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.

View More On Wikipedia.org
Recent contents Top users
  1. jbunch

    Flat Spacetime at Event Horizon?

    Hi, I'm new and uneducated. Would like to know how to reconcile space-time being considered asymptotically flat near the event horizon and beyond, with the observable fact that stars do indeed orbit the black hole. I understand those orbits are not near the horizon, and I believe all the...
  2. atyy

    Wave function collapse in curved spacetime

    In flat spacetime, there isn't any problem with wave function collapse. I think that's the "textbook" position, although the only citation I have off the top of my head is the discussion in http://arxiv.org/abs/0706.1232 (section 1.1). How about in curved spacetime (working in the regime where...
  3. R

    How to plot correctly spacetime diagrams

    Hello, after having done a bit of exercices on Taylor & Wheeler ( just for self-study ), I felt the need to go on a bit differently, i.e. trying to solve qualitative problems instead of quantitative ones, i.e. using a bit of diagrams ( all in all, as Susskind always suggest "when you face a...
  4. darida

    Hawking Mass in Schwarzschild Spacetime

    Homework Statement Metric signature: - + + + Schwarzschild metric: dS^{2}=-(1-\frac{2M}{r})dt^{2}+(1-\frac{2M}{r})^{-1}dr^{2}+r^{2}d\theta^{2}+r^{2}(sin\theta)^{2}d\phi^{2} Second fundamental form: h_{ij}=g_{kl}\Gamma^{k}_{ij}n^{l} where: i=1,2 j=1,2...
  5. R

    Scalar field lagrangian in curved spacetime

    Homework Statement I am studying inflation theory for a scalar field \phi in curved spacetime. I want to obtain Euler-Lagrange equations for the action: I\left[\phi\right] = \int \left[\frac{1}{2}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi + V\left(\phi\right) \right]\sqrt{-g} d^4x Homework...
  6. T

    Distorting spacetime: Links/references about fundamental limits

    I'm interested in reading about the fundamental limits imposed by known physics on distorting spacetime in ways that bring two masses closer together so that speed of light travel time between them is reduced. I'm familiar with the concept of inflation theory. I think of it as a rapid...
  7. F

    Spacetime expanding at a rate equal to the speed of light

    Is there anyway to figure out the distance at which the universe is expanding (rate of stretching) at a rate that is equal to the speed of light?
  8. S

    Why do objects fall through curvature of spacetime?

    Just wondering, if the way to describe the movement of objects through spacetime is to say that they fall through the curves created in 4D spacetime, then is it a stupid question to ask why objects don't rise through spacetime? Or is this the same thing and rising and falling are one of the same...
  9. omephy

    Unitary spacetime translation operator

    Srednicki eqn. (2.23) and (2.24) states: We can make this a little fancier by defining the unitary spacetime translation operator T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) Then we have T(a)^{-1} \phi(x) T(a) = \phi(x-a) How do we get the second equation from the first equation?
  10. C

    Need flat spacetime to define mass and spin?

    In his book on GR, Wald writes "the notion of the mass and spin of a field requires the presence of a flat background metric...which one has in the linear approximation but not in the full theory..." Why do we need a flat background metric to define a field's mass and spin?
  11. 4

    Can something with zero rest mass (photon) curve spacetime?

    My understanding is that the presence of energy and matter curve spacetime. Is a photon considered energy? If so, how can it curve spacetime while having zero rest mass?
  12. K

    Understanding Positive and Negative Intrinsic Curvature in General Relativity

    if gravity arises from normal accelerations due to the curvature of spacetime...what would the opposite of this "process" represent? to clarify is it possible to describe the opposite of this curvature?? thanks
  13. L

    Spacetime displacement operator in QFT

    I'm trying to fit together my understanding of quantum mechanics, quantum field theory, given my lacking maths education. In quantum mechanics we have a time displacement operator and a space displacement operator, which are respectively: \hat{T}(t) = e^{-i\hat{H}t} \hat{D}(\underline{x}) =...
  14. P

    Why is there a Minus in Spacetime Interval Formula?

    Hello everyone Please help me understand why there is a minus in the spacetime interval formula and not a plus Thanks in advance
  15. S

    On Einstein´s theory of curved spacetime.

    Now if you view the cosmos from the side like imagine all planets horizontally they say spacetime is curved in a way like heavy sphere objects lying on a trampoline. What happens to the spacetime above the middle of the objects really, it seems like according to this space can push only on one...
  16. 4

    Is there always the same amount of spacetime curvature in the uni.?

    Is there always the same "amount" of spacetime curvature in the uni.? Universe is what I meant by uni. Okay, if matter and energy cannot be created or destroyed, and since they are what causes spacetime to curve, does that mean there will always be the same amount of spacetime curvature...
  17. M

    Timelike Killing vector field and stationary spacetime

    I am trying to understand why in the definition of a stationary spacetime the Killing vector field has to be timelike. It is required that the metric is time independent, i.e. the time translations x^0 \to x^0 + \epsilon leave the metric unchanged. So the Killing vector is...
  18. M

    Can we truly understand motion through spacetime?

