The Evolution of space and time
Paul Langevin 1911
Scientia 10: 31-54

Translation of the French original, with verification from a scanned copy. A retyped version can be found here:
from :’Évolution_de_l’espace_et_du_temps (you need to select the whole address).
Another translation can be found here:

Translated with help of Google Translate. and manually corrected, in part with help of Babelfish.
-> Native English speakers, please help improve the style and word choice.
Note: as is habitual in old English texts, the word vitesse is consistently rendered "velocity". "Ligne d'universe" is rendered "world line" and "lois du monde", "laws of the universe".

I add paragraph numbers, as well as a few aids for understanding in bold face (colour #300fa3); thus note that these are not in the original text.


The attention of physicists was recently brought back to the fundamental concepts of space and time as new experimental facts require them to be revised; nothing can better show the empirical origin of these concepts than their progressive adaptation, not yet completed, based on data from ever subtler human experience.

I would like to show that the form, usually insufficiently analyzed, in which these concepts presented themselves until now, was determined, or conditioned, by a particular and provisional synthesis of the world, by the mechanistic theory. Our space and our time were those required by rational mechanics.

To the increasingly powerful new synthesis which the electromagnetic theory of physical phenomena represents, correspond a space and a time -especially a time- other than those of mechanics, and in favour of which our current means of experimental investigation come to decide. It is particularly remarkable that the increasing sophistication of our measurement methods, some with a precision that was pushed beyond a billionth, still obliges us to continue adapting the most fundamental categories of our thought to the facts. It is there that, for the philosopher, there is an excellent occasion to penetrate the intimate nature of these categories by finding them still on an evolving path, by seeing them live and transform before his eyes.

[32] There is neither space, nor time a priori: with each moment, with each level of sophistication of our theories of the physical world, corresponds a concept of space and time. Mechanics implied the old concept, electromagnetism requires a new one of which nothing enables us to say that it will be final.

It is also difficult for our brain to get used to these new forms of thought: reflexion is particularly delicate there and can be supported only by the formation of an adequate language.

This is the task on which, to facilitate the evolution of the mankind, philosophers and physicists must collaborate today.

  • 2

All living things have an interior and spontaneous power of expansion that is greater when they are better adapted to the environment in which they were born. When, as a result of this expansion, a meeting takes place between individuals or species, there may be mutual adaptation, or, if accordance is impossible, conflict with survival of the fittest, which generally assimilates the essence of the other and imposes to it a new form that life seems to have deemed better.

The same is true for our physical theories: some are particularly well established, have succeeded brilliantly in the interpretation, in the grouping of a category of experimental fact, material to which they impose a form; and following this form they then develop spontaneously this rhythm of their own, taking as substance of the building that they construct the facts already known, but scattered, and those they are directed to discover, and finally those already established in synthesis of different theories that the new one absorbs after coming in conflict with them.

Just as the construction of living beings is facilitated by the organic synthesis already realised in other creatures on which they feed, the new theory maintains and utilises more or less completely the groupings of facts already established by the theories over which it triumphed.

We are currently witnessing a conflict of this kind between two particularly important and beautiful conceptions [33] of the universe: the rational mechanics of Galileo and Newton on the one hand and on the other hand the electromagnetic theory in the mature form that it was given by Maxwell, Hertz, and Lorentz.

Rational mechanics was created for the interpretation of the phenomena of visible motion and it succeeded admirably well. All scientific effort of the eighteenth century and much of the nineteenth was devoted to extend this power to explain all physical phenomena by applying these laws to the motions of various invisible material particles or fluids.

Thus developed the doctrine known as mechanics, by the fusion of rational mechanics with atomistic hypotheses. The success was great in some areas, for example the kinetic theory of fluids, but less in others such as elasticity and optics.

One should not forget here that often the failure of mechanics was blamed on the atomistic concept, now definitely established by indisputable experimental facts, and which association with the electromagnetic theory showed over the last fifteen years to be so remarkably fertile. What actually seems to be questionable is the application of the laws of mechanics to invisible motions that were first established for visible motions, and even for them they represent only a first, although excellent, approximation.

The theory of electromagnetic phenomena, as we have today, is certainly independent of the laws prescribed in the motion of matter through rational mechanics, although it seems to intervene in some fundamental definitions: the best evidence of this independence is provided by the contradictions that currently stand between the two syntheses.

