(page in development 26.08.2025)
Our perception of time bases on our feedback with environment leaving imprints into our memory. We can tell memory trace from the actual experience. This creates abstraction of the past and a subjective way to qualify events as preceding and succeeding, eventually leading to the concepts of cause and effect. This perception is fed by the surrounding world with continuous changes and move. Perception of movement is a basic evolutionary mechanism of all animals. All senses work due to changes. Even visual perception of a stationary landscape is possible because of involuntary eyes movements and immobilization of eye balls leads to blindness. This way the light sensing cells of retina can be permanently excited on the bright/dim borders of the image projected by the lenses. Similarly hearing requires permanent activation of hair cells in organ of Corti of our ears by oscillating pressure wave of a sound. Our brain to work has to be permanently fed by stimuli often correlating distinguishable signals from our senses with signals from our moving body requiring feedback to be controlled.
Ordering of sequences of the remembered events requires repeatable reference events – sunrises, sunsets, Moon phases, seasons. To position events within this reference scale we constructed clocks, calendars and a concept of dimension of time relative to the observed changes and movements. But still the subjective measure of time is frequency of the brain stimuli – when a little happens time is getting longer.
The cause and effect are usually not reversible like many sequences of surrounding us events. We use a term of thermodynamic arrow of time. Many processes in micro-world of atoms seem reversible, equally likely forward and backwards in time but this applies to simple, isolated systems. However global interaction of many objects usually makes some states of the large system to be much more likely than the others. Gas diffuses filling the whole container and suffocation of a tenant in a room with air diffused to the other half of the room, never happens. High probability becomes practical certitude. Interaction of many particles causes gradual collapse of the wave function, similarly like in the measurement. The Schrodinger’s cat is either live or dead, not in the mixed state. The wave becomes the particle. Thermodynamic laws are time irreversible and direct macroscopic processes make some events preceding others as a cause. The origin of time is linked to non-reversibility of events.
Our subjective perception of time can be related to the time of other observers, having similar daily experiences, even when we skip some periods, losing consciousness or sleeping. Technical progress makes things harder and time synchronizing during telephone conversation with antipodes requires more care. Appointment of chat during sunset can be misunderstood. Precise synchronization of clocks at different locations became a problem during development of railway networks with timetables. Synchronizing clocks of observers quickly moving one in respect to other is even more challenging. A.Einstein, similarly like earlier H.Poincare, has proposed method assuming constant and independent on our speed, finite value of speed of light. This assumption was confirmed with good accuracy by results of Michelson-Morley experiment (lack of ether drift, end of XIX century) and many experiments during XX century. The synchronization method consists of sending to the other observer light pulse, to be reflected by the other and registered back by the first observer. The second observer sets his clock for the time at the moment of reflection to be the mean value of the reported by the first observer moments of sending and receiving the reflected pulse. This convention was used by radio operators of railway system in the second half of XIX century. From the point of view of the first observer, the light covers the same distance forward and backwards. However the second observer is aware that the pulse covered shorter distance before and longer after being reflected. The pulse sender is constantly moving away. From his point of view, the moment of reflection cannot correspond to the mean time between the pulse emission and reception and is slightly less by amount dependent on mutual distance and speed. If the pulse is repeatably back-reflected to the second observer, the time measured between consecutive reflections runs slower independently of the direction of movement (escaping or approaching) accounting to the time dilation. The situation is symmetrical and the symmetry is violated only by acceleration of the second observer on return trip accounting to the famous twin paradox.
Even without the clock synchronization method the same result can be concluded on more general philosophical grounds, assuming uniformity of space and principle of relativity (equivalence). The first requires the time and position of the second observer measured by him to be linearly dependent on time and position measured by the first observer. The second requires equivalence of both observers observations and symmetric conclusions. Both assumptions leads to so called Lorentz transformations of time and position describing time dilation and size reduction in direction of the movement – the same transformations as obtained from clock synchronization principle. Hendrik Lorentz derived these transformations earlier basing on requirement of the same form of Maxwell equations (electrodynamics) in two relatively moving with constant speed (inertial), frames of reference.
Good understanding of time dilation reconciles conclusion of both observers that the time in the other frame, runs slower. This conclusion has been confirmed experimentally using precise atomic clocks. Accepting that life processes follow the same principle, one has to admit that time can be slowed down.
One of Lorentz transformations consequences is a link between distance and time in the moving frames of reference. This led to the concept of spacetime. It was developed parallelly to Einstein’s works by Hermann Minkowski. The spacetime is buildup with momentary events characterized by a moment of time and spatial position. The distance between them (metric) is defined as spacetime interval. Its square is equal to the difference between square of the path of light passed during the time difference and square of the spatial distance. Such interval between events does not depend on inertial frame of reference from which is determined – is invariant for all observers moving with constant speed. All events that can be seen by the observer at a given moment are distanced by the interval equal to zero. It is irrelevant whether the event is next to the observer or is it star far away. If a square of the interval between events is negative the events cannot affect each other and the event is invisible by the observer watching at the other event. The spatial distance between them is too large for light (and any signal) to pass during the time difference. Each event (and observer) can thus define two parts of spacetime with events interval square positive. One corresponds to positive time difference (future) and one with negative time difference (past). In spacetime they form two cones meeting at the event. These two parts of spacetime include all events that can have cause-end-effect relationship with the event. The Minkowski (metric) spacetime extends three-dimensional Euclidean space by the time dimension and by the new definition of distance – invariant for all inertial observers.
The Minkowski spacetime is a rather simple model assuming that light propagates with constant speed along straight lines.
