Is physical time travel possible ?

AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology
	TIME TRAVEL ê - fantasy or physical reality? -   What is time ? (in macro world, micro world, megaworld) Theory of relativity - physics of space, time, universe . Physical time travel ? Vojtech Ullmann physicist A popular-scientific lecture on the unusual properties of space time and on the exciting possibilities of time travel into the future and the past , which (at least in principle) the special and general theory of relativity and unitary field theory offer us.

S y l a b u s
(a more detailed physical and mathematical analysis is in the book " Gravity, Black Holes and the Physics of Spacetime ")

INTRODUCTION
Time travel is a fascinating theme that smells of mysticism, adventure, the deepest secrets of the existence of the universe and our life and destiny.

History - Literature sci-fi :
H.G.Wells: "Time Machine" (1895) - in contradiction with previous notions of absolute time
Jakub Arbes: "Newton's brain" - it's not time travel, it's just a glimpse into the past
Common feature: superluminal speed

Pitfalls of time travel (discussed in more detail below) :

• Technical difficulty or principled impossibility ..?..
• Logical paradoxes ..?..

Within Newtonian physics, due to its concept of absolute time, "time travel" was completely impossible.
It was only in the context of a special theory of relativity, enabling the speed of time to be influenced by motion, or a general theory of relativity showing the influence of gravity on the course of time, that time travel began to be considered in a sense a physically real possibility .

WHAT IS IT TIME ?                

Actually, we do not know ..?! .. We can only say:
Time is a" something " that determines the sequence of events makes it possible to compare the duration of events and the intervals between them, to quantify the motions of objects and dynamic changes in the physical, chemical and biological systems.
This is not a definition, it would be a tautology (definition in a circle) .
The secret of time is more than 1000 years old. E.g. and 4th century Aurelius Augustinus declared :
" If no one asks me, I know what time means. But if I have to explain it to someone, I find that I don't know! "

Time measurement - chronology
Regular events (consistent and predictable) and periodic movements are the most suitable standards for measuring time. In everyday life, such periodic events are the movement of the Sun across the sky (in fact, it is the rotation of the Earth), the phases of the Moon, the alternation of seasons (the Earth's orbit around the Sun), the pendulum swing, the vibration of the spring. From these observed natural laws the time units year, month, day, hour, minute, second were derived. For historical reasons, there is no decimal recalculation, but factors 12 and 60 are used (unfortunately it was not possible to reform) . However, the natural cycles from which the original units of time were derived are not completely regular, which required a new determination for more accurate measurements:
Unit of time in the SI system - second. Current definition: 1 second is the duration of 9 192 631 770 periods of radiation emitted during the transition between two hyperfine levels in the ground state of the cesium-133 atom - "Atomic Clock"
Chronology, study of the past :
- history, archeology (tens, hundreds, thousands of years) ;
- geochronology (hundreds of thousands, millions, billions of years) ;
- the time evolution of the universe (billions of years and more) .

Physical conception of space and time :

• The metaphysical conception
  Space and time are a kind of absolute background or stage on which events take place, but which remains unaffected by these events . Such absolute space and time , which has no beginning or end, is a kind of transcendent element of reality, given by God in the Platonic conception.
  " Absolute or mathematical time flows evenly on its own, without any relation to anything external " - I. Newton , "Principia ....", 1687.
  In absolute time, "time travel" is completely impossible !
• Operationalist conception
  Space and time are secondary concepts derived from natural processes - concepts used to describe the movements of bodies and the course of all other physical processes. Therefore, they can be expected to be influenced by these processes - we perceive space and time as relative. We measure spatial distances by comparison with suitable bodies - standard scales, or by radiolocation - radar. We measure time using clocks made of matter governed by the laws of physics - we mostly use periodic movements
  such as the orbit and rotation of the Earth, pendulum oscillations or electron movements and their jumps between levels in atomic shells. The "ticks" of such clocks determine the passage of time.
  Space and time in this concept are defined by the very way of their measurement, by the operations of measurement. We do not attach real meaning to any imaginary or abstract notions of space and time outside the processes by which they are measured.

