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Practicality of Time Travel By Ryan Marr Time travel is essentially the act of moving through the fourth dimension; it is a difficult concept which often captures and challenges our imagination, and is engaging for most. Time travel suggests possibilities that are far beyond the level of knowledge to which we can summon. Time is a rate of change within the universe; this is something we are constantly experiencing [1]. The passage of time can be compared and structured as a flow. We measure this flow in set units, however, the size of the channel in which the flow exists will alter the rate of flow (similarly to the flow of a river). Time is not necessarily constant, it may flow at different rates depending on its place in time; we may conclude that time is relative. [2]&[22] We can put this idea of variability down to a direct relationship between time and space. [1] Time is what we know as a fourth dimension, accompanied by the other three: depth, width and length. It is principle that any occurrence taking place in the universe requires both space and time, these two particular dimensions cannot exist without one another, they subsist together as the space-time continuum . [2]&[3] Time Travel Into the Future In order to advance into the future at a faster rate than things around us, we need to exploit space-time. One method of exploitation is actually carried out by satellites in outerspace each second of every day. [3] Many people have the impression that time is absolute and is the same everywhere, however that is not the case. Time is variable, and we can theoretically change the rate at which time flows. [4] General relativity has shown that the rate at which time passes is related to the gravitational potential; clocks will essentially tick more slowly when they are in a ‘gravitational well’. This idea is known as graviational time dilation. [4]&[5] Therefore, for a satellite orbitting the earth at a large radius, there is less gravitational potential than for an object on earth’s surface, and so time is experienced at a faster rate. [5] The time interval measured by an observer positioned at a certain distance (R) from the earth is given by equation 1: [6]

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Practicality of Time TravelBy Ryan Marr

Time travel is essentially the act of moving through the fourth dimension; it is a difficult concept which often captures and challenges our imagination, and is engaging for most. Time travel suggests possibilities that are far beyond the level of knowledge to which we can summon.

Time is a rate of change within the universe; this is something we are constantly experiencing [1]. The passage of time can be compared and structured as a flow. We measure this flow in set units, however, the size of the channel in which the flow exists will alter the rate of flow (similarly to the flow of a river). Time is not necessarily constant, it may flow at different rates depending on its place in time; we may conclude that time is relative. [2]&[22]

We can put this idea of variability down to a direct relationship between time and space. [1]

Time is what we know as a fourth dimension, accompanied by the other three: depth, width and length. It is principle that any occurrence taking place in the universe requires both space and time, these two particular dimensions cannot exist without one another, they subsist together as the space-time continuum. [2]&[3]

Time Travel Into the Future

In order to advance into the future at a faster rate than things around us, we need to exploit space-time. One method of exploitation is actually carried out by satellites in outerspace each second of every day. [3] Many people have the impression that time is absolute and is the same everywhere, however that is not the case. Time is variable, and we can theoretically change the rate at which time flows. [4] General relativity has shown that the rate at which time passes is related to the gravitational potential; clocks will essentially tick more slowly when they are in a ‘gravitational well’. This idea is known as graviational time dilation. [4]&[5] Therefore, for a satellite orbitting the earth at a large radius, there is less gravitational potential than for an object on earth’s surface, and so time is experienced at a faster rate. [5]

The time interval measured by an observer positioned at a certain distance (R) from the earth is given by equation 1: [6]

G – Gravitational constant M – Mass of the earthc – Cosmic speed of light

In 1915, Albert Einstein proposed his theory of general relativity; but whilst putting its equations into practice, Einstein realized that massive objects caused a distortion in space-time, through their gravitational potential. [6] If a large body were to be placed in the center of a trampoline, it would press down into the fabric, causing it to dimple. A marble rolled around the edge would spiral inward towards the body, pulled in much the same way that the gravity of a planet pulls at rocks in space. [4] Figure 1 shows this effect: [7]

Equation 1 - Gravitational time dilation factor [6]

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This effect inferred that gravitational force is a curve in space-time; astronomers regularly observe this phenomenon when they study light moving near a sufficiently massive object. [7] Particularly large suns, for instance, can cause an otherwise straight beam of light to curve in what we call the ‘gravitational lensing effect’. Here we can conclude that massive objects distort space-time, as demonstrated in Figure 2: [8]&[7]

