What is Spacetime: Definition and 1000 Discussions
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.
Tad Williams’ Otherland series has a scene where the characters are drawn to a temple no matter which direction they try to walk, as if space itself is curved.
This is kind of the intuition I get when a physicist talks about the spacetime interval kind of flipping past an event horizon: if you...
Hi everybody
I saw quite a nice Youtube vid about general relativity and how gravity bends spacetime and therefor redirects angular momentum into the center of gravity. I thought the first time I begun to understand the concept but immediatly the questions poped up.
The video basically says...
Hello, i can't understand how does the author found this expression relating ##x_{c}## and v. I already tried by a lot of geometrical ways, knowing that the tangent of the angle between the dotted line and the x-axis should be v, but the results are illogical. Could you help me? I am start to...
[Moderator's note: Thread spun off to allow discussion of this topic to continue since the previous thread was closed.]
I have had something nagging at me about this for a while, and it finally hit me while looking through this paper about the Godel Universe...
The distance/difference between two points in spacetime can be written in two forms (as shown in attachment). Can anyone explain the difference in the two equations? I have read that the two equations are the same, but i don't understand the change in sign. Why is it written in two forms...
I started by inserting ##ds=\sqrt{dx'^{\mu} dx'_{\mu}}## and ##p'^{\mu}=mc \frac{dx'^{\mu}}{ds}##.
So we have:
$$\frac{dp'^{\mu}}{ds}=mc \frac{d}{dx'^{\mu}} \frac{d}{dx'_{\mu}} (x'^{\mu})$$
Now I know that
##dx'^{\mu}=C_\beta \ ^\mu dx^\beta##
and
##dx'_{\mu}=C^\gamma \ _\mu dx_\gamma##
where...
I enjoy explaining spacetime curvature to people with a rank-beginner understanding of GR. But someone asked about that favorite concept in pop-sci, spaghettification. I'm having a hard time with it.
If you fell into a black hole, there's no reference frame within which you could describe...
For the flat spacetime we could just use that partial derivatives commute as well as the antisymmetry of ##F^{ab}##, i.e. ##\partial_b \partial_a F^{ab} = -\partial_b \partial_a F^{ba} = -\partial_a \partial_b F^{ba} = -\partial_b \partial_a F^{ab} \implies \partial_b \partial_a F^{ab} = - 4\pi...
I just learned from the American Journal of Physics that the two books
Space Time Physics by Taylor and Wheeler
and
Exploring Black Holes by Tayor, Wheeler, and Bertschinger
are for free now! What a nice Christmas gift!
http://www.eftaylor.com/spacetimephysics/...
In Phillip Harris' (U. Sussex) post on special relativity he includes on p. 45 an algebraic proof of invariance of spacetime intervals. He starts with the definition S^2 =c^t^2 - x^2 -y^2 -z^2, he inserts the Lorentz transform expressions fot t and x, and he does some algebra to show that one...
Via web search found https://www.physicsforums.com/threads/what-dimension-does-space-time-curve-in.852103/
Read it and watched two videos mentioned:
I understand we cannot perceive 5D ;-), so extrinsic visualization of maximum of 2D intrinsic curvature is possible. So time+1d space is all we...
Hello there.We know that spacetime may have singularities and the current theories can not describe it very much.I want to start reading about quantum gravity but what is the progress done so far for the resolution of questions about the singularity?Could a different approach perhaps a...
Hello there.The question is as stated:does light curve spacetime?We know that bodies with mass do curve spacetime but does a massless particle or wave like light curve spacetime?Thank you.
It seems a gravitational field does not alter the electromagnetic field strength. Is this correct?
My reasoning:
With no gravity, field strength is:
F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu
Introduce gravity:
\partial_\mu A_\nu \rightarrow \nabla_\mu A_\nu = \partial_\mu A_\nu +...
Ispired by PeterDonis remark about "river model" in some thread a time ago I made next visualization picture.
The graph desctibes, how the flat Minkowski spacetime is changed in presence of mass (black hole). It do not need much explanation, almost everything is described at the picture. To me...
I'm a bit confused about GR : what is more significant about the considered spacetime, the metric, which is time-independent, or the embedding (there are already some posts on PF about it), which describes the shape of a manifold, but is time-dependent ?
I want to know whether Quantum Fluctuations could exist without the presence of Spacetime. Would it be possible, in the event of a Big Rip scenario, and if Spacetime really would get ripped apart, that quantum fluctuations could still occur? And if Spacetime is ripped apart, does that mean the...
Hi,
My question can result a bit odd.
Consider flat spacetime. We know that inertial motions are defined by 'zero proper acceleration'. Suppose there exist just one free body in the context of SR flat spacetime (an accelerometer attached to it reads zero). We know that 'zero proper...
As far as I know, the grand prize of a Theory Of Everything is mathematically uniting of all forces in the conditions close to the big bang but one of the main problems from the GR end of things is that gravity is not actually a real force to be combined with anything.
All the most popular...
Hey there, I'm aware this is a bit of a stupid question, and I think that I understand the principle fundamentally, however, my intuition is still having a little trouble catching up, and I'm trying to figure out if it is because of an important detail that I have missed/misinterpreted.
I think...
My question in specific is understanding what this line EB exactly represents. This was borrowed from the book "A first course in general relativity" by Schutz. There is a question on page 30 (number 12) which asks the following:
"Use the fact that the tangent to the hyperbola DB in Fig. 1.14 is...
