In this era of smartphones most of us will be familiar with GPS (Global Positioning System).It helps us in position tracking and navigation. But did you ever wonder how GPS works?. GPS was built by the US military and has been fully operational since 1995. Now countries like Russia(GLONASS), China, India(IRNSS-not fully operational) and European union possess their own positioning and navigation systems. GPS uses a lot of complex technologies, but basic concept is simple.
There are three parts for GPS system: A 24 to 32 solar-powered satellites orbiting the earth in orbits at an altitude of approximately 20000 kilometers(24 satellites are operational at a time), a control station and a GPS receivers such as the one in a car or a GPS enabled smartphone.
The Basic principle behind GPS: trilateration
GPS system uses a mathematical principle called trilateration to locate position. The orbits of satellites are designed so that there are always 4-6 satellites in view, from most places on the earth. At least signals from three satellites are needed to carry out trilateration process.
2D illustration of trilateration
Let us assume you are lost some where in Australia. One of your friend in Adelaide told you,you are 650 kms away from him, which means you could be any where on the circle with radius 650 kms and centre Adelaide.
Fig1
like that Another friend from Sydney told you, you are 700 kms away from him. Now you know you are on either point p1 or p2 (marked in below figure).
Fig2
If a third friend told you ,you are 1400 kms from Brisbane ,you can locate your position with respect to three cities. Your position will be intersection point of three circles.(Fig3)
Fig3
This method of locating position is called trilateration. This same concept works in 3 dimension. But , instead of circles you should think in terms of spheres.
Trilateration in 3D space
Assume 3 satellites are visible to your GPS receiver. Name them A,B and C. If you know your distance from A , you could be anywhere on the surface of a huge sphere of that radius.
Fig1
If you know your distance from satellite B you can overlap 1st sphere with 2nd and they intersect in a perfect circle. Now you know you are somewhere on circle.
Fig2
So If you know distance to a third satellite C you got a third sphere which intersects with this circle at to points. And earth acting as fourth sphere ,you can eliminate point in space because you are on earth.
Fig3
If only 3 satellites are available, the GPS receiver can get an approximate position by making the assumption that you are at mean sea level. If you really are at mean sea level, the position will be reasonably accurate. In other words, it requires only 3 satellite to determine latitude and longitude with reasonable accuracy. But calculate altitude you require a fourth satellite. A modern GPS receiver will typically track all of the available satellites simultaneously, but only a selection of them will be used to calculate your position
How GPS receiver determines distance from satellites.
The GPS receiver gets a signal from each GPS satellite. The satellites transmit the exact time the signals are sent. By subtracting the time the signal was transmitted from the time it was received, the GPS can tell how far it is from each satellite. The GPS receiver also knows the exact position in the sky of the satellites, at the moment they sent their signals. So given the travel time of the GPS signals from three satellites and their exact position in the sky, the GPS receiver can determine your position in three dimensions - latitude, longitude and altitude. Distance is calculated by the formula D=(tr - ts)C
tr= time at receiver
ts= time signal from satellite
C=Speed of light
Conventional GPS and A-GPS
Conventional GPS :To determine the location of the GPS satellites two types of data are required by the GPS receiver; the almanac and the ephemeris. This data is continuously transmitted by the GPS satellites and your GPS receiver collects and stores this data. The almanac contains information about the status of the satellites and approximate orbital information. The GPS receiver uses the almanac to calculate which satellites are currently visible. Ephemeris gives very precise information about the orbit of each satellite. Your GPS receiver can use the ephemeris data to calculate the location of a satellite precisely.
A-GPS(assisted GPS):GPS receiver in our cell phones are example of a A-GPS. The A-GPS device will use a data connection (internet connection on a cellphone) to contact an assistance server. The server can supply almanac and ephemeris data so the GPS doesn't have to wait to receive them from the satellites. This improves first locking speed considerably.
Atomic clocks
Atomic clocks are high precision clocks used in scientific applications. Since GPS satellites transmits time signal to the receivers it is important to keep precise timing equipment onboard . Every single GPS satellite is home to a family of atomic clocks (typically four) that derive their time from cesium or rubidium atoms. In these clocks the energy difference between two specific atomic states is measured. When an atom changes from the high-energy state to the lower energy state, the energy difference is emitted in the form of light. The frequency, or ticking rate, of this light is what we count and how we define time. This energy difference is always the same. These clocks are so precise that it won’t lose a second for 15 billion years.
