Spacetime Definition and 1000 Threads

In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.
Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The famous physicist Albert Einstein helped develop the idea of space-time as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Albert Einstein based a work on special relativity on two postulates:

The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference)
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.The logical consequence of taking these postulates together is the inseparable joining together of the four dimensions—hitherto assumed as independent—of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light is constant regardless of the frame of reference in which it is measured; the distances and even temporal ordering of pairs of events change when measured in different inertial frames of reference (this is the relativity of simultaneity); and the linear additivity of velocities no longer holds true.
Einstein framed his theory in terms of kinematics (the study of moving bodies). His theory was an advance over Lorentz's 1904 theory of electromagnetic phenomena and Poincaré's electrodynamic theory. Although these theories included equations identical to those that Einstein introduced (i.e., the Lorentz transformation), they were essentially ad hoc models proposed to explain the results of various experiments—including the famous Michelson–Morley interferometer experiment—that were extremely difficult to fit into existing paradigms.
In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve flat spacetime into a pseudo-Riemannian manifold.

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  1. S

    What Differentiates Wave Functions and Spacetime in Quantum Gravity?

    Quantum Gravity is the successful merging of the two.. Wave functions (or QM) and Spacetime. So it would be good to know how the two differs. They seem to have one thing in common.. they are both mathematical abstraction. But then someone said (Peterdonis): "Tidal gravity is not "just a math...
  2. S

    Spacetime desynchronized in quantum realm?

    I just watched Morgan Freeman episode Through the Wormhole "How does the Universe Work". A physicist in the show theorized that spacetime is together at larger scale but at the microscopic scale, spacetime splits with space and time no longer synchronized.. this is why particles can be in two...
  3. S

    Quantum Spacetime Points & General Covariance

    I'm trying to study the best approaches to quantum gravity and especially the interactions of quantum and the metric. But first let us settle about the so called "spacetime points". What is the proof that spacetime points can't be composed of any substance but purely an abstract. The often...
  4. D

    The unit vector normal to the curvature of spacetime

    Let us say there is a curved region of spacetime whose curvature is \kappa(s). How does one find the coordinates of the unit vector normal to a certain point on the region of spacetime? I tried searching Hamilton's principle and the general theory of relativity but I could not find any equation...
  5. J

    Special relativity under the inflation of spacetime

    Inflation says that space between objects is expanding. Matter is held together by forces carried by bosons traveling at the speed of light. At the fringes of the universe inflation is warping space faster than the speed of light so it seems that there should be a horizon beyond which matter...
  6. PeterDonis

    Family of nested spheres in Schwarzschild spacetime

    On the Wikipedia page on Schwarzschild coordinates... http://en.wikipedia.org/wiki/Schwarzschild_coordinates ...it talks about a "family of nested spheres": each surface of constant t and r is a 2-sphere (i.e., setting dt = dr = 0 and r = constant in the metric results in a Euclidean...
  7. M

    Is there a spacetime which is timelike and spacelike complete but null

    Is there a spacetime which is timelike and spacelike complete but null incomplete?
  8. D

    Quantum fluctuations and Spacetime

    Hi there. I am a layman, and I have a question. As far as I have gathered, the prevalent view in cosmology is that the universe appeared as a result of the Big Bang, which in turn occurred due to expansion of singularity. Ok. Some go further and propose that singularity appeared through...
  9. marcus

    Myth of spacetime (Gomes Koslowski)

    http://arxiv.org/abs/1110.3837 A smooth classical spacetime manifold can no more exist than can a smooth classical trajectory of a moving particle. Spacetime as a classical 4D manifold is a myth, sometimes a very useful one. Many PF people must already realize this so clearly that one hardly...
  10. D

    Exploring Spacetime Elasticity & Mass Research

    I am curious if there has been any research into the elasticity of spacetime in regards to mass. If we consider that a fabric is resistive to a degree to an object it could be said that an object must poses a certain amount of mass before it can cause a divet in spacetime.
  11. C

