theory of time travel

7/29/2019 Theory of Time Travel

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In physics

Time travel to the past is theoretically allowed using the following methods: [24]

Travelling faster than the speed of light

The use ofcosmic strings and black holes

Wormholes andAlcubierre drive

[edit]Via faster-than-light (FTL) travel

If one were able to move information or matter from one point to anotherfaster than

light, then according to special relativity, there would be some inertial frame of

reference in which the signal or object was moving backward in time. This is a

consequence of the relativity of simultaneity in special relativity, which says that in some

cases different reference frames will disagree on whether two events at differentlocations happened "at the same time" or not, and they can also disagree on the order

of the two events (technically, these disagreements occur when the spacetime

interval between the events is 'space-like', meaning that neither event lies in the

future light cone of the other).[25] If one of the two events represents the sending of a

signal from one location and the second event represents the reception of the same

signal at another location, then as long as the signal is moving at the speed of light or

slower, the mathematics of simultaneity ensures that all reference frames agree that the

transmission-event happened before the reception-event.[25]

However, in the case of a hypothetical signal moving faster than light, there would

always be some frames in which the signal was received before it was sent, so that the

signal could be said to have moved backwards in time. And since one of the two

fundamentalpostulates of special relativitysays that the laws of physics should work the

same way in every inertial frame, then if it is possible for signals to move backwards in

time in any one frame, it must be possible in all frames. This means that if observer A

sends a signal to observer B which moves FTL (faster than light) in A's frame but

backwards in time in B's frame, and then B sends a reply which moves FTL in B's frame

but backwards in time in A's frame, it could work out that A receives the reply beforesending the original signal, a clear violation ofcausality in everyframe. An illustration of

such a scenario using spacetime diagrams can be found here.[26] The scenario is

sometimes referred to as a tachyonic antitelephone.

According to special relativity, it would take an infinite amount of energy to accelerate a

slower-than-light object to the speed of light. Although relativity does not forbid the
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theoretical possibility oftachyons which move faster than light at all times, when

analyzed usingquantum field theory, it seems that it would not actually be possible to

use them to transmit information faster than light. [27] There is also no widely agreed-

upon evidence for the existence of tachyons; the faster-than-light neutrino anomaly had

suggested that neutrinoswere possibly tachyons, but the results of the experiment werefound to be invalid upon further analysis. Another group of experimenters state that a

lack of radiation posited by a theory indicates the neutrinos cannot have really been

traveling faster than light.[28] The OPERA team leader, Dario Autiero, and CERN's

research director, Sergio Bertolucci, note other explanations are possible for the lack of

neutrino energy loss via radiation.[29][30]

[edit]Special spacetime geometries

The general theory of relativity extends the special theory to cover gravity, illustrating it

in terms of curvature in spacetime caused by mass-energy and the flow of momentum.General relativity describes the universe under a system offield equations, and there

exist solutions to these equations that permit what are called "closed time-like curves,"

and hence time travel into the past.[18] The first of these was proposed by Kurt Gdel, a

solution known as the Gdel metric, but his (and many others') example requires the

universe to have physical characteristics that it does not appear to have.[18]Whether

general relativity forbids closed time-like curves for all realistic conditions is unknown.

[edit]Using wormholes

Main article: Wormhole

Wormholes are a hypothetical warped spacetime which are also permitted by

the Einstein field equations of general relativity,[31]although it would be impossible to

travel through a wormhole unless it were what is known as a traversable wormhole.

A proposed time-travel machine using a traversable wormhole would (hypothetically)

work in the following way: One end of the wormhole is accelerated to some significant

fraction of the speed of light, perhaps with some advancedpropulsion system, and then

brought back to the point of origin. Alternatively, another way is to take one entrance of

the wormhole and move it to within the gravitational field of an object that has highergravity than the other entrance, and then return it to a position near the other entrance.

