In 1916 Albert Einstein put forward his theory of gravity called General Relativity. In this theory Einstein assumes that the effects of gravity can be described in terms of the curvature of space and time together. This hybrid 4-D space, upon which Einstein formulated his theory, is called spacetime. There are three dimensions of space in the four-dimensional spacetime combined with one dimension of time. In General Relativity Einstein links the curvature of spacetime with the way matter and energy are distributed in the universe. One can summarize the coupled arrangement between matter and spacetime curvature in Einstein's gravity theory by the following statements: Mass (the source of the gravitational field) tells spacetime how to curve. Spacetime tells matter (any massive body besides the source mass) how to move. Before Einstein's radical proposal about spacetime, space was thought of as an unchanging stage upon which all the motions and interactions of matter were played out. Space was like a tabletop upon which transactions occurred independently of the structure and layout of the table. Einstein's ideas however implied that space was highly changeable. It was like a flexible material that accommodated every massive object by curving appropriately in the local vicinity of the object, much like a stretched sheet of General Relativity http://cosmology.uwinnipeg.ca/Cosmology/general_relativity.htm (1 of 21) [03/06/2002 10:51:48 AM]
Transcript
In 1916 AlbertEinstein putforward his theoryof gravity calledGeneral Relativity.In this theoryEinstein assumesthat the effects ofgravity can bedescribed in termsof the curvature ofspace and timetogether. Thishybrid 4-D space,upon whichEinstein formulatedhis theory, is calledspacetime. Thereare threedimensions ofspace in thefour-dimensionalspacetimecombined with onedimension of time.In GeneralRelativity Einsteinlinks the curvatureof spacetime withthe way matter andenergy aredistributed in theuniverse.
One can summarize the coupled arrangement between matter andspacetime curvature in Einstein's gravity theory by the following statements:
Mass (the source of the gravitational field) tells spacetime how tocurve.Spacetime tells matter (any massive body besides the source mass) how to move.
Before Einstein's radical proposal about spacetime, space was thought of asan unchanging stage upon which all the motions and interactions of matterwere played out. Space was like a tabletop upon which transactionsoccurred independently of the structure and layout of the table. Einstein'sideas however implied that space was highly changeable. It was like aflexible material that accommodated every massive object by curvingappropriately in the local vicinity of the object, much like a stretched sheet of
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elastic material would accommodate itself to a heavy ball placed on itscenter area.
Curved space is understandable by means of these analogies, butwhat does curved time mean? Curved time means that the rate offlow of time is determined by the strength of the gravitational fieldwhere it is being measured. Time passes more slowly in stronggravitational fields. Time is stretched out.
Einstein arrived at the idea that curvature is gravity by thinkingdeeply about local effects of gravity versus global effects ofgravity. He deduced that we can always find a small piece ofspace where gravity is locally zero. However, globally, gravity isanything but zero. This local-global contrast led Einstein naturallyto the idea that curvature and gravity were linked. Curvature hasthe same local-global character as gravity.
Consider the followingstatements and think aboutwhat the similarity is.Look at anycurved surfacein a smallenough regionand you willsee nocurvature.
Get into theright frame ofreference, thatof a free fallsituation andyou will feel nogravity.
In 1908 Einstein had what helater called 'the happiest thoughtof his life'. He had heard of ahouse painter falling from theroof of a house. Einstein thoughtabout what the painter had saidabout the fall after it hadhappened. The painter hadexperienced no negativerepercussions while falling. Hehad said that he just feltweightless. Only when thepainter had hit the ground did heexperience anything of anegative nature. In the fallingstate, in effect, there was nogravitational field. This 'nogravity' state can bedemonstrated in a similarsituation with the dropping ofsome objects while you are
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falling. What you discover in thisexperiment is that the droppedobjects do not fall. They stayright with you, as if nogravitational field existed at all.In a freely falling state (oralternatively, and equivalently, ina freely floating state) gravity isabolished.
Click on the skydiving ('free float') picture to make it bigger.