Note: Of course, time shifts of a few hours when traveling by plane, for example between Europe and America, have nothing to do with time travel. Here, this is only related to the rapid flight between the agreed time zones, which are the result of our measurement of time of day by rotating the Earth around the axis. We will not move in time, but only in marking the time with agreed numerical hours - day clocks, which are shifted according to longitude.

TIME ARROW
What determines the direction of the passage of time ?

• The radiation arrow of time ,
  also called the electromagnetic arrow. It is given by the fact that the island system of accelerating moving charges emits electromagnetic waves, which carry energy from the source at the speed of light, whereas these waves will affect distant bodies in the future (retarded) - §1.5, equation (1.47). The energy of the radiating system also decreases in the future.
  In addition to these "retarded" waves, the equations of electrodynamics formally allow for "advancing" waves - waves coming from infinity that the source absorbs; these waves can also be understood as waves radiated into the past. In fact, with each spontaneous emission of the source, we observe only the retarded emission of waves. The same applies to the emission of gravitational waves (§2.7 "Gravitational waves").
• The thermodynamic arrow of time
  according to the 2nd Act of thermodynamics, it is determined by the monotonic increase of the entropy of an isolated system near thermodynamic equilibrium. Time flows in the direction in which things age, hot objects cool, systems decompose, their disorder increases spontaneously (unfortunately, including the decay of our body ...).
  The very laws of motion of individual parts of the system also allow for movements leading to a decrease in entropy, but their probability is significantly less than those which, according to statistical physics, lead to an increase in disorder (entropy). This is due to the fact that in practice the number of disordered states is incomparably greater than the number of ordered states. The second thermodynamic theorem is thus a statistical consequence of the fact that there are much more disordered states than ordered states. And this situation is basically given by the initial conditions.
• The cosmological arrow of time
  is determined by the observation that as time grows, so does the expansion of the universe. Is it just a coincidence..?..
• The psychological arrow of time
  it is based on the fact, that our memory reflects the part of events that we call the past and which in our psychic understanding - in the neural network - is clearly distinguished from the future. So we have a kind of "psychic feeling" for the passage of time.
  

More detailed discussion: §5.6 " The future of the universe. The arrow of time. Dark matter. " (in the book "Gravity, Black Holes and the Physics of Spacetime").

Time travel
Within Newtonian physics, due to its concept of absolute time, "time travel" is completely impossible.
Only within the special theory of relativity, which allows influencing the speed of time flow by motion, or the general theory of relativity showing the influence of gravity on the course of time, can time travel be considered in a sense a physically real possibility .

SPECIAL THEORY OF RELATIVITY (STR)
ß
- time travel only to the future -

Special theory of relativity (more detailed explanation of §1.6 "Four- dimensional spacetime and special theory of relativity ") :

Principle of relativity + Principle of constant speed of light Þ Lorentz transformations
ß           ß
high speed Þ time dilation , length contraction  

The interval of the proper time dt = Ö (1-v2/c2) .dt of a moving body is always smaller than the corresponding coordinate time interval. An observer comparing the movement of the rest and moving clocks finds that the moving clocks go according to the relation (1.70) the slower the faster they move; This phenomenon is called relativistic dilatation time .

Lorentz transformations :

D t '=   D t / Ö (1 - v ² / c ² ) - time dilation
! The biological time also takes place in the same rhythm - the aging of cells in the organism !  

Spacetime diagram - light cone, causality in spacetime

Spacetime interval - invariant
s ²  º    x ² + y ² + z ² - c² .t ²
"Time is one of the coordinates of 4-dimensional (pseudo) Euclidean spacetime"   
  

"Mixing" of space and time in different inertial frames of reference, relativity of the present .