    If energy/matter deforms spacetime in three dimensions

    If energy/matter deforms spacetime in three dimensions... Then why do we get galaxies in (relatively) flat discs and black holes that emit radiation in a single plane?
  12. PeterDonis

    Derivation of expansion scalar for FRW spacetime - weird observation

    Derivation of expansion scalar for FRW spacetime -- weird observation In a recent thread... https://www.physicsforums.com/showpost.php?p=3567386&postcount=137 ...I posted a formula for the expansion scalar for the congruence of "comoving" observers in FRW spacetime. When I posted, I...
  13. H

    My understanding of Space, Time and spacetime

    My understanding of Space, Time and "spacetime" In thinking about time I have developed the (easy) realization that whenever we indicate a duration we are comparing two spatial changes. I believe it was Einstein himself who pronounced words the effect of time being inexorably tied to space and...
  14. C

    Spacetime expanding within galaxies?

    I understand that spacetime is expanding between galaxies, as seen with the cosmological redshift. But, is it also expanding inside galaxies, such as the Milky Way? I'm not sure if the galaxy is gravitationally bound enough to where spacetime might actually be contracting within the galaxy...
  15. S

    General relativity: a poor description of spacetime

    Everyone is congratulating the recent Nobel Prize winners, whose work uses observations of distant supernovae to attempt to show the existence of universal acceleration. Let's not forget that supernova studies of cosmology are all based on a theory (General Relativity) that has huge problems...
  16. R

    Are points of spacetime unique?

    Are any known laws of physics a function of a unique spacetime coordinate? Be careful reading my question -- I'm not asking if the laws of physics vary throughout spacetime (since they don't).
  17. K

    Time dilation and length contraction in hyperbolically-curved spacetime

    For the universe to be totally flat, and not just asymptotically closer to being flat as the universe expands, wouldn't there have to be pockets of hyperbolically-curved spacetime? In either case, I still would like to know how one expresses time dilation and length contraction in hyperbolic...
  18. T

    Is Gravity a force or the chape of spacetime?

    From my understanding Gravity is a curvature in space-time caused by mass. basically a massive object makes a dent in space and the curvature of that dent is relative to the size of the object vs. its mass(red giant vs black hole). A smaller but more massive object will make a deeper dent...
  19. J

    Slightly confused about embedding picture and imagining spacetime

    I'm slightly confused as to how we can use the picture of a 2D surface embedded in 3D space as an analogue to understand (maybe not picture!) 4D spacetime. My initial thinking was that trying to imagine a 4D spacetime isn't really possible, it's just a mathematical concept which one should not...
  20. A

    Solving Spacetime Questions - Homework Equations & Solutions

    Homework Statement Homework Equations The Attempt at a Solution
  21. T

    Spacetime curvature and the force pulling an object down the curvature

    Spacetime curvature and the force pulling an object "down" the curvature ok , I have a question about the current model of gravity. If mass bends spacetime I understand that it accounts for things like how long light takes to travel through its geodesics but "why" does this curvature make...
  22. M

    Spacetime Inverval Invariance using Lorentz Transformations

    Homework Statement Prove that the spacetime interval -(ct)^{2} + x^{2} + y^{2} + z^{2} is invariant. [/itex] Homework Equations Lorentz transformations \Deltax' = \gamma(\Deltax-u\Deltat) \Deltay' = \Deltay \Deltaz' = \Deltaz \Deltat' = \gamma(\Deltat-u\Deltax/c^{2}) The...
  23. L

    What is the fabric of spacetime made of?

    I know that the rubbersheet / fabric analogies that we see on TV and in various diagrams are only a metaphor, but I'm having difficulty getting started researching what we actually know / theorise about the make-up / workings of the "fabric"? Could you give me any pointers to good postings...
  24. O

    Question about static spacetime

    Hi, everyone I'm now reading A Relativist's Toolkit by Eric Poisson. In chapter 3, he say something about stationary and static spacetime. For static spacetime, it's just like stationary (admits timelike Killing vector t^{\alpha} ) with addition that metric should be invariant under...
  25. I

    What is the Geometry of Spacetime Near the Big Bang?

