Is physical time travel possible ?

AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology


- fantasy or physical reality? -  

What is time ?
(in macro world, micro world, megaworld)
Theory of relativity - physics of space, time, space.
Physical time travel ?

Vojtech Ullmann

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 ")

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.

What is so appealing about "time travel" for us ?
Overcoming death, dreams of eternal youth
Revision of wrong decisions in the past
Predicting the consequences of our decisions in the future
Reversing adversity, averting disasters, wars
Meeting deceased ancestors, averting their death
Reliving the beautiful moments of the past (some of which now it can no longer be repeated due to illness or old age)
Naturalists - to know what new knowledge will appear in the future
Historians - to know how distant historical events really happened
... etc.

History - Literature sci-fi :
H.G.Wells: "Time Machine" (1895) - in contradiction with contemporary notions of absolute time
Jakub Arbes: "Newton's brain" - is not it time travel, but only insight into the past in common:
superluminal speed

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

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 it is. 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 :

Theory of relativity :
"Time is what the clock shows"

"ideal" clock - isolated or corrected for all non-universal influences resp. :
Time is one of the coordinates of 4-dimensional space-time "
This time also coincides with " biological " time!

Note: Of course, time shifts of a few hours when traveling by plane have nothing to do with time travel, for example between Europe and America. 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.

What determines the direction of time?

More detailed discussion: 5.6 " The future of the universe. The arrow of time. Dark matter. " (

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 .


- time travel only to the future -

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

1. Galilei- Eistein's special principle of relativity :
The laws of physics are the same for all inertial frames of reference

Principle of constant speed of light:
The speed of light in vacuum is the same in all inertial systems regardless of any movement of the source or observer

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

The interval of the proper time
d t = (1-v 2 / c 2 ) .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 / (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
2    x 2 + y 2 + z 2 - c 2 .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:
An 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 relativity offer - at least formally - two possibilities of time travel into the past :
=> In flat spacetime STR by moving at warp speed s (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 / (1-v 2 / c 2 ) 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 :

- physics of gravity and curved spacetime -

- in the principle of time travel to the future and to the past -

Universality of gravity principle of equivalence:

The gravitational field at each point is locally equivalent (for all physical processes) to a situation where there is no gravitational field, but the reference system (observer) at this point moves with the appropriate acceleration - it is non-inertial.

Gravity = curved spacetime

Gravity - inertia - kinematics - deceleration of time

Einstein's equations of gravitational field (without cosmological term) :
an object describing the geometry of spacetime   =   an object describing the distribution of matter and energy

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: ds 2 = g ik dx i dx k ; geodesic equation:
Christoffel coefficients of an affine connection:
G for i l = ( 1/ 2) The 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 ") :

T ik    =  / energy density energy current density,
ie (momentum density) / c
| |
| energy current density,
ie (momentum density) / c
momentum current density,
pressures and stresses
(stress tensor)
\ /

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

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 as it moves.

(more detailed explanation "
General theory of relativity - physics of gravitation " - )

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) :
t   = (dx / C). (1 + 2 j / c 2 )       (1 + j / c 2 ) dt.
Then placed in a gravitational field is delayed relative to the same clock placement ofoutside 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:
=> Moving the local light speed within a sequence suitably inclined beams in strongly curved spacetime geometry - at right

=> 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? click
Black holes:

1. Large black holes - final stages of evolution of material stars after gravitational collapse, giant black holes in the center of galaxies
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
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 m (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 momentum of the source matter, excitation gravitational field - Lense-Thirring effect . - 2.5, passage " Rotating gravity ". Another 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 (Eng. 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 = e abg x b T g 0 d 3 x ), 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 / c 2 r ) .sin 2 J dt d j ; metric is then:

                                                                  A Schwarzschild metric "rotation" metric
off-diagonal members d j. dt lead to the fact that the body exerts a certain add the silo (in the geodesic equation d2 j / dt 2 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 momentum, Q - electr. charge

Spatio-temporal diagram of Kerr-Newman geometry - 3.6). The outer horizon r = r g + is the event horizon (the light cones below it face inwards towards r = 0). Below the inner horizon r = r g - , however, the light cones begin to "straighten" again, so that the light line of a body that has penetrated below the horizon r = r g + does not necessarily end in the singularity r = 0.

Full analytical extension
The O observer moving in the outer asymptotically plane region of the A 1 Kerr-Newman spacetime has three possibilities.
It will either move constantly in A
1 (solid line), so it will reach I + or + in the limit . However , if the observer penetrates below the horizon r = r g + (dashed trajectory) into the inner region B 1 , he also passes through the horizon inner r = r g - into the region C 1 , 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 A 2 . The situation in this next "universe" A 2 is not completely determined by the initial conditions on the Cauchy hyperfield S , as can be seen, for example, at the point p A 2 .

Critical assessment - what is the fact?

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 inside 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) cannot actually 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.

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-Nordstrm 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 - rather interesting ...: Gdel'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 gravities. equations, it was found that to possibly. the realization would require exotic matter , tachyons or a naked singularity - probably unrealizable ...


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 separate) .
: 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:
-- Movement of the mouths of traversible wormholes Different relativistic time dilation can be used for time travel .
-- "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 No microscopic wormhole can expand to macro- or mega-dimensions.?
.. Next: ??
Artificially created wormholes ?? - Sci-Fi ..?! ..
Problem: Instability wormholes - strangulation, the conversion of a black hole is a singularity N extinction wormhole N .
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 also - 1 / 2 T g also ) V i V to  
3  0      r 3 0,   r + p and L 0  - weak energy condition
of T
also V and V to L 0, and the vector T also in to the time or isotropic type r 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 fussing 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
just 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.
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

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 D E . D t 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 variety 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

-? logical paradoxes and disputes with the principle of causality? -

The existence of closed time-lines of world leads to logical paradoxes :
On the way to the past, there can be situations and events, when
the result cancels the cause that caused it
(reaction cancels the action that triggered it)

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 birth.
Or a less morbid situation

The Astronaut Paradox - A failed 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, 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, kd y f we were not 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 starting point: 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 variety, into which the individual worldlines are already "incorporated". From this perspective, all events on time closed world lines could be
j IT "synchronized" so that they interacted unquestionable in a closed cycle - would be self-consistent .
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 t
2 cannot be identical with the situation at an earlier time t 1.. 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, the tapping cues transmitted cue ball suitable speed toward the right wormhole mouth 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 prevents it 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", it is a purely mechanical experiment !

2. Possible starting point: 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.
So far only pure sci-fi speculation! These parallel universes are "activated" only once, otherwise they are disjunct - in principle inaccessible and unknowable
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 of " poking such nonsense ". S. Hawking put forward a hypothesis called the " principle of protection of chronology " , which would forbid causal loops .
Possible mechanism:
Destructive radiation caused by 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, "sinking" of the topological tunnel and the destruction of the time machine. It will be possible to clarify the quantum theory of gravity .

Paths time: fantasy or physically realistic possibility ?

Attempt to answer in terms of current physical knowledge and the state of the art :

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 " elementary "particles" " Nuclear physics and ionizing radiation physics ".
The general theory of relativity

is crucial in the mega-world - in astrophysics and cosmology . Can OTR, 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.

Gravity, black holes and space-time physics :
Gravity in physics General theory of relativity Geometry and topology
Black holes Relativistic cosmology Unitary field theory
Anthropic principle or cosmic God
Nuclear physics and physics of ionizing radiation
AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology - Philosophy

Vojtech Ullmann