Electromagnetism is just as remarkably adapted to its original domain as rational mechanics was at its own, with its concepts of a very special medium that transmits the actions step by step, the electric and magnetic fields characterising the state of this medium, with the very particular form of relations that it states between simultaneous variations of these fields in space and time; electromagnetism constitutes a discipline, [34] a way of thinking all of its own, quite distinct of mechanics, and endowed with a surprising strength of growth since it assimilated without effort the vast field of optics and radiant heat to which mechanics remained powerless, and in which it daily provokes new discoveries. Electromagnetism has conquered much of physics, invaded chemistry and grouped together an immense number of facts that were hitherto without form and disconnected.

Of our two opposing theories, the first possesses the titles of nobility of a long-standing past, the authority to have seen its laws verified by the most distant stars and by the most tenuous gas molecules; the second, younger and more alive, adapts itself much better to the entirety of physics and possesses an inner strength of growth that the other seems to have lost.

Maxwell had thought it possible to reconcile the two theories and show that electromagnetic phenomena are susceptible to mechanical interpretations, but his demonstration as made for the particular case of phenomena presented by closed currents, only proves that the two syntheses have common characteristics, the common property to leave certain integrals stationary, but they may remain irreconcilable on other points.

  • 3

These divergent characteristics were recently highlighted by new experimental facts, by the negative results of all experiments, some of extraordinary delicacy, which have been attempted to demonstrate the overall uniform translational motion of a material system by experiments inside this system, to perceive absolute translational motion.

We already knew - and rational mechanics perfectly accounts for this fact - that mechanics experiments of visible motions inside a material system do not allow one to detect a uniform translational motion of the whole system, however they do allow one to detect [35] rotational motion by means of a Foucault pendulum or gyroscope. In other words, from the mechanical point of view, overall uniform translation has no absolute sense while rotation does.

But in the interior of a material system, other experiments may be attempted which bring electromagnetic or optical phenomena into play. The electromagnetic theory involves in its explanations a medium, the ether, which transmits the electrical and magnetic actions and in which the electromagnetic disturbances propagate with a determined velocity, in particular light.

It was hoped that if a material system moves in uniform translation with respect to this medium, electromagnetic or optical experiments inside this system could enable to perceive or demonstrate this translation.

As the Earth in its annual motion has a translational velocity that varies constantly with amounts of up to sixty kilometres per second relative velocity, corresponding to two positions diametrically opposite of the globe in the orbit, it was hoped that at least at certain times of the year observers on Earth and their instruments would move relative to the ether with a velocity of this order and might be able to demonstrate their motion.

One could expect this, because by combining the fundamental equations of electromagnetism, believed to be accurate to observers stationary in the ether, with ordinary concepts of space and time such as rational mechanics requires, one found that these equations should change shape to observers moving in the ether, and the differences for velocities such as of the Earth in its orbit should be visible in certain experiments of extraordinary delicacy.

But the result was found to be consistently negative, and independent of any interpretation, we can state as experimental fact the contents of the following principle, namely that of relativity:

If different groups of observers are in uniform translation relative to each other (such as observers on Earth for various positions of the Earth's orbit), [36] all mechanical and physical phenomena follow the same laws for all these groups of observers. None of those can, through experiments inside the material system to which it is connected, highlight the uniform translation of this whole system.

From the electromagnetic point of view we can still say that the fundamental equations, in their usual form, are verified for all these groups of observers at the same time, that everything happens for each one as if it was stationary with respect to the ether.

  • 4

It is thus an experimental fact that the equations between physical quantities by which we translate the laws of the outside world, must have exactly the same form for different groups of observers, for various reference systems in uniform translation relative to each other.

This requires, in the language of mathematics, that these equations admit a group of transformations corresponding to the passage of one reference system to another that is moving relative to it. The equations of physics must be preserved for all transformations of this group. In such a transformation, when switching from one reference system to another, measures of various magnitudes, especially those that correspond to space and time, are modified in a manner that corresponds to the structure of these concepts.

Now, the equations of rational mechanics actually admit a group of transformations corresponding to the change of reference system, and the part of that group that is concerned with measures of space and time agrees with the usual form of these concepts.