Though GPS satellites have atomic clocks that keep very precise time, it's not feasible to equip a GPS receiver with an atomic clock. However, if the GPS receiver uses the signal from a fourth satellite it can solve an equation that lets it determine the exact time, without needing an atomic clock.
Time travel’s been one of mankind’s fantasy for centuries. You might have watched time travel and time machines in sci-fi movies like “Doctor Who” ,“Star Trek” ,“Back to future” , “Planet of Apes” and so on. Recently released interstellar also screened time travel to the future through a wormhole. The reality, however ,is more muddled. Not all scientists believe that time travel is possible.
Time travel is the concept of movement of a body between different points in time either to the past or to the future. Let us check possibility of different time travel theories. According to Einstein’s theories travelling to future is simple and travelling to past is nearly impossible. But there are some other theories which support backward time travel .Wormhole theory is the most prominent among them. Einstein’s relativity theories are the base of all time travel theories. So let us see what relativity theory is .
Einstein’s theory of relativity
The theory of relativity usually encompasses two theories by Albert Einstein: special relativity and general relativity.
Special Relativity theory
Special relativity theory was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies". The special theory of relativity was based on two main postulates:
The laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference).
That the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
According to Einstein’s special relativity theory time must change according to the speed of a moving object relative to the frame of reference of an observer. However, the special theory of relativity only held true in the absence of a gravitational field. In this theory, Einstein showed that time and length are not as absolute as everyday experience would suggest: Moving clocks run slower, and moving objects are shorter. In other words ,as the speed increases time slows down and moving object becomes shorter. This is hard to digest ,because you can’t experience this effects in our surroundings. Here everything moves much slower when compared to light.
Just imagine you are in free space. No earth , no sun , no solar system , no galaxy nothing, only empty space. Put yourself in a spaceship and your friend in another one.Let us name your ship as S1 and your friend’s ship as S2. Imagine S1 is stationary and S2 is moving at half the speed of light(c/2) .In everyday life we add or subtract velocities to get relative speed. For light, it would be natural to expect that one could similarly add and subtract velocities. Suppose you (in S1)measure a particular light signal's speed, and find the usual value of 299,792.458 kilometers (186,000 miles) per second. If you see S2 moving at half the speed of light (c/2), you would expect that your friend on that spaceship would measure the speed of your light signal at merely c - c/2 = c/2, half the value that you measured. Not so, according to special relativity! Simply subtracting speeds would only give the correct answer if the observer on that space-ship measured space and time, distance and duration in the same way that you do. As we have seen above in special relativity section, that's not the case. From your point of view, for instance, the measuring rods on the speeding spaceship are shorter than your own, and its clocks run more slowly than your’s. Taken together, all of these relativistic effects combine in precisely the right way to result in a surprising phenomenon: Even from the point of view of an observer on the speeding spaceship, your light signal moves with exactly the same speed, c=299,792.458 kilometers per second.In simple words when both observers calculate speed of light using the formula “Speed=distance/time” the answers will be same.
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Two main consequences of Special relativity are:
Time dilation : Clocks run slower for moving objects.
Length contraction: Moving objects are shorter for a stationary observer.
General Relativity Theory
Since the special theory of relativity only held true in the absence of a gravitational field, Einstein strove for 11 more years to work gravity into his equations and discover how relativity might work generally as well. The result was General Relativity Theory .Einstein published his general relativity theory in the year 1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example, when standing on the surface of the Earth) are physically identical.
deformed space due to mass of earth
General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime.Einstein considered space and time as a single entity called spacetime instead of considering them seperately. In general theory of relativity, space and time become even more flexible.According to Newton’s law of universal gravitation bodies having mass attract towards each other.This attraction is called gravity.However according to the theory of general relativity, matter causes space to curve. It is posited that gravitation is not a force, as understood by Newtonian physics, but a curved field (an area of space under the influence of a force) in the space-time continuum that is actually created by the presence of mass.
A popular explanation how general relativity works is the rubber sheet analogy. This involves a bowling ball making a depression on a trampoline and a marble either rolling around inside the depression or rolling directly into it. Here the bowling ball represents a planet, the marble a satellite, and the rubber sheet is space being bent through an additional dimension. This is just an analogy used for explaining general relativity in a simple way. In reality general relativity is much more complicated than this.
