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

    Branes: Exploring the Complex Relationship with Spacetime

    Branes are confusing subject. Branes are objects. Yet Branes are also Spacetime. But how could that be. General Relativity says geometry is not physical, but just math relationship. Now how could Branes itself be spacetime when Branes are objects like strings...
  2. R

    Inflaton Field, Cosmological Constants and Spacetime

    I can accept that spacetime has no substantial aspect to it because for General Covariance (Diffeomorphism Invariance) to be true, spacetime "points" can't be real or else General Covariance won't work. Now question. How does Inflaton Field and the Cosmological Constants for example interact...
  3. Jonnyb42

    If wormholes connect two areas in spacetime, wouldn't that require 5

    If wormholes connect two areas in spacetime, wouldn't that require 5 dimensions? (an extra dimension past 4d spacetime.)
  4. andrewkirk

    Spacetime doesn't really exist does it?

    Having studied GR as far as Einstein's tensor equation and a bit beyond, I'm just doing a bit of a double-take wondering what we mean when we talk about spacetime. Frequently it is referred to as if it is a thing that exists, like mass and energy. For example, we say that spacetime is curved...
  5. Jonnyb42

    Gravity = warping of spacetime (doesn't make sense)

    I don't see how the bending of spacetime can be a proper way of explaining to people gravity. Why would bending of space-time imply movement?, (or acceleration.) The analogy with a ball on a bed sheet can only go so far. (which isn't very far.) Is this lame analogy used only because, there...
  6. S

    Does expansion of spacetime also stretch amplitude of light waves?

    Expansion of spacetime stretches wavelengths and produces the red shift. Does it also stretch the amplitude of the wave, and make distant stars look brighter and therefor nearer?
  7. D

    Spacetime curvature: Real or Not?

    Hi, I'm new to this forum so maybe this topic has been addressed ad nauseum at some point before, so I apologize if so. But, as the title suggests, do you feel the spacetime curvature is a reality, or is it just a mathematical convenience for making predictions? dm4b
  8. J

    Static spacetime as static universe

    When Einstein conceived GR he added the cosmological constant in an attempt to create a static universe model. The problem with this was that it was unstable. I've recently read about static spacetime (static spacetime admits a global, non-vanishing, timelike Killing vector field K which is...
  9. R

    Particle Physics in Curved Spacetime (Background Independent)

    Special Relativity is just a special case where spacetime is flat and fixed. Meaning it is not really a correct picture of reality because nature chooses curved spacetime that is background independent. So quantum particles shouldn't be occurring in a flat fixed background but a dynamic...
  10. D

    Travel from one spacetime to another?

    I was wondering if such could be possible in the future, to travel from one spacetime to another (if other spacetimes exist)?
  11. tom.stoer

    Why is spacetime four-dimensional

    Are there any indications in different theories or approaches to QG explaining what could possibly single out 4-dim. spacetime? Is there an idea why string theory favours compactification of 6 dimensions? Is there an idea why purely algebraic spin networks (w/o any dependence on...
  12. P

    Spacetime Interval Relativity question.

    Homework Statement Two events occur 5 s apart in time and 3 s apart in space. A clock traveling at a speed of .6 can be present at both these events. What time interval will such a clock measure between the events? A. 8 s B. 5.8 s C. 5 s D. 4 s E. 2 s F. Other Homework Equations...
  13. J

    Causal structure of spacetime: intuitive reason for non-compactness?

    Apologies in advance if this has been asked and answered somewhere else, I searched but could not find anything. I just wanted to verify if my intuitive understanding of why space time (if it is to be physically plausible) can not be compact. According to Hawking and Ellis (and others)...
  14. H

    Spacetime, gravitational force

    Hi. If Newtons theory of gravity was changed - so that gravity is considered to propagate at the speed of light AND not only masses but all energy feels and radiates gravitational attraction - would the predictions then be identical to the ones of Einsteins generel relativity?' Thanks, Henrik
  15. M

    Does logic hold true outside our reality (spacetime)?

    We know that the laws of physics are unique to our universe, that is they only hold true in our spacetime. My question is about logic and if logic holds true outside our universe unlike the laws of physics. For example, if we say that x>y and z>x then we can conclude that z>y is true by logic...
  16. J

    Acceleration from curved spacetime

    This might be a stupid question.. Why does curved spacetime cause objects with mass to accelerate towards each other? If I placed a massive particle next to a larger massive object, at rest with respect to the large object, shouldn't the particle stay at rest?
  17. N

    Does light itself bend spacetime?