It will be the great merit of H. A. Lorentz to have shown that the fundamental equations of electromagnetism also admit a group of transformations that allow them to take the same form when we pass from one reference system to another;

This group differs profoundly from the preceding concerning the transformations of space and time.

[37] One must make a choice: if we want to maintain an absolute value to equations of rational mechanics, to mechanical processes, as well as the corresponding space and time, then we must regard as false those of electromagnetism, renounce the admirable synthesis that I mentioned here above, go back in optics to for example an emission theory, with all the difficulties that it entails and which led to its dismissal, you see, more than fifty years ago. If instead we want to keep electromagnetism, we must adapt our mind to the new concepts that it requires for space and time and consider rational mechanics as having no more value than as a first approximation, more than sufficient however when it concerns motions whose velocity does not exceed a few thousand kilometers per second. Only electromagnetism, or the laws of mechanics that admit the same transformation group as the first, allow us to go further and take the dominating place that mechanism assigned to rational mechanics.

  • 5

The world according to classical mechanics

To better highlight the opposition between the two syntheses, it is easier to merge, as proposed by Minkowski, the two concepts of "space" and "time" into the more general concept of "world".

The world is the set of all events: an event consists in that it happens or that there is something in a certain place at a certain moment. Given a reference system, that is to say a system of axes linked to a certain group of observers, an event is determined in terms of its position in space and time by four coordinates related to this reference system, three for space and one for time.

Given two events related to a reference system, they generally differ in both space and time, occurring at different points at different moments. To a pair of events corresponds thus a distance in space (of the points where the two events are happening) [38] and an interval in time.

We can thus define the time by all the events that follow one another at one point, for example in the same piece of matter related to the reference system, and define the space by all simultaneous events. This definition of space corresponds in fact to that in which the shape of a moving body is defined by all the simultaneous positions of various pieces of matter that compose it, its various material points, by the totality of events that constitute the simultaneous presence of these different material points. If one agrees with Minkowski to call the world line of a piece of matter that may be moving relative to the reference system, all events that succeed each other in this piece of matter, then the shape of a body at a given time is determined by the total of simultaneous positions on the world lines of the various material points that make up this body.

The concept of simultaneity of events that occur at different points is fundamental for the very definition of space when it comes to bodies in motion, and this is generally the case.

In the ordinary conception of time, one attributes to simultaneity an absolute sense, one assumes it independent of the reference system; it is necessary that we analyze more closely the content of this usually tacit hypothesis.

Why do we usually not admit that two events that are simultaneous for a certain group of observers, may not be so for another group moving relative to the first, or, equivalently, why don't we admit that a change of reference system allows to reverse the sequence in time of two events?

This is obviously based on our implicit assumption that if two successive events follow in a certain order for a given system of reference, the one that occurred first could have intervened as a cause and modified the conditions under which the second was produced, whatever the distance that separates them in space.

In these circumstances it is absurd to suppose that [39] for other observers, for another reference system, the second event, the effect, could be anterior to its cause.

The absolute character usually admitted to the concept of simultaneity is therefore based on the implicit assumption that causality can propagate with infinite velocity, the assumption that an event can occur instantaneously as cause at any distance.

This hypothesis is consistent with the mechanistic one and is required by it since a perfect solid in rational mechanics, or for example an inextensible interposed bell cord between the two points where events occur, would instantly report the production of the first event to the point where the latter will occur, and would therefore allow to take the first in account, to intervene as cause in the conditions that determine the second. So there is mutual adaptation of rational mechanics and ordinary conceptions of space and time in which the simultaneity of two distant events in space has an absolute sense.

We are therefore not at all surprised to note that in the transformation group which preserves the equations of mechanics, the time interval of two events is preserved, is measured the same way by all groups of observers whatever be their relative motions.

It is different for the distance in space: it is a simple fact and contained in the usual concepts that the spatial distance of two events does not usually have an absolute sense and depends on the reference system that is used.

A concrete example will illustrate how the distance in space of the same two events may be different for different groups of observers in relative motion to each other. Imagine that through a hole in the floor of a car that is moving relative to the ground, one drops two objects in succession: the two events that constitute the exits of the two objects though the hole of the car occur at the same point for observers in the car but at different points for observers on the ground. The distance in space of these two events is zero for the first observers, and to the contrary for the others, equal to [40] the product of the velocity of the car with the time interval between the falling of the two objects.

