What is Spacetime: Definition and 1000 Discussions

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. R

    I What is the Constant Speed of Movement through Spacetime?

    Hi I have been reading Brian Cox/Jeff Forshaw book on Why does E=mc2 (highly recommend it) One thing I don't get (page 95) is when they say everything moves through spacetime at the same constant speed c?! I get why a person/object A at rest moves through space time with speed c - but say...
  2. X

    I Null Spacetime Intervals and Quantum Superposition

    In Abner Shimony's paper "The Reality of the Quantum World", the choice between particle detector and wave interference detector is said to be made "after the photon had interacted with the beam splitter". A: Isn't it true that, at light speed, time is not passing for the photon? And so, with...
  3. J

    I Deriving the 4-momentum of a free particle moving in curved spacetime

    Consider a free particle with rest mass ##m## moving along a geodesic in some curved spacetime with metric ##g_{\mu\nu}##: $$S=-m\int d\tau=-m\int\Big(\frac{d\tau}{d\lambda}\Big)d\lambda=\int L\ d\lambda$$...
  4. atyy

    I Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime

    Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime Sean Carroll https://www.amazon.com/dp/1524743011/?tag=pfamazon01-20 Review of the book by Matt Leifer Does the many-worlds interpretation hold the key to spacetime? https://physicstoday.scitation.org/doi/10.1063/PT.3.4366
  5. benorin

    Spacetime Physics (2nd ed.) problem 2-2: Bathroom scale and a Trampoline

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  6. M

    Transformation from de Sitter to flat spacetime coordinates

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  7. Robin04

    I Matter movement versus spacetime expansion

    If I understood well, cosmology makes a difference between matter moving in spacetime and the expansion of spacetime itself. Are these concepts experimentally distinguishable, or this distinction is only in our theories?
  8. FireAP

    B Plotting the Space-Time Continuum: Is it Possible?

    How would one plot the space-time continuum graphically(if it were possible,obviously)?
  9. A

    A Continuity Equation for fluid in a curved spacetime

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  10. D

    I The Tensor & Metric: Spacetime Points & Momentum Flux

    The components of the energy tensor are defined sometimes as the flux of the ith component of the momentum vector across some component jth of constant surface. But isn't the tensor a function of points of spacetime just as the metric? How can you evaluate a surface of j when the tensor is a...
  11. T

    I Is Minkowski spacetime a solution of the Friedmann Equations?

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  12. BWV

    I Nash embedding theorem & curved spacetime

    Curious, is there any useful reason to translate the 4d curved Lorentzian manifold in GR to, if i read this right, either a 46 or 230 dimensional flat Euclidian space, depending whether the manifold is compact or not? (although another source listed a 39 dimensional flat embedding). ( from...
  13. S

    B Elasticity of Spacetime: Does Spacetime Stiffen?

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  14. Ehyeh Asher Ehyeh

    I Is Our Universe Finite or Infinite?

    Summary: No answer could be more important to the assumptions and approach to cosmology. The overwhelming bias is a finite Universe, and could this be a mistake? The measurements across the observable universe strongly indicate a Gaussian Curvature of Zero(Flat). Does this prove that Spacetime...
  15. E

    I Gravity as Curvature of Spacetime: Understanding Einstein's Theory

    Just wanted to point out that i have never seen a better depiction of Einsteinian gravity, if a little hard to swallow and somewhat baffling to human intuition. In the following experiment prof. Brian Cox(he used to be on this forum?) says: "Isaac Newton would say that the ball and the feather...
  16. T

    A Numerically Solving Scalar Propagation in Curved Spacetime

    Hey everybody, Background: I'm currently working on a toy model for my master thesis, the massless Klein-Gordon equation in a rotating static Kerr-Schild metric. The partial differential equations are (see http://arxiv.org/abs/1705.01071, equation 27, with V'=0): $$ \partial_t\phi =...
  17. N

    B Understanding Spacetime Diagrams

    I got the book "An Illustrated Guide To Relativity" by Tatsu Takeuchi, and have questions on how to understand spacetime diagrams from different reference points. Before I ask, please let me know how I can draw a spacetime diagram and post it on the forum. I will want to use different colors to...
  18. P

    B How does the LIGO experiment affect SpaceTime?

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  19. S

    I Find CTCs in Kerr Metric: Visualizing Spacetime Geometry

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  20. J

    A Einstein and Spacetime: Debunking the Myth of Rejecting Curvature

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  21. Q

    Wicks Contraction without contractions at the same spacetime point

    If I'm computing $$\mathcal{T} \langle 0 | \prod_i^Ne^{\imath \beta_i \phi(x_i)} | 0\rangle $$ where the contractions at the same spacetime point are ignored, can I simply insert a complete set of states (product now outside of expression) between each exponential to give $$\mathcal{T}...
  22. P

    I Coordinate time between spatially separated events in Schwarzschild spacetime

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  23. S

    I Applying the spacetime interval to regular vectors instead of curves

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  24. N

    B Julius Caesar Problem from a SpaceTime Physics book

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  25. K

    B Matter & Spacetime: How Tightly Coupled Are They?

