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
  1. Sciencemaster

    I Calculating Spacetime Around Multiple Objects

    In describing the spacetime around a massive, spherical object, one would use the Schwarzschild Metric. What metric would instead be used to describe the spacetime around multiple massive bodies? Say, for example, you want to calculate the Gravitational Time Dilation experienced by a rocket ship...
  2. S

    I Can there be some kind of photon emission caused by space expansion?

    Are there any kind of observed and experimentally verified processes or mechanisms where photon emission occurs and which are directly cause by spacetime expansion in some way?
  3. E

    A What is the formal definition of spacetime in physics?

    What is the mathematical definition of spacetime here?
  4. S

    I Matter Gaining Energy from Expanding Spacetime?

    Sean Carroll has an article (https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/) where he explains that matter can gain energy from spacetime expansion. At the end of the article, he says: In general relativity spacetime can give energy to matter, or absorb it from...
  5. P

    B Exploring Mass, Gravity & SpaceTime: Ask for Expertise Here

    Greetings. I registered to this forum because of a particular issue regarding Gravity. I'm no astrophysicist or mathematician, i searched to find an answer, but the terminology and equations are a little much for me. I feel the best direct way is to ask people with the right expertise. It is...
  6. H

    I Spacetime interval and basic properties of light

    While not having a professional physics background I was still interested in knowing more about special and general relativity. Therefore I was trying to find out where the space time interval was coming from in relation to the speed of light. Of course this is the first point to start I...
  7. Bob Walance

    B Could the source of dark energy be our parent black hole feeding?

    About a year ago, I heard Leonard Susskind discussing how entangled black holes could create spacetime. As I was listening to Prof. Susskind describe the mechanisms for creating entangled black holes, and how these black holes might create their own spacetime, it occurred to me that if we were...
  8. C

    I Calculating Relative Change in Travel Time Due to Spacetime Perturbation

    Suppose you have the following situation: We have a spacetime that is asymptotically flat. At some position A which is in the region that is approximately flat, an observer sends out a photon (for simplicity, as I presume that any calculations involved here become easier if we consider a...
  9. S

    I Please help with my spacetime diagrams (relativity problem)

    Here is a simple scenario where Object A and Object B cross past each other on an x-axis (for simplicity sake, let's just assume that they somehow passed each other on one spatial dimension). As they cross past each other, a photon gets released in the positive direction, and then gets absorbed...
  10. SH2372 General Relativity - Lecture 5

    SH2372 General Relativity - Lecture 5

    0:00 What is spacetime? 20:20 Kinematics, basic definitions 35:18 Motion of test particles 41:18 Frequency shift of light 1:10:19 Simultaneity
  11. PainterGuy

    I The curvature of space and curvature of spacetime

    Hi, The quote below has been taken from this article, https://math.ucr.edu/home/baez/einstein/node2.html, which I came across. The quote doesn't make any sense to me, especially the part in boldface. Could you please help me with it?
  12. D

    B Free Fall in Curved Spacetime: Does Minkowski Spacetime Exist?

    This topic has been discussed in the past on this forum, however there is one point that seems to be unclear. One example of the setup is the following: The universe is at a stage where all the matter is concentrated in a single black hole, except two spacecraft s A and B that orbit it far...
  13. Trysse

    I Why Is Minkowski Spacetime Non-Euclidean?

    In the meantime: What is your answer to the question: Why Is Minkowski Spacetime Non-Euclidean?
  14. Trysse

    I Searching for "Why Is Minkowski Spacetime Non-Euclidean" by Cronkhite

    I cannot find the paper that is referenced here https://www.nist.gov/publications/why-minkowski-spacetime-non-euclidean Why Is Minkowski Spacetime Non-Euclidean? Author(s) J M. Cronkhite I have looked here https://aapt.scitation.org/action/doSearch?SeriesKey=ajp&AllField=Cronkhite&ConceptID=...
  15. lindberg

    B Orthogonality in Minkowski Spacetime: Meaning & Visualization

    I have read that non-inertial frames are those, where time is not orthogonal on space. Does it just mean that the speed of light is not isotropic there or does it mean anything else? How can I picture more easily this concept (for space orthogonality I just imagine perpendicularity of one axis...
  16. S

    I Questions concerning the geometry of spacetime

    I have some questions about the space of the rectangle shown in the spacetime diagram. The red and blue lines are world lines of objects at rest with each other. 1) Does the rectangle have an area? (if no please go to question 3) 2) Is the rectangle a 2d Euclidean space? (if no please go to...
  17. S

    I Why am I getting the wrong conclusion from my spacetime diagram?

    On my diagram, a person is traveling in a spaceship to the right in red, which is displayed as a Minkowski diagram . At the origin (0,0) the person traveling travels by a stationary person. And the 2 blue lines are the worldlines of two blue stationary rocks. But when I try to figure out what...
  18. S

    I Are there types of spacetime where no symmetries are valid?

