Time is a relative quantity. As indicated by Einstein in his special theory of relativity, t’=t√(1-(V2/C2)) where t’ is time elapsed for person moving at velocity V and t is time elapsed for person at rest, in a particular frame of reference of ‘course. This has been verified over and over by putting synchronized highly accurate Cesium atom clock on a fast moving aircraft and then comparing its reading with the other clock at rest. For a person moving at speed of light C, time will completely stop, while everybody else moving at normal speed will continue to age normally. When the person moving at light speed stops, he will find himself in future having not aged at all. If the person keeps moving at speed of light, he will be immortal. Of ‘course nothing that has mass can reach speed of light, no matter how much energy you supply it. The faster a massive object gets the more its relativistic mass as E=MC2/√(1-(V2/C2)) where M is rest mass and C is constant, and therefore more and more energy is needed to accelerate it. Infinite amount of energy will be required to reach light speed. It was proven by MIT’s Bill Bertozzi when he accelerated electrons and measured their kinetic energy. We can’t accelerate massive objects to light speed yet but we can get very close to it at the cost of an enormous amount of energy. A person moving close to light speed will still find himself years into future when he stops. By one estimate you would be 500 years into future if you move at 99.99% of light speed for 7 years. Astronauts who have taken rocket trips have already traveled into future by fractions of a second, yes only by that much because speed of a rocket is nowhere close to light speed. So, is time travel really possible? Turns out Yes! In fact it’s already been done, on numerous occasions, to the future at least. Russian cosmonaut Gennady Ivanovich Padalka has spent 879 days in space moving at great speed. This has taken him a fraction of a second into future because in his case, the relative speed up in passage of time due to weaker gravity is less compared to the slow down caused by high speed. Particles such as Pi Mesons have a very short lifespan of millionth of a second which increases spectacularly when they are accelerated to near light speed. “Particle accelerators are closest thing we have to a time machine” says Stephen Hawking. LHC at CERN can accelerate particles to 99.9999991% of light speed transporting them into future on a regular basis. Such an accelerator suitable enough for humans can one day help us travel into future, once the technical limitations are overcome.
Einstein’s general relativity theory suggests that time gets slower in stronger gravitational fields. Time passes at much slower rate near black holes than it does near Earth. By one estimate, if the remnant core of a supernova explosion is heavier than 2.37 Solar mass, then not even Neutron degeneracy pressure will hold against Gravity, resulting in collapse of the core, giving birth to a singularity. The collapsed core because of its enormous mass density, creates a dark sphere of influence all around it by warping spacetime around, to extremes. This dark sphere of influence is known as Black Hole. Dark because it doesn't gives out energy, at least not in amounts that can be detected by current technology. There is no other object in known Universe that creates as strong gravitational effect as the one that causes black hole. Einstein's field equations predict the manner in which local mass-energy and momentum surrounded by local space-time affects the curvature of that space-time. Both spinning and non spinning black hole mass density warps space-time with its presence, creating extremely deep curves in spacetime around the Black Hole, making a near by wave of light to travel much greater distance to pass through the surrounding regions of the dark sphere as the comparatively straighter spacetime light was moving along, turns into a deep geodesic near it. Presence of mass-energy density turns parallel straight path along relatively flat spacetime into nearing geodesics around it. Path would be relatively straight in absence of mass-energy density. But, the speed of light still remains same. This increases the time taken by it to pass through that region, as observed by someone standing out of that region. But for a person standing inside that sphere of influence, no time delay will be observed because in that region same thing happens to every other moving entity, no matter how infinitesimally small it is. Every movement, every cycle, takes longer to complete because space-time itself has been stretched. Everything slows down in there, including a person's bioclock, the person himself wouldn't notice it though. Imagine you and your friend have synchronized Cesium atom watches and you travel to a black hole while your friend stays on Earth. Somehow its possible for you to see your friends watch and vice versa. While you go around the #Blackhole in a stable orbit, your friend will observe that second's hand on your watch is taking hours may be even days to tick but you will observe that it ticks at normal rate of 1 second per tick. On the other hand, when you look at your friend's watch, the second's arm will be rotating at speeds greater than that of a ceiling fan while for your friend, the ticking rate stays at 1 second per tick. These predictions of Einstein's general relativity has been verified by data obtained from Cassini-Huygens probe experiment.
A spinning black hole, twists the space-time around it as well, apart from warping it and most of the black holes present in universe are of spinning type. They twist and distort the space-time creating an Ergo-sphere with oblate spheroidal shape in case of a low spin central mass, around the event horizon touching it at poles. In that ergo-sphere, objects cannot be observed as stationary with respect to rest of universe as that would require the object to be moving faster than speed of light. There, things can easily go along the spin but they will require far greater energies to go against it as they will be dragged alongside the twisting space-time. Space is elastic and interconnected as predicted by field equations of #Einstein. It can inflate, it can warp, it can twist, it can warp and twist simultaneously due to mass-energy influence and it can return back to its normal geometry once that mass-energy influence goes away. Twisting of space-time by spinning objects has been named frame dragging. It was derived from field equations of general relativity by Josef Lense and Hans Thirring and is also known as Lense-Thirring effect. The theory predicts that inner regions will be dragged faster than outer regions. Earth also twists and distorts space-time continuously by a very small amount, verified by Gravity probe B experiment. Lense-Thirring effect also predicts that an object constrained in an equatorial orbit, but not in free-fall will weigh lesser while moving along the spin and will weigh more while moving against it.