For both of these methods, time dilation causes the end of the wormhole that has been

moved to have aged less than the stationary end, as seen by an external observer;

however, time connects differently through the wormhole than outside it, so

that synchronized clocks at either end of the wormhole will always remain synchronized

as seen by an observer passing through the wormhole, no matter how the two ends
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move around.[32] This means that an observer entering the accelerated end would exit

the stationary end when the stationary end was the same age that the accelerated end

had been at the moment before entry; for example, if prior to entering the wormhole the

observer noted that a clock at the accelerated end read a date of 2007 while a clock at

the stationary end read 2012, then the observer would exit the stationary end when itsclock also read 2007, a trip backwards in time as seen by other observers outside. One

significant limitation of such a time machine is that it is only possible to go as far back in

time as the initial creation of the machine;[33] in essence, it is more of a path through

time than it is a device that itself moves through time, and it would not allow the

technology itself to be moved backwards in time. This could provide an alternative

explanation forHawking's observation: a time machine will be built someday, but has

not yet been built, so the tourists from the future cannot reach this far back in time.

According to current theories on the nature of wormholes, construction of a traversable

wormhole would require the existence of a substance with negative energy (often

referred to as "exotic matter"). More technically, the wormhole spacetime requires a

distribution of energy that violates various energy conditions, such as the null energy

condition along with the weak, strong, and dominant energy conditions. [34] However, it is

known that quantum effects can lead to small measurable violations of the null energy

condition,[34] and many physicists believe that the required negative energy may actually

be possible due to the Casimir effect in quantum physics.[35]Although early calculations

suggested a very large amount of negative energy would be required, later calculations

showed that the amount of negative energy can be made arbitrarily small.[36]

In 1993, Matt Visserargued that the two mouths of a wormhole with such an induced

clock difference could not be brought together without inducing quantum field and

gravitational effects that would either make the wormhole collapse or the two mouths

repel each other.[37] Because of this, the two mouths could not be brought close enough

forcausality violation to take place. However, in a 1997 paper, Visser hypothesized that

a complex "Roman ring" (named afterTom Roman) configuration of an N number of

wormholes arranged in a symmetric polygon could still act as a time machine, although

he concludes that this is more likely a flaw in classical quantum gravity theory rather

than proof that causality violation is possible. [38]

ime Travel: Fact or Fiction?

We define time travel to mean departure from a certain place and time followed (from

the traveller's point of view) by arrival at the same place at an earlier (from the
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sedentary observer's point of view) time. Time travel paradoxes arise from the fact

that departure occurs after arrival according to one observer and before arrival

according to another. In the terminology of special relativity time travel implies that

the timelike ordering of events is not invariant. This violates our intuitive notions of

causality. However, intuition is not an infallible guide, so we must be careful. Is time

travel really impossible, or is it merely another phenomenon where "impossible"

means "nature is weirder than we think?" The answer is more interesting than you

might think.

The Science Fiction Paradigm

The B-movie image of the intrepid chrononaut climbing into his time machine and

watching the clock outside spin backwards while those outside the time machine

watch the him revert to callow youth is, according to current theory, impossible. In

current theory, the arrow of time flows in only one direction at any particular place. Ifthis were not true, then one could not impose a 4-dimensional co-ordinate system on

space-time, and many nasty consequences would result. Nevertheless, there is a

scenario which is not ruled out by present knowledge. This usually requires an

unusual spacetime topology (due to wormholes or strings in general relativity) which

has not yet seen, but which may be possible. In this scenario the universe is well

behaved in every local region; only by exploring the global properties does one

discover time travel.

Conservation Laws

It is sometimes argued that time travel violates conservation laws. For example,

sending mass back in time increases the amount of energy that exists at that time.

Doesn't this violate conservation of energy? This argument uses the concept of a

global conservation law, whereas relativistically invariant formulations of the

equations of physics only imply local conservation. A local conservation law tells us

that the amount of stuff inside a small volume changes only when stuff flows in or out

through the surface. A global conservation law is derived from this by integrating

over all space and assuming that there is no flow in or out at infinity. If this integral

cannot be performed, then global conservation does not follow. So, sending mass

back in time might be all right, but it implies that something strange is happening.(Why shouldn't we be able to do the integral?)