Time travel to the future :
Relativistic time dilation in STR:
For the observer moving at high speed close to the speed of light passes time slower than the reference "rest" observer, so that even a large time interval in the rest frame can bridge a much shorter time interval, ie. " travel to the future " of the rest reference system.
The paradox of time - twins - solved within STR, it is not necessary to use the general theory of relativity :
Time is delayed by the observer whose motion takes place in two frames of reference (inertial or non-inertial).
Note: In the popularization literature, it is often argued that the general theory of relativity must be used to solve the twin paradox, because the traveler's frame of reference is non-inertial - that the time difference arises in the phase of braking and reversing the second observer's motion. This statement is misleading and unconvincing; in fact, the twin paradox can be correctly solved within the special theory of relativity itself using three inertial frames of reference: the rest systems of the first observer and the two different moving systems of the second observer as they move back and forth.
Detailed analysis: §1.6 "Four- dimensional spacetime and special theory of relativity ", passage "The paradox of time".

Time travel into the past :
Kinematic effects of the theory of relativity offer - at least formally - three possibilities of time travel into the past :
=> In flat spacetime STR by moving superluminal speed (pictured left);
=> In the curved spacetime of the general theory of relativity by moving at a locally sublight speed within a sequence of suitably inclined light cones in an area with a strongly curved geometry of spacetime (pictured right) - will be discussed below.

=> Another hypothetical possibility is the complex topological structure of spacetime - "abbreviations, tunnels, wormholes" (discussed below) .

The need to exceed the speed of light - STR forbids !

Although: tachyons - particles faster than light?
Tachyons are purely speculative particles that can move only at superluminal velocities and have (in connection with the known relationship of mass versus velocity m = m_o /Ö(1-v²/c²) in the special theory of relativity) an imaginary mass. The motivation for the introduction of tachyons is only speculation about a kind of symmetry with respect to the speed of light, no physical arguments for them; rather, they would raise serious problems with the principle of causality .

In reality, therefore, only the solution within the general theory of relativity remains for travel into the past :

GENERAL THEORY OF RELATIVITY
- physics of gravity and curved spacetime -
ß
- in the principle of time travel to the future and to the past -

Universality of gravity Þ principle of equivalence:

ß
Gravity = curved spacetime

Gravity - inertia - kinematics - deceleration of time

R_ik - Ricci spacetime curvature tensor, g_ik - metric spacetime tensor, G - Newton's gravitational constant, c - speed of light, T_ik - energy-momentum tensor; G_ik - Einstein's curvature tensor
spacetime interval: ds² = g_ik dxⁱ dx^k ; geodesic equation:
Christoffel coefficients of an affine connection: G_kⁱ_l = (1/2) g^im (¶g_mk/¶x^l + ¶g_ml/¶x^k + ¶g_kl/¶x^m)

Curvature of spacetime :
Curvature tensor :

The energy-momentum tensor, which completely describes the distribution and motion of energy and momentum in a given physical system, generally has a structure (§1.6, section " Energy-momentum tensor ") :

The physical significance of the individual components of the energy-momentum tensor T ⁱ is thus as follows:

• T°° - energy density (~ mass); this component is the most important and dominant in physically real situations
• T^a° - a -component of energy flow = a -component of momentum density
• T^b - a -component density of b -component momentum, i.e. a -component forces acting on a given volume element through the pad unit normal vector e_b .

The gravitational body M curves spacetime in its vicinity

The dialectic of the general theory of relativity :
Matter dictates spacetime as it should curve ;
(curved) Spacetime dictates matter how it should move .
(more detailed explanation "General theory of relativity - physics of gravitation" - in the book "Gravity, Black Holes and the Physics of Spacetime" )

Time travel to the future:
Gravitational time dilation :
The actual time with respect to the coordinate time (which corresponds to the zero gravitational potential) flows the slower , the higher the value of the gravitational potential j at a given location (gravitational potential is negative) :
                        dt = (dx°/c).Ö(1 + 2j/c²) » (1 + j/c²) dt .
The clock located in the gravitational field is delayed relative to the same clock located outside the field (or in a place with a weaker field).

Gravitational dilation of time. The clock located in the gravitational field is delayed compared to the same clock located outside the field (or in a place with a weaker field).