    We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no symmetries, no matter how fundamental, would be valid? Any special metric, geometry or shape?
  19. Narasoma

    I Spacetime Curvature via Triangle

    I understand the mechanism of defining the curvature of a 2D manifold via triangle. But I don't understand how this works in 3D. Meanwhile, Lawrence Krauss mentioned in his book A Universe from Nothing it does. How does this work in 3D?
  20. wcivch

    B Ride Gravitational Waves to Increase Speed?

    This is my first post so I apologize if i am in error anywhere. I recently had a thought that I have had trouble confirming. Based on the following assumptions. 1.) As you accelerate an object near the speed of light it’s mass increases exponentially. 2.) Mass warps space time. 3.) Spacetime...
  21. A

    I Time Travel in Newtonian Spacetime: Is it Possible?

    Is time travel possible in Newtonian curved spacetime?
  22. S

    A Does Spacetime Absorb Energy in General Relativity?

    Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...
  23. Tertius

    A Local phase invariance of complex scalar field in curved spacetime

    I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...
  24. cianfa72

    I Definition of "Spatial X Direction" in Spacetime Context

    Hi, although there is a lot of discussion here in PF, I'd like to ask for a clarification about the definition of 'spatial x direction' in the context of flat or curved spacetime. Consider a set of free-falling gyroscopes (zero proper acceleration) passing through an event A with different...
  25. F

    I Gamma - A Minkowski Spacetime Diagram Generator

    Gamma is a Minkowski spacetime diagram generator. I probably started this project in August and have been working on it almost full-time since. It will be a free, open-source application. The program can draw all the usual things: axes, grids events, and worldlines, etc. It's easy to create...
  26. H

    A Entangled particles in curved spacetime

    i do not know if the question about entangled particles has found mainstream answers; Suppose that pairs of maximally entangled particles are shared by Bob and Alice in a time independant gravitational field. Bob measures the spin in the direction of far fixed stars. There is a direction in...
  27. cianfa72

    I Minkowski Spacetime KVF Symmetries

    Hi, reading Carrol chapter 5 (More Geometry), he claims that a maximal symmetric space such as Minkowski spacetime has got ##4(4+1)/2 = 10## indipendent Killing Vector Fields (KVFs). Indeed we can just count the isometries of such spacetime in terms of translations (4) and rotations (6). By...
  28. cianfa72

    I Comparing Spacetime and Thermodynamic State Space Manifolds

    Hi, I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space. To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the...
  29. Trysse

    I Exploring Physicists' Opinion on 'Moving Through Time

    I recently had a discussion with my brother, about what it means to "move through time". His opinion is, that physicists cannot take this literally. His opinion is, that time is just an expression for change that takes place at different rates for different observers depending on their speed...
  30. C

    Space-like trajectory in Schwarzschild spacetime

    I'm not sure how to approach this question. So I start off with the fact the path taken is space-like, $$ds^2>0$$ Input the Schwarzschild metric, $$−(1−\frac{2GM}{r})dt^2+(1−\frac{2GM}{r})^{−1}dr^2>0$$ Where I assume the mass doesn't move in angular direction. How should I continue?
  31. cianfa72

    B Basic introduction to gravitation as curved spacetime

    Hi, my daughter saw my MTW copy on the desk and she asked me about the picture with the apple in front. To introduce her to the idea of gravitation as curved spacetime I answered like this: Consider you (A) and a your friend (B) at two different spots on a garden each with a firecracker. Take...
  32. F

    I Request for Input: 2D Minkowski Spacetime Diagram Generator

    I’m planning to write a 2D Minkowsky spacetime diagram generator tool. At this point, I am looking for help reviewing the specification. I am not looking for help with the implemenation. To be clear, I’ve written a complete specification, but it would be a waste if it was missing features that...
  33. F

    I Uncover Traps in Spacetime Diagrams: Bob & Alice's Cases

    There are some traps for the unwary in spacetime diagrams. I'll note a few; does anyone have more? Let me use my favorite actors, Bob and Alice. Bob is the stationary observer; Alice is the moving one. Both are in inertial frames (or however one prefers to phrase it). We look at Alice's...
  34. fee_de

    B Understanding Spacetime Diagrams from "Reality is not What it Seems

    I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity. https://i.stack.imgur.com/JgBDJ.jpg Before this image Rovelli writes: "It's not...
  35. LCSphysicist

    Special relativity - Trivial exercise with spacetime interval

    For a observer on Earth, a rocket takes Mike from Earth to Pluto with a speed of 0.82 c for 33.72 yr. Find the space-time interval for the two events such as Mike leaving the Earth and reaching Pluto considering Pluto is at rest relative to Earth for the observer on Earth. I confess that i am...
  36. W

    I Does a Magnet Curve Spacetime More Than a Non-Magnetic Mass?