    Ok, I understand what the motion through space is, but I have difficulty in understanding what the motion through spacetime is. Spacetime is a 4 dimensional manifold with time being one of the 4 dimensions. When a particle moves through spacetime with some velocity, it moves through space...
  19. M

    Spherically symmetric spacetime

    I know from classical physics that, for example, an electric field is spherically symmetric if its magnitude depends only on the distance r to the origin (and not on the angles \phi, \theta) and it's in radially inward or outward direction. But, what does it mean when spacetime is spherically...
  20. B

    Doppler shift, c, observation, recession, spacetime expansion

    Hi all, It is my understanding that a Doppler shift is the result of a change in wave frequency due to a change in distance of a signal source, relative to the observer. I assume that the change in distance must be continuous, in order to observe a Doppler effect: frequency increase =...
  21. soothsayer

    Spacetime is smooth after all?

    Just came across this article, which details findings from the Fermi telescope that have an interesting consequence to quantum gravity theories: www.space.com/19202-einstein-space-time-smooth.html First, what do you guys think of this finding? Is it legitimate, or flawed? It's obviously...
  22. S

    Question about spacetime curvature

    This maybe a simple question, but if Earth orbits the Sun due to the Sun's mass 'curving' spacetime, wouldn't we be moving closer to the sun? like if you spun a marble around within a bowl, it ends up in the center. What am I missing here?
  23. V

    Varying the action of a point particle in curved spacetime

    Homework Statement What I have to do is vary the action S =-mc \int ds = -mc \int \sqrt{-g_{\mu\nu}(x(t))\frac{dx^\mu(t)}{dt} \frac{dx^\nu(t)}{dt}} \ \ dt to find the equation of motion for x^\mu(t) The Attempt at a Solution Now, to begin with, I have to admit that I am having...
  24. Z

    How Does Relativity Affect Time and Space Measurements Between Events?

    The question... Two events are observed in a frame of reference S to occur at the same space point, with the second event occurring after a time of 1.70s. In a second frame S' moving relative to S, the second event is observed to occur after a time of 2.25 s. What is the difference Δx...
  25. F

    Local flatness at r = 0 for star interior spacetime

    Hi All, I am interested in the discussion in section 10.5 of Schutz's First Course in GR book. Specifically, the conditions at r = 0 of a static, spherically symmetric interior star (or whatever) solution e.g. Schwarzschild interior solution. He argues that by enforcing local flatness one...
  26. H

    Spacetime Physics (1966) Fig 23 on page 40

    I am self-studying and have followed everything in Taylor and Wheel up to the exploded view of the spacetime diagram on page 40. The diagram in lower right hand corner of Fig 23 on page 40 refers to "Events that an observer at A may yet experience if nothing is shrouded from his gaze."...
  27. V

    Question about the curvature of spacetime:

    There's something very fundamental about the curved structure of spacetime that is confusing me. Einstein is saying that gravity can bend starlight. In other words, if I have this right, a star's light will follow the curvatures of spacetime created by a large body of mass, like the sun. Here's...
  28. V

    Quote about movement through spacetime that is confusing me:

    The quote is from Jake Goldberg's Albert Einstein: the rebel behind relativity: p. 53: "As objects begin to move rapidly through the dimension of space, their movement throught the dimension of time must slow down, because no object can move through space-time faster than the speed of light."...
  29. P

    Evidence of Electromagnetic fields causing spacetime curvature?

    Hi All, Just wanted to know, is there any experimental or observational evidence today, that electromagnetic fields can cause spacetime curvature? Either direct or indirect?
  30. V

    Thought experiment involving spacetime curvature:

    Peter Donis and Nugatory taught me a lot about spacetime curvature yesterday, but it has left me with so many questions. It sounds like mass slows down time as it warps spacetime. So, I suppose this means: more mass = more spacetime curvature = less time elapsing. Okay, in addition to...
  31. P

    Tension Shells & Tension Stars: Exploring the Israel Formalism

    I've been learning the Israel formalism (see original article here) for thin shells. I think I understand the formalism well and how to do the matching given two manifolds (that are solutions of the Einstein's field equations - EFE). I've been studying several articles that use the matching...
  32. C

    Spacetime, Gravity & My Theory - A Year 9 Perspective

    This is not a homework question- it's a theory of mine. We had this Indian lady come and teach us Einsteinium physics. She talked about spacetime and gravity and free fall etc., but there is one thing I don't get. In Google images, if you type 'spacetime' you get images of a body in the middle...
  33. D

    Spacetime separation and dilation/contraction

    I'm trying to understand the relationship between the spacetime metric \Delta s^2 = \Delta x^2 - c^2\Delta t^2 and the simple formulas for time dilation and length contraction in special relativity x = \frac{1}{\gamma} \bar{x} and t = \gamma \cdot \bar{t}. Suppose from an inertial reference...
  34. B

    Differentiation in Minkowski Spacetime

    Hello everybody, I'm currently reading the book Special Relativity in General Frames by Gourgoulhon. There, Minkowski Spacetime is introduced as an affine space \mathscr{E} over \mathbb{R} with a bilinear form g on the underlying vector space E that is symmetric, nondegenerate an has signature...
  35. D

    Does Gravity Have Lines of Force Like Magnetism?

