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. E

    Simple spacetime interval question

    Homework Statement on a spacetime plot (y-axis) = t (x-axis) = x find the spacetime interval between points (0,0) and (300,700) Homework Equations Interval = (c^2(del t)^2 - (del r)^2)^1/2 The Attempt at a Solution So I can see clearly my del t is 700 (700 - 0 = 700 ) but for the...
  2. M

    Gravity from spacetime curvature

    After a while of trying to understand this, it's still kind of confusing. I get how the planets orbit around the sun because of the sun's spacetime curve, but if one were to drop something, how does spacetime curvature cause it to fall? How can everything in the universe have a gravitational...
  3. T

    Can spacetime be created ? if yes how if not why ?

    Can spacetime be created ? if yes how if not why ? I understand that spacetime is not physical and more of geometry. Still bec it exist virtualy ,as gravity depends on warping of spacetime. So can we ever create this spacetime , does it existing before big bang ??
  4. P

    Lorentz transformations for spacetime

    I've tried several hours to understand Lorentz transformations(for space and for time)...it simply dosn't make any sense...I've posted here,on math section,because I need a better mathematical view over it... whitout this I can not understand much out of the restricted theory of relativity,thus...
  5. Z

    Do particles without a rest mass bend spacetime?

    Hi guys, simple question I have: Do particles without a rest mass (including EM radiation) cause spacetime to bend? Or only those with a rest mass have gravity?
  6. G

    How do we know that spacetime is expanding

    What are the facts by which we believe that it's spacetime itself which is expanding since the big bang and not that it's only the matter-energy in the universe which expands in a pre-existing unchanging spacetime canvas?
  7. A

    Unravelling Metrics of Spacetime

    In a space time with metrics : ds^2=f(t)(-dt^2+dx^2+dy^2+dz^2) which is the unit that measures time t? second?, meter of time?
  8. K

    Minkowski spacetime diagrams, what does the hyperbola represent?

    Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame...
  9. L

    Spacetime Curvature: Matter & Metric Influence Explained

    in this article http://en.wikipedia.org/wiki/General_relativity it says in the first paragraph that the curvature of spacetime is related to the stress energy tensor i.e. the matter in the universe. i.e. the curvature at a particular point depends on the matter present at that point...
  10. H

    Does spacetime could curved in a square way ?

    Does spacetime could curved in a "square way"? Suppose there is a square mass object in the universe (I know its impossible, but suppose...). Does spacetime will curved in a "square way"? I believe that not as GR is defined on a smooth manifold. Am I right?
  11. P

    Is Spacetime the Cause of Inertia?

    Brian Greene describes in The Fabric of the Cosmos how spacetime itself is now thought to be the cause of the inertial effects behind Newton's bucket experiment (rising water, etc.). That is, rather than the "fixed stars" being the cause, as was the commonly held notion before Einstein...
  12. Rasalhague

    Evaluating T(A,A) and Components of T(A,__) in Minkowski Spacetime

    Excercise Exercise 1.6 of Roger Blandford and Kip Thorne's online textbook Applications of Classical Physics: "In Minkowski spacetime, in some inertial reference frame, the vector A and second rank tensor T have as their only nonzero components A0 = 1, A1 = 2, A2 = A3 = 0. T00 = 3, T01 = T10...
  13. J

    Kruskal and Penrose diagrams for a Minkosky spacetime

    Hello I'm looking for diagrams (Kruskal and Penrose diagrams) representing Minkosky spacetime. I found two diagrams at http://nrumiano.free.fr/Estars/int_bh.html (the two first diagrams of the page). Do they represent a Minkowski spacetime ? Thanks, Jeff
  14. B

    Spacetime and gravity: question about how they work together

    Hello, I have had this lingering curiosity for a while. I read through https://www.physicsforums.com/showthread.php?t=5732" thread a second ago and would like to kind of take it a step further on a tangent. I have only read about gravity effects and space-time as such they are...
  15. Rasalhague

    Minkowski Norms and Lorentz Metric in Spacetime

    From my reading of introductory texts on special relativity, I've seen this defined in various ways, and I'm curious about whether any of these definitions are preferable to others, for example because they're more convenient, consistent, logical, clearer, more widely used or more easily...
  16. O

    Curved spacetime and imaginary coordinate

    In Misner, Thorne, Wheeler: "Gravitation" it is stated on that "no one has discovered a way to make an imaginary coordinate work in the general curved spacetime manifold" (p.51). Can anyone elaborate on this? Right now, I don't get why it wouldn't work and nothing more is said in the book.
  17. A

    Schwarzchild spacetime singularity

    Hi all! I'm studying black holes and there's a point that I cannot understand. The book I'm reading is Modeling black hole evaporation, by Fabbri and Navarro Salas. The path is the following. After introducing the Schwarzschild metric ds^2 = \left(1 - \frac{2M}{r} \right) \ dt^2 - \left(1 -...
  18. J

    Spacetime manifold: initial condition or result of GR?

