I General Relativity & Curvature Explained: How Objects Fall

[Gadhav]

TL;DR

Describe how objects fall on earth

I always was confused on how objects fall on Earth due to curvature of space. All I see everywhere is a flat stretched piece of fabric and balls going round and round the central massive ball. But that does not explain anything, how objects actually fall. Finally I saw this video where it explains that it is due to curvature of time dimension, not space.
Why this information is not widespread?

 

[PeterDonis]

Why this information is not widespread?

What makes you think it isn't?

 

[Gadhav]

Probably known in expert worlds but not for novices. Because whatever books I read and YouTube videos I saw, show a stretched disk and balls moving around but no where it dais that specifically. It is hard to visualize that curvature of space will cause an apple to fall, as curvature of Earth is very small. So I always questioned what makes apple fall to ground due to that small curvature. No book as I read mentions specifically that "While lines curve slightly inwards to earth, Earth itself moves fast through time dimension and hence objects follows the line towards Earth and hence apple falls, (Due to Curvature of Time axis, not space axis)
These videos are good.

 

[A.T.]

What makes you think it isn't?

All the people who come to this forum, because they are confused by the balls on rubber sheet analogy? The term "widespread" is of course relative. Compare the view numbers:Rubber sheet: 66M.



Geodesics with time dimension: ~100k:

 

[PeterDonis]

whatever books I read and YouTube videos I saw

Ah, so your question was really, why isn't this information widespread in pop science sources? And the only answer to that is, because they're pop science sources and their purpose is not to actually teach you the science. It's to sell things.

Btw, even the video you linked to is pop science and is not really teaching you the actual science:

"While lines curve slightly inwards to earth, Earth itself moves fast through time dimension and hence objects follows the line towards Earth and hence apple falls, (Due to Curvature of Time axis, not space axis)

This sounds nice, but it's really no better than the "stretched piece of fabric" explanation. What "lines" are these that "curve slightly inwards to earth"? Why are they curved? Why does the Earth "moving fast through the time dimension" mean the objects follow the lines towards earth?

 

[PeterDonis]

even the video you linked to is pop science and is not really teaching you the actual science

In addition to the issues I raised in my previous post, there is this one, which is really the key misconception in the video: the idea that "different parts of the object want to move through time at different rates". There are a number of issues with this, but the simplest one to raise for a person not already familiar with the details of GR is this: it implies that the path of an object free-falling towards the Earth should be different depending on its radial extension, since its radial extension determines how "different" the "rate of time flow" is from one end of the object to the other. But experimentally, this is not what we observe: all objects free-fall towards Earth with the same acceleration (once complications like air resistance are removed). So the "explanation" in the video can't be right.

My advice is to stop looking at pop science and work your way through a textbook. Carroll's online lecture notes on GR are one possible good start.

 

[A.T.]

No book as I read mentions specifically that "While lines curve slightly inwards to earth, Earth itself moves fast through time dimension and hence objects follows the line towards Earth and hence apple falls, (Due to Curvature of Time axis, not space axis)

You might try Relativity Visualized, by Lewis Carroll Epstein.

 

[PeterDonis]

So the "explanation" in the video can't be right.

And note carefully that the video by @A.T. (the second one in his post), which is a much better one to start from if you absolutely have to have a video, shows the worldine of the free-falling particle as straight, not curved! The curved worldline is the one of an object that is at constant altitude relative to the Earth. (And the region shown by that video is only a small "local" region of spacetime, not a region large enough to contain the entire Earth.)

 

[A.T.]

And note carefully that the video by @A.T. (the second one in his post), which is a much better one to start from if you absolutely have to have a video, shows the worldine of the free-falling particle as straight, not curved!

I think these are just two different ways to visualize qualitatively, how gravitational time dilation can be related to coordinate acceleration of free falling objects. To represent the gradient of gravitational time dilation, one vary the distances along the time dimension (my video), or the rate of advancement through the time dimension (the video in the OP).

 

[Gadhav]

, since its radial extension determines how "different" the "rate of time flow" is from one end of the object to the other. But experimentally, this is not what we observe: all objects free-fall towards Earth with the same acceleration (once complications like air resistance are removed). So the "explanation" in the video can't be right.

Yes I noticed that and clearly the video is wrong there. But not sure whether these videos are just pop science. While there are likely some errors, most of visual effects are really good. Visual effects do help for someone trying to get into it. It also has a video on how magnetic field and electric field are one and same. People probably know this after spending 3 decades i n Physics but Visual effect tells you its relativistic significance.
(I also like AT's video (and reasoning too) that explains a lot but problem is that video does not necessarily comes in search) Otherwise there is a chance that everyone gets lost in math without having clear understanding. My humble opinion which can be wrong...

 

[PeterDonis]

I think these are just two different ways to visualize qualitatively, how gravitational time dilation can be related to coordinate acceleration of free falling objects.

No, they aren't. Your way shows the object as a pointlike test object with a single (straight) worldline, and then describes why this worldline appears to vary in height, by showing the relationship between the object's worldline and the worldlines of constant height. In other words, it (correctly) attributes the object's apparent motion to the difference in shape between the object's worldline and the worldlines of constant height.

The other way requires the object to have radial extension; it (incorrectly) attributes the object's apparent motion to the difference between the worldlines of different parts of the object. That is simply wrong.

 

[PeterDonis]

not sure whether these videos are just pop science

Are they textbooks or peer-reviewed papers? Have they been critiqued by other experts in the field prior to being published?

If the answer to those questions is no (and as far as I can tell it is), then it's pop science.

Visual effects do help for someone trying to get into it

It depends on what you mean by "help". If the video is giving you incorrect information, it's not helping you, no matter how good its visual effects are.

 

[Orodruin]

Otherwise there is a chance that everyone gets lost in math without having clear understanding. My humble opinion which can be wrong...

Understanding the math is having a clear understanding. Everything else is mental images.

 

[PAllen]

Worth noting is that some real understanding does not require the most advanced treatment. Thus, for general relativity, there are 'physics first' texts (e.g. Hartle's) that are accessible pretty much following a standard 3 semesters of calculus, yet give real understanding rather than popsci.

 

[Tomas Vencl]

Nice article :
visualizing curved spacetime

 

[PAllen]

Nice article :
visualizing curved spacetime

Very interesting, but as noted in the article itself, given a GR solution, you have one model of their type (absolute metric) per family of observers. Thus, for SC geometry, you have one model for stationary observers and a completely different one for free fallers. Each can only be used to compute for or understand the chosen family of observers. I don’t see it as that much harder to directly confront the non-positive definite metric of GR, from which all observers can be handled with one metric. It seems a lot of machinery just to be able to use a positive definite induced metric on a surface embedded in a Euclidean space, good for only one family of observers.

 

[A.T.]

Nice article :
visualizing curved spacetime

Here is more from the same author:
http://www.relativitet.se/articles.html

@Gadhav As an introduction I recommend chapter 2 of this thesis:
http://www.relativitet.se/Webtheses/tes.pdf