In theory of General Relativity Einstein considered how masses affect the spacetime interval. Masses create gravitation forces – the source of acceleration. One of formulations of the equivalence principle is that gravitational effects are equivalent to phenomena in accelerating frame of reference. Thus, effect of masses can be studied considering clocks synchronization between accelerating frames. Since explanation by Max Planck of black body radiation spectrum (1900), physicists believe that energy of the light carrier – photon, is proportional to the frequency of its wave. The massive elementary particles can be fully transformed into light – annihilated conserving the energy. The particle in gravitational field (accelerated) gains energy, thus the photon increases frequency and the photon escaping from mas is red-shifted (to lower frequencies). It has consequences for time. Frequency of photon- oscillations of electric/magnetic field, can drive the clock and its rate agrees with the synchronization rules. Masses affecting time rate, affect spacetime interval in the spacetime model including mas and accelerating frames. They modify spacetime geometry introducing curvature. To spacetime curvature contribute also momentum, pressure or strain. Action principles in this geometry result in photon path deviating from the straight line. This effect, was used to predict shift of the observed position of star visible close to a large mass e.g. Sun. It was calculated by Einstein and confirmed during famous expedition of Arthur Eddington to the Island of Principe (1919) to observe total solar eclipse. The observed (Hyades cluster) shifts of star positions close to the Sun (1.75 arcsecond) fully agreed with Einstein calculations and were double of the classic theory expectations. It became then the first experimental proof of Einstein’s General Relativity and Einstein himself quickly became the world celebrity.
Like usual, the proof was initially questioned by the second evidence, collected by the other expedition to observe the solar eclipse led by Frank Dyson in Sobral, Brasil. Their results were closer to Newtonian model of light but over years, these results were questioned and finally rejected with errors attributed to a defect in the astrographic lenses setting (see Physics Today 62 (3), 37–42 (2009)). The solar eclipse star shift experiments were later repeated few times with the last, the most accurate, led by University of Texas in 1973. Even more accurate data was provided later by radio astronomers observing occulting of quasars by the Sun. The general relativity stands then on a quite solid experimental base. Also the very assumption of the relativity- constancy of the speed of light, was questioned during XX century, but convincingly confirmed in a number of good quality studies (e.g. Phys. Rev. Lett. 39, 1051). The principal difficulty comes from the fact, that most experiments involve interferometric measurements (the most accurate) of light produced by moving long distance sources, and measure phase velocity of light propagating through air, with characteristic refraction index (or dielectric constant) responsible for the light phase propagation being sum of the phase shifted waves produced by the local dipoles. Also extraterrestrial sources are seen as light affected by interstellar extinction. The light is then produced not by a moving source but by local medium. The Michelson-Morley experiment was addressing solely the question of ether-drift and attempted to measure difference of light (produced by a local oil lamp) velocity in different directions – e.g. parallel and perpendicular to the Earth orbital direction. Many subsequent experiments consider independently effect of the source speed and of the receiver speed. The zero effect seems to be quite convincingly proven.
The General Relativity admitting spacetime curvature can theoretically describe tunnel joining two remote areas. It can connect future and past offering possibility of time travel. Such geometric models, in terms of topology are called not simply connected. In the simply connected space all closed curves can be continuously contracted to a point. Not simply connected is e.g. ring torus surface. Any closed curve around the ring cannot be contracted to a point. Spaces not simply connected can make difference in validity of some electrodynamics laws. Concepts of spacetime tunnels do not violate laws of physics. However they involve usually huge gravity force gradients that are able to tear off most of known forms of matter. The question of spacetime tunnels existence is still open. Many theoretical works on the subject appeared during XX century. Some candidate for the tunnel would be a pair, black hole and white hole, however there is no evidence of existence of white holes (besides Bing Bang itself).
Leaving aside the technical problems such possibilities open up fundamental philosophical questions. The past existed some time ago but appears real as a fragment of the spacetime. Does the past exist in the real way and is the future determined although non existent at the moment? If we accept the Copenhagen interpretation of quantum mechanics suggested by experimental violation of Bell’s inequality, the answer to the second question is ‘not’. Consequences of current events are to large extent random and driven by probability. Then, unpredictable journey back in time would transfer us to the world not known from the history and real only for us. The traveler would simply vanish from our world into parallel, possibly humanless world. The assumption of the determined future is similarly not attractive encompassing non existence of free will. But why we want to know and understand our world if we cannot change anything ? Why the nature equipped us in self-preservation instinct to run away from the attacking lion if it is pointless and not changing evolutionary survival rate ? Negating the free will leads to conceptually vain and non prolific attributing everything to the God’s plan. Anyway time travel forward without tunnels would be possible when we lose consciousness and could hibernate for a longer time. However more attractive variant would be to travel forward and back, returning to the present. Then, the discussed above limitations appear again.
The above considerations concern human perception of time and not structure of time in cosmological scale. At this end various models consider beginning of time, its end or cyclicality. They assume spacetime geometry attempting to arrive on solutions of the General Relativity field equations. Those ultimate models describe world where man can not exist so have purely theoretical importance. They can be based on contemporary sophisticated measurements like angular distribution of cosmic microwave background, but their credibility is supported only by precision and consequence of the used mathematics. In physics, good mathematical model often allowed prediction of new phenomena, not known before but discovered afterwards. The math appeared wiser than men. When James Maxwell in XIX century gave mathematical formulation to set of rules describing all then known laws of electrodynamics, he was not fully aware of consequences. Years after, Hendrik Lorentz conceived on their basis, set of transformations of position and time that revolutionized thinking about space and time.