What is the safest way to free float? The safest way is to getyourself into orbit around the Earth. Then you are moving forwardwith a certain speed while you are directly falling in towards theEarth. The moving forward and the moving inwards compensateeach other such that you continuously encircle the curved Earthsurface. You are continuously falling but you never hit the ground.
In any free-float situation, such as that in a freely fallingspaceship, the paths of objects will never bend in any directionwhen they are given a certain speed. These objects will move incompletely straight lines.
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Any object - a coin, a key, or a ball - follows a straight trackin a free-float spaceship.
As soon as the spaceship lands, and is not in a freelyfalling frame anymore, a big difference occurs.Throwing the objects away from you now makes theobjects travel in a curved path towards the floor.
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When the Earth (or a rocket) pushes on the spaceship, the trackscurve relative to the spaceship.
Question: What is the most natural situation? Why does thecurved path suddenly appear when the spaceship lands on theEarth? Is there some mysterious force that causes the curvedpath of the released objects?
From the Greeks to Galileo to Newton, the best thinkers of the daytried to describe the force that made objects move in this way.Einstein brought a revolutionary point of view to the solution ofthe problem. Einstein said that there was no gravity force curvingthe path of the objects. Einstein also said that the composition ofthe objects had nothing to do with the curves. The curved path isthe fault of the floor that forces us and all other objects away fromthe natural state of motion, the state of free float. Theelectromagnetic forces between the atoms in the floor pushupwards, stopping our downward natural motion. This upwardsforce makes us feel heavy.
Let the room be cut away at the moment that we (who are in the room) throw the ball. The ballwill pass through the same space as before. The same ball thrown in the same direction withthe same speed appears to move quite differently when it is not in free float (left), and when itis (right). Yet in the two pictures, the ball arrives after the same time at the same location inspacetime.
The ball appears to move in the familiar curvedpath which we have come to view (since thetime of Newton) as the effect of a gravitationalforce directed towards the center of the Earth.
With the platform severed from its attachmentto the Earth, the small house is in a free-fallsituation. This time the ball will move in astraight line, unaffected by any so-called'gravity' force.
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Einstein recognized that falling is an illusion. The illusion arises fromlooking at motion from a reference frame (the room at the left) that is notin free float. The thing that keeps us from the free-float condition is theelectromagnetic forces from the atoms in the floor pushing up on ourfeet. We, who stand securely, see things the wrong way around becausethe ground beneath our feet is all the time pushing us away from a naturalstate. This natural state is a state of motion equivalent to free falling orfree floating.
To be in tune with the universe weshould be freely surfing thespacetime curvature just as theMarvel Comics superhero SilverSurfer freely surfed through hisspace.
click to make bigger
The perverse way that Einstein wants us to view gravity is summed up by the following poem written by a 15year old girl (Frances Ruml, granddaughter of the gravityexpert John A. Wheeler).
What’s the fault of the force on my feet?
What pushes my feet down on the floor?
Says Newton, the fault’s at the Earth’s core.
Einstein says, the fault’s with the floor;
Remove that and gravity’s beat.
What first strikes us about the concept of free float is its paradoxicalcharacter. As a first step to explaining gravity, Einstein got rid of gravity!
The second feature that is evident to us is the local character of the free floatframe. Free falling rooms at different locations above the surface of the Earthcan be 'falling' in completely different directions. Free fall here and free fallthere are not the same. The concept only applies within a limited localregion. A way of measuring spacetime curvature is to look at the differencebetween nearby free-fall frames. The bigger the difference , the bigger will bethe gravitational curvature. If we lay down postage stamps on a largespherical object, sooner or later we will notice discrepancies in the coveringof the curved surface. Similarly if we jump into free fall frames all around amassive object, sooner or later we will notice discrepancies in the motion ofobjects in nearby frames.
