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. RisingSun361

    How does the curvature of spacetime affect space?

    If the fabric of the universe is made of both space and time, and curving spacetime affects time, then I'm guessing it also affects space. I'm aware that an object shortens in length as it approaches the speed of light. But in the case of gravity, is space relative like time? Does an object on...
  2. bcrowell

    Computing trajectories in Schwarzschild spacetime

    I want to produce some realistic figures showing the spatial trajectories of test particles in a Schwarzschild spacetime. For instance, I'd like to start a massive test particle at aponegricon (how often do you get to use that word!?) in an orbit that Kepler and Newton would have predicted to be...
  3. Q

    Does the mass of a spinning object twist spacetime?

    Does the mass of a spinning object twist space time? If so is this why all natural satellites orbit in the same direction as the spin of the said object?
  4. Spinnor

    K.G. eq. verses Dirac eq. in 1+1 spacetime, differences

    Solutions to the Klein-Gordon equation can be interpreted as spin-0 particles of mass m and charge +1, 0, -1? See here. I think same can be said for solutions to the Dirac equation in 1+1 dimensional space-time, solutions can be interpreted as spin-0 particles of mass m and charge +1, 0, -1...
  5. T

    Static universe, spacetime and the stress-energy tensor

    Einstein's static universe obeys ##\rho = 2\lambda##. So, attractive and repelling gravity cancel each other. I'm curious about the spacetime in this universe. Because the scale factor is constant, it seems that neighboring co-moving test particles don't show relative acceleration, thus no...
  6. 5

    Realizing Warp Drive with Matter-Antimatter Fuel Cells

    My question is related to M. Alcubierres paper on the warp drive within general relativity. I was wondering about the realizability of this, setting the three energy conditions aside for the moment. Assuming the highest energy density known to me as an energy source, namely something like...
  7. L

    Can Quantum Gravity Allow Spacetime and Matter to Interchange?

    Supersymmetry interachanges bosons and fermions and can make bosons transform into fermions and vice versa... is there equivalent in quantum gravity where spacetime and matter can transform to each other and spacetime can become matter and matter can become spacetime.. isn't something akin to...
  8. L

    Understanding Spacetime in QM and QFT: Time Treatment and Particle Tracking

    spacetime is classical and continuous.. so when quantum system form superposition or entanglement, how is time treated esp in qft? how does spacetime keep track of the particles of fields? or how does the fields or particles able to jump in spacetime.. how is this handle in qm or qft?
  9. A

    Trampoline analogy for gravity

    The trampoline analogy tries to explain gravity in terms of space time curvature the orbit of objects around a massive object can be understood, but what about centre of gravity of the massive object, the images of trampoline is generally shown as seen from top where the massive object is making...
  10. T

    Curved Spacetime & Mass Movement: Exploring the Possibilities

    Is the movement of a mass affected by its curvature in spacetime? For instance will a forward moving planet diverges from its original straight line path due to the curvature of spacetime cause by it?
  11. BiGyElLoWhAt

    How Did Clifford's Theories Influence Modern Physics and String Theory?

    http://en.wikipedia.org/wiki/Kaluza–Klein_theory ##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche) http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf (this author makes some interesting arguments) Also, a lot (if not all...
  12. T

    Mass Warping Spacetime Explained: Quantum Field Theory

    How do u use quantum field theory to explain why mass warped spacetime? Is it something like spacetime is like a field and mass can only interact with it. The presence of mass excites the field (spacetime) producing graviton which distort spacetime. Is it something like that? If not can some1...
  13. T

    Mass Warping Spacetime: QFT & Gravitons Explained

    Is it something like that involves gravitons? Like mass producing gravitons that warp spacetime? All is it something like qft whereby spacetime is just a field and only those with mass can interact with it, resulting in warped in spacetime which is equivalent to excitation of fields in quantum...
  14. I

    Interplay of space and time in Spacetime invariant interval

    According to Special Relativity, the same event could have a different time duration and a different space extension for different observers, depending on their frame of reference. Relativity subsequently introduced the the notions of Spacetime as a continuum ( as opposed to the classical...
  15. H

    Relative Motion & Rotation of Axes of Reference

    I'm still very early on in my reading, so forgive me if this question isn't coherent. In the "historical introduction" section of the 1920 University of Calcutta translation of the original papers of Einstein and Minkowski available via the MIT online archive, mention is made of the fact that...
  16. michael879

    Quantum Mechanics in 1+1 spacetime

    I was trying to make a problem simpler by working in 1+1 spacetime, and I realized that it's far from obvious that quantum physics would even work in this case. Any non-spin related phenomenon could still work (e.g. quantum scalar fields, schrodinger equation) but in less than 2 spatial...
  17. E

    Does energy level determine the smallest region of spacetime that can be probed?

