What do you think?
Rate this book
“Collector’s Edition” Space And Time In Contemporary Physics An Introduction To The Theory Of Relativity And Gravitation 1920 [Premium Leather Bound]
Indulge in the luxury of a unique, premium leather-bound book designed for elite readers and collectors of rare, old books. We specialize in printing hard-to-find books not listed in our store, aiming to bring rare books back to the shelves and preserve literary history for future generations. We welcome your comments and suggestions to continually improve our offerings. Our exceptional editions feature genuine leather binding, handcrafted using original leather in various colors, including Red, Green, Blue, Magenta, Tan, Deep Brown, and Black. Customize your book by choosing any color and sending us your preference. The exquisite golden leaf design on the spine, front, and back, complemented by edge gilding, gives the book a truly distinguished appearance. We use high-quality, natural shade paper for black and white printing, with pages sewn bound for enhanced durability and longevity. The original edition was first published Long Back [1920] and faithfully reprinted in 2024. Each page has been meticulously processed to ensure readability, preserving the original content while addressing occasional issues such as blurs, missing pages, or black spots. Our dedicated team strives to restore these historical treasures to their former glory. The book is in English, contains 115 pages. If it is multi volume set, then it is only single volume. We offers custom labels in different colors for further personalization. A folio edition is available in size 12x19 inches upon request. Please note that leather is a natural material, and slight variations in color or texture may occur. Complete - “Collector’s Edition” Space And Time In Contemporary Physics An Introduction To The Theory Of Relativity And Gravitation 1920 [Premium Leather Bound] by Moritz Schlick
115 pages, Leather Bound
First published January 1, 1917
2 people are currently reading
78 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 2 of 2 reviews
January 13, 2019
[Disclaimer: I'm not a physicist, so please take my review - where it deals with physics - with a grain of salt. I think I understand the main concepts, up to a point, but it's always possible to make a mistake. I'd love to hear where I'm wrong!]
Originally published in 1920, Space and Time in Contemporary Physics was philosopher Moritz Schlick’s attempt to elucidate and interpret Einstein’s theory of general relativity. The book offers an exposé of one of the most important and fundamental scientific theories ever developed.
In 1905, Albert Einstein came up with the special theory of relativity, which explained uniform, rectilinear movements of objects in terms of invariant spacetime. If both space and time were absolute, then different people, within different coordinate systems, had to perceive different lightspeeds. Obviously, lightspeed was known to be a constant: light travels at 300.000 km/s – this was already established through observation and experiment. But if lightspeed is set; and speed is nothing but travelled distance in a given time; then space and time had to differ for different observers. But this was blocked by Newton’s principles.
So Einstein threw away the notions of absolute space and absolute time. According to him, different observers are bound to different systems of coordinates (in spacetime) in which they all perceive the exact same lightspeed. With reference to a particular observer another systems of coordinates is distorted, in the sense that time and space seem to shorten or lengthen. But with reference to the observer in that other frame of reference, it is exactly the other way around. The moral of the story? The four spacetime dimensions are invariant – they are bound up to the frame of reference of the observer and all observers experience their own spacetime. Any frame of reference can be transformed into any other frame of reference by using the Lorentz-transformation equations.
But of course, objects don’t only move in a uniform rectilinear fashion. Most of the motions in our universe are actually motions were forces play a huge role in accelerating and decelerating objects. Newton taught us that this was because of the gravitational force, so Einstein tried to expand his special theory of relativity to fit in accelerating motions.
Now, what is acceleration? An object accelerates if its speed increases in a particular fashion. But for an observer, locked in a (fictitious) box, an accelerating object is only one part of the story. If the said object seems to ‘fall’ to the ‘ground’, this can, of course, be explained in terms of gravitation – the object accelerates to the floor. But the exact same motion can be described as well by saying that the box and observer move ‘upward’ and the object is at rest – the ‘floor’ hitting the object. So now the exact same motion is described in terms of inertia (an object at rest, resisting forces).
What Einstein’s general theory of relativity does, is to establish an equivalence between gravitation and inertia. The common denominator here is mass. Mass is both proportional to gravitation as well as to inertia. It doesn’t matter if you explain accelerations in terms of inertial masses or gravitational masses – both are identical.
