Einstein & Gravity: Explained by HallsofIvy

[aychamo]

Hello there!

I asked this question in a different forum, and was directed to ask this here:

----
My next question also involves Einstein. It's about gravity not really being a force or whatever. According to the program the Earth revolved about the sun because the sun warps the space time around it. So if I drop my cell phone and it hits the earth, is this because the Earth warps the space time around it? I don't understand this part.

Thank you kindly
AYCHAMO
----

I received this answer from HallsofIvy which I really don't understand. May someone break this down for me?

--
Geometrically, any surface or "curved" 3 dimensional volume has "geodesics" that act like straight lines: they are the shortest distance between points. Gallilean relativity says things move in a straight line unless acted on by an external force. Einsteinian relativity says things move in a geodesic unless acted on by an external force. Since we are used to "thinking in straight lines", when we see things move on a geodesic that is not a straight line, we interpret it as a force. For normal experience it doesn't matter which "model" you use but very precise experiments indicate that the "curved geodesic" model works better than the "force" model.

You might get better answers by putting this in the "special and general relativity forum".
--

Thank you!

 

[selfAdjoint]

First think of the surface of the earth. Geometry suggests that "The shortest distance between two points is a straight line". But this isn't true on the surface of the Earth because it is curved. Instead the shortest distance is an arc of a great circle (a circle whose center is at the center of the Earth - I am asuming a perfect sphere here for simplicity). You probably know that airliners follow a great circle course on long distance flights. The great circles are the geodesic on the surface of the earth. The air currents of the world atmosphere also follow great circle paths - or would if it weren't for the coriolis force.

Now imagine another surface, the inside of a whirlpool. Sort of a cone with an exta trumpet shape curvature. If you tried to go from one point to another staying on this surface, you would have to go around the curvature. And you might have to go right aroung the eye of the whirlpool in a circle. This would be another geodesic, the quickest way from one point to another, within this geometry. If you drop a bit of paper into the eddy, is will folow such a curve because a geodesic is the least energy curve.

Now step up in imagination to four dimensional spacetime - one time dimension and the usual three space dimensions. We can't imagine this being curved, we can't visualize it. But we can see the results in the movement of ordinary things. You drop your phone and it follows a bit of a radius toward the center of the earth. If on the other hand you had thrown it as far as you could, it would follow an arc, another path. Leaving out the atmospheric effects, once you drop or throw it, there will be no forces acting on it until it hits the ground. So the set of points the phone passes throug, with the times it passes through them, make a curve in spacetime, and in both cases that curve is a geodesic wending through the geometry resulting from the Earth's gravity.

Some geodesics make orbits - the thrown phone was briefly in orbit. Other geodesics are the ones light moves along. They have a special name and special physics, NULL geodesics. But in spite of the special physics, they are still geodesics.

 

[R0man]

Hello there,

I am not an expert in physics, but I will try my best to break down the explanation given by HallsofIvy.

First, let's define some terms. Geodesics are the shortest distance between two points on a curved surface. In this case, the curved surface is the space-time that is warped by massive objects like the sun and the Earth. Gallilean relativity is the concept that objects move in a straight line unless acted upon by an external force. Einsteinian relativity, on the other hand, states that objects move along geodesics unless acted upon by an external force.

Now, let's apply this to the example of dropping a cell phone on Earth. When the cell phone is dropped, it follows a geodesic, which is the shortest distance between the starting point (your hand) and the end point (the ground). However, because the Earth's mass warps the space-time around it, the geodesic that the cell phone follows is not a straight line, but a curved one. This is what we interpret as gravity - the cell phone appears to be pulled towards the Earth, but in reality, it is just following a curved geodesic.

The reason why we are more familiar with the concept of forces is because we are used to thinking in straight lines. But when it comes to very precise experiments, the curved geodesic model of gravity works better than the force model.

I hope this helps to clarify the explanation given by HallsofIvy. If you have any further questions, I would recommend posting in a forum specifically for special and general relativity, as suggested by HallsofIvy. They will be able to provide more in-depth and accurate explanations.