    Is it true that as you go higher in energy, from 1 eV to GeV to 10 TeV, you can probe smaller spacetime region. Since the LHC has only probed up to the 4 TeV or so, it means they have probed the corresponding tiny region of spacetime.. meaning it is still possible spacetime becomes discrete at...
  18. S

    Do free-falling objects also curve spacetime?

    First of all, I'm having a difficulty in defining what a static spacetime is. Does it presume that the objects with mass in the system are just sitting around and doing nothing, with no motion, relative to our frame, so there can be no motion and change in curvature of spacetime through time...
  19. K

    Dynamical Spacetime: Time or Space Dependent?

    when do you call a spacetime dynamical...when metric is time dependent or it depends on space ??...
  20. J

    Spacetime Interval & Metric: Equivalent?

    This may seem an odd question but it will clear something up for me. Are "The spacetime interval is invariant." and the "The spacetime metric is a tensor." exactly equivalent statements? Does one imply more or less information than the other? Thanks!
  21. Spinnor

    Do spinors still do "funky" weird stuff in 1+1 spacetime?

    Apparently we still need spinors for the Dirac equation in 1+1 dimensional space-time. Do spinors still do "funky" weird stuff in 1+1 dimensional space-time? Thanks for any help!
  22. tom.stoer

    Newtonian Spacetime: MTW Chap 12 Q&A by Tom

    I have some questions regarding Newtonian spacetime; reference is MTW chap. 12. MTW translate the Lagrange e.o.m. for Newtonian mechanics (with a potential phi derived from a mass density rho via Poisson eq.) into a geodesic equation in 4-dim. spacetime. They explicitly construct the...
  23. J

    Spacetime Curvature by Mass: Gravity Impact?

    Is there an attribute of spacetime that determines the curvature that will be caused by a specific mass thus resulting to the corresponding gravity? In other words: can there be "harder" or "softer" regions of spacetime where the same mass will bend spacetime less or more thus resulting to less...
  24. D

    How Does Blood Flow Velocity Relate to Spacetime?

    What is the velocity of a person's blood flow relative to the earth?
  25. B

    Exploring 4 Axes of Spacetime: Understanding the Unification of Space and Time

    below the speed of light we experience one axis if time and three of space. So at the speed of light the space and time unify and we get 4 isotropic axes of spacetime. 4 identical dimensions. is this correct?
  26. R

    Ball Thrown Up Follows Curvature of Spacetime

    A ball thrown up comes down again because the ball follows the curvature of spacetime. So is it possible that the ball comes down and before hitting the surface, goes up again due to curvature of the spacetime,which now point upward.
  27. F

    Sean Carroll's Spacetime and Geometry Chapter 5. Questions 3

    Homework Statement I'm not in grad school but I've been trying to teach myself some GR and I asked a professor what problems he thought would be good to study. He mentioned this one. I'd ask him for help, but he's out of town this week. I've also attached a picture to this problem. (It seems...
  28. W

    Basic question about spacetime and matter

    I'm trying to understand the concepts of physics, but there's one thing I don't fully get... If there is some matter with a spatial and temporal coordinate, let's say coordinate X, is the matter "in" that time and place, or "is" the matter that time and place? In other words, does space-time...
  29. Q

    Is Spacetime Flat? Answers to Orbit Questions

    Is space-time flat and if the answer is yes then how can objects orbit vertically and diagonally(since gravity is the warping of space-time)? Or does it exist from all sides?
  30. A

    Exploring Space-Time: Dilation & Concentration

    Hi all, I was wondering if anybody else here thinks the concept of space-time dilation/concentration (curvature) is a little bit funny, not in the sense of it having an effect on the neighbouring particles, but in the sense of actually stretching or contracting, as though it itself had certain...
  31. T

    Big Bang: Spacetime Created in 1 Sec

    During the first second of the Big Bang a mind boggling amount happened. So much so that we need to measure it in plank time to appreciate all the stages that occur. And in that 'bang' spacetime was created. My question is this. As space dilated would time not dilate? Meaning. If I were able to...
  32. R

    Spacetime: How It Is One & How It Moves

    Why do we say spacetime is moving and not space is moving in time dimension. And how is spacetime one. Also, there is only space, where changes(event) occur, and the rate of changes is describe with term time. That is, time is just a term and not actually a dimension like space(3 dimension).
  33. rmoh13

    Is the speed of light truly constant?

    The question that ponders upon the thought if the speed of light really is constant is a fairly common question. However, I was wondering about something and MAYBE this can provide some backup to the theory that the speed of light isn't constant, please point out any mistakes I make in stating...
  34. Thinkor

    Evidence for Variable Speed of Gravity in Coordinate Spacetime

    Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space. The same is theoretically true of the speed of gravity. But is there any supporting empirical evidence?
  35. V

    Topology of Relativity: Implications of Niels Bohr's Arguments

    I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal representation of the universe: "Neither does the theory of relativity, Bohr argued, provide us...
  36. C

    Schwarzschild Spacetime: Ellipsoidal for Moving Observers?