When we describe objects in motion – be it uniform rectilinear motion or a form of accelerating motion – we always use a system of coordinates that contains the three spatial and the temporal coordinates (spacetime). Now, this system of coordinates describes in geometrical terms what is happening. But geometry had always been Euclidean geometry – geometry of plane surfaces. In the nineteenth century, mathematicians discovered non-Euclidean geometries, and now the question became: is the universe best described in Euclidean, or in non-Euclidean terms? And if the latter: which geometry, exactly?
And now we are at the core of Einstein’s general theory. Basically, what he says is: it doesn’t matter which system of coordinates or which geometry you pick. Any randomly chosen system of coordinates can be transformed into any other arbitrarily chosen system of coordinates. And any geometry can be used to describe a particular spacetime within a given system of coordinates. Also, each system contains the exact same natural laws, and all objects, their positions, speeds and locations are equivalent.
What this means is that space and time do not exist independent of physical objects (matter). They only exist in relationship to matter within a given system of coordinates. Within a given coordinate system, it is a matter of utility which geometry we pick to describe the movement of matter through spacetime. Simplicity is the criterion here – the most simple system is the best. There’s no question of truth involved, though. Matter curves spacetime, so we know that plane surface geometry can only be used if the necessary corrections are made. Other geometries, describing curved surfaces, can be used as well.
(This can be compared to the question whether the Ptolemaic geocentric model or the Copernican heliocentric model is true? Both are descriptions of reality and describe the movements of the planets, Sun, moon and the stars in their own terms. Both can be applied, although the Copernican model is the simpler one and hence is used as default.)
In sum: Einstein’s theory of general relativity is, ultimately, based on the principle of covariance. Any system of coordinates can be transformed into any other system of coordinates; and the physical objects within such a system determine spacetime coordinates.
Einstein’s theory literally transformed our whole conception of the universe – space and time were no longer a priori all-important absolute notions, but were relegated to mere dependents of physical objects. Without matter there’s no spacetime. The postulate of equivalence is truly ground-breaking and is a scientific landmark that can be compared to Copernicus’ heliocentric model – in ingenuity as well as in its after-effects.
But Einstein’s theory is very interesting in yet another sense. It is a perfect illustration of the scientific method. It shows us how science works; how new theories replace old, established ones and how rigid the rules of the scientific game are.
The general theory of relativity had five implications. (1) When the differential equations were applied to the empirical universe, the values were such that these equations transformed into Newton’s equations. This means that Einstein’s theory incorporates Newton’s mechanics and hence explains the whole body of knowledge that had been acquired up to that point. It’s always required that a scientific theory incorporates the established theories.
(2) Newton’s mechanics could not deal with the observed motion of the planet Mercury. This planet is described by a perihelion – a peculiar motion unique (in our Solar system) to this planet. Over time, scientists tried to explain it within the Newtonian framework by coming up with all kinds of ad hoc hypotheses, but of course this is not very satisfying. Einstein’s theory explained the perihelion perfectly, even quantitively, in terms of its own equations. Hence, this was an important plus compared to Newton’s physics.
(3) The theory explains how mass curves spacetime. Another way of putting it is that objects which travel in straight lines, such as light waves, are slowed down due to gravitational effects. The theory thus predicts lengthening of wavelengths of light waves which travel through a strong gravitational field. A longer wavelength means a shift towards the red end of the light spectrum – a redshift. In short: general relativity predicts that light that is being emitted by huge gravitational objects (stars) becomes redshifted – we can compare the spectral lines of these stars with stars which contain the same elements and then look if certain spectral lines are redshifted. This has been confirmed in astronomical observations.
(4) Also, if gravitational effects curve spacetime, we would predict that a light ray (which travels in a straight line) will acquire a curved trajectory, i.e. bend, in the neighbourhood of a strong gravitational field. So, for example, a star that is located behind our Sun and hence is blocked from our view, with reference to an Earthly observer of course, could actually be observed due to the bending of the light rays. So the theory predicts that we can observe a star that is right now not observable to us due to blockage by our Sun. This was the first prediction of Einstein’s theory that was actually observed during an eclipse in 1919 – it is called the Eddington Expedition, after the astronomer Arthur Eddington who wanted to confirm Einstein’s theory.