    What did spacetime look like some time after the big bang? 1) Euclidian space. Imagine yourself in empty space, no mass, with (x,y,z) coordinates ranging from –infinity to +infinity. Somewhere within this infinite space was a volume with high matter-energy density from the Big Bang. 2)...
  26. zonde

    Backreaction of accelerated motion on spacetime curvature

    Curvature of spacetime tells us how the body is moving when it moves inertially. But if the body is not moving inertially does it causes backreaction by affecting spacetime curvature? Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.
  27. A

    The General Relativity Metric and Flat Spacetime

    Let us consider the General Relativity metric: {ds}^{2}{=}{g}_{00}{dt}^{2}{-}{g}_{11}{{dx}_{1}}^{2}{-}{g}_{22}{{dx}_{2}}^{2}{-}{{g}_{33}}{{dx}_{3}}^{2} ---------------- (1) Using the substitutions: {dT}{=}\sqrt{{g}_{00}}{dt} {dX}_{1}{=}\sqrt{{g}_{11}}{dx}_{1}...
  28. T

    Exploring Spacetime Curvature: The Role of Mass and Gravitational Force

    1) Is it always a given that the spacetime curvature will be flat in a region in which there is no mass? 2) Therefore is the curvature directly dependent on the mass in a particular region? 3) Also, what exactly is included in the term "mass"? 4) If there are no matter fields to curve...
  29. W

    Trying to understand spacetime curvature

    I'm familiar with space and time together being 4 dimensions and that mass causes a curvature in this spacetime. When I consider a line that is curved, I can view the curvature because the line is drawn on a 2D surface (plane). So, it seems an additional dimension is required for a...
  30. Y

    Gravity: A Matter of Spacetime Compression?

    I have always thought of gravity as being a phenomenon related to matter. I have always envisioned it as a "contraction" in spacetime reaching out in all directions from an object. What I mean by contraction is that the closer you get to a body of mass the more spacetime is compressed. Due...
  31. A

    Computing Lagrangian for Light Propagation in Spacetime

    Does anyone know the Lagrangian for the propagation of light in curved spacetime? I'm disappointed to discover that I don't actually know how to compute the action for a given null curve.
  32. T

    Can measurements of red shift be affected by the shape of spacetime?

    I have read on some threads that there are other possible shapes for spacetime and I wondered could any of these spacetime shapes, or their change over time, affect our measurement of red shift? Also does the matter density at the location where a photon is emitted relative to our own...
  33. T

    Rotation of coordinate system in minkowsky spacetime

    Does performing a rotation of the usual coordinate system ct,x in the minkowsky spacetime makes sense? I guess it doesn't, but more than this i think that there is something that forbids it, since i could make coincident the 'lenght' axis of the non rotated coordinate system (observer A) with...
  34. N

    Why Is Gravity Viewed as Spacetime Distortion Rather Than a Force?

    Please teach me this: Why we do not infer the gravity for the force(a type of interaction of fields) but for the distortion of space-time. Thank you very much in advance.
  35. V

    Beables in or NOT in Spacetime?

    How do you understand Beables? How do you define Beables? Are these supposed to be located in spacetime or behind spacetime? m_wan wrote in the QM forum: Do you agree with this? Why and why not? I think understanding beables and its connection to spacetime is key to solving the secret of...
  36. Islam Hassan

    Gravitons vs Attraction Due to Curvature of Spacetime

    If one day gravitons are discovered, would their action be complementary to the gravitational attraction due to curved spacetime? Can gravity arise from both curved spacetime and exchange of gravitons? IH
  37. S

    Exploring Quantum Mechanics & QFT in Curved Spacetime: Latest Research Updates

    Hi PF I know that a goal of the current research in High Energy physics is to get a describtion of QFT in curved spacetime. I assume this has yet to be described fully, but how about plain quantum mechanics in curved spacetime? Has it yet been described? Schreiber
  38. R

    What effect does the expanding universe have on spacetime?