It is only in the case that the two events are simultaneous that their distance in space has an absolute sense, does not vary with the reference system. It follows immediately that the dimensions of an object - the length of a ruler for example - have an absolute sense, are the same for observers at rest or in motion with respect to this object: we have in fact noticed that for any observations, the length of a ruler is the distance between two simultaneous positions of the ends of the ruler, that is to say the distance in space of two simultaneous events, of the two simultaneous presences of both ends of the ruler. We have seen that simultaneity as well as the distance in the space of two simultaneous events, have an absolute sense in the habitual conceptions of time and space.

Given two arbitrary successive events, two events separated in time, we can always find a reference system with respect to which these two events coincide in space, observers for whom these two events happen at the same point. It will in fact suffice to give these observers, compared to the original reference system, a motion such that having attended to the first event, they next attend to the second, so that the two events happen for them at the same point nearby; it suffices to give the observers a velocity equal to the ratio of distance in space by the time interval of the two events as reported in the original reference system, and that will always be possible if the time interval is not zero, if the two events are not simultaneous.

What one can thus realise for space, the coincidence of two events in space by means of a suitable choice of reference system, we have seen that one can not achieve that for time, since the time interval of two events has an absolute sense, is measured in the same way in all reference systems.

One has there an asymmetry that is habitually made between space and time but which the new conceptions make disappear: the time interval, just like [41] the distance in space becomes variable with the reference system, with the motion of observers.

The world according to the new mechanics

In the new conceptions, a single case exists and must exist where the change of reference system is ineffective: it is where the two events coincide in both space and time: this double coincidence must in fact have an absolute sense since it corresponds to the encounter of the two events and from this encounter may well emerge a phenomenon, a new event, which necessarily has an absolute sense. Retaking the previous example, if the two objects that exit the car through the same hole, leave it simultaneously, if their releases coincide in both space and time, this can result in collision, a breaking of objects; and the phenomenon of collision has an absolute sense, so that in any conception of the universe (electromagnetic or mechanic), the coincidence in both space and time, if it exists for a group of observers, can not be denied by another group, regardless of its motion relative to the first. For those who see the car pass by as well as for those who find themselves in the car, the two objects will have broken each other because they passed at the same time at the same point.

Except for this very special case, it is easy to see that the electromagnetic design requires a major overhaul of the concept of world. The equations of electromagnetism imply in their habitual form that an electromagnetic disturbance, a light wave for example, propagates in the vacuum with the same velocity in all directions, equal to about three hundred thousand kilometers per second.

The newly established experimental facts have shown that if these equations are exact for a group of observers, they should also be exact for all others regardless of their motions relative to the first; of this results the paradoxical fact that a given light disturbance must propagate with the same velocity for different groups of observers in motion relative to each other. A first group of observers sees a light wave propagating in a certain direction with a velocity of three hundred thousand kilometers per second and sees another group of observers chasing this wave with [42] whatever velocity; and nevertheless, for this second group the light wave will move with respect to it with the same velocity of three hundred thousand kilometres per second.

Einstein first showed how this necessary consequence of the electromagnetic theory is sufficient to determine the characteristics of space and time required by the new conception of the world. One conceives, from the preceding, that the velocity of light must play an essential role in the new formulations: it is the only velocity that is preserved when switching from one reference system to another and it plays in the electromagnetic world the role played by the infinite velocity in the mechanical world. This will be clear from the results that follow.

For any pair of events, changing the reference system changes both the distance in space and the time interval, but in view of the importance of these changes, we are led to classify pairs of events into two broad categories for which time and space play symmetric roles.

The first category consists of pairs of events such that their distance in space is greater than the path travelled by light during the time interval, that is to say, such that if the emission of light signals accompanies the production of two events, each of them will take place before the passage of the signal from the other. Such a relationship has an absolute sense, that is to say, it holds for all reference systems if it holds for one of them.

The transformation equations required by the electromagnetic theory show that in this case, the sequence of two events in time has no absolute sense. If for a first reference system, the two events follow each other in a certain order, this order will be reversed for observers moving with respect to the first with a velocity less than that of light, that is to say with a physically feasible velocity.

It is obviously impossible that two events whose sequence could thus be reversed would be united by a relationship of cause and effect, for if such a relationship existed between our two events, certain observers would see the cause after the effect, which is absurd.