    So magnetism has definite lines of force. Does gravity have an equivalent device. References would be good just looking to learn up. P.S. I am aware that mass warps space time. I am having difficulty visualizing this in three dimensions.
  36. Luca_Mantani

    Proof of the Komar formula for the mass of a spacetime

    Homework Statement Hi, I'm italian but i hope to write in decent english :wink: Here's my problem. I want to proof the Komar formula for the mass M=-\frac{1}{8\pi}\int_S\epsilon_{abcd}\nabla^c\xi^d \, , where ##\epsilon_{abcd}## is the Levi-Civita tensor and \xi^a is the timelike Killing...
  37. andrewkirk

    Energy conservation in a FLRW spacetime

    Consequences of Energy conservation in a FLRW spacetime This entry uses the local energy conservation law to derive an equation that can be used, together with the Einstein field equation, to derive Friedman's equations for the dynamics of a homogeneous, isotropic universe. The energy...
  38. homer

    Christoffel symbols in flat spacetime

    Homework Statement Consider a particle moving through Minkowski space with worldline x^\mu(\lambda). Here \lambda is a continuous parameter which labels different points on the worldline and x^\mu = (t,x,y,z) denotes the usual Cartesian coordinates. We will denote \partial/\partial \lambda by a...
  39. 2

    Why can't we determine our motion relative to spacetime?

    Hi all, I was thinking about special relativity and spacetime and had the thought of measuring our velocity with respect to spacetime. I was wondering why this would't work and what makes it different from the ether, which we would be able to measure our velocity with repsect to to determine...
  40. N

    Why does spacetime warp around mass if it doesn't have mass?

    Whatever spacetime be made of strings or some other erotic substance it seems that it doesn't have mass so what causes it to warp around mass, shouldn't it pass right through?
  41. N

    Does Cosmic inflation cause spacetime to move?

    I've thought about this a lot and have tried to find the answer but have been unsuccessful. In the event of the big bang did it inflate through spacetime without effecting it other than warping by mass or did it actually cause the spacetime to flow or move outwards with the inflation?
  42. T

    How did Einstein come to the Conclusion of Spacetime?

    What led Albert Einstein to conclude that space and time were not two separate entities but merely one spacetime. Also, has there been experiment to prove this notion?
  43. DiracPool

    3-d versus 4-d spacetime curvature

    A second SR question that has been on my mind lately is that of hyperbolic nature of Minkowski space. The fact that the invariant interval, or lines of constant delta S trace out a hyperbola according to the equation, ##x^2-(ct)^2=S^2##, is fascinating to me and seems to imply that space-time...
  44. L

    Moving objects in Stationary and Static Spacetimes

    Hi, I understand the definition of stationary as existence of a timelike Killing vector field and as a result the fields (metric plus anything else e.g. gauge fields etc) cannot have any time dependence. Static is a stronger constraint that satisfies the above plus requires the Killing vector...
  45. twistor

    Read Witten's Reflections on Spacetime

    I found an now historical article of witten speaking about the fate of spacetime, and I wanted to share it with you. Here it goes: http://www.sns.ias.edu/~witten/papers/Reflections.pdf :rolleyes::wink: I hope you enjoy it
  46. B

    Spacetime and gravity and fields

    this might be a dumb question, but, if spacetime isn't a field and gravity is a property of spacetime. then gravity isn't a field either? (at least not a quantum field.)
  47. N

    Drawing lines through spacetime warped by the mass of the earth

    Been reading laymen's books on general relativity and I'm in need some clarification! ... Line 1: The shortest path from a point 9.8 meters above the surface of the Earth to another point at the same location in space but 1 second later in time. Line 2: The shortest path from a point 9.8...
  48. m4r35n357

    Geodesic Deviation in Spacetime: Exploring the Possibilities

    I've been meaning to ask this for some time, and now I've plucked up the courage! It is puzzling to me that many fundamental relationships in GR are explained in terms of euclidean space. Taking for example the geodesic deviation equation, it occurs to me that if defined in 3+1 spacetime there...
  49. T

    Radial motion in the Schwarzshild spacetime

    Hello, The following has been confusing my friends and I, I want to make sure I have this clear as it is fairly elementary. (note set c = 1) Ed is falling radially into a black hole, the Schwarzschild metric is: ds2 = (1-2μ/r) dt2 - (1- 2μ/r)-1 dr2 his proper time is dτ2 = (1-2μ/r) dt2 -...
  50. S

    Energy-stress tenor = 0 => flat spacetime?

    Mathematically, ##T_{\mu_\nu} = 0## ##\Rightarrow~R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = 0## Now multiply both sides by ##g_{\mu\nu}## with definition of ##R = g^{\mu\nu} R_{\mu\nu}## ##R - \frac{1}{2} R = 0## ##R = 0## Is that my imagination wrong? I thought 'empty space' might not...
Back
Top