Gravity is proportional to warping of space-time geometry. Warping of space-time formed by Earth is nothing compared to the warping caused by a black hole. Time on Earth's surface, where Earth's gravity is stronger, passes at a slightly slower rate than it does in orbit around it. This is the reason why GPS clocks have to be compensated to match Earth time. GPS Satellites move at 3874 m/s relative to Earth's center, making their clocks get slower by about 7200 ns/day compared to Earth clocks, yet due to gravitational time dilation, those clocks get ahead by about 45900 ns/day, which gives us a figure of ahead by 38700 ns/day which is consistent with practical observations. Time dilation caused by a height difference of less than a meter has been verified in laboratories around the world using highly precise Cesium atom clocks. Due to curved space, the cycles take longer to complete. Greater the curvature longer it will take the cycle to complete and hence lesser will be the frequency of the wave. So a light wave passing through high gravity field will appear redder to a person standing outside that field or in weaker gravity field, and this is exactly what we see in observations. This phenomena has been named Gravitational red shift. As predicted by field equations of general relativity theory, light or any other object moves along the curvature of space-time, which could be close, open or flat. When light passes through nearby regions of mass-energy density, its path changes as it moves from a relatively flatter curvature to a more bent curvature, causing lensing. This is yet another prediction of general relativity named gravitational lensing. When images are formed with this light, the lensing effect shows up clearly. Arthur Eddington was the first to observe and measure the extent of lensing caused by celestial bodies and found the results to be in close proximity to figure predicted by Einstein's field equations of general relativity, thus verifying the theory in 1919. But it was not until the 1960's when radio frequency observatories started to come up that the observed values started to get extremely close to figure predicted by Einstein's theory. Since dark matter has far greater presence in Universe than normal matter, the extent of lensing gives us an indirect measure of amount of dark matter present in that locality. People spending time in much stronger gravitational fields may find themselves years into the future on returning to Earth. Gravity stretches space, brings geodesics closer and since time is relative, this affects time as well, even though the co-ordinates of time are different from the co-ordinates of space as indicated in Einstein's field equations. Closer the geodesics are brought by warping, stronger will be the gravitational field intensity. The field equation is usually written as
Karl Schwarzschild came up with first exact solution of field equations. Schwarzschild radius is the radius of non spinning black hole, equation for which was given by him as
Rs=(2GM)/c2
Here G is the gravitational constant whose value is 6.67408*10-11 in SI units, M is the mass of object and c is speed of light in vacuum. Any mass density with radius smaller than its Schwarzschild radius will collapse under its own gravity creating a black hole around it. Anything that gets into the black hole will not be able to escape the gravity well no matter how much energy it burns, as predicted by the theory. Black Holes are dark spheres with radius Rs caused by a Planck length mass density, a singularity. Schwarzschild also gave the equation for calculating gravitational time dilation due to non spinning energy density (celestial bodies), which can be written as
tr/t=√(1-(rs/r))
where, tr=elapsed time for an observer at radial coordinate "r" within the gravitational field t=elapsed time for an observer standing outside the gravitational field rs=Schwarzschild radius of the energy density or object r=radial coordinate of the observer from the gravitating object Using this equation you can calculate the figures for your time travel to future, yourself. When technology becomes sufficiently advanced and it becomes possible to take a trip to a black hole, a person taking his ship near a #Blackhole and spending a few months there may find himself 100s of years into future on returning to Earth, because super gravity of black hole will slow time down for him while time on Earth will continue to pass at much faster rate due to Earth’s much weaker gravity.
Einstein’s general relativity also predicts a worm hole. These are conduits across space-time that forms for a very short while and then pinches off before anything can pass through because of pile up of quantum mechanical fluctuations of radiation called vacuum fluctuations which become infinitely energetic and explode, but in that short while it may be connecting two extremely distant regions in space and time, forming a shortcut between them. If the worm hole can be stabilized it may make it possible to travel to far regions of space which would otherwise take 1000’s of years to reach. Conditions have been found within general relativity which allows worm holes to be used as a time machine to the past. Physicists have argued that negative matter will be needed to stabilize a worm hole. Negative matter is non-baryonic and has opposite properties to normal matter. If normal matter is represented as 2kg then negative matter will be represented as -2kg. It has not been detected yet although efforts are underway.