(5) Finally, the general theory, developed as an alternative to Newton’s mechanics, could be applied to the universe as a whole as well. We can observe the amount of stars in given areas; we also can calculate the volume of the entire universe; and hence we can arrive at an average density of matter (matter/volume). The theory tells us that matter curves spacetime, so the amount of matter in the universe (i.e. the matter density) determines the curvature of spacetime and hence which type of universe we live in. Although Space and Time was written in 1920, later developments in science led to the conclusion that our universe is spherical, i.e. finite yet unbounded, and that it is expanding ever faster because of the matter density and dark energy (the latter working as a repulsive force in empty space).
So in summary: general theory of relativity (1) incorporated all earlier established theories; (2) explained old problems better than alternative theories; (3-4) led to new verifiable predictions as criteria of truth; and (5) led to new applications and, in a sense, to the establishment of a whole new scientific field (cosmology).
Now, in the last chapter in Space and Time Schlick mainly occupies himself with the philosophical implications of Einstein’s theory. This is a very hard chapter to grasp, but I think I got the main ideas:
Schlick distinguishes between psychological (or subjective) space and time and physical (or objective) space and time. Psychological space is the amalgam of sense data. Different types of senses lead to different types of perceptions of space: visual and tactual. But physical space, on the other hand, is the product of our conceptions. The difference is this: we perceive certain sense data to be properties of objects, but physics occupies itself solely with physical concepts. For example, we perceive red to be a property of that ball over there, but physics only describes colour in terms of the surface area of the ball absorbing certain frequencies of light waves and reflecting other frequencies of light waves. The same thing applies to time. We perceive time to be duration, but physical time is nothing but order – an arrangement on a one-dimensional continuum.
Why is this important? Well, for millennia, certain philosophical schools claimed intuitions (our perceptions of sense data) are a source of knowledge, while others claimed this was absolutely impossible. Schlick’s perspective on this is that the different types of sense data (visual, tactual) correspond to one another and through this correspondence are arranged into one perceptual scheme of space. This coincidence of experiences then becomes a conception of a point in space.
“In order to fix a point in space, we must in some way or other, directly or indirectly, point to it.” (p. 81)
Physical space and time are nothing but a construction out of coincidences of different types of perceptions. According to Schlick, this is to be contributed to Einstein, who “founded physics on the conception of the coincidence of events.” Through the use of concepts, we can express these coincidences in symbols, for example, differential equations – and this allows us to enter the domain of non-experiential reality.
“We might just as well assume that elements or qualities which cannot be directly experienced also exist.” (p.83)
What this means is that science, physics in this case, offers us an image of the world: a system of symbols arranged into a four-dimensional scheme. We can use this system to gather knowledge about reality. But how do we know this symbolic representation of the world is true? How do we know, for example, that atoms exist? Atoms are concepts, symbolic representations, but they cannot directly be perceived. We can only decide on knowledge – matters of truth – by resorting to observation, if not directly, then indirectly. Measurement is a prerequisite for knowledge. Atoms are real because we can measure their effects.
What does this have to do with Einstein’s general theory of relativity? Well, Einstein offered us a symbolic system as a representation of reality; a system in which each symbol is necessarily true, since they are fundamental building blocks of the theory and the theory is confirmed by the facts.
I don’t know why Schlick included such an abstract epistemological discussion in an introduction to general relativity. It is an interesting approach, but I can’t really place it in the broader picture? It seems to be his alternative to positivism, which claimed that only things that can be positively verified do exist. As Schlick cleverly puts it:
“The pencil in my hand is to be regarded as real, whereas the molecules which compose it are to be pure fictions.” (p. 84)
His answer to this positivist problem:
“It is avoided by the assumption, which is certainly allowable, that every conception which is actually of use for a description of physical nature can likewise be regarded as a sign of something real.” (p. 85)
The conclusion of this abstract discussion is that utility of concepts becomes the measurement of scientific theories: questions of truth are irrational, since different points of view can be used equally well to explain the same collection of sense-data and perceptions. In other words: different symbolic systems can represent the same underlying reality. Only the criterion of simplicity is deemed to be useful: the best theories are the most simplest.