Three main consequences of general relativity are:
States of accelerated motion and being at rest in a gravitational field (for example, when standing on the surface of the Earth) are physically identical.
Clocks run slower in deeper gravitational wells. This is called gravitational time dilation.
Rays of light bend in the presence of a gravitational field.
Proofs of relativity theory
Countless experiments have been carried out and Einstein’s theories hold true. Modern GPS uses Einstein’s theory of relativity to locate our position accurately. Clocks on GPS satellites are adjusted based on the predictions of special and general relativity theories.
In 1971 an experiment was conducted with four super accurate atomic clocks which were set to exact same time as reference clock. The clocks were placed aboard commercial flights and planes flew twice around the world. First eastward and the westward. When the clocks were returned and when compared with reference clock, clocks were no longer synchronized and differences were consistent with the predictions of special and general theory of relativity.
Special Relativity theory and time travel
According to Special Relativity theory time slows down for object travelling close to the speed of light. In other words if you are traveling at a high speed , you are moving forwarding in time.And time stops altogether for objects travelling at speed of light.Then follows ‘time must go backward for objects traveling faster than speed of light’. So far it’s been seen that no object can travel at the speed of light. On approaching speed of light object start to increase mass rather than speed. Look at the Einstein’s equation E=MC^2 .In this equation C=Speed of light remains constant. As the speed of object approaches light speed mass M approaches infinity. So it would require infinite amount of energy to accelerate object from there. In short it would take infinite energy for an object to achieve light speed. This is why we cannot travel back in time. We simply have not been able to reach greater speed than the speed of light. So, according to Einstein’s special relativity time travel to the past is impossible. Are you disappointed? No. There is still another possibility for time travel. The Wormholes.
Wormholes
A wormhole is a hypothetical topological feature that would fundamentally be a shortcut connecting two separate points in spacetime. A wormhole, in theory, might be able to connect extremely far distances such as a billion light years or more, short distances such as a few feet, different universes, and different points in time. A wormhole is much like a tunnel with two ends, each at separate points in spacetime. Spacetime can be viewed as a 2D surface (to simplify understanding) that, when 'folded' over, allows the formation of a wormhole bridge. A wormhole has at least two mouths that are connected to a single throat or tube.In three dimensional space a wormhole will appear spherical to our eyes and you can see through it the other end of wormhole.
2D representation of a wormhole
According to Einstein and his colleague Nathan Rosen, a wormhole is actually deformed space that has warped in such a way to connect two different points in space-time. The result is a tunnel-like structure that could be straight or curved, linking two areas of the Universe that are incredibly far apart. Einsteinian mathematical models predict that wormholes exist, but none have ever been found. So far, physicists haven’t determined a way in which wormholes would form naturally in the Universe.In 1962 two physicist John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable, and that it will pinch off instantly as soon as it forms, preventing even light from making it through.
3D illustration of a wormhole
Even if wormholes exist they are too tiny for a human or spaceship to fly through. In 1988 noted theoretical physicist Kip Thorne and his graduate student Mike Morris demonstrated the possibility of traversable wormholes in general relativity. The type of traversable wormhole they proposed, held open by exotic matter. Exotic matter is a matter that has negative energy density and/or negative pressure. Negative properties of exotic matter might push the sides of a wormhole outward, making it large enough—and stable enough—for a person or a spaceship to fly through it. But exotic matter exists only in theory, we don't know what it looks like, and we have yet to know where to find it.
Wormholes and time travel
The theory of general relativity predicts that if traversable wormholes exist, they can also alter the speed of time. They could allow time travel.This would be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back. relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry.
For example, consider two clocks at both mouths both showing the date as 2010. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2012 while the stationary mouth's clock read 2020. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2012, in the same region but now eight years in the past. Theoretically you can convert a wormhole into a time machine. But you need to solve three problems 1. Existence of wormholes 2.Stabilization of worm holes using exotic matter and 3.Existence of exotic matter. Many more traversable worm holes have been proposed. But they also exist theoretically.
Conclusion
According to Einstein’s special relativity theory nothing can travel faster than light. To go backward in time ,faster than light travel is the only way. Faster than light travel can be achieved if we find out some shortcuts through space-time. Wormhole is one such shortcut which exist theoretically . So, for coming hundreds or thousands of years time travel will remain fantasy only. Let us wish after thousands of years our descendants will solve this mystery and come and visit us from future .
