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. HowardHughes

    Imagining spacetime curvature more accurately

    I am intrigued to see what spacetime curvature is like in reality. Most images or ways to imagine it tend to look at spacetime as a fabric which it is not precisely. So how would be best to imagine it... Do any of the picture demonstrate this? What is the best way to imagine it?
  2. B

    Homogeneous spacetime - Lie groups

    All Bianchi type spacetimes have metrics that admits a 3-dimensional killing algebra. They are in general not isotropic. Bianchi type IX have a killing algebra that is isomorphic to SO(3), i.e. the rotation group. But what does it mean? If the fourdimensional spacetime is invariant under the...
  3. R

    If gravity is curvature of spacetime, why unified force @ Planck epoch

    Hi Bear with my possible ignorant. I am puzzled over this dilemma. If General Relativity states that gravity is the curvature of spacetime, that is, no spacetime no gravity, and the cause of curvature is matter (mass), it means that if no matter, there is no gravity. I understand that...
  4. marcus

    How many spacetime quanta are there? (depends how you count.)

    http://arxiv.org/abs/1404.1750 How many quanta are there in a quantum spacetime? Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli, Freddy P. Zen (Submitted on 7 Apr 2014) Following earlier insights by Livine and Terno, we develop a technique for describing quantum states of the...
  5. TrickyDicky

    Is Schwarzschild spacetime parallelizable?

    I was wondering since it is usually foliated into 2-spheres and these are not themselves parallelizable(only the n-spheres S1, S3 and S7 are). I know the timelike Killing vector field is not global, but is the a global basis of vector fields in Schwarzschild spacetime? I mean a basis in a...
  6. berkeman

    New Cosmos: A Spacetime Odyssey 2014 TV Series

    Looks like the new Cosmos TV series is about to start. We'd like to keep discussions about the series in a single thread, so feel free to post your thoughts and reactions and questions in this thread. I really enjoyed the original Cosmos TV series with Carl Sagan. It was a bit over-done at...
  7. R

    A thermal expansion coefficient of spacetime?

    Are there any theories or thoughts that view spacetime as 'having' a coefficient of thermal expansion... analogous to the CTE of water? An inflection with density in regards to temperature?
  8. W

    Transformations in curved spacetime?

    I know that the spacetime in special relativity is not curved and that the axis can be transformed via the lorentz transformations. I was wondering if the curved spacetime in general relativity can be transformed in such a way, and if so, how?
  9. B

    Is Spacetime a Field in General Relativity?

    Could spacetime itself be a field?
  10. P

    Spacetime symmetries vs. diffeomorphism invariance

    This is a very basic question, but I cannot get my head around the following: Any physical system should be invariant under changes of coordinates, because these are just a way of parametrizing the manifold/space in which my physical system is embedded. Now, let us consider a system that...
  11. D

    Maxwell's equations and spacetime

    Hi, I'm just beginning to learn relativity, but I have a question about why gravity is so different from other forces of nature in GR. As a start, I read that Einstein tried to find a differential geometric representation of the physical universe which represents the Maxwell equations in a...
  12. S

    Science fictiony questions about spacetime curvature

    I'm writing a sci-fi story and I'd like to make it, at the very least, scientifically plausible (in the way that alcubirre warp drives are possible assuming we could get our hands on something with negative mass which, as far as we know, doesn't exist). The basic assumption for these questions...
  13. B

    Are the S' Axes Nonorthogonal in a Spacetime Diagram?

    Homework Statement Show that the S' axes, x' and ct', are nonorthogonal in a spacetime diagram. Assume that t = t' = 0 when x = x' = 0. (Hint: use the fact that the ct' axis is the world line of the origin of S' to show that the ct' axis is inclined with respect to the ct' axis. Next, note...
  14. R

    Could spacetime be a condensate?

    Are there any theories/papers/thoughts that view spacetime as being a condensate, basically a superfluid of spacetime, akin to the Higgs field? I see the pictures and equations that describe the inflation of the (observable) universe- the curvature of spacetime... and wonder if there might be a...
  15. D

    Spacetime 'loaf' according to Fabric of the Cosmos

    Spacetime 'loaf' according to "Fabric of the Cosmos" From what I learned watching Brian Greene's "Fabric of the Cosmos" episode on Nova, if you look at spacetime like a loaf of bread, then each 'slice' depends on your relative speed compared to another point in the loaf. This I have no problem...
  16. Markus Hanke

    Is Weyl Curvature Present in Interior Spacetimes?

    I am just wondering - is space-time curvature in the presence of energy-momentum ( i.e. in interior solutions to the EFEs ) always pure Ricci in nature ? I had a discussion recently with someone who claimed that, but personally I would suspect that not to be the case in general, since I see no...
  17. M

    A couple basic spacetime questions.

