# I Gravity and balls on rubber sheets

#### jeffinbath

I have never felt comfortable about trying to explain gravitational attraction to children by using heavy balls running around elastic rubber sheets. After all, it is using gravity to explain gravity. It would be so much better to explain it more like it really is, thanks to that originally astounding concept of Albert Einstein. i.e. that increasing gravity causes time to increasingly lengthen. So when an observer watches say a spaceship being attracted straight to a planet, then snapshots of the scene will show that at a given second its speed of travel must be less than it will be in the next second because the next second will be longer and therefore the distance travelled during that second will be greater. Thus the effect of gravitational acceleration is explained. When it comes to the observer seeing a spaceship being deviated by the gravitation from a planet on say its lefthand side, then time is slowing more on the left side of the ship than on the right and consequently the ship will be constantly trying to travel faster on the its left side and therefore the whole ship will bend to the left and it will swing around the planet anti-clockwise to the observer.

Related Special and General Relativity News on Phys.org

#### PeroK

Homework Helper
Gold Member
2018 Award
I have never felt comfortable about trying to explain gravitational attraction to children by using heavy balls running around elastic rubber sheets. After all, it is using gravity to explain gravity. It would be so much better to explain it more like it really is, thanks to that originally astounding concept of Albert Einstein. i.e. that increasing gravity causes time to increasingly lengthen. So when an observer watches say a spaceship being attracted straight to a planet, then snapshots of the scene will show that at a given second its speed of travel must be less than it will be in the next second because the next second will be longer and therefore the distance travelled during that second will be greater. Thus the effect of gravitational acceleration is explained. When it comes to the observer seeing a spaceship being deviated by the gravitation from a planet on say its lefthand side, then time is slowing more on the left side of the ship than on the right and consequently the ship will be constantly trying to travel faster on the its left side and therefore the whole ship will bend to the left and it will swing around the planet anti-clockwise to the observer.
That's not at all how gravity as the geometry of spacetime works.

Your model would not explain why a ball dropped from rest above the Earth would start to move at all. The gravitational time dilation between points close to the Earth is so small that it makes no practical difference.

#### jeffinbath

I am sorry that I do not agree with you. You describe the object “at rest”. If it is at rest then that means that some force must be initially preventing it from gravitationally accelerating. You say “The gravitational time dilation between points close to the Earth is so small that it makes no practical difference.” That cannot be right either, and is perhaps best paraphrased in the expression “The longest march always starts with one step”.

#### PeroK

Homework Helper
Gold Member
2018 Award
I am sorry that I do not agree with you. You describe the object “at rest”. If it is at rest then that means that some force must be initially preventing it from gravitationally accelerating. You say “The gravitational time dilation between points close to the Earth is so small that it makes no practical difference.” That cannot be right either, and is perhaps best paraphrased in the expression “The longest march always starts with one step”.
A ball falling from 5m, say, is a not a long march of 100 years! It takes about 1s to fall 5m, at which point the object is moving at about 10m/s.

Gravitational time dilation is negligible over these times and distances.

A ball that accelerates from rest to 10m/s is certainly not doing so because time is 10 times longer or shorter a few metres apart!

#### jeffinbath

You have chosen to drop the ball from a window 5 m up. That means you were holding the ball using a force that counteracted gravity and therefore cancelled time dilation. Instead of dropping it over a 5m distance we should drop it from a virtually infinite distance away and it should be coming in without any air resistance to travel across that same 5 metres at a near “relativistic” speed! At the end of the day, would you agree that time dilation is the only game in town at the moment that explains the behaviour of Gravity?

#### PeroK

Homework Helper
Gold Member
2018 Award
You have chosen to drop the ball from a window 5 m up. That means you were holding the ball using a force that counteracted gravity and therefore cancelled time dilation. Instead of dropping it over a 5m distance we should drop it from a virtually infinite distance away and it should be coming in without any air resistance to travel across that same 5 metres at a near “relativistic” speed!
I can drop a ball from 5m if I want to. Once I've removed the initial sustaining force, the ball is free to fall under gravity. The theory of gravity must explain that. It can't just say: that's an experiment you're not allowed to do.

An object dropped from a large distance from the Earth will reach the surface at the Earth's escape velocity, which is about $11km/s$, which is pretty fast, but not relativistic.

At the end of the day, would you agree that time dilation is the only game in town at the moment that explains the behaviour of Gravity?
Of course not. GR is more than just gravitational time dilation. The reason for the path of any projectile is the equations of motions derived from the metric, which itself is implied by Einstein's field equations for the curvature of spacetime in the presence of a mass (or, more generally, the presence of stress-energy).

And, in fact, the reason for moving at all (why should an object care if spacetime is curved?) is the Lagrangian principle - in the case of GR in terms of maximising the proper time experienced.

There's a reasonable good summary here:

#### Dale

Mentor
I have never felt comfortable about trying to explain gravitational attraction to children by using heavy balls running around elastic rubber sheets.
Yes, this is a fairly bad analogy for many reasons. It is unfortunately kept alive by pop science authors.

increasing gravity causes time to increasingly lengthen
Unfortunately, this is not a good fix. The first problem is that increasing time dilation is related to decreasing gravitational potential not increasing gravitational force.

The second problem is that if you work this out quantitatively you wind up with the wrong answers. This approach can replicate some basic Newtonian gravitational effects, plus time dilation, but it misses almost everything else. It gets the wrong deflection of light, it misses gravitational waves, it doesn’t produce the Lense Thiring effect, etc.

You are, in effect “throwing the baby out with the bath water”. The “baby” is curved spacetime, the “bath water” is the rubber sheet analogy. While the rubber sheet analogy is bad and should be discarded, spacetime curvature itself should not be discarded. It correctly predicts all of the above and more. The better approach is to actually understand how spacetime curvature actually works and why the rubber sheet analogy doesn’t work.

At the end of the day, would you agree that time dilation is the only game in town at the moment that explains the behaviour of Gravity?
Most emphatically no!

#### Nugatory

Mentor
This video (by our member @A.T. ) is a pretty good explanation of how general relativity does explain the apparent acceleration of a dropped object:

#### A.T.

hus the effect of gravitational acceleration is explained. When it comes to the observer seeing a spaceship being deviated by the gravitation from a planet on say its lefthand side, then time is slowing more on the left side of the ship than on the right and consequently the ship will be constantly trying to travel faster on the its left side and therefore the whole ship will bend to the left and it will swing around the planet anti-clockwise to the observer.
This is going in the right direction, but you have to replace "moving in space" with "advancing in spacetime", so it works for objects initially at rest as well. Additionally to the video above, this might help es well:

#### jeffinbath

Thank you all for pointing me to those really helpful videos. As an 80 yr old it is astounding to me to see how much knowledge about the universe is available out there to us now with a few mouse clicks. It’s a bit sad that we don’t use it more often instead of spending so much time watching the non-educative stuff.

#### FactChecker

Gold Member
2018 Award
Thank you all for pointing me to those really helpful videos. As an 80 yr old it is astounding to me to see how much knowledge about the universe is available out there to us now with a few mouse clicks. It’s a bit sad that we don’t use it more often instead of spending so much time watching the non-educative stuff.
As always, those who want to will search out the educational resources. It is just much, much easier now.

"Gravity and balls on rubber sheets"

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