To me personally, this reeks too much of pragmatism. (1) As long as the theory is useful it is true or (2) questions of truth aren’t even sensible questions. To escape this conundrum, I think we have to distinguish between different types of theories. I can see how special relativity and Newtonian mechanics are both specific instances of general relativity; and how Copernicus’ Sun-centred system is just as valid as Ptolemy’s Earth-centred system in explaining the facts. The problem is, though, that we all know of theories that have been discarded because they were deemed to be utterly false. For example, the vitalism theory in biology which claimed that living organisms were alive due a ‘life force’ (how about a monumental question-begging?). We know evolution by natural selection explains life. So there seems to be a place of asking questions of truth in science. That leaves open the option of pragmatism: focus on utility of theories.
I love it when a book makes you ponder new questions and makes you want to learn more. This short book by Moritz Schlick provides plenty of options for pondering new questions. I can definitely recommend it to anyone interested in the overlap between science and philosophy!
Originally published in 1920, Space and Time in Contemporary Physics was philosopher Moritz Schlick’s attempt to elucidate and interpret Einstein’s theory of general relativity. The book offers an exposé of one of the most important and fundamental scientific theories ever developed.
In 1905, Albert Einstein came up with the special theory of relativity, which explained uniform, rectilinear movements of objects in terms of invariant spacetime. If both space and time were absolute, then different people, within different coordinate systems, had to perceive different lightspeeds. Obviously, lightspeed was known to be a constant: light travels at 300.000 km/s – this was already established through observation and experiment. But if lightspeed is set; and speed is nothing but travelled distance in a given time; then space and time had to differ for different observers. But this was blocked by Newton’s principles.
So Einstein threw away the notions of absolute space and absolute time. According to him, different observers are bound to different systems of coordinates (in spacetime) in which they all perceive the exact same lightspeed. With reference to a particular observer another systems of coordinates is distorted, in the sense that time and space seem to shorten or lengthen. But with reference to the observer in that other frame of reference, it is exactly the other way around. The moral of the story? The four spacetime dimensions are invariant – they are bound up to the frame of reference of the observer and all observers experience their own spacetime. Any frame of reference can be transformed into any other frame of reference by using the Lorentz-transformation equations.
But of course, objects don’t only move in a uniform rectilinear fashion. Most of the motions in our universe are actually motions were forces play a huge role in accelerating and decelerating objects. Newton taught us that this was because of the gravitational force, so Einstein tried to expand his special theory of relativity to fit in accelerating motions.
Now, what is acceleration? An object accelerates if its speed increases in a particular fashion. But for an observer, locked in a (fictitious) box, an accelerating object is only one part of the story. If the said object seems to ‘fall’ to the ‘ground’, this can, of course, be explained in terms of gravitation – the object accelerates to the floor. But the exact same motion can be described as well by saying that the box and observer move ‘upward’ and the object is at rest – the ‘floor’ hitting the object. So now the exact same motion is described in terms of inertia (an object at rest, resisting forces).
What Einstein’s general theory of relativity does, is to establish an equivalence between gravitation and inertia. The common denominator here is mass. Mass is both proportional to gravitation as well as to inertia. It doesn’t matter if you explain accelerations in terms of inertial masses or gravitational masses – both are identical.
When we describe objects in motion – be it uniform rectilinear motion or a form of accelerating motion – we always use a system of coordinates that contains the three spatial and the temporal coordinates (spacetime). Now, this system of coordinates describes in geometrical terms what is happening. But geometry had always been Euclidean geometry – geometry of plane surfaces. In the nineteenth century, mathematicians discovered non-Euclidean geometries, and now the question became: is the universe best described in Euclidean, or in non-Euclidean terms? And if the latter: which geometry, exactly?
And now we are at the core of Einstein’s general theory. Basically, what he says is: it doesn’t matter which system of coordinates or which geometry you pick. Any randomly chosen system of coordinates can be transformed into any other arbitrarily chosen system of coordinates. And any geometry can be used to describe a particular spacetime within a given system of coordinates. Also, each system contains the exact same natural laws, and all objects, their positions, speeds and locations are equivalent.
What this means is that space and time do not exist independent of physical objects (matter). They only exist in relationship to matter within a given system of coordinates. Within a given coordinate system, it is a matter of utility which geometry we pick to describe the movement of matter through spacetime. Simplicity is the criterion here – the most simple system is the best. There’s no question of truth involved, though. Matter curves spacetime, so we know that plane surface geometry can only be used if the necessary corrections are made. Other geometries, describing curved surfaces, can be used as well.