I had a thought that I wanted to share in another thread, but it wandered way off track and quite properly was closed. But I thought the separate idea that I had spawned from the old thread was worthy of posting in a new thread. I do not want to re-open the old thread, though!
In flat...
1) We know that for a given Killing vector ##K^\mu## the quantity ##g_{\mu\nu}K^\mu \dot q^\nu## is conserved along the geodesic ##q^k##, ##k\in\{t,r,x,y\}## . Therefore we find, with the three given Killing vectors ##\delta^t_0, \delta^x_0## and ##\delta^y_0## the conserved quantities
$$Q^t :=...
When people try to explain how gravity works, the following example is constantly used .
However, I don’t understand how this explains HOW gravity works. By using this example, gravity itself is used as a bias to explain how gravity works. How can explain gravity by saying “things fall along...
Hi,
in general relativity I'm aware of the spacetime 'distance' between two timelike related events is maximized by the free falling timelike path (zero proper acceleration) joining them.
Consider now a couple of events belonging to a spacelike hypersurface (AFAIK it is an hypersurface with...
I'm studying differential geometry basics for general relativity (no specific source, just googling around). I know that spacetime is modeled as a ##4##-dimensional smooth manifold. Smooth manifold means that we consider a restriction of the maximal atlas such that all charts in it are...
I was just reading about de Sitter space and the following question occurred to me:
de Sitter spacetime is curved despite containing no mass-energy, because it has a positive cosmological constant. Does it have a foliation into spatially flat, constant-time hypersurfaces though?
Maybe it's...
This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is:
##A## has set up a space-time co-ordinate system with some arbitrary event along his...
I was looking at this chart and I didn't understand how increased angular momentum of the test particle curves the spacetime around the center mass. If that is how it's interpreted. Now the way it looks like is that the curvature is dependent on the angular momentum of the test particle.
In de Sitter-Schwarzschild spacetime things close to the black hole are falling towards it whereas in greater distance they are receding. So there should be a certain (unstable) ##r##-coordinate, where things are static. The de Sitter-Schwarzschild metric has according to Wikipedia...
In a spacetime diagram the spatialized time direction is the vertical y-axis and the pure space direction is the horizontal x-axis, ct and x, respectively.
The faster you go and therefore the more kinetic energy you have, you'll have a greater component of your spacetime vector in the...
Since it is nonlinear, the 3 leg lengths would be limited to differentials?
But how would the metric coefficients be incorporated into those leg lengths?
It seems like the leg differential lengths would have to vary inversely with the magnitudes of the metric coefficients? For example, near...
If I make two rods with 1 meter length here on the surface of earth, and send one of them near a black hole that is at rest relative to earth, placing it there with its length alligned in the radial direction of the black hole, would I see the rod close to the black hole with a length shorter...
I am trying to understand the basic conceptual ideas about the space-time diagrams. In spacetime diagrams we have events which are labeled as points on the diagram.
Let us call we have an event on point ##A(0,0)##and another event on ##B(4,0)## measured by an inertial frame ##S##. This inertial...
I built the tool initially for myself to better understand how Lorentz Transforms and spacetime diagrams work. Then while trying to discuss it with a friend I need to put it online and it snowballed from there.
Now I am wondering whether there is any value for others in what I have created...
I am reading this book and in there the spacetime defined as a manifold such that an affine space of dimension 4. I am having trouble to understand the affine space. I made some reasearch but I couldn't grasp the idea of it. In the books its also stated that " We are familiar with the structure...
I am still new to the theory of relativity (both SR and GR), but I've read few books which gave me an insight about the subject (not a mathematical insight though). There's a question that I really would like to know the answer of: Is there a time delay for the bending of spacetime to occur...
Now that gravitational waves are more famous because of LIGO, it got me to thinking about what we (lay people) are usually told would happen, which is that the Earth will continue in a straight line at a tangent to its orbit at that moment that information arrives eight minutes later. Which is...
I know that the mathematical form of the line element of spacetime is invariant in all inertial reference frames, namely
$$ds^2 = -(cdt^2) + dx^2 + dy^2 + dz^2$$
From what I understand, the actual spacetime distance between two events is the same numerical quantity in all reference frames...
Hi,
reading the book "The Road to Reality" by Roger Penrose I was a bit confused about the notion of Galilean spacetime as fiber bundle (section 17.2).
As explained there, each fiber over absolute time ##t## is a copy of ##\mathbf E^3## (an instance of it over each ##t##), there exist no...
I have been at this exercise for the past two days now, and I finally decided to get some help. I am learning General Relativity using Carrolls Spacetime and Geometry on my own, so I can't really ask a tutor or something. I think I have a solution, but I am really unsure about it and I found 6...
Okay, so, while discussing Rindler space with my professor, I was asked to prove that for a free-falling observer, proper time for passing through the Rindler horizon is finite. That is at least how the question is phrased.
So, the professor obviously assumes that it is clear and trivial to me...
How can space time emerge from nothing, I mean nothing in the absolute case is voide of any thing, I can imagine the BB where there is a primordial plasma the expands and creates the matter and space, but space time from nothing is beyond me, me being stupid and uneducated.
Hi,
starting from this very interesting thread
I'm still a bit confused about the conclusions.
The main point, as far as I can understand, is all about conditions for a quadrilateral to be considered a parallelogram.
My first basic doubt is: the concept of 'parallel' applies just to geodesic...
My question comes from the following confusing aspect of the big bang theory. Since at different stages during development of the current universe, we know that fundamental particles, atoms and large masses started to form. And if all large masses are embedded in spacetime when during the...