    I apologize for the poorly worded title. Let me try to explain my question better. A scientific theory must be predictive to be useful. Since we only know what happened in the past, the global topology of spacetime cannot be an input to the theory. Given space-like slices/"chunk" of the...
  19. D

    Curved spacetime: embedded or not?

    Can we think about 2 different "interpretations" of GR: 1. Without embedding: space is curved, that's all 2. With embedding: curved non-euclidean space can be embedded in higher-demensional euclidean space. In another words, spacetime is just curved (1), or it is curved is something (2)...
  20. morrobay

    Less elapsed time: Lorentz Transformation or Spacetime Interval ?

    With one clock stationary at the common origin for 10 time units and the other rocket clock traveling out and back at v=.6c. When both clocks are compared at the origin the elapsed time on the traveling clock will show less time by a factor of (.8) from the Lorentz Transformation. The...
  21. S

    Understanding Spacetime: Clarifying Misconceptions and the Role of Gravity

    Please clarify / correct my misunderstanding. I'm not a physics pro (just a personal interest). Also, please excuse the complete lack of technical terms! It has been said that to move beyond the speed of light is to move backwards in time? (Though it's also stated that this isn't possible...
  22. MTd2

    Energy Gaps in a Spacetime Crystal (paper title)

    Energy Gaps in a Spacetime Crystal L.P. Horwitz, E.Z. Engelberg (Submitted on 14 Oct 2009) This paper presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and...
  23. F

    Mass/energy as a condition of spacetime

    Mass/energy as a "condition of spacetime" I recently read somewhere (I think here) that mass is not something you "drop into" space, rather it's a condition of space, and that gravity waves are also a "condition of space". a) is this correct? b) If so, is it more generally correct to say...
  24. N

    Special Relativity spacetime intervals HW help

    Homework Statement The Tale: The Klingon home world of Kronos is located at x=0. At time ct=-4 , a wonderful event occurs: Federation emissaries negotiate a peace treatywith the Klingons, bringing many years of warfare to an end! As part of this treaty, the Federation agrees to share its vast...
  25. L

    Spacetime Invariance and Lorentz Equations

    Homework Statement So, I am working on a question that requires me to prove that s^2 = s'^2 from the Lorentz equations. It seemed like it'd be trivial... and then I ended up here a few hours later, not willing to waste any more time. Homework Equations By definition: s^2 = x^2 - (ct)^2 &...
  26. E

    Spacetime, curvature, orbit, matter and reactions

    In the BBC film Einstein and Eddington, Eddington describes the theory of spacetime using a table cloth (space), a loaf of bread (sun) and a piece of fruit (a planet). The Bread is placed in the middle of the table cloth, this forms curves in the cloth. He then takes a piece of fruit and...
  27. J

    Spacetime - formal description of No Rip/Tear

    Could someone point me in the direction of the relevant differential geometry/topology terminology/definitions/explanation etc. to express the idea that spacetime cannot be "torn". Methinks it's "diffeomorphic invariance" but, even if it is, a few nice words and/or an example (or two...) of...
  28. U

    The structure of quantum geometry of spacetime at the Planck scale

    http://img233.imageshack.us/img233/5816/espaotempoquntico1.th.jpg Two pictures of quantum spacetimes... The theory of quantum gravity (LQG) can perform calculations and predictions on the concrete structure of space and time at the Planck scale. Equations formulas that describe...
  29. E

    SM particles in highly curved spacetime

    I'm curious as to whether parameters like rest mass and mixing angles, half-life for 2nd/3rd gen and other properties change for SM particles like muons in highly curved spacetimes.
  30. N

    What Holds People on Earth if Gravity is the Spacetime Fabric?

    Ok, so according to Einstein, the Earth is held in by a "fabric" due the the Sun pulling on said "fabric." So my question, what holds people on Earth if gravity is this "spacetime fabric?"
  31. X

    The vacuum Einstein equations and flat spacetime

    Rencently, I found myself confused by some fundamental concepts in GR. I hope someone can help me with that. We all know the vacuum Einstein equation (VEE) without the cosmological constant \Lambda is Rab=0. Since I learn GR the words " matters bend the spacetime " been told again and...
  32. E

    Is spacetime in string theory 4D or 12D?

    Spacetime is 3D + 1T = 4D Is spacetime in string theory 4D as a result of compactification, or 12D, 11D+1T?
  33. N

    Is spacetime a physical entity?

