Space-Time - Special and General Relativity - The Physics of the Universe
In physics, spacetime is any mathematical model that fuses the three dimensions of space and . In the context of special relativity, time cannot be separated from the three dimensions of space, because the observed rate at . superseded previous attempts of an electromagnetic mass-energy relation by introducing the. It's not too hard for us to think of space as a big, concrete whole and ignore Everything further away is “time-like separated” from that event. Some people have greater needs for space, or for togetherness, than others. Every relationship is a balance of time spent together and time spent alone. We can do this in the same room or in separate rooms, being.
Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to the presence of some third thing—absolute space.
Leibniz describes a space that exists only as a relation between objects, and which has no existence apart from the existence of those objects. Motion exists only as a relation between those objects. Newtonian space provided the absolute frame of reference within which objects can have motion. In Newton's system, the frame of reference exists independently of the objects contained within it.
These objects can be described as moving in relation to space itself. For almost two centuries, the evidence of a concave water surface held authority. Mach[ edit ] Another important figure in this debate is 19th-century physicist Ernst Mach. While he did not deny the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclusion by offering a different answer as to what the bucket was rotating in relation to: Mach suggested that thought experiments like the bucket argument are problematic.
If we were to imagine a universe that only contains a bucket, on Newton's account, this bucket could be set to spin relative to absolute space, and the water it contained would form the characteristic concave surface.
But in the absence of anything else in the universe, it would be difficult to confirm that the bucket was indeed spinning. It seems equally possible that the surface of the water in the bucket would remain flat. Mach argued that, in effect, the water experiment in an otherwise empty universe would remain flat. But if another object were introduced into this universe, perhaps a distant star, there would now be something relative to which the bucket could be seen as rotating.
The water inside the bucket could possibly have a slight curve.
To account for the curve that we observe, an increase in the number of objects in the universe also increases the curvature in the water. Mach argued that the momentum of an object, whether angular or linear, exists as a result of the sum of the effects of other objects in the universe Mach's Principle.
Einstein[ edit ] Albert Einstein proposed that the laws of physics should be based on the principle of relativity. This principle holds that the rules of physics must be the same for all observers, regardless of the frame of reference that is used, and that light propagates at the same speed in all reference frames. This theory was motivated by Maxwell's equationswhich show that electromagnetic waves propagate in a vacuum at the speed of light.
However, Maxwell's equations give no indication of what this speed is relative to. Prior to Einstein, it was thought that this speed was relative to a fixed medium, called the luminiferous ether. In contrast, the theory of special relativity postulates that light propagates at the speed of light in all inertial frames, and examines the implications of this postulate. All attempts to measure any speed relative to this ether failed, which can be seen as a confirmation of Einstein's postulate that light propagates at the same speed in all reference frames.
Special relativity is a formalization of the principle of relativity that does not contain a privileged inertial frame of reference, such as the luminiferous ether or absolute space, from which Einstein inferred that no such frame exists. Einstein generalized relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principlewhich states that the force felt by an observer in a given gravitational field and that felt by an observer in an accelerating frame of reference are indistinguishable.
This led to the conclusion that the mass of an object warps the geometry of the space-time surrounding it, as described in Einstein's field equations. In classical physics, an inertial reference frame is one in which an object that experiences no forces does not accelerate.
In general relativity, an inertial frame of reference is one that is following a geodesic of space-time. An object that moves against a geodesic experiences a force.
An object in free fall does not experience a force, because it is following a geodesic. An object standing on the earth, however, will experience a force, as it is being held against the geodesic by the surface of the planet.
Einstein partially advocates Mach's principle in that distant stars explain inertia because they provide the gravitational field against which acceleration and inertia occur.
But contrary to Leibniz's account, this warped space-time is as integral a part of an object as are its other defining characteristics, such as volume and mass. If one holds, contrary to idealist beliefs, that objects exist independently of the mind, it seems that relativistics commits them to also hold that space and temporality have exactly the same type of independent existence.
Relativity and the Separation Formula
Conventionalism[ edit ] The position of conventionalism states that there is no fact of the matter as to the geometry of space and time, but that it is decided by convention. This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach. Reichenbach's conventionalism, applying to space and time, focuses around the idea of coordinative definition. Coordinative definition has two major features. The first has to do with coordinating units of length with certain physical objects.
This is motivated by the fact that we can never directly apprehend length. Instead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures International Bureau of Weights and Measuresor the wavelength of cadmium to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equality of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another.
Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects.
Sameness of length, to the contrary, must be set by definition. Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is assumed, i. After this setting of coordinative definition, however, the geometry of spacetime is set. Structure of space-time[ edit ] This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources.
Unsourced material may be challenged and removed. August Learn how and when to remove this template message Building from a mix of insights from the historical debates of absolutism and conventionalism as well as reflecting on the import of the technical apparatus of the General Theory of Relativity, details as to the structure of space-time have made up a large proportion of discussion within the philosophy of space and time, as well as the philosophy of physics.
Relativity and the Separation Formula
The following is a short list of topics. Relativity of simultaneity[ edit ] According to special relativity each point in the universe can have a different set of events that compose its present instant. This has been used in the Rietdijk—Putnam argument to demonstrate that relativity predicts a block universe in which events are fixed in four dimensions.
Invariance, or symmetry, applies to objects, i. Covariance applies to formulations of theories, i. This distinction can be illustrated by revisiting Leibniz's thought experiment, in which the universe is shifted over five feet.