Gravitational lensing is essentially where the gravitational attraction of an object or mass intervenes, as a lens, to redirect light rays. [7] If a bright object, such as a quasar, is a large distance away from earth (e.g. 10 billion light-years), the light rays picked up on earth will have been redirected in some way. If a large mass, such as a large galaxy (or cluster of galaxies), is blocking the direct view of the quasar, the light will have been bent by the gravitational field around the galaxy. [9] This is shown in Figure 3: [10]

Figure 1 - Earth's gravitational potential causing distortion in space-time; similar to the effect caused by a body on a trampoline. [7]

Figure 2 - Further distortion of space-time due to Earth's 'gravitational lensing' [8]

Figure 3 - A diagram of gravitational lensing [10]

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In general relativity, a ‘point mass’ (in this case the massive galaxy) will deflect light rays through a certain angle (aplha) in accordance to Equation 2: [11]

G – Gravitational constant M – Mass of defelcting object C – Speed of light b – Impact parameter

An impact parameter is defined as the perpendicular distance between the path of light rays and the centre of mass which is causing the gravitational deflection. [12]

At the centre of the galaxy, physicists discovered a supermassive black hole, Sagittarius, where the mass of 4 million suns exists as a single, infinitely dense point, known as a singularity. [13] To put this relationship between gravitational potential and the rate of flow of time into perspective, astrophysisits of NASA belive, though impossible, orbiting a point such as Sagittarius would cause the ‘orbiter’ to experience time at half the Earth rate. [13]&[5]

Another way scientists have proposed exploiting space-time is to travel at varying speeds. The speed at which matter moves through the course of space also affects the rate of time experienced relative to a stationary observer [14]. As the cosmic speed limit (what we call the speed of light: approximately 300,000,000 meters per second [15]) is approached by matter, the rate of time experienced by that matter becomes increasingly slower, relatively; we call this effect relativistic time dilation [14]. If a stationary observer measures the time interval between two events, they will attain a value for the ‘proper time’ (Ta). However, an observer moving at a constant velocity close to the speed of light (c) will measure a longer interval (Tb) between the two events (shown contextually in Equation 4). [16] The time measured by the moving observer (Tb) is an increase of the time measured by the stationary observer (Ta) by a varying scale factor known as the relativistic factor (shown in Equation 3). [16]&[17]

Relativistic Factor: Hence:

To put this factor into perspective, if such a train could attain 99.999% of the cosmic speed, only one year would pass onboard for every 223 years back at the train station. In effect, this hypothetical commuter would have traveled into the future. [17]

Time Travel Into the Past

There was nothing in Einstein's theories of general or special relativity [5] that precluded time travel into the past, however, the laws of causality (or cause and effect) are violated by the concept of traveling back to previous positions in time. [19] When any event occurs in the universe, it leads into an endless one-way string of events and possibilites, and in every

Equation 2 - Gravitational Lensing Formalism [11]

Equation 3 – Relativistic Factor [18] Equation 4 – Time interval measured by a moving observer, using the relativistic factor [18]

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instance the cause occurs before the effect. A concept as such violates reality as we know it; thus many scientists dismiss time travel into the past as an impossibility. [19]&[9]

Some scientists have proposed the idea that exceeding the cosmic speed of light may cause a backward flow in time for the travelling observer, however, this is just one hypothesis that (even in modern day) cannot be proven. [5] In order to represent velocities in space-time, we can use a space-time diagram as shown in Figure 4: [4]

The cosmic speed of light, c, is represented by a line 45 degreees above the x-axis.[5] When exceeding the speed of light, it is unknown what happens, therefore it is hypothetical to assume that exceeding this speed can be represented by a line less than 45 degrees (represented by the dashed line).[20] The reason for this uncertainty is that there are many possibilities as to what could really happen when ‘c’ is exceeded; for instance, the line could curve back on itself. This, as we know it, is an unknown phenominon yet to be discovered. [5]