[43] However, since the distance in space of our two events is greater than the path travelled by light during their time interval, the first could not intervene as cause in the production of the other, the second could not be informed of the first, except if the causal connection could propagate with a velocity faster than light. We must therefore, according to the preceding, eliminate such a possibility: causality, whatever its nature, must not be able to propagate with a velocity faster than light, there can be neither messenger nor signal that can surpass three hundred thousand kilometres per second.

We must therefore admit that an event cannot act instantly as remote cause, that its impact cannot be felt immediately but on the spot, at the very point where it takes place, and subsequently at increasing distances, and spreading with at most the velocity of light. This plays thus in the new conceptions, already in this view, the role that in the old conceptions infinite velocity plays, which there represents the speed limit with which causality can propagate.

This goes to show that the current antagonism between mechanics and electromagnetism merely manifests in a new form the opposition between two concepts that have succeeded each other in the development of electrical theories: that of the instantaneous action at a distance consistent with mechanics, and the one introduced by Faraday of transmission through a medium, by local action. This ancient opposition affects today even the most fundamental concepts.

From the preceding follow various consequences: firstly it is impossible for a piece of matter to move with respect to an other with a velocity exceeding that of light. This paradoxical result is contained in the formulas that led to the new kinematics of velocities: the composition of any number of velocities below the velocity of light always gives a lower velocity than light. Similarly in the ordinary conception, the composition of any number of finite velocities always gives a finite velocity.

[44] We can attest then that no action at a distance, gravitation for example, can propagate faster than light, and we know that this condition is not contradicted by the currently established astronomical results.

Finally it is necessary to renounce the perfectly rigid body of mechanics in which we could find a way to signal immediately at a distance, to establish a causal connection propagating faster than light. Nothing of what we know about real solid objects opposes the idea that any action, any wave must propagate through it less fast than light; in fact elastic waves in the most rigid solids propagate with a velocity much lower than that. The important thing is that we must reject the very concept of a perfect rigid body, a body that could be put in motion simultaneously at all its points.

One can summarise the preceding reasoning as follows: if there were a signal that could propagate with a velocity faster than that of light, one could find observers for whom the signal would have arrived before having left, for whom the causal link that the signal allows to establish would have been reversed: we could telegraph into the past, as Mr. Einstein remarked and we believe that that would be absurd.

The two events of the pair in question, with no definite sequence in time, are thus necessarily without possible mutual influence, they are truly independent events. Evidently, having no causal connection between them, they can not succeed each other in the same piece of matter, they can not belong to the same world line, the life of a single being. This impossibility is moreover in agreement with the fact that to be successively the seat of these two events, this piece of matter should displace itself with a velocity exceeding that of light.

Both events can thus not be brought to coincide in space for any choice of reference system, but they can be brought to coincide in time: since their order can be reversed, there are reference systems for which the two events are simultaneous.

One may call pairs in space, the pairs of events [45] that have just been considered, whose sequence in time has no absolute sense, but which, in an absolute manner, are distant in space.

It is noteworthy that, if the spatial distance between two events can not be canceled, it reaches a minimum precisely for reference systems with respect to which the two events are simultaneous.

ds2 = invariant = (dx2 + dy2 + dz2) - c2dt2

Hence the following statement:

The spatial distance between two events that are simultaneous for a certain group of observers is shorter for them than for all other observers that are in any motion with respect to them.

This statement contains as particular case what is called the Lorentz contraction, that is to say, the fact that the same ruler as examined by different groups of observers, some resting, others in motion with respect to it, is shorter for those who see it passing by than for those who are connected to it. We have in fact seen that the length of a ruler to observers who see it passing by is defined by the distance in space of two positions simultaneously (for those observers) at both ends of the ruler. And this distance, according to the preceding, will be shorter for these observers than for all others, in particular for those who are connected to the ruler.

One also easily understands how the Lorentz contraction can be reciprocal, i.e. how two rulers, equal at rest, see themselves mutually shortened when they slide against each other, as the observers connected to one of the two rulers, see the other shorter than theirs. This reciprocity is based on the fact that observers attached to the two rulers in relative motion do not define simultaneity in the same way.

