Even without regard to this, at some point, I'll collide with my friend, so obviously the distance between us changed.
 
Matterwave said:
A light pulse will take shorter and shorter time to bounce from me to my friend and back

That's what I don't understand.

Why will it take shorter time?
Light (or equivalent pulse) would allways pass the same number of molecules (the same amount of paper) regardless of how the paper is bent.
 
I'm getting closer to my friend. The proper distance between us decreases. The proper distance is not "number of molecules" between me and my friend.

The distance between two points is not governed by some "counting" of molecules or intermediate particles.
 
molecules of paper are equivalent to fabric of space, not particles.

If we assume that space is discrete, the distance between two points is the number of points of fabric of space (= molecules of paper) between them.

If we bend the space/paper, we don't change the distance.
 
  • #10
As far as I know, no successful quantization procedure of space-time is known. If you want to deal with causets or something, I am not well versed in those theories.

In general relativity, the proper distance between two points is given by the metric, and this proper distance changes if the space-time changes. There is no way to count the events of space-time, as they are uncountably infinite.

The events of space-time form a differentiable manifold. As such, we can make a differentiable mapping between some small region of space-time to an open set of R^4. Any open region of R^4 necessarily contains an uncountably infinite set of points, just as there is an uncountably infinite set of points between the numbers 0 and 1 on the real line.
 
  • #11
You can bend a non-stretchy piece of paper into some shapes (like cylinders) without changing any distances, but you can't, for instance, make a flat non-stretching piece of paper smoothly cover a sphere, for the same reason that you can't make a flat, continuous map of the Earth's surface that preserves the size and shape of continents (i.e. doesn't stretch them or distort them).

This is because a cylinder has no intrinsic curvature, though it has an extrinsic curvature. See for instance the Wikipedia:

http://en.wikipedia.org/w/index.php?title=Curvature&oldid=460970826

wiki said:
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context. There is a key distinction between extrinsic curvature, which is defined for objects embedded in another space (usually a Euclidean space) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic curvature, which is defined at each point in a Riemannian manifold. This article deals primarily with the first concept.

While the article above, and your post, deals with the first sense of the ambiguous word, curvature, GR is most interested in the second - "intrinsic" curvature, not "extrinsic" curvature.

The curvature of space-time that's of interest for gravity is intrisic curvature, not extrinsic curvature.
 
  • #12
thanks o lot, I think that answers my question
 
  • #13
  • #14
I think I get what OP is saying. I think he is saying that "distance" is just the number of points between two points, and that YOU an intrinsic are part of the "space" or "set of points". He thinks it doesn't matter what direction a point is from you... it doesn't matter WHERE it is, but rather how many points are between you and that point.

However, this ignores the concept of "distance" - which basically HAS to be used in physics for any meaningful theories to arise. And "distance" is also well-defined in maths - and I advice you to look up the concept of a "metric"/"metric space".

Also, pervect's post is very good and may have already answered OP's question, but oh well.

Edit: Also OP, you mentioned discrete space-time, and theories involving this always interest me. However, many theories based on discrete space-time apparently violates the Lorentz Invariance Principle (according to a lecturer).
 
  • #15
Think about it this way: we exist in spacetime. You say things wouldn't move? Well, let's use your paper example. If I set a paper clip on the paper, and then curved the piece of paper to a convexed (hump) shape, would it slide of? Yes. The same occurs with spacetime in a general sense.
 
  • #16
pervect said:
You can bend a non-stretchy piece of paper into some shapes (like cylinders) without changing any distances, but you can't, for instance, make a flat non-stretching piece of paper smoothly cover a sphere, for the same reason that you can't make a flat, continuous map of the Earth's surface that preserves the size and shape of continents (i.e. doesn't stretch them or distort them).