General Relativity

The possibility of time travel in GR has been known at least since 1949 (by Kurt

Godel, discussed in [1], page 168). The GR spacetime found by Godel has what are


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now called "closed timelike curves" (CTCs). A CTC is a worldline that a particle or a

person can follow which ends at the same spacetime point (the same position and

time) as it started. A solution to GR which contains CTCs cannot have a spacelike

embedding - space must have "holes" (as in donut holes, not holes punched in a sheet

of paper). A would-be time traveller must go around or through the holes in a clever

way.

The Godel solution is a curiosity, not useful for constructing a time machine. Two

recent proposals, one by Morris, et al. [2] and one by Gott [3], have the possibility of

actually leading to practical devices (if you believe this, I have a bridge to sell you).

As with Godel, in these schemes nothing is locally strange; time travel results from

the unusual topology of spacetime. The first uses a wormhole (the inner part of a

black hole, see figure 1 of [2]) which is held open and manipulated by

electromagnetic forces. The second uses the conical geometry generated by an

infinitely long string of mass. If two strings pass by each other, a clever person can

go into the past by travelling a figure-eight path around the strings. In this scenario, if

the string has non-zero diameter and finite mass density, there is a CTC without any

unusual topology.

Grandfather Paradoxes

With the demonstration that general relativity contains CTCs, people began studying

the problem of self-consistency. Basically, the problem is that of the "grandfather

paradox": What happens if our time traveller kills her grandmother before her mother

was born? In more readily analyzable terms, one can ask what are the implications ofthe quantum mechanical interference of the particle with its future self. Boulware [5]

shows that there is a problem - unitarity is violated. This is related to the question of

when one can do the global conservation integral discussed above. It is an example of

the "Cauchy problem" [1, chapter 7].

Other Problems (and an escape hatch?)

How does one avoid the paradox that a simple solution to GR has CTCs which QM

does not like? This is not a matter of applying a theory in a domain where it is

expected to fail. One relevant issue is the construction of the time machine. After all,infinite strings aren't easily obtained. In fact, it has been shown [4] that Gott's

scenario implies that the total 4-momentum of spacetime must be spacelike. This

seems to imply that one cannot build a time machine from any collection of non-

tachyonic objects, whose 4-momentum must be timelike. There are implementation

problems with the wormhole method as well.


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Tachyons

Finally, a diversion on a possibly related topic.

If tachyons exist as physical objects, causality is no longer invariant. Different

observers will see different causal sequences. This effect requires only special

relativity (not GR), and follows from the fact that for any spacelike trajectory,

reference frames can be found in which the particle moves backward or forward in

time. This is illustrated by the pair of spacetime diagrams below. One must be

careful about what is actually observed; a particle moving backward in time is

observed to be a forward moving anti-particle, so no observer interprets this as time

t

One reference | Events A and C are at the same

frame: | place. C occurs first.

|

| Event B lies outside the causal

| B domain of events A and C.

-----------A----------- x (The intervals are spacelike).

|

C In this frame, tachyon signals

| travel from A-->B and from C-->B.

| That is, A and C are possible causes

of event B.

Another t

reference | Events A and C are not at the same

frame: | place. C occurs first.

|

| Event B lies outside the causal

-----------A----------- x domain of events A and C. (The

| intervals are spacelike)

|

| C In this frame, signals travel from

| B-->A and from B-->C. B is the cause

| B of both of the other two events.


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The unusual situation here arises because conventional causality assumes no

superluminal motion. This tachyon example is presented to demonstrate that our

intuitive notion of causality may be flawed, so one must be careful when appealing to

common sense. See the FAQ article on tachyons, for more about these weird

hypothetical particles.

Conclusion

The possible existence of time machines remains an open question. None of the

papers criticizing the two proposals are willing to categorically rule out the

possibility. Nevertheless, the notion of time machines seems to carry with it a serious

set of problems.
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