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. naima

    Integration by parts in spacetime

    In this paper we have p18 an integral on space time M. The author takes a 3 dimensional space like Cauchy surface ##\Sigma## which separates M in two regions, the future and the past of ##\Sigma##. He gets so the sum of two integrals on these regions. He writes then let us integrate each of them...
  2. Jim Hasty

    Is the metric basis for space expanding as the universe expands?

    I have read that as the universe expands that the "fabric" of spacetime expands. Does this mean that the metric basis for a given space is expanding? Also, does this mean the distances between the atoms in the lattice of matter is also increasing proportional to the expansion of the cosmos?
  3. F

    Gravitational Lenses: Does Gravity Distort Spacetime?

    If gravitational lens can "focus" light, is it possible with gravitation, so that the resulting gravitation would be strangely unhomogenous? (If it is a dumb/noob question just tell we pls.)
  4. K

    Space-Time Curvature in General Relativity

    Suppose we are in a Minkowskian space, away from all the source of gravity, and observe an accelerated frame from this frame. Acoording to Equivalence principle, we can consider the accelerated frame to be at rest and assume we have gravity in the accelerated frame. Thus, observer in the...
  5. K

    Confusion in General Relativity

    According to equivalence principle, gravity can be treated like acceleration "locally". Based on this principle we can treat a non-inertial frame at rest and explain the fictitious forces (of Newton's Laws) as gravity. From this we can prove that time elapses at different rates at different...
  6. R

    Are spatial and temporal dimensions interchangeable?

    According to general relativity, time is a dimension, one of four dimensions that form 4D spacetime - a structure which is mathematically symmetrical and homogeneous. Should not all four dimensions, therefore, be mathematically interchangeable? Assuming that we are 3-dimensional bodies...
  7. E

    What is the difference between standard and isotropic metrics?

    The metric $$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$ when changed to $$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$ upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric. My question what is the difference between the first and the second...
  8. nomadreid

    Understanding Invariance of Spacetime Intervals

    Category of simple questions Obviously I am misunderstanding how an interval of space- time can be invariant under coordinate transformations. The following elementary (but obviously incorrect) calculation will illustrate my difficulty. Alice is leaving her two boyfriends, Bob and Charlie. Bob...
  9. DaniV

    Does acceleration curve spacetime?

    When Einstein wrote the special realvity he said that inertional acceleration and gravitational acceleration are the same, my question: Does it mean that any source of somthing that making body accelerate (force) is also curving the space-time? for example- spaceship that accelerating in empty...
  10. S

    Dirac equation and structure of spacetime

    I've been reading about the Dirac equation, and most authors eventually make some statement to the effect that the fact of spin and antiparticles falling out of the equation reflects a deep connection to the structure of spacetime. Is the implication that the math requires four particle states...
  11. Dimitri655

    Understanding Spacetime: Exploring the 2D Concept of Space and Time

    Hi guys, I was wondering if anybody could help me understand the concept of spacetime. My physics knowledge is quite limited but so far what I have gathered is: Spacetime is like a piece of paper (assuming it is 2d) but instead of width and length it has space on one axis and time on another...
  12. K

    Spacetime scaling invariance and quantum gravity

    Neil Turok, Director of the Perimeter Institute of Theoretical Physics in Ontario, Canada suggests scaling invariance is a fundamental property of nature, including spacetime. that nature does not recognize any kind of scale, including Planck scale. if true how would this affect the leading...
  13. Pejeu

    Spaghettification and gravity in theory of relativity?

    Per my layman's understanding, the apparent force of gravity, as explained by the general theory of relativity, is actually the result of rectilinear motion at uniform speed through warped spacetime. 1. If that's the case, what actually causes gravity for objects at rest with respect to the...
  14. E

    Non-Static Spacetime: Is It an Approximation?

    I have a problem with static/non-static spacetime. The problem is that the notion of spacetime includes time itself, so how can it change with time? Imagine an asteroid approaching the Earth-Moon system. The Earth-Moon system is a non-static spacetime, so presumably is giving off gravitational...
  15. DaniV

    I The Curious Case of White Holes: Unraveling the Mysteries of Spacetime Curvature

    How does white holes curving the space-time manifold? (I prefer see picture of white hole influence in addition to the explanation).
  16. R

    Why does light have a speed at all?

    I appreciate that this may be the 100th time this is asked but I am yet to see an answer which addresses the question head on. Given that reaching light speed creates both a length and time singularity; both length and time amount to zero for the propagating wave/photon. Why does that photon...
  17. E

    Does space have a velocity in spacetime?

    Hello, i try to find some opinions on these points a) If a brane action in a bulk is defined, in that case, that a brane is modelwise moving through a bulk, how is this ratio defined? Is this a regular "velocity" in that meaning, that space is being passed in a period of time? b) If a...
  18. RyanH42

    What is the volume of the universe using a spacetime metric approach?