It is enough for the observer to stay long enough in a place with strong gravity (high gravitational potential), where time passes more slowly, to return to the starting point at a time when a much larger interval of time has passed in the meantime.

Time travel into the past :
The geometry of curved spacetime of general relativity offers two possibilities of time travel into the past :
=> By moving at a locally sublight speed within a sequence suitably inclined light cones in an area with a strongly curved space-time geometry - in the picture on the right î

=> Another hypothetical possibility is the complex geometric-topological structure of spacetime .
Gravity affects both the passage of time and spatial scales and proportions. In such a globally curved spacetime, there may be some "shortcuts" over spacetime - geometric-topological "tunnels" that allow the observer to in a sense "overtake" the light beam and "travel" back to the past. At the same time, locally everything runs according to STR, the speed of light is not exceeded anywhere.
It's similar to the fact that a sailor sailing here on Earth across the ocean, still facing forward, may eventually find that he has returned to the place from which he sailed. Moving in curved spacetime, the observer can, in principle, find out over time that he has not only reached the starting point, but that he has "visited" an event from his past again, even though locally his time has flowed towards the future.

Are "time machines" physically possible ?

Black holes - bridges to other universes? Time machines? ï click
Black holes:
1. Large black holes - final stages of evolution of massive stars after gravitational collapse, giant black holes in the center of galaxies (quasars);
2. Black "microholes" - primordial, formed at the beginning of the universe during big-bang.
Spacetime singularities: Apparent (coordinate)- removable; Real (physical) - irremovable.
Rotating black holes - Kerr-Newman geometry, ring singularity ;
Naked singularities (R.Penrose:The principle of cosmic censorship- every singularity must be "dressed" to the horizon) ;
Analytical extension of black hole spacetime ® tunnels to other universes - or to other places in the same universe ?

Schwarzschild geometry of a centrally symmetric non-rotating black hole :
Kruskal's spacetime diagram of the analytical extension of Schwarzschild geometry. a) Coordinate network in relation to the Schwarzschild coordinates r and t . b) Overall structure of spacetime and motion of test particles and photons. A is the outer asymptotically planar region, B is the inner region below the horizon.		Penrose-Kruskal conformal space-time diagram of the complete extension of Schwarzschild geometry. a) Coordinate lines in relation to the Schwarzschild coordinates (hyperplanes r = const. and t = const.). b) Shapes of light cones and radial geodesics of time and light type.
a) Einstein-Rosen bridge between two universes. b) Topological tunnel between two places in space. c) "Wormhole" connecting two places in one universe.
The analytical extension of Schwarzschild's geometry contains two asymptotically planar regions - two "universes", between which the Einstein-Rosen bridge can form for a short time. However, it disappears very quickly - it is impassable, not even a light photon penetrates it !

Rotating gravity
The only known physically real possibility of such a deformation of spacetime in which there would be a suitable rotation of spacetime light cones is rotating gravity : entrainment (drift, towing) of local inertial systems by the rotational angular momentum of the source matter, that excited the gravitational field - Lense-Thirring effect - §2.5, passage "Rotating gravity". Another hypothetical possibility - "electrogravity" using an extremely strong electric charge, is mentioned below.

Hydrodynamic analogy of the influence of the rotation of the source body on the properties of the excited gravitational field. Left: In Newton's theory, the gravitational field of a body is given only by the distribution of matter and does not depend at all on its possible rotation (unless it leads to changes in the distribution of matter). Similarly, a smooth and symmetrical body (such as a sphere) rotating in an ideal liquid without viscosity does not cause the liquid to move around it. Right: In general relativity, but rotation of the source, leaving the outer gravitational field (on spacetime metric) characteristic "tracks" - leads to entrainment of local inertial system (frame dragging) - entrainment of free bodies by a rotating gravitational field in the direction of rotation of the source.  Like a body rotating in a viscous liquid, it entrains the liquid near its surface.