    Hey everyone, for anyone who saw my thread in the chemistry section you know I'm changing my view point to that of the "there are no dumb questions", and with that I have a couple of things I've been curious about for a while regarding spacetime. First off, from reading and research I am...
  18. A

    Invariant Spacetime Interval for Classical Spacetime

    In special relativity we have the invariant spacetime interval ds2 = dx2 - c2dt2. If we think about classical (non-relativistic) space and time as one spacetime in which the transformation between reference frames is given by the Galilean transformation, is there a corresponding spacetime...
  19. stevendaryl

    Square-Integrable Functions in Curved Spacetime

    In non-relativistic quantum mechanics, an important set of functions are the normalized square-integrable ones. Those are functions on \mathcal{R}^3 such that \int |\Psi(x,y,z)|^2 dx dy dz = 1 I'm just curious as to whether there is some analogous concept for curved spacetime. One...
  20. T

    The book: Spacetime Physics (Taylor - Wheeler) - missing solutions

    Hi I have buyed the book Spacetime physics - Introduction to Special Relativity; Second Edition. It is a great book, although I am currently only at second chapter. There are exercises with solutions in this book. The problem is, there are solutions only to odd numbered exercises. Can I...
  21. atyy

    Time & Probability: Relativistic Bohmian Mechanics

    http://arxiv.org/abs/1309.0400v2 Time and probability: From classical mechanics to relativistic Bohmian mechanics H. Nikolic (Submitted on 2 Sep 2013 (v1), last revised 30 Sep 2013 (this version, v2)) Bohmian mechanics can be generalized to a relativistic theory without preferred foliation...
  22. M

    The Classical Path, QM Path Integrals and Paths in Curved Spacetime

    "The" Classical Path, QM Path Integrals and Paths in Curved Spacetime Hey Guys! I've got an exciting question! It's been burning on my mind for years, but I think I can formulate it now. It's not so much a specific question, but rather a physical story which perhaps this thread can uncover...
  23. J

    The affect of spacetime curvatures on the speed of light

    I understand that the speed of light can be slowed down when it passes through different mediums. I also understand that general relativity describes how space time is cured and this curvature depends on the mass of local objects and that it can influence the direction of light. So my...
  24. L

    Following a light ray through a curved spacetime.

    Here goes a conceptual question that has been bugging me: Consider the famous eclipse experiment that shows the Sun's gravitational lensing effect, allowing a star that would otherwise be obscured by the Sun to be visible from Earth. Say an observer wanted to travel to the star from Earth and...
  25. M

    Spacetime/Proper Length

    In special relativity, length dilation is defined as follows: X' = X0√(1 - V2/c2), where X' is the apparent/dilated length and X0 is the "proper length" Therefore proper length: X0 = X'/√(1 - V2/c2), where c > V > -c I read a book on the spacetime approach to relativity using the...
  26. Q

    Curvature of space and spacetime

    i am trying to understand the relationship between the two on a local and global scale and how these two concepts are related to the Ricci scalar. Is it correct to say that as far as we know on a global scale, spacetime is flat so that the Ricci scalar is zero. If so, what can be said about...
  27. darida

    Exploring Ansatz Metric of 4D Spacetime

    Ansatz metric of the 4 dimensional spacetime: ds^2=a^2 g_{ij}dx^i dx^j + du^2 (1) where: Signature: - + + + Metric g_{ij} \equiv g_{ij} (x^i) describes 3 dimensional AdS spacetime i,j = 0,1,2 = 3 dimensional curved spacetime indices a(u)= warped factor u = x^D =...
  28. A

    Exploring Spacetime Geometry: Change in the Worldtube?

    I've been thinking about the geometry of spacetime itself, and it has really been mind-blowing in some way. If space and time are so alike that we can treat them in a way that objects have a temporal extension as well as a spatial one, my question will be about this fact. So let's suppose...
  29. C

    Why is spacetime shown on a 2 dimensional plane?

    I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space...
  30. M

    Curvature of Spacetime: Is the Universe Flat or Curved?

    Hi there. I have a dump question for you guys. I really wonder about curvature of spacetime. I read that due to Omega_tot=1 the Universe is assumed to be flat. But on the other hand something like the curvature of the universe is mentioned... I also thought that the energy stress tensor...
  31. S

    Is spacetime independent of its universe?

    Something is throwing me here. No matter how fast one is going, relatively speaking, one is in the same universe as everyone (and everything) else. We're all going through the same spacetime, albeit at different velocities. You're in the same universe as I am and we both see the same space...
  32. S

    Question: does the physical curvature of spacetime ever move ?

    Question: does the physical curvature of spacetime ever "move"? Something isn't adding up with Einstein's theory--or, more likely, I'm just not understanding it correctly! How can we say that the curvatures of spacetime created by the presence of stress-energy is giving us a continuum? When I...
  33. O

    Is the future just an illusion in the block universe model?