We're going to find pairs of events in the second category of properties exactly correlative to the previous by permutation of space and time. These pairs, which I will call pairs in time, are defined by the following condition, which has an absolute sense: the distance in space between two events is less than the path traveled by light during their time interval; said otherwise, the second event occurs after the passage of the light signal of which the emission coincides [46] in space and time with the first. This introduces, from the point of view of time, an asymmetry between the two events, the first is anterior to the passage of the light signal whose emission coincides in space and time with the second event, while the second is posterior to the passage of the light signal which accompanies the first event. A causal relationship may exist, at least by means of the light, between the two events, as the latter could have been informed of the first, and this requires that the sequence has an absolute sense, cannot be reversed by any change of reference system. One sees immediately that such a reversal would require a velocity exceeding that of light for the second reference system with respect to the first.

Two events between which thus exists a real possibility of influence, if they cannot be brought to coincide in time, can always be brought to coincide in space by a suitable choice of reference system. Especially if the two events belong to the same world line, or succeed with an absolute order in the life of a piece of matter, they coincide in space for observers linked to this piece of matter.

In connection with what happened just now, if the time interval of two events cannot be cancelled, it reaches a minimum, particularly for the reference system with respect to which the two events coincide in space .

Hence the statement:

The time interval between two events that coincide in space, which succeed in a single point for a certain reference system, is less for that one than for any other one that is in whatever uniform translation relative to the first.

  • 6

In all of the foregoing, the used reference systems are supposed to be driven by uniform translational motion: for such systems only, attached observers cannot experimentally detect their overall motion; only for such systems must the equations of physics [47] preserve their form when switching from one to another. For such systems it is as if they were stationary with respect to the ether: a uniform translation in the ether has no experimental sense.

But one should not conclude from this, as has sometimes been done prematurely, that the ether concept must be abandoned, that the ether is non-existent, inaccessible to experiment. Only a uniform velocity with respect to it cannot be detected, but any change of velocity, any acceleration has an absolute sense. It is in particular a fundamental point in the electromagnetic theory that any change of velocity, any acceleration of an electrified centre is accompanied by the emission of a wave that propagates in the medium with the velocity of light, and the existence of this wave has an absolute sense; conversely any electromagnetic wave - light for example - has its origins in the change of velocity of an electrified centre.

We have therefore hold on the ether by means of accelerations; acceleration has an absolute sense as it determines the production of waves that leave matter that underwent a change in velocity, and the ether manifests its reality as a vehicle, as support for the energy that is carried by these waves.

The theory provides the opportunity to demonstrate, by means of electromagnetic or optical experiments, any acceleration of the overall motion of a material system by means of experiments inside this system, if only by finding the wave emission of electrified bodies that are attached to the system, immobile with respect to it. We also know that if the acceleration of the whole system is provided by external actions that are only exerted on certain parts of the system, contrary to what happens with gravity, we have ample other means to demonstrate it, such as internal deformations in the system by means of which the acceleration is transmitted from parts of the system that are subjected to the external actions, to other parts that do not undergo them.

In a uniform gravitational field, where each part of the system undergoes direct external action which transmits the overall acceleration, as in the projectile of Jules Verne, similar reactions do not occur; but there [48] remains as I said above, the possibility of electromagnetic or optical experiments to detect the change of velocity of the ensemble: the laws of electromagnetism are not the same with respect to axes attached to this material system as with respect to axes in uniform translational motion of the ensemble.

  • 7

We will see this absolute character of acceleration manifest itself in another form.

Consider a piece of matter in arbitrary motion and the succession of events that constitute the life of this piece of matter, its world line.

For two of such sufficiently close events, observers in uniform motion who successively assist to these two events can be considered attached to the piece of matter, the change of velocity of the latter being imperceptible in the interval of the two events. For those observers, the time interval between the two events, which constitute an element of what we call the proper time of the piece of matter, will be shorter than for any other group of observers attached to a reference system in any uniform motion.

If we now take any two events in the life of our piece of matter, their time interval as measured by observers in non-uniform motion which will have constantly monitored the piece of matter, will, by integrating the previous result, be shorter than for the reference system in uniform motion.