The rotational momentum J of the source system (has components J_a= ne_abgx^bT^g0d³x), described by non-diagonal components of the energy-momentum tensor, leads in the solution of Einstein's equations to non-diagonal terms in the metric tensor (4GJ/c²r).sin²J dt dj; metric is then :

                                              a Schwarzschild metric ä                   "rotation" metric
These off-diagonal members dj.dt lead to the fact that that a certain additional force acts on the bodies (in the geodesic equation d²j/dt² ¹ 0 becomes non-zero) causing entrainment of local inertial systems (frame dragging) - entrainment of free bodies by a rotating gravitational field in the direction of rotation of the source .

Kerr-Newman geometry of rotating axially symmetric black holes :
a = J / M - specific angular momentum, Q - electr. charge
Spatio-temporal diagram of Kerr-Newman geometry - §3.6). The outer horizon r = rg+ is the event horizon (the light cones below it face inwards towards r = 0). Below the inner horizon r = rg- , however, the light cones begin to "straighten" again, so that the light line of a body that has penetrated below the horizon r = rg+ does not necessarily end in the singularity r = 0.	Full analytical extension	The O observer moving in the outer asymptotically plane region of the A1 Kerr-Newman spacetime has three possibilities. It will either move constantly in A1 (solid line), so it will reach infinities I+ or Á+ in the limit. However , if the observer penetrates below the horizon r = rg+ (dashed trajectory) into the inner region B1, he also passes through the inner horizon r = rg- into the region C1, where he has two possibilities: he either encounters singularity (dotted path) where it is absorbed and destroyed, or it can avoid singularity (dashed trajectory) and reach another asymptotically planar outer region A2 . The situation in this next "universe" A2 is not completely determined by the initial conditions on the Cauchy hyperfield S , as can be seen, for example, at the point pÎA2 .

Critical assessment - what is the reality ?

The space-time structure of a real black hole.
a) In Schwarzschild's spacetime of a static black hole created by the collapse of a (non-rotating) star, a large part of the structure of the Kruskal's diagram is cut off by interior of the the collapsing star. b) The collapse of a rotating star into a black hole could theoretically create a space-time structure allowing it to travel to another universe. The collapsing matter could then emerge in the second universe in the form of a "white hole". c) However, due to the diverging intensity of the incoming radiation at the inner horizon and the quantum production of particles around the singularity, much of the theoretical structure of Kerrr-Newman geometry (including inner horizons and other universes on the Penrose diagram) actually cannot be realized. The collapse creates a singularity that is in the future and takes on a spatial character, which does not allow any travel to other universes .

Thought model experiment: Tipler's massive infinitely long relativistically rotating cylinder

A thin, infinitely long supermassive (tens of masses of the Sun) and a super-dense cylinder, rotating at a tremendous speed (of the order of billions of revolutions per second, circumferential speed > c/2).   At great distances from the cylinder (in asymptotically planar spacetime), the light cones will point vertically upwards (along the time axis), so that the sublight speed allows the body to move only in the positive time direction + t (enlarged section in the figure on the left).   There is a strong curvature of space-time near the massively gravitational cylinder, and due to the effect of entrainment of local inertial systems by the momentum of the cylinder (Lense-Thirring effect) the light cones will be inclined by more than 45°, so that part of them points backwards along the time axis on the space-time diagram. Within these entrained light cones, the helical path (light line) of the particle can move at a sublight speed both into the future and into the past - in the negative direction - t .

Problem: Requires the infinitely long cylinder. Implementation with a finite length of cylinder would be possible only with the violation of a weak energy condition - the need for "exotic matter" with a negative energy density in the Cauchy horizon - see below.

Electrogravity
Another hypothetical possibility is the application of an extremely strong electric field. Einstein's gravitational equations using the energy-momentum tensor of the electric field lead to the Reissner-Nordström geometry of spacetime , containing an inner horizon and a topological tunnel to other universes. From the quantum point of view, the Casimir effect between parallel superconducting plates, caused by quantum electromagnetic fluctuations of the vacuum, is considered. .....