    Hello, I understand light can be accelerated in a gravitational field, because it follows the curves in the spacetimecontinuum. Now I was wondering: does light itself also create a distortion in spacetime and thus attract other things? And are there experiments to confirm this? (E.g. two...
  18. marcus

    Merging NCG matter with Spinfoam LQG spacetime (new Pfaeffle-Stephan)

    This thread is in case discussion of the following paper is wished. http://arxiv.org/abs/1102.0954 The Holst Action by the Spectral Action Principle Frank Pfaeffle, Christoph A. Stephan 11 pages (Submitted on 4 Feb 2011) "We investigate the Holst action for closed Riemannian 4-manifolds with...
  19. P

    Quantum Electrodynamics in Curved Spacetime

    Does anyone know if there exist a formulation of QED in curved spacetime. If yes could you give me some references to papers in which solution to these problem is described?
  20. M

    Calculating spacetime intervals between events

    Hi, I am new to this forum so hello to everybody. I have this problem to solve: Homework Statement Q is moving away from P at speed 4/5 c. After 3 years (in Q's frame of reference) he turns around (assuming that turning takes no time) and is moving back to P at speed 4/5 c. What are spacetime...
  21. D

    How could spacetime become discretised at the Planck scale?

    In early 2010 I attended this inaugural lecture by string theorist- Prof. Mavromatos entitled 'MAGIC strings'. In it he proposes that some string theory models may violate Lorentz symmetry at the Planck scale resulting in a kind-of foamy spacetime that could be observed by differing arrival...
  22. G

    Spacetime represented in coordinate geometry

    if the 3 spatial dimensions are represented on a 3 axis graph. would time be a straight line through the origin? if not could your direct me to some reading that i may find answers? I'm uncertain whether space-time can be represented using euclidean geometry.
  23. nomadreid

    What is k-Minkowski spacetime, and is it a tool in a theory of quantum gravity?

    What is k-Minkowski spacetime, and... In http://www.physorg.com/news157203574.html, k-Minkowski spacetime, which decreases down towards zero at small scales, is mentioned as a possible tool in a theory of quantum gravity and spacetime. But it is very, very vague. First, how is k-Minkowski...
  24. B

    Is spacetime a matter?how can this matter be detected?

    Someone told me that spacetime is a matter. I know that matter must be a mass or energy. Is spacetime a matter (mass or energy) , and if it is a mass. why can't we see it? Is it due to the presence of dark matter? If it is an energy. what is its source? The sun?? If it is not mass or...
  25. H

    Lorentz transformations on spacetime

    Homework Statement A3. Show that the Lorentz transformations on a spacetime 4-vector can be written as x'μ = (Lμν)*(χν) . Find the matrix L. Prove that (in matrix notation) Lτ gL = g where g is the Minkowski spacetime metric.Homework Equations Any help suggesting at least equations will be...
  26. A

    Spacetime inside Quantum Vacuum or vice versa

    Hi, Is Spacetime inside the Quantum Vacuum or is the Quantum Vacuum inside or fill up Spacetime?
  27. G

    On the interpretation of a spacetime diagram

    Below is a spacetime diagram which depicts the movement of a rod, four units long, relative to another rod of equal length. The red lines are the "moving" rod; the purple lines are the "stationary" rod. The gray lines are the world lines of the unit marks (0, 1, 2, 3, 4) on each rod. As I...
  28. W

    Analyzing Spacetime Diagrams: Finding Coordinates and Checking Invariance

    Homework Statement Two rockets are sent off at t=0, one from x=0 and the other at x=4. The rocket leaving from x=0 is moving at .8c and the rocket leaving x=4 is moving at .2c. When the paths of the two rockets meet, they send a light signal to x=0. Read off the coordinates in the S frame...
  29. D

    Tears in spacetime shielded by strings

    Hi all, Alright so while reading through some stuff, I came across something peciluar, string/M-theory state that rips in spacetime are a natural phenomenon and happen all the time. "Edward Witten showed that strings, which have spatial extant, can travel while encircling the tear as it...
  30. F

    Where does a photon distort spacetime?

    Lets say I have a very low energy photon moving through space and I want to visualize how space-time is effected by the motion of the photon thru space. Photons are supposed to be quantized.. If it were possible to build a machine to measure the "gravitational" effect of a single photon would...
  31. A

    Spacetime Expansion in Big Bang 100% Certainty?

    In Big Bang theory, Spacetime itself expands from Planck size to the universe today. This means there is no existing space before the bang. But what if we assume space and time already existed in the universe and the Big Bang was an explosion of just matter. Is there no cosmology theory or...
  32. pellman

    What is the EM Lagrangian in curved spacetime?

    In flat space time the Lagrangian for the EM potential is (neglecting the source term) \mathcal{L}_{flat}=-\frac{1}{16\pi}(\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu})(\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}) which is a scalar for flat spacetime. I would have expected the...
  33. A

    Rate of expansion of spacetime

    I understand that Spacetime is expanding, as demonstrated by the increase in red-shift with distance. And I also understand that light travels *through* spacetime which itself is expanding. It seems rational to me that one may compare the rate of spacetime expansion to the speed of light...
  34. L

    Exploring Spacetime Metric for Clock A's Time Interval

    Consider the spacetime metric ds^2=-(1+r)dt^2+\frac{dr^2}{(1+r)} + r^2 ( d \theta^2 + \sin^2{\theta} d \phi^2) where \theta, \phi are polar coordinates on the sphere and r \geq 0. Consider an observer whose worldline is r=0. He has two identical clocks, A and B. He keeps clock A with...
  35. S

    Why more than 4 spacetime dimensions

    hi, I have a very simple question: why is there really a need for more than 4 spacetime dimensions? are there any concepts for which 4 dimensions are not sufficient? thank you!
  36. B

    How can matter change the geometry of spacetime?