In particular, this reference system may be such that the two events under consideration will happen there at the same point, so that with respect to it the piece of matter has run in a closed circle, has returned to its starting point thanks to its non-uniform motion. And we can affirm that for observers attached to that piece of matter, the elapsed time period between the departure and return, the proper time of the piece of matter will be shorter than for observers who would have remained attached to the reference system in uniform motion. In other words, the piece of matter [49] will have less aged between its departure and its return than if it had not sustained an acceleration, if it had remained stationary with respect to a reference system in uniform translation.

We can also say that it is sufficient to be agitated, to undergo accelerations in order to age less fast; we'll see in a moment how much we can hope to gain this way.

Let's provide concrete examples: imagine a laboratory attached to the Earth, whose motion can be regarded as a uniform translation, and in this laboratory two perfectly identical samples of radium. What we know about the spontaneous evolution of radioactive materials allows us to assert that if the samples remain in the laboratory, both will lose their radioactivity in the same way over time and keep continuously equal activities. But let us send one of these samples out with a sufficiently high velocity and then bring it back to the laboratory; this requires that at least at certain times this sample undergoes accelerations. We can affirm that at return, its proper time between departure and return being less than the measured time interval between these events by observers related to the laboratory, it will have less evolved than the other sample. Consequently it will be more radioactive than the latter, it will have aged less, having been more agitated. Calculation shows that for a difference of one ten-thousandth in the variation of radioactivity of the two samples, one would have to maintain the wandering sample during the separation at a velocity of about four thousand kilometres per second.

  • 8

Before providing another example, let's present our results in a different light. Suppose that two pieces of matter meet for the first time, separate, and then meet again. We can say that observers related to the one and the other during the separation have not evaluated the duration the same way, that some have not aged as much as the others. It follows from the foregoing that those who during the separation will [50] have aged the least are those of whom the motion has been the farthest from uniform, who have undergone the greatest accelerations.

This observation provides the means, to whoever of us who is willing to devote two years of his life, of knowing what the Earth will be in two hundred years from now, to explore the future Earth by making during his life a leap forward which for the Earth will last two centuries and for him will last two years, but this without hope of return, without possibility to come back to inform us of the outcome of the voyage as any similar attempt could only transport him further and further forward.

This would only require that the traveller agrees to be locked up in a projectile that the Earth would launch with a velocity that is sufficiently close to that of light but lower, which is physically possible, while arranging himself such that an encounter, with a star for example, occurs after one year of the traveller's life and which sends him back to Earth with the same velocity. Back on Earth having aged two years, he leaves his ark and will find our world aged by two hundred years if his velocity remained in the interval of only one twenty-thousandth less than the velocity of light. The experimental facts of physics that are most surely established allow us to affirm that it will be so.

It is fun to realise how our explorer and the Earth would see each other live if they could, by means of lights or by wireless telegraphy, remain in constant communication during their separation, and thus understand how the asymmetry is possible between the two measurements of the duration of separation.

As they move away from each other with a velocity close to that of light, each seems to flee from before the electromagnetic or optical signals that are sent to each other, so that it will take a very long time to receive the signals emitted during a given time. Calculation thus shows that each of them will see one another live two hundred times more slowly than usual. During the year that this moving away takes for him, the explorer will receive from Earth only news about the first two days after his departure; during this year he has seen the earth make the motions of two days. Moreover, for the same reason, because of the Doppler [51] principle, the radiations that he receives from the Earth during this time will for him have a wavelength that is two hundred times greater than for the Earth. What for him seems to be light radiation by means of which he can see the Earth has been emitted by it as extreme ultraviolet, maybe close to Röntgen rays. And if one wants to maintain communication between them by radio signals, by wireless telegraphy, the explorer having brought with him receiving devices with a certain antenna length, the transmission devices used by the Earth during these two days following the departure should have an antenna length of two hundred times shorter than his.

During the return the conditions are reversed: each of them will see the other live a remarkably accelerated life, two hundred times faster than usual, and during the year that for him the return will last, the Explorer will see the Earth perform the actions of two centuries: one sees that he will find it back at his return aged by two hundred years. Also, during this period he will see it by means of waves that are bright for him but that for Earth belong to the far infra-red, by the rays of around one hundred microns in wavelength that Mr Rubens and Wood recently discovered in the emission spectrum of a Welsbach mantle. So that he continues to receive the radio signals from Earth, one will have to, after the first two days and during the two centuries that follow, use a transmitting antenna that is two hundred times longer than that of the traveller, forty thousand times longer than that used during the first two days.

