Spacetime Definition and 1000 Threads

The poincare' group is the group of isometries of Minkowski spacetime, in a nutshell. In terms of an actual physical definition it is the group of all distance preserving maps between metric-spaces in Minkowski spacetime. What is the difference between this and geodesics?

Quantum Gravity is the successful merging of the two.. Wave functions (or QM) and Spacetime. So it would be good to know how the two differs. They seem to have one thing in common.. they are both mathematical abstraction. But then someone said (Peterdonis): "Tidal gravity is not "just a math...

I just watched Morgan Freeman episode Through the Wormhole "How does the Universe Work". A physicist in the show theorized that spacetime is together at larger scale but at the microscopic scale, spacetime splits with space and time no longer synchronized.. this is why particles can be in two...

I'm trying to study the best approaches to quantum gravity and especially the interactions of quantum and the metric. But first let us settle about the so called "spacetime points". What is the proof that spacetime points can't be composed of any substance but purely an abstract. The often...

Let us say there is a curved region of spacetime whose curvature is \kappa(s). How does one find the coordinates of the unit vector normal to a certain point on the region of spacetime? I tried searching Hamilton's principle and the general theory of relativity but I could not find any equation...

Inflation says that space between objects is expanding. Matter is held together by forces carried by bosons traveling at the speed of light. At the fringes of the universe inflation is warping space faster than the speed of light so it seems that there should be a horizon beyond which matter...

On the Wikipedia page on Schwarzschild coordinates... http://en.wikipedia.org/wiki/Schwarzschild_coordinates ...it talks about a "family of nested spheres": each surface of constant t and r is a 2-sphere (i.e., setting dt = dr = 0 and r = constant in the metric results in a Euclidean...

Is there a spacetime which is timelike and spacelike complete but null incomplete?

Hi there. I am a layman, and I have a question. As far as I have gathered, the prevalent view in cosmology is that the universe appeared as a result of the Big Bang, which in turn occurred due to expansion of singularity. Ok. Some go further and propose that singularity appeared through...

http://arxiv.org/abs/1110.3837 A smooth classical spacetime manifold can no more exist than can a smooth classical trajectory of a moving particle. Spacetime as a classical 4D manifold is a myth, sometimes a very useful one. Many PF people must already realize this so clearly that one hardly...

I am curious if there has been any research into the elasticity of spacetime in regards to mass. If we consider that a fabric is resistive to a degree to an object it could be said that an object must poses a certain amount of mass before it can cause a divet in spacetime.

If energy/matter deforms spacetime in three dimensions... Then why do we get galaxies in (relatively) flat discs and black holes that emit radiation in a single plane?

Derivation of expansion scalar for FRW spacetime -- weird observation In a recent thread... https://www.physicsforums.com/showpost.php?p=3567386&postcount=137 ...I posted a formula for the expansion scalar for the congruence of "comoving" observers in FRW spacetime. When I posted, I...

My understanding of Space, Time and "spacetime" In thinking about time I have developed the (easy) realization that whenever we indicate a duration we are comparing two spatial changes. I believe it was Einstein himself who pronounced words the effect of time being inexorably tied to space and...

I understand that spacetime is expanding between galaxies, as seen with the cosmological redshift. But, is it also expanding inside galaxies, such as the Milky Way? I'm not sure if the galaxy is gravitationally bound enough to where spacetime might actually be contracting within the galaxy...

Everyone is congratulating the recent Nobel Prize winners, whose work uses observations of distant supernovae to attempt to show the existence of universal acceleration. Let's not forget that supernova studies of cosmology are all based on a theory (General Relativity) that has huge problems...

Are any known laws of physics a function of a unique spacetime coordinate? Be careful reading my question -- I'm not asking if the laws of physics vary throughout spacetime (since they don't).

For the universe to be totally flat, and not just asymptotically closer to being flat as the universe expands, wouldn't there have to be pockets of hyperbolically-curved spacetime? In either case, I still would like to know how one expresses time dilation and length contraction in hyperbolic...

From my understanding Gravity is a curvature in space-time caused by mass. basically a massive object makes a dent in space and the curvature of that dent is relative to the size of the object vs. its mass(red giant vs black hole). A smaller but more massive object will make a deeper dent...

I'm slightly confused as to how we can use the picture of a 2D surface embedded in 3D space as an analogue to understand (maybe not picture!) 4D spacetime. My initial thinking was that trying to imagine a 4D spacetime isn't really possible, it's just a mathematical concept which one should not...

Homework Statement Homework Equations The Attempt at a Solution

Spacetime curvature and the force pulling an object "down" the curvature ok , I have a question about the current model of gravity. If mass bends spacetime I understand that it accounts for things like how long light takes to travel through its geodesics but "why" does this curvature make...

Homework Statement Prove that the spacetime interval -(ct)^{2} + x^{2} + y^{2} + z^{2} is invariant. [/itex] Homework Equations Lorentz transformations \Deltax' = \gamma(\Deltax-u\Deltat) \Deltay' = \Deltay \Deltaz' = \Deltaz \Deltat' = \gamma(\Deltat-u\Deltax/c^{2}) The...

I know that the rubbersheet / fabric analogies that we see on TV and in various diagrams are only a metaphor, but I'm having difficulty getting started researching what we actually know / theorise about the make-up / workings of the "fabric"? Could you give me any pointers to good postings...

Hi, everyone I'm now reading A Relativist's Toolkit by Eric Poisson. In chapter 3, he say something about stationary and static spacetime. For static spacetime, it's just like stationary (admits timelike Killing vector t^{\alpha} ) with addition that metric should be invariant under...