    How can matter change the geometry of spacetime?
  37. D

    Please explain the paths that planets take in regards to spacetime.

    Do planets follow the curvature of spacetime as they orbit, or what is their path considered to be?
  38. Y

    Device to measure curvature of spacetime.

    While posting a reply in another thread, I had an inspiration for a device to measure spacetime curvature. It is well know that we can measure this curvature by measuring the angles of a large triangle or comparing the circumference of a circle to its radius, but his device may may be simpler or...
  39. L

    Solutions to Killing's equation in flat spacetime

    Hi, Killing equation in flat space is just \partial_{\mu}K_{\nu}+\partial_{\nu}K_{\mu}=0 . I've seen in various places the solutions to this written as K^{\mu}=\Lambda^{\mu}_{\nu}x^{\nu}+P^{\mu} where P is a constant 4 vector, and \Lambda_{(\mu\nu)}=0 (i.e. symmetric part vanishes and it is...
  40. G

    Contradiction in Taylor-Wheeler's example of spacetime invariance

    In section 1.2 of Taylor and Wheeler's Spacetime Physics, a rocket moves past a laboratory (on Earth). Attached to the rocket is a pin. From that pin a spark is emitted at two locations in the lab, separated by 2 meters. The observer in the rocket measures the elapsed time between the sparks, as...
  41. G

    Contradiction in Relativistic Simultaneity in Taylor-Wheeler Spacetime Physics?

    In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously. I see two problems with this. 1. The narrative in figure 3-1 contradicts the text in...
  42. PeterDonis

    Conditions for spacetime to have flat spatial slices

    In another thread, https://www.physicsforums.com/showpost.php?p=2973770&postcount=45, some questions came up about what the conditions are for a spacetime to admit flat spatial slices, and for a spacetime to have a time-independent "scale factor" (see definition below). These questions...
  43. C

    Algebra of Physical Space vs. Spacetime Algebra

    What is the difference between the Algebra of Physical Space (APS) and the Spacetime Algebra (STA), and why do we need them both?
  44. L

    The Fall of Physical Momentum in an FRW Spacetime

    General particle motion in an FRW spacetime is governed by the geodesic equation, \frac{du^\mu}{ds} + \Gamma^\mu{}_{\nu \alpha} u^\nu u^\alpha=0, with u^\mu = \frac{dx^\mu}{ds} and where the Christoffel symbols are given in the notes. Show that the physical momentum of any particle always falls...
  45. C

    Free particle in Minkowski spacetime

    Homework Statement A free particle is moving in the x direction through Minkowski spacetime, and has velocity V as measured by a stationary observer at x = 0; t = 0. Express the particle's world-line parametrically in terms of V , parametrized by the particle's proper time  Homework...
  46. V

    Eddington Finkelstein coordinates in the Schwarzschild spacetime

    Do the Eddington-Finkelstein coordinates allow to cover the maximal analytic extension of the Schwarzschild spacetime? ans if not what region do they cover?
  47. V

    Orbit of Moons & Shapes of Planets due to Warped spacetime

    First post, I am just a layman, so go easy. The way I understand it, the moon is following a straight line through space. However, the mass of the Earth is so great that it warps the fabric of spacetime and it appears that the moon is going around the earth. Same with any moon or planet, they...
  48. J

    Is Spacetime Everywhere and Does it Stack Infinitely?

    So I have just recently started thinking about the universe and things like that, and I had a question about spacetime. I was curious as to how exactly spacetime works in the universe. Pictures usually show only one plane of spacetime, such as this picture...
  49. J

    Pauli matrices with two spacetime indices

    "Pauli matrices with two spacetime indices" Hi all. This is my first post so forgive me if my latex doesn't show up correctly. I am familiar with defining a zeroth Pauli matrix as the 2x2 identity matrix to construct a four-vector of 2x2 matrices, $\sigma^\mu$. I'm trying to read a paper...
  50. nomadreid

    Exploring the Mystery of an Equation in Spacetime

    In my reading I came across the equation ds2 = −dt2 + 2t/r dtdr + (1 − (t/r)2)dr2 + (BKr)2(dθ2 + sin2 θdϕ2) where s is spacetime, t is time, r is radius and the others are not important for my question. What I do not get is the "1" in the (1 − (t/r)2)dr2, or dr2− ((t/r)2)dr2 . This seems...
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