    I want to calculate two things (This is not a homework question so I am posting here or actually I don't have homework like this) First question is finding universe volume using spacetime metric approach.The second thing is find a smallest volume of a spacetime metric (related to plank...
  19. Fractalm

    Stretched piece of spacetime example appropriate for student

    I would like to hear different examples of presenting the difference that general theory of relativity relates between a stretched piece of spacetime around a planet and a not stretched one far away from any kind of mass or energy distortions...these examples i would like to be written in a...
  20. T

    Heory of Spacetime Curvature and Gravity

    Do gravitational forces have to follow spacetime in the same way as light? Or does gravity act in a higher dimension? Thanks, T
  21. diegzumillo

    Apple and Worm: Patching holes in spacetime game

    I mean, I'm making a game, not making a gamer. I talked about making a gamer with my wife but she just grabs my head, analyzes, sees how big it is and says "nah, thanks". (this paragraph made sense because the topic title was "any gamers here?I am developing one") Anyway, the title of the game...
  22. Jaami M.

    Are light and time somehow intertwined?

    I'm wondering if time and light(entire spectrum) can only coexist simotanuously. When we look out into the cosmos and see stars they can be many light years away. Because it takes time for light to travel. That may have not been relevant. But what I'm saying is... Time is manipulated by the...
  23. Tony Stark

    Curvature of spacetime inside hollow sphere

    If mass curves spacetime in its vicinity, then consider the following case- Take a heavy hollow lead sphere which has 2 smaller lead balls placed in it. The Outer Sphere will curve spacetime around itself and thus will have its own gravity, but what about the 2 balls placed in it? The spacetime...
  24. Finny

    Why is gravity but not EM 'ripples' in spacetime?

    Why do we say gravity [GR] is a theory about ‘spacetime curvature’ and gravitational waves are ‘ripples’ but nobody uses such a description for electromagnetic fields? Don't EM waves 'ripple' spacetime? For example, one might imagine different types of spacetime curvature associated with each...
  25. D

    B How did spacetime pop out into existence?

    Hello, Cosmology for the layman says that there was a time t=0 when the universe was created out of infinitesimal length distance and before that nothing existed not even time. OK, but this rests on the assumption that there is always a manifold from which we cut off our space slices in the...
  26. AaromTheBritt

    I Anti-gravitons effect on spacetime

    So, I'm still a bit new to the realm of physics but I was discussing theorized particles with my professor the other day and came to the conclusion, if gravitons do exist, could anti-gravitons be an explanation for why the universe is expanding? I was reading around and came across a similar...
  27. H

    Question on quantum entanglement

    I am not a physicist but felt compelled to create an account to pose a question/idea. Don't beat me up over this please... I was reading on Quantum Entanglement and how entangled particles seem to pass information between them at "faster than light" speeds. Now, given that entanglement is an...
  28. K

    In LQG, do objects attract via gravitons or curved spacetime

    planet Earth and the sun. in GR, gravity is not a force but simply a manifestation of spacetime curvature. the sun curves spacetime and the Earth is simply traveling through geodesic motion through curved spacetime. in string theory, the sun and Earth exchange virtual gravitons through a...
  29. K

    Is spacetime a massless spin 2 field?

    since a massless spin 2 field when perturbatively quantized gives rise to gravitons, which couple to everything and is identical to gravitation, is spacetime itself massless spin 2 field? do virtual graviton exchange also modify time and space?
  30. D

    Coincidence of spacetime events & frame independence

    I have been reading these notes: http://isites.harvard.edu/fs/docs/icb.topic455971.files/l10.pdf in which they claim that if two spacetime events are coincident in one frame of reference then they are coincident in all inertial frames of reference, thus spacetime events are absolute i.e. they...
  31. B

    Is there measureable spacetime distortion from EM fields

    Please forgive me if I am posting in the wrong forum. Also the board limits the length of the title. I wanted to ask about Effect of high intensity electric and magnetic fields on spacetime. To begin, 15 years ago this was published...
  32. P

    Momentum Operator In Curved Spacetime

    Hello, I'm sorry if this question sounds silly, but in QM the Momentum Operator is ##{\hat{p}}=-i{\hbar}{\nabla}## . In Relativistic QM in Flat Space, this operator can be written ##{\hat{P}_{\mu}}=-i{\hbar}{\partial}_{\mu}## . Would it be correct, then, to say that in curved spacetime the...
  33. btouellette

    Flat Spacetime at Event Horizon of Black Hole?

    I've been working through Leonard Susskind's "The Theoretical Minimum" lecture series (which are a fantastic introduction to the topics covered by the way) and a couple of his comments confused me when he was covering the Kruskal-Szekeres metric/coordinates in General Relativity. The end of the...
  34. S

    Like spacetime -- can sound be taken as a fifth dimension?

    Like spacetime , can sound be taken as a fifth dimension?
  35. S

    Gravity & Spacetime Curvature: Have I Understood?

