# Einsteins relativity gravity and acceleration relationship

### Einstein's Pathway

Einstein's general theory of relativity has an unusual answer to that question Overall, gravity is intimately connected with the geometry of space and time. This accelerated observer feels as heavy as we would feel on earth, since In the plane, as on paper, the shortest connection between two points is a straight line. Einstein felt a compelling need to generalize the principle of relativity from inertial He was transfixed by the ability of acceleration to mimic gravity and by the . He now imagined a uniformly accelerated observer, in relation to whom all free. General relativity was Einstein's theory of gravity, published in , which extended special relativity to take into account non-inertial frames of reference.

This was the theory of special relativity. It introduced a new framework for all of physics and proposed new concepts of space and time. Einstein then spent 10 years trying to include acceleration in the theory and published his theory of general relativity in In it, he determined that massive objects cause a distortion in space-time, which is felt as gravity. The tug of gravity Two objects exert a force of attraction on one another known as "gravity.

The force tugging between two bodies depends on how massive each one is and how far apart the two lie. Even as the center of the Earth is pulling you toward it keeping you firmly lodged on the groundyour center of mass is pulling back at the Earth.

But the more massive body barely feels the tug from you, while with your much smaller mass you find yourself firmly rooted thanks to that same force. Yet Newton's laws assume that gravity is an innate force of an object that can act over a distance. Albert Einsteinin his theory of special relativitydetermined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels.

As a result, he found that space and time were interwoven into a single continuum known as space-time. Events that occur at the same time for one observer could occur at different times for another. As he worked out the equations for his general theory of relativity, Einstein realized that massive objects caused a distortion in space-time.

## Einstein's Pathway to General Relativity

Imagine setting a large body in the center of a trampoline. The body would press down into the fabric, causing it to dimple. A marble rolled around the edge would spiral inward toward the body, pulled in much the same way that the gravity of a planet pulls at rocks in space. How To See Spacetime Stretch ] Experimental evidence Although instruments can neither see nor measure space-time, several of the phenomena predicted by its warping have been confirmed. Einstein's Cross is an example of gravitational lensing.

### Equivalence principle - Wikipedia

Light around a massive object, such as a black hole, is bent, causing it to act as a lens for the things that lie behind it. Astronomers routinely use this method to study stars and galaxies behind massive objects. Einstein's Cross, a quasar in the Pegasus constellationis an excellent example of gravitational lensing.

**Gravity - From Newton to Einstein - The Elegant Universe**

The quasar is about 8 billion light-years from Earth, and sits behind a galaxy that is million light-years away. Four images of the quasar appear around the galaxy because the intense gravity of the galaxy bends the light coming from the quasar.

Gravitational lensing can allow scientists to see some pretty cool things, but until recently, what they spotted around the lens has remained fairly static.

However, since the light traveling around the lens takes a different path, each traveling over a different amount of time, scientists were able to observe a supernova occur four different times as it was magnified by a massive galaxy. But there is no gravity in this situation. All the observers in freely drifting spaceships rocket engines shut off are in agreement: The fact that the accelerated observer sees objects "fall" is merely an artefact, brought about by his spaceship's acceleration - it vanishes as soon as you leave the accelerated reference frame and change to a free-falling one.

Is the same true for gravity here on earth? Is it an artefact of the unnatural, accelerated reference frame from which we observe the world - and does it vanish as soon as we change to a freely falling reference frame? The remains of gravity In fact, earth's gravity does not vanish completely even in a free-falling reference frame it cannot be "transformed away", as physicists would say.

To see why, have a look at this freely falling elevator of gigantic size, with two freely floating gigantic spheres inside. The following animation shows the elevator falling towards the earth, following our planet's gravitational pull: Under these circumstances, it becomes important to note that bodies falling towards the earth do not all move in the same direction "down" - they move towards one and the same point in space, namely towards the earth's center of gravity.