Next - artificial solutions ...: Gödel's rotating universe; cosmic strings; warp (Alcubierr) propulsion - pure sci-fi ...

Cosmic strings - hypothetical 1-dimensional topological defects in space-time, which perhaps could have occurred during the Big Bang and due to the expansion of space (especially inflation) could be expanded to macroscopic to cosmic dimensions *). According to some, a combination of two moving cosmic strings, or strings + black holes, would make it possible to create closed time curves and tunnels that would allow travel to different places and times. *) Although there is no direct connection between cosmic strings and superstrings in unitary field theories, according to some hypotheses, cosmic strings could be inflation-expanded D-gates from superstring theory ..?..

Warp drive - a speculative image of a special "bubble" of curved space, which propagates like a wave through flat space and inside it, the observer can travel locally at sublight, but globally at super-light speed. M. Alcubierre constructed a special space-time metric that could model such a curvature. Formal substitution into Einstein gravit. equations, it was found that to possibly the realization would require exotic matter, tachyons or a naked singularity - probably unrealizable ...

Wormholes

Wormhole = tunnel connecting different places in space-time
® Hypothetical abbreviation for traveling between distant places in space, or for traveling between places in other universes (otherwise separated) .
Wormholes : permeable ( traversible ) , impermeable ( non-traversible )
Possibilities of using wormholes for time travel :
It is necessary to achieve a violation of time synchronization between the two mouths of wormholes. Theoretically, this can be done in basically two ways:
c Movement of the mouths of traversible wormholes ® Different relativistic time dilation ®can be used for time travel .
c "Park" one mouth of a wormhole in a place with a high gravitational potential ® gravitational dilation of time ...
One end of the wormhole would end up on Earth and the other near the horizon of the black hole. If we enter its initial opening and then travel towards the black hole, then time will begin to flow much slower than when entering. Only a few hours pass in the hole at the horizon of the black hole, while many years may pass in the entrance hole on Earth. In this way, traveling the wormhole "here and there" gives us a hypothetical opportunity to look into the distant future or past... If we wanted to achieve large time differences, the second mouth of the wormhole would have to be located close to the horizon of the black hole. Then, however, there would be a problem of leaving them without being irreversibly drawn into a black hole..!.. Another problem with the instability and explosion of a wormhole is mentioned below.
Wormholes :
× Microscopic - quantum - arise everywhere and constantly due to quantum fluctuations in the geometry and topology of spacetime:
      
    "Topological foam"

× Macroscopic - cosmic Inflationary expansion of the universe cmicroscopic wormhole can expand to macro- or mega-dimensions..?..
.. Next: ?? Artificially created wormholes ?? - Sci-Fi ..?!..
Problem: Instability of wormholes - strangulation, the conversion of a black hole is a singularity ®Nextinction of a wormholeN.
To ensure stability of wormholes is needed of "reinforcement" field using the negative energy density:®"exotic field", "exotic material" or "exotic mater" (Kip Thorne).
Violation weak energy conditions or energy dominance (§2.6 "Deviation and focus of geodesics") .
(T_ik - ¹/₂ T g_ik ) Vⁱ V^k l 0 ® r l 0 , r + p_a l 0 - weak energy condition
T^ikV_iV_k l 0 and vector T^ikV_k is the time or isotropic type ® r ³ 0 , -r £ p_a £ r (a = 1,2,3)  - energy dominance
(local energy density is non-negative and in addition the local energy flow takes place only inside or on the mantle of the light cone) - energy "dominates" over other components of the energy-momentum tensor ; - the pressure does not exceed the energy density, the speed of "sound" does not exceed the speed of light.
According to Raychaudhuri's equation of deviation and focusing of geodesics :
When the energy conditions (inequalities) for the energy-momentum tensor are met, gravity has an attractive character  and on geodesics of time resp. isotropic type focusing effect .
On the contrary: The wormhole needs "exotic matter" with a negative energy density - antigravity !!
Exotic matter
Matter with special, rare occurrences - " exotic " - properties.
How "exotic" would a mass with a negative energy density have to be to reinforce topological tunnels acting as time machines? ...
She is crazy exotic! - above all our imagination ..!..
Any exotic substance that has been created on the largest accelerators is "ordinary" in this respect ..!.. 