    When spacetime is not bent the two objects, red ball and blue ball, will move strait up the y-axis as they move through time. (Space is x and time is y). Now I've made the assumption that either a) All things want to move the smallest possible distance to the next point in time or b) all...
  36. vanhees71

    Electrodynamics in Robertson Walker spacetime

    I've a (perhaps somewhat stupid) question. Is there a good source, where one finds the plane-wave solutions (or what comes closest to it) for electrodynamics for the closed and open (non-flat) Friedmann-Lemaitre-Robertson-Walker metric. I try this myself for a while, because to my surprise I...
  37. S

    Graviton vs Einstein's Curvature of Spacetime

    As far as I understand it, Einstein theorized that gravity was the result of the curvature of space created by the presence of mater/energy, but that idea seems like it does not meld well with the idea that gravity is the result of a specific force carrying particle, as with the other...
  38. G

    Could energy be extracted from spacetime expansion?

    Purely theoretically, could it be possible to extract energy from spacetime's expansion? Like, say, imagine two celestial bodies far away enough so that they are not bound enough by gravity, they get farther away from each other due to spacetime expansion. We tie them to each other with a rope...
  39. D

    Solving the Shorter Distance Puzzle with Spacetime

    I see an example from book stated that a muon that are created at high altitudes can travel to the ground because of time dilation about its lifetime. In the view of muon, it travels shorter distance compared with the view of the Earth. Suppose there are two muons. In view of muon A, muon B is...
  40. R

    Measuring Relative Speed of Frames Using Spacetime Interval

    Hi all, Say two events happen in the same place according to one observer (1). They are separated in time by 3 years. According to another observer (2) that is moving relative to the first, the events are separated by 5 years. We can calculate, using the invariance of the spacetime interval...
  41. M

    Is Deja Vu the Brain's misinterpretation of Spacetime?

    Hi! Not sure if this is properly categorized,please correct me if it isn't. What if deja vu is just our brain misinterpreting 'reality' and exposing us to spacetime. Like skipping ahead in time(according to the definition of time in spacetime) but then it calibrates us back into the present...
  42. I

    Exploring Spacetime Curvature and Light

    Hi, So according to GR, energy bends spacetime, right? So that would include both light and mass. If I am understanding this right, light bends spacetime, and is also affected by the spacetime curvature. Could someone explain exactly what the spacetime curvature does to light (I mean like how...
  43. J

    Spacetime Curvature: Which Tensor Gives Coordinates?

    In the Einstein Field Equations: Rμν - 1/2gμνR + Λgμν = 8πG/c^4 × Tμν, which tensor will describe the coordinates for the curvature of spacetime? The equations above describe the curvature of spacetime as it relates to mass and energy, but if I were to want to graph the curvature of spacetime...
  44. J

    Conformal symmetry of FRW spacetime

    The standard spatially flat FRW metric in Cartesian co-moving co-ordinates is given by: $$ds^2=dt^2-a(t)^2(dx^2+dy^2+dz^2)$$ As far as I understand it the fact that the metric can be written in a form that is independent of ##x,y,z## implies that the Universe has the physical qualities of being...
  45. Spinnor

    Bose and Fermi statistics in 1+1 spacetime?

    Do we have Bose like and Fermi like particles (fields) in 1+1 dimensional spacetime, Fermi like particles (fields) that obey the Pauli Exclusion Principle? For what space dimensions does the Pauli Exclusion Principle operate? Thanks for any help!
  46. U

    Satellite orbiting around Earth - Spacetime Metric

    Homework Statement The metric near Earth is ##ds^2 = -c^2 \left(1-\frac{2GM}{rc^2} \right)dt^2 + \left(1+\frac{2GM}{rc^2} \right)\left( dx^2+dy^2+dz^2\right)##. (a) Find all non-zero christoffel symbols for this metric. (b) Find satellite's period. (c) Why does ##R^i_{0j0} \simeq \partial_j...
  47. Atlas3

    Does light receive a spacetime curvature upon refraction?

    could the bend be described mathematically? Not the vector the curvature.
  48. H

    Hypothetical Shape of a Spacetime and Time Travel

    Disclaimer: I am an aeronautical engineer with a background in fluids. My knowledge of cosmology only extends to articles and things I read before I go to sleep. So, here is my question: I have though about time travel, as many other people have. Currently we think it may not be possible, as it...
  49. RisingSun361

    Does spacetime imply fatalism?

    I'm currently reading Relativity: A Very Short Introduction. One part caught my attention: Does this mean that the future is already embedded in spacetime?
  50. Strange design

    Spacetime: Is There Zero Separation for Charged Particles?

    Is it correct to say that two arbitrary charged particles in space have a spacetime separation of zero? And if so, is this the explanation for how the electrostatic force between them acts instantaneously across any 3 dimensional distance. (By "instantaneously" I mean that the force would...
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