    Hi. My question is described in the summary. I'm seeking some advice. The Reissner-Nordstrom solution for charged spherical bodies seems to indicate that electrostatic fields will be a source of gravitation. I've not seen anything similar for magnetic fields but I can't imagine how it could be...
  37. Wannabe Physicist

    Is There a Flaw in Understanding Proper Time and Time Dilation?

    Let us denote the events in spacetime before the trip has started by subscript 1 and those after the trip is over by subscript 2. So before the trip has begun, the coordinates in spacetime for A and B are ##A = (t_{A_1},x,y,z)## and ##B = (t_{B_1},x,y,z) = (t_{A_1},x,y,z)##. After the trip is...
  38. D

    I Discussion about quantum mechanics and spacetime

    Robert Lawrence Kuhn: It seems that special relativity suggests time is like gravity and electromagnetism, not built into the absolute fabric of reality like logic and causation. David J Gross: Yes, time is dynamical. The phenomena are dynamical and are labeled by what we call time. Including...
  39. thegroundhog

    I Why are gravitons expected to exist when gravity is just warped spacetime?

    As per the summary I don't understand why physicists talk as if gravitons are inevitable, when gravity is just curved spacetime? Why would curved spacetime have a particle?
  40. Buckethead

    B Spacetime: The cause of matter?

    In a paper written by Jonathan Schaffer entitled Spacetime the one substance (https://philpapers.org/rec/SCHSTO-7) which I have not read but which I found as a reference in a book by philosopher Philip Goff, Goff suggests that matter is actually created by a curvature in spacetime rather than...
  41. MidgetDwarf

    Relativity Question Regarding Different Editions of Spacetime Physics by Wheeler

    Greetings! I have misplaced my copy of Spacetime Physics by Wheeler (1966 ed/red cover) and wanted to read it again. Was wondering if there is a major difference between the earlier blue hardback?
  42. C

    I Electromagnetic Field & Space-Time: Relationship Explained

    What is the relationship between the electromagnetic field and space-time? I am basically assuming that space-time is one big gravitational field. Is there a relationship between space-time and the field (I presume) created by the strong force (however negligible it may be at any significant...
  43. Paulpaulpa

    Spacetime translations and general Lagrangian density for Field Theory

    In Sydney Coleman Lectures on Quantum field Theory (p48), he finds : $$D\mathcal{L} = e^{\mu} \partial _{\mu} \mathcal{L}$$ My calulation, with ##\phi## my field and the variation of the field under space time tranlation ##D\phi = e^{\mu} \frac{\partial \phi}{\partial x^{\mu}}## ...
  44. Halc

    I Coordinate System for Minkowskian Spacetime Relative to Event

    I have been using a coordinate system that is anchored on an event (rather than a speed reference) in Minkowskian spacetime. This makes it sort of a special case (no gravity or dark energy, just like special relativity) of the cosmological (or CMB-isotropic) coordinate system used to foliate the...
  45. morrobay

    B Time like spacetime interval, proper time, and time dilation

    Since the time like spacetime interval is equal to proper time for stationary or traveling observers, then it seems time dilation (proper time) seen with traveling clock is necessarily frame invariant. Then the so called time between ticks of both identical clocks, with stationary and traveling...
  46. J

    I Could spacetime be non-orientable?

    Einstein's general relativity theory assumes that spacetime is a manifold with intrinsic curvature proportional to stress-energy tensor. But manifolds, in principle, can be non-orientable, like Möbius strip or Klein bottle: So could spacetime be non-orientable? If not, is that because of...
  47. A

    I Is mass the source of spacetime?

    Mass curves the spacetime. In electrodynamics, an electron curves an electric field (if there is one) - because it has an electric field of its own. The electron is the source of an electric field(maxwell equations) Is there an analogy to space-time, is mass the source of the space-time field as...
  48. P

    A De-Sitter Spacetime: Is it Homogeneous & Isotropic?

    The question is in the title. I believe the answer is yes.
  49. Ranku

    I What Is the Difference Between Spacetime Curvature and Spatial Curvature?

    Why do we call it spacetime curvature of gravitation and spatial curvature of the universe? Why don't we call it spacetime curvature of the universe?
  50. C

    Calculation Involving Projection Tensor in Minkowski Spacetime

    In Minkowski spacetime, calculate ##P^{\gamma}_{\alpha}U^{\beta}\partial_{\beta}U^{\alpha}##. I had calculated previously that ##P^{\gamma}_{\alpha}=\delta^{\gamma}_{\alpha}+U_{\alpha}U^{\gamma}## When I subsitute it back into the expression...
Back
Top