    If our universe is indeed expanding, would this have an effect on spacetime? For example as space and time are related, if I change one, shouldn’t it have an effect on the other? Also, wouldn’t it make gravity weaker as it is stretching space?
  39. G

    Electric field in curved spacetime

    hi i am looking for an equation that gives me the electric field( if possible in 3-dim form) of a point charge in a distance r in a schwarzschild spacetime, where the point charge and the the gravitating body should not be the same position.
  40. L

    Issues entering a spacetime in GRTensor II

    Hi, I'm trying to enter a spacetime with makeg(spacetime_name): on GRTensor II. I'm just following the simple example in the documentation, but instead of doing what it's supposed to (e.g presenting me with text offering me certain options and then me selecting say option 1-4) and presenting...
  41. J

    Questions on Redshift, Hubble’s Law, spacetime expansion and the standard model

    The current state of NASA’s version of cosmology is amazing to watch – According to modern cosmology, which NASA endorses, the Milky Way is moving through space at 600km/s and the Earth is moving through space at 30km/s and the sun is moving through space at 250km/s. So if we total up these...
  42. narrator

    Spacetime, like an isometric weather map?

    Novice question :blushing: I've been reading Brian Greene's "The Hidden Reality". It occurred to me that spacetime across the 2D analog of the U could be much like an isometric weather map. Could it be that the U isn't expanding, but that our region, like a High on a weather map is rushing...
  43. V

    Exploring Quantum Spacetime: Unifying Matter, Space, and Time in Quantum Gravity

    Do you believe that in Quantum Gravity, quantization of gravity is only a small part and it is really Quantum Spacetime or the unification of Matter, Space and Time that is the general feature or attraction?
  44. L

    Why can't a static spacetime have an ergosphere?An ergoregion is

    Why can't a static spacetime have an ergosphere? An ergoregion is just a region outside the event horizon where k can become negative (k being a Killing vector field that is timelike near infinity). Both stationary and static spacetimes have such a KVF so surely static spacetimes could also...
  45. Y

    Can I express stationary spacetime and static spacetime in this way?

    Can I express "stationary spacetime" and "static spacetime" in this way? Can I express "stationary spacetime" and "static spacetime" in this way? stationary spacetime: if we arrange a set of observers locating in any places, then each of them should observe nothing change at the place where...
  46. Demon117

    The set of allowed trajectories in spacetime

    I was reading Spacetime and Geometry by Caroll and I came across this notion: I have never understood this and I was wondering if someone could enlighten me.
  47. V

    Entanglement more primary than Spacetime?

    What do you think of the following passage from Scientific American (June 2011): Do you believe it? That entanglement are more primary than space and time and "relativity theory must give way to a deeper theory in which space and time do not exist."? Or does entanglement work inside...
  48. F

    Understanding Spacetime Bending & Gravity Effects

    I'm having some troubles understanding how spacetime actually looks and what causes gravity and unifying the idea with the general relativity consequences, like light bending. So, if spacetime is bent by massive objects like in this picture: HOW does the light bend outwards that massive...
  49. C

    Topology of Minkowski spacetime

    I recently Googled "spacetime topology" and found that the topology of Minkowski spacetime is generally described as that of an R4 manifold. This is not my field, but I'm surprised. Perhaps mathematically the (---+) "Lorentz signature" can be taken as a secondary characteristic of the...
  50. V

    Finding Lorentz Factor of a Point Particle in Curved Spacetime

    Hello, Is there a way to find the lorentz factor of a point particle in a curved spacetime in terms of metric elements(diagonal) More specifically I was trying to write energy of a point particle in a curved space. thanks
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