An example of curvature becoming evident concerns the use of grids tomark out parcels of land on the Earth's surface by geographers. Eventuallythe grids will not be adjacent to each other and the grid system will not bewithheld. See the picture below of the grid areas (ten-mile-square townships)
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laid down in the flat prairie land of North Dakota. Click the picture to make itlarger. Even though the grid areas start off nicely lined up, it does not takelong for the curved surface of the Earth to mess up the alignment.
Principle of EquivalenceThe idea that a free fall frame is possible for any object leads toone of the strongest predictions of Einstein's theory. If all objectsfeel no force when they achieve a free float state then thecomposition of materials will never be important for gravitation. Ifsomething is in free fall, and it has no weight, then it can donothing else but float. A zero weight of gold is just the same as azero weight of feathers. They both should float weightless atexactly the same height in a free fall frame. The principle that saysthat all objects, no matter what their compositions, fall or float inexactly the same way is called the Principle of Equivalence. Thisprinciple also has another form that equates acceleration withgravity. It is not possible to distinguish, in a small region ofspacetime, the difference between the acceleration of an objectand the existence of traditionally postulated gravitational force.
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It is easy to visualize curvature of space caused by massive bodies. Onethinks of objects sunken into the space.
However it is not so easy to think of curvature of the hybrid space callspacetime. What does curvature of spacetime look like? To get an idea ofwhat this means we consider a simple experiment where two balls arethrown across a room. Click here to see the details of the experiment.
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Energy, by the above formula,must act like a mass. Hencespacetime should tell lightrayshow to move. This is the crucialdeduction that leads to one of theclassic tests of general relativityhaving to do with the bending oflight by stars.
The bending of light is seen everyday by astronomers. It ispossible for intervening massive galaxies to bend the light of evenmore far-off galaxies in such a way that multiple images of thefar-off galaxies are produced. This effect is called a gravitationallens.
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The collection of galaxies in the middle of the picturerepresents such a bending of spacetime that images ofgalaxies behind the collection are multiplied. These multipleimages of the same extremely distant galaxy are shownencircling the central mass collection.
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General Relativistic Predictions
The Four Standard TestsTime Slows Down Near Massive Objects. Scientists use radar to bounce off planets andsatellites to check for this slowing down effect. The diagram below shows a radar beam sentto Mars and reflected there being curved by the Sun's gravitational field. This extra curveddistance, that the radar beam has to go through, delays the signal. This delay can bemeasured. It agrees with GR's prediction.
Light bends around stars. Thisbending can be measured. The firstmeasurement that confirmedEinstein's prediction took place in1919. Scientists wait for the moon toblock the Sun and then look for starsthat should not be observable unlesstheir light has been bent to come inour direction.
Light Bending video 1
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Another example of light bending by gravitational field is the gravitational lens effectdiscussed earlier. Below is a picture of a multiple Quasar image (4 images surrounding adense galaxy). This image is only seeable in the Southern Hemisphere. It has been named the'Einstein Cross'.
Orbits of all planets get disturbed with Mercury having the biggest disturbance. Most of thedisturbance is due to the natural disturbance induced by the other eight planets. However alittle bit that is measurable is due to general relativity's prediction that space is curvedaround the Sun. Click here to see a movie of the precession effect of spacetime curvature ona planet.
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Light gets dragged back when light isclose to massive objects such asstars (called the gravitational redshifteffect). This forces the wavelength ofthe escaping light to stretch. Thisstretch results in the light wavegetting more in the direction of thered end of the electromagneticspectrum. It is therefore said to bered-shifted.See The Spacetime Wrinkles Site for more pictures : Click Here.
BLACK HOLES
Black holes form when matter accumulates in a smallregion of space. This can happen at the center ofgalaxies such as our own galaxy the Milky Way (whichhas a central 3 million solar mass black hole), or it canhappen when a huge star dies and does not throw offmost of its mass when it collapses near the end of itsexistence. This latter type of black hole requires thatthe star have at least three times the mass of the Sunbefore it will have sufficient gravity to completely traplight.