(This can be compared to the question whether the Ptolemaic geocentric model or the Copernican heliocentric model is true? Both are descriptions of reality and describe the movements of the planets, Sun, moon and the stars in their own terms. Both can be applied, although the Copernican model is the simpler one and hence is used as default.)
In sum: Einstein’s theory of general relativity is, ultimately, based on the principle of covariance. Any system of coordinates can be transformed into any other system of coordinates; and the physical objects within such a system determine spacetime coordinates.
Einstein’s theory literally transformed our whole conception of the universe – space and time were no longer a priori all-important absolute notions, but were relegated to mere dependents of physical objects. Without matter there’s no spacetime. The postulate of equivalence is truly ground-breaking and is a scientific landmark that can be compared to Copernicus’ heliocentric model – in ingenuity as well as in its after-effects.
But Einstein’s theory is very interesting in yet another sense. It is a perfect illustration of the scientific method. It shows us how science works; how new theories replace old, established ones and how rigid the rules of the scientific game are.
The general theory of relativity had five implications. (1) When the differential equations were applied to the empirical universe, the values were such that these equations transformed into Newton’s equations. This means that Einstein’s theory incorporates Newton’s mechanics and hence explains the whole body of knowledge that had been acquired up to that point. It’s always required that a scientific theory incorporates the established theories.
(2) Newton’s mechanics could not deal with the observed motion of the planet Mercury. This planet is described by a perihelion – a peculiar motion unique (in our Solar system) to this planet. Over time, scientists tried to explain it within the Newtonian framework by coming up with all kinds of ad hoc hypotheses, but of course this is not very satisfying. Einstein’s theory explained the perihelion perfectly, even quantitively, in terms of its own equations. Hence, this was an important plus compared to Newton’s physics.
(3) The theory explains how mass curves spacetime. Another way of putting it is that objects which travel in straight lines, such as light waves, are slowed down due to gravitational effects. The theory thus predicts lengthening of wavelengths of light waves which travel through a strong gravitational field. A longer wavelength means a shift towards the red end of the light spectrum – a redshift. In short: general relativity predicts that light that is being emitted by huge gravitational objects (stars) becomes redshifted – we can compare the spectral lines of these stars with stars which contain the same elements and then look if certain spectral lines are redshifted. This has been confirmed in astronomical observations.
(4) Also, if gravitational effects curve spacetime, we would predict that a light ray (which travels in a straight line) will acquire a curved trajectory, i.e. bend, in the neighbourhood of a strong gravitational field. So, for example, a star that is located behind our Sun and hence is blocked from our view, with reference to an Earthly observer of course, could actually be observed due to the bending of the light rays. So the theory predicts that we can observe a star that is right now not observable to us due to blockage by our Sun. This was the first prediction of Einstein’s theory that was actually observed during an eclipse in 1919 – it is called the Eddington Expedition, after the astronomer Arthur Eddington who wanted to confirm Einstein’s theory.
(5) Finally, the general theory, developed as an alternative to Newton’s mechanics, could be applied to the universe as a whole as well. We can observe the amount of stars in given areas; we also can calculate the volume of the entire universe; and hence we can arrive at an average density of matter (matter/volume). The theory tells us that matter curves spacetime, so the amount of matter in the universe (i.e. the matter density) determines the curvature of spacetime and hence which type of universe we live in. Although Space and Time was written in 1920, later developments in science led to the conclusion that our universe is spherical, i.e. finite yet unbounded, and that it is expanding ever faster because of the matter density and dark energy (the latter working as a repulsive force in empty space).
So in summary: general theory of relativity (1) incorporated all earlier established theories; (2) explained old problems better than alternative theories; (3-4) led to new verifiable predictions as criteria of truth; and (5) led to new applications and, in a sense, to the establishment of a whole new scientific field (cosmology).