This is because a cylinder has no intrinsic curvature, though it has an extrinsic curvature. See for instance the Wikipedia:

http://en.wikipedia.org/w/index.php?title=Curvature&oldid=460970826



While the article above, and your post, deals with the first sense of the ambiguous word, curvature, GR is most interested in the second - "intrinsic" curvature, not "extrinsic" curvature.

The curvature of space-time that's of interest for gravity is intrisic curvature, not extrinsic curvature.




The point you are conveying here sounds similar to the hairy ball theorem and how all the hair can't be combed in on direction because there is always a point where the vector is 0.
 
  • #17
mdl said:
If I bend a paper, it doesn't change the things written on it.

If gravity is bent space(time), we shouldn't be able to detect it. (e.g. things shouldn't be dragged by it)So why are we talking about bending space, if it's not the space itself that is bending?
it's only our mental concept of how things will be that is "bending".

Hmmm. I agree that ALL physics theories are just mental concepts. But everyone seems to find they have a useful relation with the real world.

If you want to use General Relativity then you use its concepts and definitions. If you don't want to, fine.

But I will mention that if you bend the paper then it affects the motion of grains of sand on the paper, right?
 
Last edited:
  • #18
PatrickPowers said:
But I will mention that if you bend the paper then it affects the motion of grains of sand on the paper, right?

IMHO that model is misleading, because you need another external space (where grains could exist, where the observer is, and where you actually can bend a paper).

As was said earlier (by pervect), spacetimes curvatures are different.
 
  • #19
PatrickPowers said:
Hmmm. I agree that ALL physics theories are just mental concepts. But everyone seems to find they have a useful relation with the real world.

If you want to use General Relativity then you use its concepts and definitions. If you don't want to, fine.

But I will mention that if you bend the paper then it affects the motion of grains of sand on the paper, right?

mdl said:
IMHO that model is misleading, because you need another external space (where grains could exist, where the observer is, and where you actually can bend a paper).

Yes, grains of sand rolling on a bend paper have nothing to do with General Relativity. This is a better analogy:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html
 
  • #20
Obviously there's some conflict between everyday usages of these words and their mathematical definitions. I agree with the OP about people living on a sheet of paper not being able to tell if it had been rolled or not.

This caught me eye though:
mdl said:
That's what I don't understand.

Why will it take shorter time?
Light (or equivalent pulse) would allways pass the same number of molecules (the same amount of paper) regardless of how the paper is bent.

Please correct me if I'm wrong, but isn't this exactly the kind of thing the curvature of space-time effects? If you have a massive object, space-time curves around it. Think about if you were surveying distances by how long it took you to walk from place to place, moving at a steady pace. Of course since gravity sucks you in, you would get to that massive object much faster than you had expected, based upon how long it took you to get to that same spot when it was empty. Therefore (absent a proper understanding of higher physics) you would have to conclude that somehow the distance between the two spots had shrunk.

So it seems like the curvature would produce results suggesting the distance between the points really had shrunk, even though maybe at first glance no "space" had evaporated?
 

Similar threads

High School Does Spacetime Have Physical Existence?
  • · Replies 58 ·
2
Replies
58
Views
4K
High School Does a gyroscope bend spacetime?
  • · Replies 21 ·
Replies
21
Views
5K
High School Does Gravity Really Bend Space-Time or Just Create Confusion?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Curved spacetime bulging in time direction
  • · Replies 30 ·
2
Replies
30
Views
2K
Undergrad General Relativity: Angular Momentum, Gravity & Questions
  • · Replies 7 ·
Replies
7
Views
2K
High School Warping Spacetime: Classical Physics & Relativity
  • · Replies 3 ·
Replies
3
Views
2K
High School Mechanics behind curved time causing gravitation/geodesics
  • · Replies 27 ·
Replies
27
Views
7K
Undergrad Speed of light around a (massive) object in space ...(i.e.sun
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Space and time as fields of mass-energy
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Questions regarding traveling speed in time and gravity as a force
  • · Replies 95 ·
4
Replies
95
Views
7K