It is proposed that the rate of flow of time tends towards zero as the speed of light is approached.[15]&[21] This idea derives from the relativistic factor, where if ‘v’ and ‘c’ are equal, the factor will equal a value of ‘1 over 0’.[18] Here, a common assumption is made that this gives an infinite value; hence the time period measured by the travelling observer will also be infinite and so the rate of flow of time is simply zero. However, dividing through by zero does not necessarily equal an infinite value; this is an assumption. Division by the value zero is undefined and often dismissed as being meaningless. [23]&[24]

But taking the assumption that approaching the cosmic speed does cause the time flow to tend towards zero, it is then questionable as to how this can be represented graphically. If we use a different graph, for instance a distance-time graph, we can demonstrate this assumption simply; shown in Figure 5: [15]

Figure 4 – A space-time diagram

Figure 5 - Distance-time diagram showing a particle approaching the cosmic speed, from rest.

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If the rate of flow of time tended towards zero when approaching the cosmic speed, the timeline of a particle should theoretically tend towards a horizontal curve in correspondence, for relativistic velocities. [5]

A common dismissal is that as an object nears the speed of light, its relativistic mass increases until, at the speed of light, it becomes infinite.[5] Newton’s law of motion states that the magnitudal force of an object is its mass multiplied by acceleration, therefore this can be re-arranged to find that accelleration of an object is its magnitude of resultant force per unit of mass.[22] However, if mass tends towards and infinite value when reaching the speed of light, accelleration will tend towards a value of zero; therefore no further positive acceleration can occur, hence accellerating an infinite mass (or any initial mass) any faster than the speed of light is impossible as we know it. [5]&[25]

Conclusion

For many, the concept of travelling through time involves imagination and creation far beyond our technological capabilities; this concept is almost trivial. However, it is evident that our current understanding and ability to ‘time-travel’ revolves primarily around the variations in the rate at which time flows. It is almost certain, that in our generation, this concept could only be tested to certain extents.

Time travel ‘into the future’ is an aspect which can be summoned through altering the rate of time which an object or observer experiences. Albert Einstein’s theory of general relativity was revolutionary in these findings, introducing both gravitational potential and velocity as factors which can ‘distort’ space-time in order to change the rate of time for an observer. With our current advancement in technology, these findings are still to be explored by physicists.

Time travel ‘into the past’ on the other hand is a limited, and almost dismissed, concept whose proofs as in impossobility outweighs those of possibility. The dismissals proposed by physicists suggest that any technological advancement would only be deferred by the laws of physics; for example, the impossibility of accellerating an infinite mass. It is therefore difficult to predict or understand the limits to which time travel into the past can extend to.

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Bibliography

1. http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/four_dimensions

2. http://science.howstuffworks.com/science-vs-myth/everyday-myths/time-travel.htm

3. http://einstein.stanford.edu/content/relativity/q411.html

4. http://www.youtube.com/watch?v=g73iuRlfl8E

5. Einstein – Program from the History Channel – AlternativeNews4U

6. http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

7. http://casa.colorado.edu/~ajsh/approach.html

8. www.scienceblogs.com/startswithabang/files/2013/03/spacetimelu31.jpeg

9. http://relativity.livingreviews.org/Articles/lrr-1998-12/

10. http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html

11. http://en.wikipedia.org/wiki/Gravitational_lensing_formalism

12. http://en.wikipedia.org/wiki/Impact_parameter

13. http://www.astrology-online.com/sagittar.htm

14. http://www.space.com/17661-theory-general-relativity.html

15. http://nvaspeedoflight.org.uk/

16. http://webs.morningside.edu/slaven/Physics/relativity/relativity6.html

17. http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html

18. http://www.1728.org/reltivty.htm

19. http://en.wikipedia.org/wiki/Causality_(physics)

20. http://en.wikipedia.org/wiki/Faster-than-light

21. http://users.wfu.edu/brehme/time.htm

22. CGP OCR Advancing Physics B – A2 level revision guide

23. http://en.wikipedia.org/wiki/Division_by_zero

24. http://www.mathsisfun.com/numbers/dividing-by-zero.html

25. http://www.frihost.com/forums/vt-115312.html