Now, in the last chapter in Space and Time Schlick mainly occupies himself with the philosophical implications of Einstein’s theory. This is a very hard chapter to grasp, but I think I got the main ideas:
Schlick distinguishes between psychological (or subjective) space and time and physical (or objective) space and time. Psychological space is the amalgam of sense data. Different types of senses lead to different types of perceptions of space: visual and tactual. But physical space, on the other hand, is the product of our conceptions. The difference is this: we perceive certain sense data to be properties of objects, but physics occupies itself solely with physical concepts. For example, we perceive red to be a property of that ball over there, but physics only describes colour in terms of the surface area of the ball absorbing certain frequencies of light waves and reflecting other frequencies of light waves. The same thing applies to time. We perceive time to be duration, but physical time is nothing but order – an arrangement on a one-dimensional continuum.
Why is this important? Well, for millennia, certain philosophical schools claimed intuitions (our perceptions of sense data) are a source of knowledge, while others claimed this was absolutely impossible. Schlick’s perspective on this is that the different types of sense data (visual, tactual) correspond to one another and through this correspondence are arranged into one perceptual scheme of space. This coincidence of experiences then becomes a conception of a point in space.
“In order to fix a point in space, we must in some way or other, directly or indirectly, point to it.” (p. 81)
Physical space and time are nothing but a construction out of coincidences of different types of perceptions. According to Schlick, this is to be contributed to Einstein, who “founded physics on the conception of the coincidence of events.” Through the use of concepts, we can express these coincidences in symbols, for example, differential equations – and this allows us to enter the domain of non-experiential reality.
“We might just as well assume that elements or qualities which cannot be directly experienced also exist.” (p.83)
What this means is that science, physics in this case, offers us an image of the world: a system of symbols arranged into a four-dimensional scheme. We can use this system to gather knowledge about reality. But how do we know this symbolic representation of the world is true? How do we know, for example, that atoms exist? Atoms are concepts, symbolic representations, but they cannot directly be perceived. We can only decide on knowledge – matters of truth – by resorting to observation, if not directly, then indirectly. Measurement is a prerequisite for knowledge. Atoms are real because we can measure their effects.
What does this have to do with Einstein’s general theory of relativity? Well, Einstein offered us a symbolic system as a representation of reality; a system in which each symbol is necessarily true, since they are fundamental building blocks of the theory and the theory is confirmed by the facts.
I don’t know why Schlick included such an abstract epistemological discussion in an introduction to general relativity. It is an interesting approach, but I can’t really place it in the broader picture? It seems to be his alternative to positivism, which claimed that only things that can be positively verified do exist. As Schlick cleverly puts it:
“The pencil in my hand is to be regarded as real, whereas the molecules which compose it are to be pure fictions.” (p. 84)
His answer to this positivist problem:
“It is avoided by the assumption, which is certainly allowable, that every conception which is actually of use for a description of physical nature can likewise be regarded as a sign of something real.” (p. 85)
The conclusion of this abstract discussion is that utility of concepts becomes the measurement of scientific theories: questions of truth are irrational, since different points of view can be used equally well to explain the same collection of sense-data and perceptions. In other words: different symbolic systems can represent the same underlying reality. Only the criterion of simplicity is deemed to be useful: the best theories are the most simplest.
To me personally, this reeks too much of pragmatism. (1) As long as the theory is useful it is true or (2) questions of truth aren’t even sensible questions. To escape this conundrum, I think we have to distinguish between different types of theories. I can see how special relativity and Newtonian mechanics are both specific instances of general relativity; and how Copernicus’ Sun-centred system is just as valid as Ptolemy’s Earth-centred system in explaining the facts. The problem is, though, that we all know of theories that have been discarded because they were deemed to be utterly false. For example, the vitalism theory in biology which claimed that living organisms were alive due a ‘life force’ (how about a monumental question-begging?). We know evolution by natural selection explains life. So there seems to be a place of asking questions of truth in science. That leaves open the option of pragmatism: focus on utility of theories.
I love it when a book makes you ponder new questions and makes you want to learn more. This short book by Moritz Schlick provides plenty of options for pondering new questions. I can definitely recommend it to anyone interested in the overlap between science and philosophy!
April 2, 2011
This was good, another short read. I got it free on my ereader so I can't exactly complain. It is just that there are so many better books on this subject that are more up to date at this point, that reading something of this nature seems utterly pointless, unless like I mentioned before you got it free.
Displaying 1 - 2 of 2 reviews