    I have maintained here several times , amid howls of objection from a few, that spacetime IS something more than a mathematical construct or that at least we should maintain an open mind about that possibility. I have been thinking WHY I have that view and a significant reason is the presence of...
  34. P

    Spacetime & Rotating Planet: Velocities Impact

    What affect does spacetime have on a rotating planet? (Velocities in the center differ from surface velocities)
  35. T

    Does the curvature of SpaceTime Disprove gravity?

    Obviously not. But I am confused on this. Newtons laws of gravity did not fit with Einsteins Relativity theories because Newton said that a change in matter of an object would cause a shift to be felt by others in the universe because of the change in gravity. This would mean that the movement/...
  36. G

    Curvature of spacetime, Matter vs Energy

    Hello, I have what is probably a relatively (no pun intended) simple question pertaining to general relativity. I thought that I had achieved a solid understanding of the theory (and its special counterpart), until this question formed in my mind. My problem is based on the following...
  37. M

    Thermodynamics of Spacetime: The Einstein Equation of State?

    Hi, I have recently been delving into Quantum gravity related material... and I came across a paper by Ted Jacobson "Thermodynamics of Spacetime: The Einstein Equation of State" http://arxiv.org/abs/gr-qc/9504004 and as far as I understand the argument it is very impressive who would have...
  38. V

    Gravitation: curved spacetime or a force?

    In the Einstein's theory of general relativity, the gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies. But the quest for the famous graviton does not presume that gravitation is due to a force? Is the quantum gravity conflicting with the...
  39. D

    Can spacetime exist without energy?

    As I understand it a vacuum is space that doesn't contain matter, however is it possible to have space that is a vacuum that also doesn't have any energy?
  40. Pythagorean

    Exploring Smoothness of Spacetime

    Is Spacetime Smooth? Smooth: infinitely differentiable If there were a limit to the differentiability of matter's motion through time, I'd assume it would be at the quantum level (where particles are not actually point particles). Example: When I accelerate in my car, the value of my...
  41. Spinnor

    Hidden dimensions of string theory hiding in 4D spacetime?

    Hidden dimensions of string theory "hiding" in 4D spacetime? Could the hidden dimensions of string theory be "hiding" in 4D spacetime? Thank you for any thoughts.
  42. C

    Large Scale Structure of Spacetime Study Group

    Is anyone interested in going through Hawking and Ellis' book by the title above and posting questions and insights? My interest is in singularities in higher dimensional spacetime, and whether there are other ways to achieve singularities (and their zoology) besides large enough mass. I am...
  43. T

    Spacetime Translational Invariance vs(?) Lorentz Covariance

    Hello, I have been reviewing some relativity notes, and I am confused over something. I apologize if this seems like a silly or obvious point, but humor me. When we are talking about Lagrangians in field theory and in regular mechanics, we are often looking at symmetries. Namely, almost...
  44. M

    Interpretation of spacetime diagrams.

    Hello all I have been at ease with spacetime diagrams of the usual sort where the y and z dimensions are suppressed until I came across this passage from the following book. Problems of Space and Time. A reader edited and with an introduction by J.J.C.Smart. Page 293 of the chapter...
  45. S

    Does spacetime curvature of EM field affect zero-charge particles?

    I've read in a few places that the energy and momentum of the electromagnetic field will itself induce a curvature of spacetime, much like the presence of matter. I'm not very familiar with general relativity, but does this imply that particles with mass and zero charge will still be affected...
  46. A

    Exploring the Contradiction of Vacuum: Empty Spacetime?

    Okay, here’s the concept. Is it just “empty space” or something else? But since relativity; we know that space cannot, and does not exist without time, And it’s a continuum "spacetime" rather than space and time. So does it means that vacuum is just “empty spacetime” There arises a...
  47. G

    How to draw a spacetime diagram

    here is my poor effort at teaching newbies how to draw spacetime diagrams (somebody has to do it): first draw your x axis. this represents space. (one dimension of it anyway. one dimension is enough for most thought experiments) the y-axis represents time. imagine there is a stationary...
  48. Spinnor

    Is spacetime the surface of a 5 dimensional ball.

    At one time it was thought(still is?) that we live in a closed universe? So if we live in a closed universe we might try to get a picture of this space by thinking of the space S^3? remember, S^1 surface of a 2 dimensional ball, S^2 surface of a 3 dimensional ball, S^3 surface of a 4...
  49. C

    The Present Moment in Spacetime?

    It’s often asserted that there’s a contradiction between Special Relativity and our experience of living in the present moment. Einstein made a few statements like that, and it seems many physicists assume that if the theory is correct, this very basic feature of our awareness of the world must...
  50. M

    Is spacetime truly flat without gravitational influences?

    If someone were to remove all of the gravitational influences on a portion of space would that essentially make that portion of spacetime flat? (Just curious):-p
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