Nuclear reactions in collisions of two heavy atomic nuclei.
Above: When two nuclei collide at low or medium energies, their electrical (Coulombic) scattering, inelastic scattering with direct interactions by nucleon transfer or ejection, fragmentation or composition (fusion) of the nuclei can occur to form a new heavy nucleus.
Bottom: In a high-energy collision of two nuclei for a brief moment of 10^-20 sec. a quark-gluon plasma is formed, followed by hadronization.

However, we may have exotic matter with a negative energy density all around: DARK ENERGY _î

Different possibilities for the dynamics of the evolution of the universe. a) Closed space. b) Open space. c) Open space with final accelerated expansion - is caused by dark energy with antigravity effects.

Quantum fluctuations - by the uncertainty principle of quantum DE.Dt ³ h can briefly "swing" the local energy density to negative values. However, accumulating extremely dilute dark energy in the universe, or extracting negative micro-quantum fluctuations, into macroscopic scales is completely sci-fi ..!..   

Another sci-fi option: ?? Develop and uncover hidden compacted extra-dimensions of the Calabi-Yau manifold in multidimensional superstring theories ?? ...?... thus we could get into a completely different reality with other physical laws ...?!... - different kinds of interactions ..?.. ® N

The physics of black holes is discussed in detail in Chapter 4 "Black Holes" of the book "Gravity, Black Holes and the Physics of Spacetime".
On our topic: "Black holes - bridges to other universes? Time machines?".
In the same monograph, see also: §3.3, section "Closed worldlines and time travel" .

Time travel to the past
ß
- ? logical paradoxes and disputes with the principle of causality ? -

The paradox of the murder of our ancestors (the paradox of maternal murder, grandfather murder, etc.) :
After a closed time world, we could go back in time and kill our own parents (or grandparents) before his own birth.
Or a less morbid situation :

The Astronaut Paradox - A prevented start and a space flight
	The astronaut launches into space in a rocket and flies into the mouth of a "wormhole", which acts as a "time machine". After a closed time world-line, he could then return in space and time to his launch, damage the rocket and prevent himself from this original launch .

What it would then be possible to reconcile the two controversial alternatives in the future: our existence, when we could not be born ?; or the flight of an astronaut in a rocket, when he prevented himself from taking off ? Thus, such a traveler could not even go back to the past and perform the mentioned interventions ..!? ..
Monograph "Gravity, Black Holes and the Physics of Spacetime", §3.3, section "Closed World Lines and Time Travel".

1. Possible solution: Self-consistent synchronization - negation of "freedom of will"
Logical paradoxes and disputes with the principle of causality in time travel typically arise under the assumption of " freedom of will " - that the competent entity can decide in principle any intervention in running events. If freedom of will did not exist (and there really is no such thing in classical physics), there would not have to be a dispute with the principle of causality: the traveler does not change the past over time, because he has always been an immanent part of it (he can fulfill the past, not change it). The universe can be imagined as a "finished" and unique 4-dimensional manifold, into which the individual worldlines are already "incorporated". From this perspective, all events on time closed world lines could already be "synchronized" so that they interacted without contradiction in a closed cycle - would be self-consistent .
Objection:
However, if we take into account the irreversibility of the evolution of the universe (existence of dissipative processes, 2nd law of thermodynamics), the existence of closed time curves is physically unlikely, because the situation at a later time t2 cannot be identical with the situation at an earlier time t1. Thus, closed curves leading to a "time machine" could perhaps function at most within elementary particles .
Key objection: "billiard ball paradox" :