    Firstly, I’m not a mathematician. My understanding of Einstein’s theories comes from popular science books (Cox, Greene, Gardner) so this is at the level of the ‘block universe’ model (or Brian Greene’s loaf, if that’s more familiar) and spacemen flying around the universe. So, on the face of it...
  34. M

    Nature of spacetime and interest in the field

    I am not quite sure what field the study of spacetime and energy would apply, considering I'm looking at it from a very, very big-picture point of view. I have a few theories and have done some math in regard to these three fields, and some of my conclusions have been quite interesting. I desire...
  35. Spinnor

    An angle at each point in spacetime and A_μ?

    Suppose we have a field that is represented at each point in space by an angle that is a function of time, θ(X,t). Can we make the following identification with the electromagnetic vector potential A_μ(X,t) of a moving point charge with velocity v_x, v_y, and v_z? θ(X,t) = A_0(X,t)...
  36. Z

    Higgs Boson vs GR's Spacetime: Is Mass Effect Obsolete?

    i was just reading a article that said that if the higgs boson is proven for fact, then the concept of the mass effect (spacetime pressure and curvature) would be obsolete. Is this true? i spent so much time teaching my self about SR and GR.
  37. T

    Relative acceleration of geodesics and spacetime curvature

    Mass curves spacetime. The relative acceleration of nearby geodesics of free test particles indicates the sign of the spacetime curvature. Convergent geodesics mean positive, divergent negative curvature. But also the metric expansion of space curves spacetime. The geodesics may be convergent...
  38. ChrisXenon

    Is There a Connection Between Movement Through Space-time and Aging?

    I'm getting older and dumber, it seems. In his book "The Fabric of the Cosmos", from page 49, Green points out some basic vector thinking. Given a fixed speed over the ground, as you head more West of North, your speed North decreases, whilst your speed West increases. He suggests that this...
  39. M

    Quantum mechanics without spacetime

    Hi, I am wondering what everyone here thinks about some of the work that has gone into researching quantum mechanics without spacetime. I am only a third year physics student at college (having done classical mechanics, electromagnetism and quantum mechanics upto perturbation theory, special...
  40. X

    Gravity question: force vs spacetime curvature

    So Newton says that gravity is an attractive force and some people believe in gravitons to transmit that attractive force, but Einstein says the attraction is actually due to moving along the curvature of spacetime (caused by the bodies' mass). I'm not asking which is correct, but my question is...
  41. jaumzaum

    Spacetime diagram - Twin paradox

    I was studying the twin paradox (of Einstein special relativity) and everything was working well until I get to the traveler's spacetime diagram. First let me introduce the paradox for you to understand the diagram. Pam is the twin sister of Joe. Pam goes out Earth in 2007 in a spaceship...
  42. A

    Why spacetime quantization does not prevent blackhole formation?

    Hi, This is my first post and first of all I would like to thank all the contributors to this forum for the amazing amount of information provided here. I’m not a physicist, but I like physics (although I have only a qualitative understanding of it) and I like to smash my brain on difficult and...
  43. Spinnor

    Picture of electro-magnetic vector potential in 1+1 dimension spacetime?

    "Picture" of electro-magnetic vector potential in 1+1 dimension spacetime? I'm trying to model the electro-magnetic vector potential, does the following come close for 1 + 1 dimension spacetime? See sketches below. Consider an elastic string, under tension, between two fixed points A and B...
  44. tom.stoer

    Hehl on gauge aspects of spacetime - beyond Riemann

    http://arxiv.org/abs/1204.3672 Gauge Theory of Gravity and Spacetime Friedrich W. Hehl (U Cologne and U of Missouri, Columbia) (Submitted on 17 Apr 2012) The advent of general relativity settled it once and for all that a theory of spacetime is inextricably linked to the theory of gravity...
  45. Greg Bernhardt

    Cosmology Spacetime, Geometry, Cosmology by William Lewis Burke

    Author: William Lewis Burke Title: Spacetime, Geometry, Cosmology Amazon Link: https://www.amazon.com/dp/0935702016/?tag=pfamazon01-20 Prerequisities: Level:
  46. P

    Why Doesn't Ether Equal Spacetime?

    EM radiation seems like a wave traveling through spacetime so, why isn't spacetime the same as ether?
  47. J

    Curvature of Spacetime on Earth

    I am trying to improve my understand of the basic elements of GR. I have read that the Earth orbits the sun because spacetime between the Earth and the sun is warped, mainly due to the sun’s mass. The Earth follows a geodesic, which is the equivalent of a straight line in curved space...
  48. bcrowell

    Relativity Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll

    Author: Sean M. Carroll Title: Spacetime and Geometry: An Introduction to General Relativity Amazon Link: https://www.amazon.com/dp/0805387323/?tag=pfamazon01-20 Download Link: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html Prerequisities: Contents: Contents: 1...
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