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  26. bland

    I Spacetime Geodesics at Sea Level & Zoomed Out

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  27. diazdaiz

    B Spacetime Curve: Mass Effects & 5th Dimension

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  28. PeterDonis

    Insights Maxwell’s Equations in a Static, Spherically Symmetric Spacetime

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  29. L

    B Professional debates about Spacetime

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  30. Ranku

    I Spacetime curvature and curvature index

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  31. R

    I Spacetime and Events in (x,y,z,t)

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  32. PeterDonis

    Insights The Einstein Field Equation in a Static, Spherically Symmetric Spacetime

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  33. platosuniverse

    B Is spacetime a quantum error correcting code?

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  34. W

    B Spacetime interval - alternative view - maybe?

    With regard to special relativity… Whenever, I come across the spacetime interval, written like this, say, (Δs)2 = (Δt)2 – (Δx)2 – (Δy)2 – (Δz)2 , it is as if it has to be that way. However, it seems to me it is this way by definition and does not have to be so. Sometimes, it seems to be...
  35. M

    I What happens to spacetime during the expansion of the Universe?

    What happens to the fabric of spacetime during the expansion of the universe? Does it stretch or expand? If it does not stretch or expand, does new spacetime form to "fill the gap" as such? Hypethotically speaking, I have two celestial objects separated by a gap 1 mile wide. Due to the...
  36. C

    I Is a photon simply a vibration of the spacetime lattice?

    Is a photon simply a propagating vibration of the spacetime lattice similar to gravitational waves but at a different wavelength and amplitude, and the electron that creates it plucks a single lattice string rather than a bunch? Therefore it has no mass and travels differently through spacetime...
  37. A

    A Do we need stochasticity in a discrete spacetime?

    Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a...
  38. jk22

    A Fractional spacetime, dimension equation

    Suppose we use fractional derivatives (https://en.m.wikipedia.org/wiki/Fractional_calculus) in GR, hence we have a local group symmetry ##SO(3-\epsilon,1+\epsilon)## does any reference exist about an equation for ##\epsilon## ?, since it could depend on coordinates too.
  39. LightAintSoFast

    A Equations for computing null geodesics in Schwarzschild spacetime

    My project for obtaining my master's degree in computer science involved ray tracing in Schwarzschild spacetime in order to render images of black holes. These light rays had to be computed numerically using the geodesic equation. However, I ran into a problem. The geodesic equation is given as...
  40. A

    A Why is this Pilot-wave model on a discrete spacetime stochastic?

    Look at the paper in the link below: https://link.springer.com/content/pdf/10.1007%2Fs10701-016-0026-7.pdf It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed...
  41. S

    I Is spacetime emergent - and in which theories?

    Some physicists, like Nima, Ed. Witten, Gross, and others have said/suggested that space-time is doomed, or emergent from something more fundamental. What ideas would replace space-time? Something similar to a perfect material? A fluid? Geometry? Quantum field theory of some sort? Entanglement...
  42. PeterDonis

    Insights Fermi-Walker Transport in Kerr Spacetime - Comments

    Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Kerr Spacetime Continue reading the Original Blog Post.
  43. PeterDonis

    Insights Fermi-Walker Transport in Schwarzschild Spacetime - Comments

    Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Schwarzschild Spacetime Continue reading the Original Blog Post.
  44. PeterDonis

    A Extra Killing Vector Field in Kerr Spacetime?

    In a recent thread, the following was posted regarding the "no hair" theorem for black holes: In the arxiv paper linked to, it says the following (p. 2, after Theorem 1.1): "Hawking has shown that in addition to the original, stationary, Killing field, which has to be tangent to the event...
  45. G

    I Electromagnetic Curr. in Curved Spacetime: Questions Answered

    I assume this forum to be the appropriate one, since the real problem is about covariance rather than electromagnetism. In electrodynamics in a curved background, the relation ##F^{\mu \nu} = A^{\mu , \nu} - A^{\mu , \nu}## stays in terms of ordinary derivatives. So, in particular ##F_{,\mu...
  46. A

    I Geodesics in 4D Spacetime: An Overview

    The geodesic for 2-D, 3-D are straight lines. For a 4-D spacetime (x1,x2,x3,t) what would be it's geodesic.?? The tangent vector components are ##V^0=\frac{∂t}{∂λ} , V^i=\frac{∂x^i}{∂λ},i=1,2,3## & ##(\nabla_V V)^\mu=(V^\nu \nabla_\nu V)^\mu=0,(\nu,\mu=0,1,2,3)##
  47. PeterDonis

    Insights How to Study Fermi-Walker Transport in Minkowski Spacetime

    Greg Bernhardt submitted a new blog post How to Study Fermi-Walker Transport in Minkowski Spacetime Continue reading the Original Blog Post.
  48. F

    B Any interest in a spacetime diagram generator?

    Hi, I've written a script-based spacetime diagram generator. I have no idea if it has any value for anyone besides myself—you may have access to better tools than I do. When I looked for spacetime generators, I only found some very limited web tools and one downloadable program that wasn't much...
  49. M

    I Spacetime as emergent quantum phenomenon

    Published in the peer reviewed Journal of Applied Mathematics and Physics is the intriguing paper with the following abstract: https://file.scirp.org/Html/11-1721242_88041.htm "Entanglement and the tunnel effect phenomena have been repeatedly observed and are generically accepted under...
  50. Osvaldo

    I Spacetime Curvature: Eliptical Orbital Paths & Keppler Laws

    Though it is hard not to believe in the spacetime curvature that cause planets to follow curved path arround massive objects, I wander how come these paths are eliptical, the object change velocity when moving arround the massive object and what is more obeys the Keppler laws. If there is not...
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