In this example the position of an object is seen not to be a property of that object, i. Similarly, the covariance group for classical mechanics will be any coordinate systems that are obtained from one another by shifts in position as well as other translations allowed by a Galilean transformation. In the classical case, the invariance, or symmetry, group and the covariance group coincide, but they part ways in relativistic physics.
The symmetry group of the general theory of relativity includes all differentiable transformations, i. The formulations of the general theory of relativity, unlike those of classical mechanics, do not share a standard, i. As such the covariance group of the general theory of relativity is just the covariance group of every theory.
Historical frameworks[ edit ] A further application of the modern mathematical methods, in league with the idea of invariance and covariance groups, is to try to interpret historical views of space and time in modern, mathematical language.
In these translations, a theory of space and time is seen as a manifold paired with vector spacesthe more vector spaces the more facts there are about objects in that theory. The historical development of spacetime theories is generally seen to start from a position where many facts about objects are incorporated in that theory, and as history progresses, more and more structure is removed.
For example, Aristotelian space and time has both absolute position and special places, such as the center of the cosmos, and the circumference. Newtonian space and time has absolute position and is Galilean invariantbut does not have special positions.
Holes[ edit ] With the general theory of relativity, the traditional debate between absolutism and relationalism has been shifted to whether spacetime is a substance, since the general theory of relativity largely rules out the existence of, e. One powerful argument against spacetime substantivalismoffered by John Earman is known as the " hole argument ".
This is a technical mathematical argument but can be paraphrased as follows: Define a function d as the identity function over all elements over the manifold M, excepting a small neighbourhood H belonging to M.
Over H d comes to differ from identity by a smooth function. These considerations show that, since substantivalism allows the construction of holes, that the universe must, on that view, be indeterministic. Which, Earman argues, is a case against substantivalism, as the case between determinism or indeterminism should be a question of physics, not of our commitment to substantivalism.
In Einstein's view, this simply preserves the absolute universality of the laws of nature, since the velocity of light turns out to be an artifact of Maxwell's Equations for electromagnetic interactions. Maxwell's Equationsand so the velocity of light, are equally valid for every inertial frame of reference the original "Galilean" form of Relativitywhich means however it is that one is moving, as long as one is moving at a constant velocity which means the same speed and directionthe velocity of light in a vacuum will be a constant.
The change in mass itself explains why ordinary objects cannot attain the velocity of light: They would have an infinite mass there and so would need an infinite force to accelerate themselves to that velocity. This circumstance is not always appreciated, even by great science fiction writers like Robert Heinlein, who has one character in a story ask why we can't go faster than the velocity of light and the answer is given that "we don't know" but "we'll see when we get there".
Another science fiction story speculates that a ship hitting the velocity of light would be bounced back into the past. The original formulae for the transformation of coordinates, from one frame of reference moving past another in the x axis [as given in The Universe and Dr.
Einstein, by Lincoln Barnett, Mentor,footnote pp. Lorentz to account for the anomaly of the Michelson-Morley experiment inwhere the velocity of light had not varied regardless of the direction in which it was measured.
The form of the equations is for the x coordinate, and time t. The y and z coordinates are unaffected. The equation is also given for the addition of velocities v. Lorentz did not know, however, why this effect had occurred, so these were just ad hoc mathematical descriptions.
Einstein provided the reason. Simpler equations for the length l contraction for the object, the dilation for a unit of time tand for the increase in the mass m of the moving object are all given at right [versions given in Physics, The Foundation of Modern Science, Jerry B. The Lorentz Transformations are not mathematically very difficult, but they do not transparently relate space and time to each other, and they do not relate to any intuitive sense of why this all would happen.
Another equation that does provide a better sense of things, called the "Separation Formula," is given at right, where s is the "separation" or "proper time," which is the elapsed time for a moving object, while t, x, y, and z are the changes in the coordinates in time and space as an object moves [cf.
At first this may not seem like an improvement over the previous equations. But, as with many equations, it can be simplified. First of all, the Greek delta, which indicates the change in the coordinates, can be left out, as in the first equation at left, giving us variables for the movement in each of four dimensions.
Then we should take into account that the Separation Formula is really an extension of the Pythagorean Theorem. This all by itself is revealing, since it answers the question whether time is treated exactly like a dimension of space in Relativity. This can then be further simplified by picking the right units.
The velocity of light can be set equal to one with the choice of light years LY and years y. The velocity of light is, indeed, one light year per year that is the definition of a light year. With all those simplifications, the Separation Formula ends up as a very simple equation indeed: Although the velocity of light term has been eliminated, it should be remembered that its units of velocity are there and that the "separation" comes out in units of time.
With the simplified equation, we can inspect some Relativistic effects. The graph at left, in vertical units of years and horizontal units of light years, shows two trips in space-time. The blue path is the movement of light itself -- 5 light years in five years. The green line is a stationary object in this inertial frame of reference -- we could think of it as the Earth, from which the spaceship travels 3 light years away.
We discover from the Separation Formula, that while 5 years have elapsed on Earth, the ship has arrived at its destination in only 4 years, according to its clocks. That is called "light-like" separation, in comparison to the "time-like" separation of the other object. It can be seen from this that the longest path in space-time is the shortest separation.
On the other hand, what if an object had gone faster than light?