Why is the earth's gravity easy to feel and measure but the curvature of space caused by earth's gravity is way too small to observe?

Question

General relativity says gravity is due to a curvature of space. The non-Euclidean geometry of space around earth is much too slight to measure. So why is the effect of gravity so noticeable?

Answer 1

It can be easily understood - unfortunately using a very hard equation. The way to resolve this is to understand under what conditions general relativity approximates Newtonian gravity.



As it turns out, you can approximate Newtonian gravity from general relativity when fields are weak and fr LOW velocities. The observed ‘acceleration’ of gravity depends not only on the strength of gravity but also depends on the velocity of the object in the field. If we assume a weak field such as the gravity of earth, then the earth Newtonian approximation depends depends mostl on the components of the 4-velocity of an object. The 4-velocity is the spacetime version of regular velocity but has an additional component of velocity in the time direction. If the three components of space velocity are small compared to the speed of light, then the time component of the objects velocity will be really large. So, the contribution to acceleration from the space components of gravity (spatial curvature) is negligible for low spatial velocities - the vast majority of the acceleration on earth comes the time effects of gravity since the component of time velocity is so much greater (near ‘c’).



As I said, the actual equation is quite difficult but I will update my answer with the equation (and explanation) if you request it. You will need calculus and differential equations at a minimum to understand it ...

Answer 2

"curvature of space" should be "curvature of space-time"



The deviation from Euclidean space-time geometry is a small effect but can be measured using atomic clocks in airplanes or satellites. First done in 1971 - see link.

Answer 3

The entire mass of the planet is needed to keep you stuck to the ground, yet you can easily pick up some objects with a relatively weak fridge magnet against the entire gravity of the Earth. So the spacetime curvature produced by the Earth is weak, despite it being so all-encompassing to our lives on this planet.

Answer 4

Gravity is not the curvature of SPACE but the curvature of SPACETIME. There is a big difference! And the curvature of spacetime is easy to feel and measure, it's gravity! That being said, gravity is a relatively weak effect when comparing with say electrostatic forces. Some small pieces of paper are easily drawn up by a rubbing-charged ballpoint pen. Not even a whole massive Earth can hold them on the table!

Answer 5

Gravity is NOT CAUSED by the curvature of space time. FALSE PREMISES and CIRCULAR LOGIC. Gravity is caused by MASS,. and Earth has a LOT of mass.



Because the ACCELERATION of gravity on Earth is an average of 9.81 meters per second squared or 32 feet per second squared., but the curvature of the horizon is VERY VERY SMALL because Earth's radius and diameter is SO LARGE.. The Higher above the ground your eye level is, the more the curvature of the horizon but the DISTANCE TO the horizon is INCREASES. The horizon is about 3.1 miles away at ground levl. Earth is HUGE. compared to the hight of human being at ground level.. I could see the curvature of the horizon from Pikes Pead looking east when i was 20 or 11 years old, and i could see it from DC-# planes, but you HAVE to look closely. The curvature of the horizon is NOT OBVIOUS., because the Earth SO BIG in comparison to your eye level hight. not everyone is 6 feet

tall. My horizon will be closer to me than YOUR horizon probably will be because I less than 5 feet tall. At my

tallest was only 5/8 f inch over 5 feet...



https://en.wikipedia.org/wiki/Horizon



"...For an observer on the ground with eye level at h = 5 ft 7 in (1.70 m), the horizon is at a distance of 2.9 miles (4.7 km). For an observer standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 12.2 miles (19.6 km)...."



https://en.wikipedia.org/wiki/Horizon



When you trip and fall or fall down a flight of stirs you are falling at rate of almost 10 METERS or 32 feet EVERY second.SQUARED. You are ACCELERATING, your velocity INCREASING BECAUSE OF EARTH'S MASS, NOT the CURVATURE OF SPACE TIME.





The curvature of Earth's horizon IS visible AND MEASURABLE. If you don't pay attention to details and small differences. that just means YOU are not very observant, because the curvature of the horizon IS visibleIF the horizon is NOT BLOCKED, which it frequently is.