Negative matter could also make it possible to travel at faster than light as Miguel Alcubierre suggests. He tells us that a spaceship could travel faster than light by contracting space in front and expanding it behind, creating a warp bubble or Alcubierre warp drive. It's something like a dust particle riding a ripple on a sheet of fabric. Metric suggested by Alcubierre is mathematically valid but it requires negative energy density to make sense, which means it requires negative matter. We haven’t detected the presence of negative matter yet. That’s a problem we need to solve before this becomes a possible means of time travel, even remotely.
Special theory of relativity allows for a hypothetical particle with imaginary rest mass. Such a particle is called a Tachyon. E=MC2/√(1-(V2/C2)), for imaginary rest mass the denominator must be imaginary and for that V must be greater than C. Therefore Tachyons will always travel faster than light. If ever detected, these particles could provide a means to send communication back in one’s past. A device which would make that happen has been named Tachyonic Antitelephone. As for paradoxes involving traveling to past, it is been argued that nature always finds a way to stay self consistent.
Galaxy's flat rotation curve corroborated by the observations from the Radio Telescope in Puerto Rico, accelerating expansion rate of Universe and the data from Wilkinson Microwave Anisotropy Probe (WMAP) and Planck space observatory has given us the standard model of Astronomy. Universe is composed of- 4.9% Baryonic matter or matter made of atoms, 26.8% Dark matter or non baryonic matter and 68.3% Dark energy. These figures may get better with improved data from future missions and deeper analysis. Nobody has detected either Dark matter or Dark energy yet. We know Dark Energy is out there causing the accelerating expansion of space-time around us and Dark Matter from the flat rotation curve of Galaxies. Who knows what secrets lie ahead or what doors might open? But one thing is certain, the future is full of mind warping possibilities. Theories of relativity and Quantum mechanics is about how much we know so far about reality and with String theory, Quantum gravity and Quantum cosmology, we continue our relentless effort to grow our awareness of reality. References: 1) http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf 2) https://arxiv.org/ftp/arxiv/papers/1002/1002.4154.pdf 3) https://www.its.caltech.edu/~kip/index.html/PubScans/VI-47.pdf 4) http://www.hawking.org.uk/space-and-time-warps.html 5) http://cse.ssl.berkeley.edu/bmendez/html/time.html
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Einstein’s general relativity theory suggests that time gets slower in stronger gravitational fields. Time passes at much slower rate near black holes than it does near Earth. By one estimate, if the remnant core of a supernova explosion is heavier than 2.37 Solar mass, then not even Neutron degeneracy pressure will hold against Gravity, resulting in collapse of the core, giving birth to a singularity. The collapsed core because of its enormous mass density, creates a dark sphere of influence all around it by warping spacetime around, to extremes. This dark sphere of influence is known as Black Hole. Dark because it doesn't gives out energy, at least not in amounts that can be detected by current technology. There is no other object in known Universe that creates as strong gravitational effect as the one that causes black hole. Einstein's field equations predict the manner in which local mass-energy and momentum surrounded by local space-time affects the curvature of that space-time. Both spinning and non spinning black hole mass density warps space-time with its presence, creating extremely deep curves in spacetime around the Black Hole, making a near by wave of light to travel much greater distance to pass through the surrounding regions of the dark sphere as the comparatively straighter spacetime light was moving along, turns into a deep geodesic near it. Presence of mass-energy density turns parallel straight path along relatively flat spacetime into nearing geodesics around it. Path would be relatively straight in absence of mass-energy density. But, the speed of light still remains same. This increases the time taken by it to pass through that region, as observed by someone standing out of that region. But for a person standing inside that sphere of influence, no time delay will be observed because in that region same thing happens to every other moving entity, no matter how infinitesimally small it is. Every movement, every cycle, takes longer to complete because space-time itself has been stretched. Everything slows down in there, including a person's bioclock, the person himself wouldn't notice it though. Imagine you and your friend have synchronized Cesium atom watches and you travel to a black hole while your friend stays on Earth. Somehow its possible for you to see your friends watch and vice versa. While you go around the 
is the Ricci curvature tensor, 
is the scalar curvature, 
is the metric tensor, 
is the cosmological constant, 
is Newton's gravitational constant, 
is the speed of light in vacuum, and 
is the stress–energy tensor.
Einstein’s general relativity also predicts a worm hole. These are conduits across space-time that forms for a very short while and then pinches off before anything can pass through because of pile up of quantum mechanical fluctuations of radiation called vacuum fluctuations which become infinitely energetic and explode, but in that short while it may be connecting two extremely distant regions in space and time, forming a shortcut between them. If the worm hole can be stabilized it may make it possible to travel to far regions of space which would otherwise take 1000’s of years to reach. Conditions have been found within general relativity which allows worm holes to be used as a time machine to the past. Physicists have argued that negative matter will be needed to stabilize a worm hole. Negative matter is non-baryonic and has opposite properties to normal matter. If normal matter is represented as 2kg then negative matter will be represented as -2kg. It has not been detected yet although efforts are underway.