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. DLeuPel

    B What is the fabric of spacetime?

    The question is in the title. Nothing more to add.
  2. L

    I Are displaced dark matter and curved spacetime same thing?

    If dark matter is a supersolid that fills 'empty' space and is displaced by visible matter, then is this the same notion as the spacetime fabric having mass and being curved by visible matter?
  3. C

    I Gravitational DE(?) from Schwartzschild spacetime

    Imagining that an object spining around a spherical mass M has angular momentum that has z-component(θ=0) only, then $$g_{μν}\frac{dx^μ}{dτ}\frac{dx^ν}{dτ}=(1-\frac{r_s}{r})c^2(\frac{dt}{dτ})^2-\frac{1}{1-\frac{r_s}{r}}(\frac{dr}{dτ})^2-r^2(\frac{dθ}{dτ})^2-r^2\sin^2θ(\frac{dφ}{dτ})^2=c^2$$...
  4. M

    B Testing spacetime collapse at absolute zero

    The other day I was pondering what happens at/near absolute zero so I did some googling and found articles talking about how it has been demonstrate that as you near absolute zero, the quantum effect start to have an increased range. However, is seems that perhaps the quantum effects only get...
  5. TheQuestionGuy14

    B Is Spacetime a Discrete Lattice? - Prof. Sila Beane's Experiment

    Recently I found an experiment done by Prof. Sila Beane. In this experiment he simulates a tiny porportion of the universe using a QCD Lattice where spacetime is a discrete lattice. He inputs the GZK cutoff point of a cosmic ray into the lattice and what happens is, the result is that the...
  6. BookWei

    I Solving Boundary Conditions in 4D Spacetime Volume

    Hi, my classmate asks me an interesting question: For a finite 4D volume in spacetime, its boundary is a 3D close surface. If the 4D volume is a 4D rectangular, the boundary consists of eight 3D surfaces. The boundary condition is specified on these eight 3D surface. Please explain the physical...
  7. E

    Casimir effect in 1+1 Minkowski spacetime

    Homework Statement https://i.imgur.com/sI3JiB4.jpg https://i.imgur.com/PLpnPZw.jpg I have no idea how to solve the first question about the vacuum energy. I solved the second and third problems, but I'm hopelessly stuck at the first. 2. Homework Equations The Hamiltonian can be written as...
  8. T

    I Origin of Deformation Energy in Curved Spacetime?

    If a gravitational wave passes an elastic body it will be deformed. The source of the work done on it comes from the energy of the gravitational wave. In curved spacetime e.g. an accelerated expanding FRW- or static Schwarzschild-spacetime an elastic body will be deformed too. What is the...
  9. BookWei

    I Spacetime is homogeneous and isotropic

    I read the Special Theory of Relativity in Jackson's textbook, Classical Electrodynamics 3rd edition. Consider the wave front reaches a point ##(x,y,z)## in the frame ##K## at a time t given by the equation, $$c^{2}t^{2}-(x^{2}+y^{2}+z^{2})=0 --- (1)$$ Similarly, in the frame ##K^{'}## the wave...
  10. Mr_Phil_Osophy

    Which forum should I post in for....

    Hi, I have a question about the bending of spacetime and its proportion and relation to the mass which causes the bending; and also how the bent space would interact with other objects as they come closer. I'm going to ask a more detailed question with some possible problems I would like to...
  11. N

    B Is Gravity a Force or Effect? Exploring the Theories Behind Gravity's Nature

    If what we perceive as the force of gravity is really just the effect of curvature of spacetime, why do theorists hypothesize the graviton as the force carrier for gravity? I thought that GR does away with the notion that gravity is a "force." So, is gravity a force or is it merely an effect?
  12. DaveC426913

    B Flat spacetime in a gravity well

    I am trying to explain to someone why there is still gravitational time dilation at the centre of the Earth. (Not to over-tax the rubber sheet analogy, but...) When we sketch a gravity well, we show a curve that starts out nearly flat, then curves away from the flat plane, until it reaches the...
  13. Demystifier

    A Quantum field theory, spacetime, and coordinates

    [Moderator's note: This thread is spun off from another thread since it was dealing with a more technical point that is out of scope for the previous thread. The quote that starts this post is from the previous thread.] I feel the same about transformations of Dirac matrices and Dirac field...
  14. L

    The inverse of spacetime curvature?