That is why even an observer inside the falling elevator will see some residual of the earth's gravitational force at work: She doesn't notice the downward pull - after all, she is falling alongside all other objects within the elevator. But she does notice the fact that the distance between the two spheres is shrinking steadily, little by little, over time. The reason for the shrinking distance? The gravitational force pulls the left sphere into a slightly different direction than the right - simply because both spheres get pulled towards the earth's center.

It is this difference in directions that's responsible for the two sphere's decreasing distance, a force difference that physicists call a tidal force. Just such a difference in the moon's gravitational attraction on the earth and on the earth's oceans is responsible for the tides.

Tidal effects become even more drastic when an observer considers falling bodies on opposite sides of the earth. Sure, the falling bodies at his side still float as if there were no gravity at all. But bodies on the opposite side of the earth accelerate towards our observer with twice the usual gravitational acceleration! All this serves to show the difference between an observer on earth and an accelerated observer in gravity-free space: The accelerated observer need simply change his frame of reference - for instance, switch off his rocket engine.

Immediately, what he thought to be a constant "gravitational force" vanishes. Earth's gravity cannot be made to vanish simply by letting go and falling freely. Sure, if we restrict ourselves to a limited observation period in a small, freely falling cabin, we won't notice the difference to floating freely in gravity-free space.

But the larger our elevator, the longer our period of observation, the better are our chances of noticing residual gravity - tidal forces.

### Gravity and Acceleration - Special and General Relativity - The Physics of the Universe

Planes and curved surfaces Oddly enough, this elusiveness of gravity has an analogue in pure mathematics, more specifically: The plane is the simplest of two-dimensional surfaces - like a sheet of paper, but infinitely extended in all directions. In the plane, as on paper, the shortest connection between two points is a straight line.

- Gravity and Acceleration
- Equivalence principle
- Einstein's Theory of General Relativity

Straight lines can be used to construct more complicated geometric objects, such as triangles: The properties of geometric objects obey a set of rigid laws.

For instance, the sum of all the angles of a given triangle will always be degrees, and for triangles with a right angle, Pythagoras' theorem holds true.

A perfect plane is only the simplest example of a surface. From everyday experience, we know of distorted, curved surfaces - say, the surface of a sphere, that of a saddle, or the undulating surface left in the sand when the flood has receeded. On those more general surfaces, the laws of geometry are somewhat different. As an example, take a surface that is, in itself, rather simple: There are no straight lines on a sphere - all one can construct are straightest lines.

## General Relativity

Mathematicians call such lines-that-are-as-straight-as-possible geodesics. In the case of the sphere, they are also called great circlesas they are the largest circles that one can possibly construct on that surface, the best-known example being the equator. The shortest connection between two points on a sphere will always correspond to some part of a suitably chosen great circle.

The following figure shows a sphere as well as, in green, a triangle formed by three intersecting geodesics: The two angles of the triangle that lie along the equator red line are both right angles - they alone add up to degrees. The total sum, which includes the angle that is at the North pole, is evidently larger than degrees. The surplus can, in fact, be used to define a measure for the sphere's curvature and thus for the difference between its geometry and that of a plane.

The elusiveness of curvature But in spite of the differences in geometry, the following still holds: If you look at a tiny region of the sphere's surface, you'll be hard-pressed to find a difference between it and the corresponding region on a plane. In fact, that's what we do every day: We draw city maps, which show a comparatively small part of the earth's surface, just as if the city had the same geometry as that flat sheet of paper we're drawing on: This works quite well, although, in reality, the city region is part not of a gigantic plane, but of the surface of a gigantic sphere, the earth.

Only when you look at larger regions will you notice that the surface is, in fact, curved; the larger the region, the more distinct the signs of curvature.

The same is true for any curved surface: This indistinguishability is exactly analogous to the elusiveness of gravity that has been described above: For a very small spacetime region, say, the elevator of a free-falling observer, gravity is absent.

Over a brief observation period, the interior of the elevator looks as if it were part of the spacetime of special relativity, where there is no gravity at all.

Only in a larger spacetime region, the differences become measurable. Residual gravity, tidal forces come into play.