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One of theweirdestpredictions ofGeneral Relativityinvolves the ideaofsuper-collapsedgigantic stars thatcollapse so muchthat a tear in thespacetime fabricis created. Lightand nothing elseis able to escapefrom thesegravitationallysupreme objects.The puncture inthe spacetimecontinuum iscalled asingularity.
Black Holes have aninterior region that cannotbe observed. The boundarybetween where light canpotentially escape andwhere light and nothingelse, can escape is calledthe Event Horizon. The factthat a singularity exists atthe center of a black holeimplies that the Einsteinequations are incompletethere. The radius of theevent horizon is called theSchwarzschild Radius.
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Since the collapsed starsthat they are formed fromare rotating, most blackholes should also berotating. Rotating blackholes are called Kerr BlackHoles. The picture to theleft shows such a rotatingblack hole with a jet ofparticles coming out of itscentral region.Astrophysical objects havebeen observed with suchhigh energy jets. Nodefinitive proof existshowever that black holesexist. They are alwaysinferred from indirectevidence such as theradiation released whencharged particles fall intothe black hole. Justbecause a jet comes outfrom the center region ofthe black hole doesn'tmean that the black hole isemitting these particles.The jet phenomenon arisesfrom too many particlestrying to get into therelatively small eventhorizon of the black hole.So many things try to get inthat some are energeticallyflung out from the centerby the intense pressureclose to the mouth of theblack hole.
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Some people speculated in the past that the black hole might be away of traveling to another universe or to another part of thisuniverse. However, it can be shown that black holes pinch off assoon as you continue down their throats. All matter that passesinside a black hole gets crushed into nonexistence.
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The violent deaths of large stars (supernovas) and thecollisions of extremely dense stars such as neutron starswith each other can cause spacetime disturbances tohappen and to spread out in a wavelike manner. Thesewaves are called gravity waves or gravitational radiation.Within the next five years gravitational radiation should beseen for the first time.
Below is an example of a supernova induced spacetime wave disturbance. This disturbance can bedetected by placing two masses side by side and observing any change in their relative positionswhen a gravitational wave passes by. Does the distance between them stretch or compress? Theanswer has to be very high resolution since the effect is so very small. Lasers are used to opticallydeduce the minute distances that the gravity waves make the two masses travel.
Recently there has been serious scientific discussion of theidea of warp drive to boost spaceships to apparent speedsconsiderably in excess of the speed of light. No known wayof actually doing this exists at the moment, but theoreticallyit's not too hard to see how it might work.
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As the diagram shows, what one needs to do is tocompress the spacetime in front of the ship whileexpanding the spacetime in the rear of the ship. The overalleffect of doing this would be to warp space in front of theship so much that the distance between where the sip isnow and where it wants to be is lessened. Then, althoughlocally the ship is always traveling less than the speed oflight, the global transport is in effect much faster than thespeed of light. The captain of such a spaceship would haveto keep well away from other ships and communities whilethe ship was in warp drive mode since much damage couldbe done to anyone nearby.
The idea that global situations are quite different from localsituations runs deeply through everything in cosmology andespecially in general relativity. You have to be very careful whenmaking statements about the universe. Humans live only in aninsignificant piece of the overall universe. We have also only livedin this universe for a negligible amount of time. Yet we can makedeductions about regions that we can never hope to reach andtimes that we can never hope to find out about in a local way.
As an example of a local versus global tension, much like thatrunning through general relativity, consider the drawing by M.Escher, a famous 20th century Dutch artist. Below we see a pieceof that drawing. Although it is somewhat otherworldly, theenvironment portrayed seems to follow rules similar to what weare familiar with. This world is however far stranger than what isshown.
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Click on this picture to see what the global situation is like.
The Einstein Gravitational Field Equation is shown below. This equationstates that the spacetime curvature of anyplace in the universe (left-handside of the equation) must be equal to the distribution of matter andenergy in that part of the universe (right-hand side of the equation).
It is this equation that was 50 years ahead of its time when Einstein put
forward his general theory of relativity in 1916.
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