What did spacetime look like some time after the big bang? 1) Euclidian space. Imagine yourself in empty space, no mass, with (x,y,z) coordinates ranging from –infinity to +infinity. Somewhere within this infinite space was a volume with high matter-energy density from the Big Bang. 2)...

Curvature of spacetime tells us how the body is moving when it moves inertially. But if the body is not moving inertially does it causes backreaction by affecting spacetime curvature? Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.

Let us consider the General Relativity metric: {ds}^{2}{=}{g}_{00}{dt}^{2}{-}{g}_{11}{{dx}_{1}}^{2}{-}{g}_{22}{{dx}_{2}}^{2}{-}{{g}_{33}}{{dx}_{3}}^{2} ---------------- (1) Using the substitutions: {dT}{=}\sqrt{{g}_{00}}{dt} {dX}_{1}{=}\sqrt{{g}_{11}}{dx}_{1}...

1) Is it always a given that the spacetime curvature will be flat in a region in which there is no mass? 2) Therefore is the curvature directly dependent on the mass in a particular region? 3) Also, what exactly is included in the term "mass"? 4) If there are no matter fields to curve...

I'm familiar with space and time together being 4 dimensions and that mass causes a curvature in this spacetime. When I consider a line that is curved, I can view the curvature because the line is drawn on a 2D surface (plane). So, it seems an additional dimension is required for a...

I have always thought of gravity as being a phenomenon related to matter. I have always envisioned it as a "contraction" in spacetime reaching out in all directions from an object. What I mean by contraction is that the closer you get to a body of mass the more spacetime is compressed. Due...

Does anyone know the Lagrangian for the propagation of light in curved spacetime? I'm disappointed to discover that I don't actually know how to compute the action for a given null curve.

I have read on some threads that there are other possible shapes for spacetime and I wondered could any of these spacetime shapes, or their change over time, affect our measurement of red shift? Also does the matter density at the location where a photon is emitted relative to our own...

Does performing a rotation of the usual coordinate system ct,x in the minkowsky spacetime makes sense? I guess it doesn't, but more than this i think that there is something that forbids it, since i could make coincident the 'lenght' axis of the non rotated coordinate system (observer A) with...

Please teach me this: Why we do not infer the gravity for the force(a type of interaction of fields) but for the distortion of space-time. Thank you very much in advance.

How do you understand Beables? How do you define Beables? Are these supposed to be located in spacetime or behind spacetime? m_wan wrote in the QM forum: Do you agree with this? Why and why not? I think understanding beables and its connection to spacetime is key to solving the secret of...

If one day gravitons are discovered, would their action be complementary to the gravitational attraction due to curved spacetime? Can gravity arise from both curved spacetime and exchange of gravitons? IH

Hi PF I know that a goal of the current research in High Energy physics is to get a describtion of QFT in curved spacetime. I assume this has yet to be described fully, but how about plain quantum mechanics in curved spacetime? Has it yet been described? Schreiber

If our universe is indeed expanding, would this have an effect on spacetime? For example as space and time are related, if I change one, shouldn’t it have an effect on the other? Also, wouldn’t it make gravity weaker as it is stretching space?

hi i am looking for an equation that gives me the electric field( if possible in 3-dim form) of a point charge in a distance r in a schwarzschild spacetime, where the point charge and the the gravitating body should not be the same position.

Hi, I'm trying to enter a spacetime with makeg(spacetime_name): on GRTensor II. I'm just following the simple example in the documentation, but instead of doing what it's supposed to (e.g presenting me with text offering me certain options and then me selecting say option 1-4) and presenting...

The current state of NASA’s version of cosmology is amazing to watch – According to modern cosmology, which NASA endorses, the Milky Way is moving through space at 600km/s and the Earth is moving through space at 30km/s and the sun is moving through space at 250km/s. So if we total up these...

Novice question :blushing: I've been reading Brian Greene's "The Hidden Reality". It occurred to me that spacetime across the 2D analog of the U could be much like an isometric weather map. Could it be that the U isn't expanding, but that our region, like a High on a weather map is rushing...

Do you believe that in Quantum Gravity, quantization of gravity is only a small part and it is really Quantum Spacetime or the unification of Matter, Space and Time that is the general feature or attraction?

Why can't a static spacetime have an ergosphere? An ergoregion is just a region outside the event horizon where k can become negative (k being a Killing vector field that is timelike near infinity). Both stationary and static spacetimes have such a KVF so surely static spacetimes could also...

Can I express "stationary spacetime" and "static spacetime" in this way? Can I express "stationary spacetime" and "static spacetime" in this way? stationary spacetime: if we arrange a set of observers locating in any places, then each of them should observe nothing change at the place where...

I was reading Spacetime and Geometry by Caroll and I came across this notion: I have never understood this and I was wondering if someone could enlighten me.

What do you think of the following passage from Scientific American (June 2011): Do you believe it? That entanglement are more primary than space and time and "relativity theory must give way to a deeper theory in which space and time do not exist."? Or does entanglement work inside...

I'm having some troubles understanding how spacetime actually looks and what causes gravity and unifying the idea with the general relativity consequences, like light bending. So, if spacetime is bent by massive objects like in this picture: HOW does the light bend outwards that massive...

I recently Googled "spacetime topology" and found that the topology of Minkowski spacetime is generally described as that of an R4 manifold. This is not my field, but I'm surprised. Perhaps mathematically the (---+) "Lorentz signature" can be taken as a secondary characteristic of the...