To understand the asymmetry, it should be noted that the earth will need two centuries to receive the signals sent by the explorer during his moving away which for him lasts one year: one will see him during this time in his ark live his life two hundred times slowed down; the Earth will see him perform the gestures of one year. During the two centuries that the Earth will see him move away, one will, to receive radio signals emitted by him, use an antenna two hundred times longer than his. At the end of the two centuries, news will reach Earth of the meeting of the projectile with the star that marks the beginning of the [52] return voyage. The arrival of the traveller will happen after two days during which the Earth will see him live two hundred times faster than usual, one will see him perform the gestures of another year to find him at return aged by only two years. During these last two days, to hear from him one must use a receiving antenna that is two hundred times shorter than the antenna of the traveller.

Thus the asymmetry being that the traveller only has undergone, in the midst of his voyage, an acceleration that changed the direction of his velocity and brought him back to the starting point on Earth, is reflected by the fact that the traveller sees the Earth move away and approach him for equal times of one year, while the Earth, only informed about this acceleration by the arrival of light waves, sees the traveller move away from it for two centuries and come back during two days, during a time that is forty thousand times shorter.

If we now look under what conditions a similar program could be realised, we encounter of course enormous material difficulties.

The theory allows to calculate the work that the Earth would have to spend to launch the projectile, to transmit the kinetic energy corresponding to its enormous velocity. Assuming the mass of the projectile only equal to one tonne it is calculated easily if we want to spend no more than a year to launch it, by turning it at the end of a sling for example before releasing it, it should run non-stop for this year for four hundred milliard horse powers and to produce that, burn at least a thousand cubic kilometres of coal.

These initial difficulties would also be followed by equally large difficulties when bouncing or stopping. One should first of all, for bouncing, find a system capable of storing the enormous kinetic energy of the projectile, then rend it back to return in opposite direction with the same velocity. To stop it one should gradually dissipate the same energy without causing at any moment an acceleration or temperature rise that is detrimental to the projectile, while the quantity of heat equal to its kinetic energy suffices to reach a temperature of 1016 degrees or more.

[53] We moreover have every reason to think that if a projectile arrives at the Earth with such a velocity, it does not even notice its passing and it would stop only at a certain depth in the soil without even leaving a hole at the place on the surface where it passed. There would hardly be on its path through the atmosphere a slight increase in electrical conductivity of the air. We know indeed that, for example a particles of radium, that is material helium atoms with a velocity of just 20,000 kilometers per second, can follow a perfectly straight path through matter and cross other atoms without leaving any trace of their passage other than increased conductivity, and our projectile will have, per unit of mass, a kinetic energy a hundred thousand times greater than the alpha particles. It would constitute an extraordinarily penetrating radiation. One should, in order to avoid these difficulties, find a way to gradually slow down its motion as it approaches the Earth. It seems that one can also not attempt here to use the principle of the rocket that my friend Mr. Perrin proposes to use for interplanetary travel.

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I only developed these speculations in order to show by means of a striking example to what consequences, so far away from our usual conceptions, the new form of space and time concepts leads. It must be remembered that this is a perfectly correct development of findings as required by experimental indisputable facts, of which our ancestors were not aware when they formed, from their experience that synthesized mechanics, the categories of space and time which we have inherited from them. Up to us to extend their work by pursuing with greater precision, in correspondence to the means at our disposal, the adaptation of thought to the facts.

It is not only in the field of space and time that a realignment of the most fundamental concepts of the mechanistic synthesis is required. Mass, by means of which one measured inertia, the essential attribute of matter, was regarded as an essentially unchanging element, [54] characterizing a given piece of matter. This concept now vanishes and merges with that of energy: the mass of a piece of matter varies with the internal energy of the latter, increases and decreases with it. A piece of matter which radiates loses its inertia in amounts proportional to the radiated energy. It is energy that is inert; matter resists a change in velocity only in proportion to the energy it contains.

The concept of energy itself loses its absolute sense: its measurement varies with the reference system to which the phenomena are related, and nowadays physicists search what are, in the expression of the laws of the universe, the real elements that have an absolute sense, elements that remain invariant when switching from one reference system to another, and which will play in the electromagnetic conception of the world the role that played in the mechanistic synthesis, time, mass and energy.

Paris, Collège de France.