    In special relativity a sphere in the rest frame for some observer looks like an ellipsoid for an observer with a relative velocity. Can we use the same reasoning for the Schwarzschild spacetime? Namely that a spherically symmetric spacetime produced by a spherical mass look ellipsoidal for an...
  37. V

    Mathematical Considerations of Spacetime in Classical Mechanics

    When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any...
  38. Q

    Length contraction and time dilation in spacetime

    Observers that pass each other with a relative speed close to the speed of light will observe length contraction and time dilation at the other observer. In a spacetime diagram, this would be represented by two worldlines making an angle, right? Some textbooks suggest that some of the length...
  39. C

    Relativity & Spacetime: Interval Explained

    Hi! I'm a student reading a book given to me by my teacher about relativity and spacetime. It says that the separation between events in spacetime is measured in "intervals," and I can understand that part. What I don't understand is why you subtract the squares of the distance in space instead...
  40. R

    How does one get time dilation, length contraction, and E=mc^2 from spacetime metric?

    How does one get time dilation, length contraction, and E=mc^2 from the spacetime metric? Suppose all that you are given is x12 + x22 + x32 - c2t2 = s2 How do you derive time dilation, length contraction, and E=mc^2 from this? What is the most direct way to do this?
  41. E

    Diffeomorphism and removal of all matter from the spacetime

    It is unclear to me (1) what precisely diffeomorphism means and (2) what happens when all matter is removed from the spacetime. Sean Carrol says that: "the theory is free of "prior geometry" and there is no preferred coordinate system for spacetime." http://arxiv.org/pdf/gr-qc/9712019v1.pdf page...
  42. R

    Sinking instead of expanding universe?

    We all know the concept of the universe expanding. Would it be possible that the universe is not expanding at all, but the spacetime between objects is increasing? My question comes from the idea that spacetime is changed due to the presence of gravitational objects and the idea that gravity is...
  43. julcab12

    The birth of spacetime atoms as the passage of time

    http://arxiv.org/pdf/1405.3492v1.pdf The birth of spacetime atoms as the passage of time The view that the passage of time is physical finds expression in the classical sequential growth models of Rideout and Sorkin in which a discrete spacetime grows by the partially ordered accretion of new...
  44. H

    Locally Maximally Symmetric Spacetimes

    Can one say that every general curved spacetime, locally is maximally symmetric? I know that one can say that every general curved spacetime is locally flat (and therefore maximally symmetric with R=0), but I'm talking about a very high curvature spacetime, where still we can consider nonzero...
  45. T

    Spacetime diagram drawing problem

    I was drawing a spacetime diagram to relate Doppler shift effect but i stuck at a point which i can't understand This is what I'm trying to draw An object with mirror is moving away from me with a velocity of 50% speed of light When each second passes in my clock i send light pulses at that...
  46. nomadreid

    Units of spacetime in Minkowski metric

    In the equation ds2=dx2+dy2+dz2-c2*dt2 the units on the RHS are units of distance squared. But it would seem that units for a spacetime metric should somehow be in units which incorporate both space and time units. Undoubtedly this is an elementary question, but one has to start somewhere...
  47. C

    Relation between det(spacetime metric) and det(spatial metric)

    I have a metric g on spacetime and a spatial metric ##\gamma## such that the components of g can be written in matrix form as $$ g_ {\alpha, \beta} = \begin{pmatrix} g_{00} & g_{0 j} \\ g_{i 0} & \gamma_{ij} \end{pmatrix} $$ where ##i,j = 1,2,3## and ##\alpha = 0,1,2,3##. Now I want to find a...
  48. K

    Hamiltonian Formulation of GR for Elliptic Spacetime?

    This has bothered me for some time. In the ADM formulation, we foliate spacetime into 3+1 dimensions by creating 3 dimensional hypersurfaces via ##T = constant## along the worldline of some observer whose proper time is ##T##. This allows us to write dynamical equations for the evolution of some...
  49. B

    Solving Spacetime Diagram Homework: Ship Reversal from Cape Canaveral

    Homework Statement At time t = 0, a spaceship leaves Cape Canaveral (x = 0) at speed 2/3c, heading directly upwards (+x direction) toward a satellite in orbit. The satellite is located a distance 2 AU (see footnote2 if you forget what that is) above the earth’s surface. When the ship...
  50. E

    Is Spacetime Infinitely Elastic or Does it Have an Elastic Limit?

    I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions. It would seem that spacetime gets stretched. Does spacetime have an elastic limit, such that it could "break" at some point...
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