    Let's say you can bend a paper...how about bending it upward. a slope I'm saying as we saw spactime in 3d...we all know how it looks..the lines are attracted toward Earth but why doesn't it deflects them and maybe negative mass is linked with it. In other words, someone under the trampoline...
  15. bland

    I Explaining Spacetime Dragging: Gravity, EM & Smooth Objects

    I'm looking for a simple explanation or decent analogy whereby something that is symmetrical and smooth like a black hole or even a spinning neutron star can drag spacetime as if spacetime was a viscous liquid. It guess it might make sense to me if gravity was unified with EM. I can see how two...
  16. Buckethead

    B Curvature of space vs. curvature of spacetime

    Regarding curvature of spacetime/space: At some given point in a gravitational field, spacetime is curved at that point and this is a constant. (I'm assuming this is true). Although we can talk about the curvature of spacetime, I never hear anyone talking about the curvature of space. Can...
  17. T

    B I'm a rookie and I have a question about spacetime

    I'm very new to this site and most assuredly and not a physicist (or a scientist) , but I have a question I'm hoping y'all can help me with. If I were traveling at or near the speed of light for a set distance- say Andromeda and back, time will slow down for me relative to the static observer...
  18. Gabriele99

    I Spacetime of Flatland: Exploring a 2D Universe

    I started this post on physics.stackexchange but it's too vague for that site, so here I am! :) I'm trying to really get the intuition of spacetime. This video explains how Minkoswki was the first to think that maybe our universe does not consist of a 3d space which evolves in time, but rather...
  19. Arman777

    Insights A Journey Into the Cosmos - FLRW Metric and The Friedmann Equation - Comments

    Greg Bernhardt submitted a new PF Insights post This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METU A Journey Into the Cosmos - FLRW Metric and The Friedmann Equation Continue reading the Original PF Insights Post.
  20. J

    I Alcubierre Drive & Bending of Spacetime

    Hello, I've been wondering about this... If something like the Alcubierre drive is possible, that bends spacetime around it in order to reach great distances faster, why would this not affect other matter in its vicinity? If I'm understanding correctly, in order to move faster than light, a big...
  21. Spinnor

    I Open string end points, their motion in spacetime

    I have some questions and refer you to the image below the caption of which states, "D-branes may be of exceptional importance in the explanation of elementary particles of the Standard Model. However, it still remains to find a solid connection between the M-theory and the Standard Model."...
  22. S

    A Kerr-Bolt Spacetime: Derivation & Resources

    I am unable to find any paper or book on Kerr-Bolt solution. I need to know its derivation. Please if anyone can suggest some material on it? I will be very thankful.
  23. RUTA

    Insights The Schwarzschild Metric: Part 1, GPS Satellites - Comments

    Greg Bernhardt submitted a new PF Insights post The Schwarzschild Metric: Part 1, GPS Satellites Continue reading the Original PF Insights Post.
  24. E

    I Embedding Curved Spacetime in Noncurved Spacetime

    Let us say, that we have a curved spacetime, for instance, Schwarzschild metric. Can it be embedded in five dimensional noncurved Lorentzian spacetime, or we need six dimensional Lorentzian spacetime with two time dimensions? Books only write that it is not necessary that this space is...
  25. F

    I Alice Observes Bob at Event Horizon: DarkLink's Question

    Hello physics forum. I am not very well versed in physics, so this question could be a misfire, but I just wanted to clear this up. I watched one of Susskinds holographic principle lectures. So I get that Bob would see Alice turn into a hot mush of energy as she approaches an event horizon...
  26. O

    B Can We Stop Gravity? Exploring the Possibility

    I know this is probably going to sound stupid but I'm really curious for the opinion of someone who has knowledge. Well spacetime is like a stretched bed linen. Putting on an object with a big mass, will cause its curvature. Now imagine having a piece of fabric holding it stretced from both...
  27. Mcbleak

    B Expanding space time and Virtual particles

    If space time (the universe) is infinitely expanding what happens when it rips? Have we observed Virtual particles in an area and counted them? Does the expansion of space time affect the amount of Virtual particles in a particular area? Is it theoretically possible to expand space time to a...
  28. L

    B Spacetime Geometry: Understanding Causality & Effects

    I still have some confusion of the concept of spacetime as geometry. Specifically, what confuses me is causality related to this geometry. My understanding is that stress-energy of matter/energy curves spacetime, the curvature of spacetime tells matter/energy how to move, and dictates to...
  29. K

    I String theory on complex spacetime, twistor string

    bosonic string theory requires 26 dimensions superstring theory requires 10, 9 spatial 1 dimension of time Witten has researched twistor string theory has there been any serious research with (super) string theory written on 4 complex -valued dimensions of spacetime? the additional dimensions...
  30. B

    I Dirac's Rest Mass in Minowski Spacetime

    Dirac's rest mass seems to be expressed as a fourth dimension. If we were to try to include this rest-mass dimension into Minowski space time, could it be expressed as a distance in space? S^2=x^2+y^2+z^2+(rest-mass dimension)^2-(ct)^2?
  31. K

    I Can complex spacetime solve the Higgs hierarchy problem?

    thus far the LHC hasn't found any evidence of SUSY or technicolor. thus far it's just 1 fundamental scalar there is an extensive literature on the Higgs hierarchy problem with various proposals and solutions offered has there been any scientific papers and research on the physical properties...
  32. dreens

    I Can the Electromagnetic Force be Explained by Curving Spacetime?