The paradox of billiard balls - conflicting trajectories of bodies
	From a starting position, by tapping of cue, a billiard ball is sent at a suitable speed towards the right mouth of the wormhole, functioning as a "time machine" - along a path A. This sphere flies through a wormhole, goes back in time and flies out of the left mouth before it has flown into trajectory A into the right mouth. It can then crash "into itself" (into its "younger version"), divert path A to an alternative trajectory B, out of the wormhole. However, this will prevent itself from flying into the right mouth - and thus hitting itself.   When moving, starting with exactly the same initial conditions (from the same position and at the same speed), thus creating two conflicting trajectories A and B, along which the sphere would move simultaneously. With proper orientation, the ball can fly through the wormhole several times - there are an infinite number of trajectories, differing in the number of passes through the wormhole.
There is no subjective decision-making and "freedom of will" here, it is a purely mechanical experiment !

2. Possible solution: The concept of many universes
A certain way to circumvent disputes and logical paradoxes in time travel could also be represented by Everett's and Wheeler's quantum-mechanical hypothesis of "many worlds" [79] (it is also discussed in §5.7 "Anthropic principle and the existence of multiple universes"), according to which the universe contains not only a unique history of the world, but many histories parallel. Whenever there is an interaction (or, from the observer's point of view, a "decision"), there is a "branching of history" into different universes. If the traveler eventually flies back to the past and changes his history there (for example, kills his mother before his birth), there will be a "turn" to another history in the universe, which will coexist with the original universe - the traveler will actually move to another universe, where it will be part of the changed history. There will be no unacceptable influence on the future of the present - our, default, original - universe.
Objection:
So far only pure sci-fi speculation! These parallel universes are "activated" only once, otherwise they are disjunct - in principle inaccessible and unknowable Þ from the point of view of gnoseology they do not effectively exist ..?..

Protection of causality - chronology - time sequences
These strange, even "pathological" consequences of time travel naturally lead to an effort to find mechanisms that would prevent the space-time events from "making such nonsense". S. Hawking put forward a hypothesis called the "principle of protection of chronology", which would forbid causal loops.
Possible mechanism: Destructive strong radiation, caused by the amplification of quantum vacuum fluctuations.  
The operation of a "time machine" would allow particles to repeatedly hit their own past through a time loop. The resulting quantum perturbations would amplify to macroscopic scales and their energy would destroy the wormhole.
This would cause the collapse, "burried" the topological tunnel and the destruction of the time machine. It will be possible to clarify perhaps the quantum theory of gravity .

Conclusion
Time travel: fantasy or physically real possibility ?

Let's try to answer in terms of current physical knowledge and the state of the technology :

• From a technical point of view ,
  any "time travel" is still just science fiction, even travel into the future.
  We can't develop enough speed (our rockets are "slow snails"!), we don't have strong gravity, we don't know about any topological tunnels ...
• From a physical point of view ,
  traveling to the future is realistically possible using the effects of STR (speed close to light) or GTR (strong gravity, black holes). Traveling into the past is probably impossible for macroscopic objects ... For elementary particles, closed time worldlines are in principle possible, their consequences are investigated in various variants of unitary field theory (eg in superstring theory). Here, too, most experts are skeptical ...

Concluding remark - reflection - on the theory of relativity:  
The role of the theory of relativity in science
Special theory of relativity
is applied not only in the macro- and mega-world - in astrophysics and cosmology - but also in the microworld - in atomic and nuclear physics + particle physics 
(physics of "elementary" particles ® "Nuclear physics and ionizing radiation physics".
The general theory of relativity
is crucial in the mega-world - in astrophysics and cosmology. Can GTR, as the physics of gravity and spacetime, have a role in the microworld ? Probably not in atomic and nuclear physics. But in the deepest the structure of particles, which unitary field theory seeks to understand, probably yes !
  Relativistic astrophysics and cosmology are discussed in Chapter 4 "Black Holes" and Chapter 5 "Cosmology" of the book "Gravity, Black Holes and the Physics of Spacetime".
  The unitary theory of fields and particles is discussed in Chapter B "Unitary theory of Fields" of the same monograph.

Vojtech Ullmann