    So General Relativity explains the force of gravity as mass/energy induced curvature of spacetime. This correctly predicts gravitational time distortion, nonlinear geodesics and gravitational lensing, the anomalous precession of planetary orbits, the schwarzchild metric, and so on. Could the...
  33. mr1batman

    B Spacetime: Real or Not? LIGO Lab Explores Ripples

    how does scientists discover the spacetime ripples and this things while the spacetime is not a real fabric is this all returns to the LIGO lab and the machine that was built there ?
  34. nomadreid

    I Exploring Malament-Hogarth Spacetime: Simplified Alice/Bob Experiment

    The article https://en.wikipedia.org/wiki/Malament%E2%80%93Hogarth_spacetime, the possibility of a space with a "worldline λ and an event p such that all events along λ are a finite interval in the past of p, but the proper time along λ is infinite" is discussed, and the suggestion is made that...
  35. Urs Schreiber

    Mathematical Quantum Field Theory - Spacetime - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Spacetime Continue reading the Original PF Insights Post.
  36. T

    I Geodesic Deviation in Static Spacetime: Flat Geometry

    Regarding Einstein's static universe John Baez explains in The Meaning of Einstein's Equation To see this, consider a small ball of test particles, initially at rest relative to each other, that is moving with respect to the matter in the universe. In the 13 local rest frame of such a ball, the...
  37. P

    I Why must the spacetime we inhabit be a geodesically complete manifold?

    Can someone tell me how we know that our physical universe is geodesically complete? In response to a question I had about why we assign any meaning to the other side of a black hole’s event horizon (or its interior), I got an answer prompting me to look into the concept of geodesic...
  38. R

    Minkowski spacetime - Overall Distance

    Hi guys, I'm not exactly sure how to go about doing this problem. The question has no additional information, so I'm stuck. Any help I could get would be appreciated. 1. Homework Statement In four dimensional Minkowski spacetime an event, A, has components labelled Aμ and another event B has...
  39. Marrrrrrr

    A Virtual Fermions and Pauli Principle

    Hi guys, Do virtual particles, when they are fermions, obey Pauli exclusion principle as real fermions do? More specifically, what I am wondering is the following: Fermion fields would have some energy at every point in spacetime due to the uncertainty principle. Now, is it possible for the...
  40. T

    I Non-radial geodesics in Schwarzschild spacetime

    Consider a non-radial timelike geodesic outside the event horizon. Will it nevertheless cross the horizon radially or are non-radial geodesics also possible inside? I couldn't find any reference regarding a possible angle dependence in this respect.
  41. F

    B Fourier Transform of Spacetime

    When you do a Fourier transform of spacetime.. what do you get? (or how does spacetime look in frequency domain? And what applications do this and what results are they looking or solving for?
  42. weezy

    I Why do people keep saying photons are timeless?

    If you search for "does a photon experience time", almost every other link says that they travel at the speed of light and so STR tells us that its clock doesn't tick at all. However why do they use the arguments for special relativity which was developed for massive particles moving close to...
  43. L

    I The Expanding Universe: A Scientist's Perspective on Infinite vs Finite Space

    I have read some of the other posts about this topic but am still left unsatisfied. Could just be me. :cool: Did the universe, one minute after the big bang, consist of a finite volume of spacetime? If so, then is it not logically inconsistent that the universe can possibly be infinite now...
  44. G

    I Curvature of space and spacetime

    General relativity suggests that path of light is curved around sun. This curvature is not dependent upon frequency of the photon. What is the physical difference between 'curvature of space' and 'curvature of space-time' ? We can make measurements at two points in space at same time. But there...
  45. K

    I The spacetime curvature changed by an object

    Does the amount by which an object changes the spacetime curvature depend on relativistic mass or the rest mass? Through this question I just want to answer whether momentum equals [relativistic mass * velocity] or is it [rest mass * gamma * velocity]. Both the formulas might be the same but I...
  46. W

    B If spacetime can be bent can it be broken?

    A planet or star can bend space time around it.The greater the mass the greater the gravitational well.Could a black hole actually be such an enormous mass as to pierce space time and create a worm hole to another dimension?Also could the effects of the other dimension explain the weird effects...
  47. haushofer

    I Gravitational time dilation, proper time and spacetime interval

    Dear all, I'm having confusion about the standard derivation of Schwarzschild's gravitational time dilation. For concreteness I'll follow the explanation of Schutz' "gravity from the ground up", but other texts argue the same. So let me rephrase Schutz's explanation (I surpress factors of c in...
  48. deuce123

    I Explaining Extreme Spacetime Curvature & Time Physics

    Can someone please explain to me why time drastically slows for anyone near an extremely curves spacetime. I see it as the flow of time almost becomes slowed due to extreme curvature, what can explain this? What do physicists "see" time as? Also, I'm not entirely educated on this topic but I...
  49. V

    I Does Spacetime Have Elastic Properties?

    I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?
  50. jaketodd

    I Question about modeling continuous spacetime

    Since determining how many points there are in a given volume of continuous spacetime would require divisibility by infinity, is set theory's infinite sets the only way to model continuous spacetime? Thanks, Jake
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