Spacetime Definition and 1000 Threads

Jacobson’s work (1995) [1] demonstrated that Einstein’s equations can be derived from thermodynamic principles, suggesting gravity might emerge from the thermodynamic behavior of spacetime, tied to the entropy of horizons. Other researchers, such as Bekenstein [2] and Verlinde [3], have explored...

Hello! I considered connections between spacetime intervals in 2D (see pic below) and their coordinates/times. I derived following equations (##A_1## and ##A_2## are coefficients that depend on coordinates and times): ##A_1(x_1,x_2,t_1,t_2)(c^2\Delta t^2-\Delta x^2) =...

Spacetime is the foundation of General Relativity, describing how mass and energy influence the curvature of space and the flow of time. However, an important question arises: Is spacetime a physical entity, or is it merely a mathematical framework? Physics relies on measurable quantities and...

What do you interpret from this equation. G μν(g αβ)+Λg μν= 8πG/C^4 T μν({φ i,θ i}) Spacetime geometry = Interference-driven stress-energy>> I'm not looking for conformation. Just a little help n interpretation. Plz

I try to figure out how to calculate the proper time between two events for a moving frame of reference. Knowing that the proper time is: ##(d \tau)^2 = \frac{- (ds)^2}{c^2}##, and thus it is the same for all frame of reference. Following This example from wikipedia, we have an observer A who...

I've already got "Personal Speculation Warning" and I had a private conversation with @Nugatory, who told me, that I have to publish it in an appropriate peer-reviewed journal before it can be posted for discussion here. I replied with a question, if he is willing to believe, that...

I tried to come up with answers using the spacetime interval equation. (Δs)^2 = (c*Δt)^2 - (Δx)^2 Let train's frame of reference be S. Δt = 0 Δx = 500 m (since proper length is measured in object's rest frame) Then I get (Δs)^2 = -250,000 Since L = L0 / lorentz factor, where L0 is the proper...

The conventional picture We often describe two perspectives of infalling matter: Outside observers see the object asymptotically approach but never cross the horizon, with signals becoming increasingly redshifted The infalling object supposedly experiences a finite proper time to cross the...

Are there any images to show CTC such as many images are available in Google to show curvature of general relativity. As far as I understand two points of space time fabric are curved and joined . If we travel from one point to future we will again come back to the same point and now we are in...

In the context of the model of eternal inflation, if an inflating "pocket universe" disconnects from an the background spacetime, does it mean that the baby universe itself can have its own spacetime? can they be described by a different spacetime metric than the background? if the original...

As discussed in this thread, for a symmetric spacetime (i.e. with a KVF) there are conserved quantities as constants of motion. For instance in Schwarzschild spacetime there is a timelike KVF, hence for example the contraction of a geodesic tangent vector (4-velocity) and the timelike KVF...

Given that physics is the study of the physical world, what exactly is spacetime if it is an actual "real world thing", a curved medium or "fabric" guiding the movements of masses, and what is the physics of how this guidance works. As far as I know, space is a vacuum (where not occupied of...

The waterfall model is used in several places such as https://jila.colorado.edu/~ajsh/insidebh/waterfall.html how do we know so sure that the speed of the falling in arrows (wheatver that may be) can exceed the speed of light while on the other hand we assue the speed of light is the speed...

For this problem and solution, I'm confused by part (c) and (d). I don't understand how the Lorentz formula ##ct' = \gamma (ct - \frac{v}{c}x)## can be used to find the ##ct'## axis. This is because they found the ##ct = \frac{v}{c}x## which is in terms of ##x## not ##x'##. Does anybody...

According to general relativity, mass and energy cause the curvature of spacetime. To have perfectly flat spacetime, there must be a completely empty vacuum state with no mass or energy. Does this mean that perfectly flat spacetime cannot exist if mass and energy are present? Let's assume that...

I am on Chapter one and have not yet reached this formula yet but i wanted to know in advance because i was a bit curious Also i noticed it written as (c²t²- x² ) in some places while (x² - c²t²) in some places ,is there a difference?

How is humanity technologically ready for testing below: Something analogous to Bell's theorem testing: for particle(s) in superposition of locations detecting spacetime curvature to test if spacetime can be in superposition. Does above test make sense theoretically even if far from...

Context, To start with? You all know the original twin paradox. Quick review so nobody is confused : Original Twin Paradox: Traveling twin travels at v=0.8c out 4 light years (5 earth years pass)and then he returns home. Earth twin ages 10 years and traveling twin ages 6 because the...

There is a gravitational wave spacetime described by$$g = a(u) (x^2-y^2)du^2 + 2du dw + dx^2 + dy^2$$There is one obvious Killing vector field, ##\partial/\partial w \equiv \partial_w##. To find some more, it's suggested to try:$$X = xf(u) \frac{\partial}{\partial w} + p(u)...

If gravity is caused by the warping of spacetime - how did gravity compress the mass of the post Big Bang universe? Does said compression indicate the force of gravity exists independent of space time? Was Newtonian gravity responsible for the compression? On the other hand, if spacetime was the...

I found this paper (https://arxiv.org/pdf/hep-th/0211160.pdf) which argues against the possibility of a decay from a metastable vacuum to a true vacuum state. However, this is the first time I've read this. Is it then impossible that a vacuum decay from a false vacuum may occur (even in...

Can the holographic principle be applied to spacetimes and metrics that are (fundamentally) continuous/smooth? Or only to discrete ones?

Hi, I would like to ask for a clarification about the terms time dilation vs differential aging vs gravitational redshit. As far as I can tell, time dilation is nothing but the rate of change of an object's proper time ##\tau## w.r.t. the coordinate time ##t## of a given coordinate chart (aka...

Let us start with a simple two-dimensional space that is asymptotically flat, like e.g. sheet of paper on a desk. Geodesics in this space are straight lines in the traditional sense. Now add a bulge in the center of this space. without affecting the asymptotic flatness. Say, we simply distort...

Consider the Lorentz transformations with c=1, and consider any point in space whose x coordinate isn't zero, starting from ##t_{inital }= t'_{inital }=0## ##t' =\gamma (t-xv)## ##t= \frac { t'}{\gamma} + xv## ##\Delta t' = t'-0## ##\Delta t = t-0## Time dilation provides ##\Delta t' =\gamma...

What is the math for projecting a Killing vector onto a Schwarzschild field of spacetime? How would you do it?

Which one would you use in order to map out a black hole and its connection to a white hole?

I'd like to start with: Does the rubber sheet analogy still hold true enough? Or is there really no visualization (it's all mathematical constructs)? Does this picture analogy hold at all here? With the curved geodesics influencing the paths of things. Thanks!

In the Minkowski space time equation in one dimensional space , ds^2 = dx^2 - (ct)^2, what is the value to use for x and t, and what does the space time interval ds represent? For example, if Alpha Centauri is 4 light years away, what values are. used for x and t, based on speed I guess, and...

Hi, Penrose in his book "The Road to Reality" claims that Newton/Galilean spacetime has actually a structure of fiber bundle. The base is one-dimensional Euclidean space (time) and each fiber is a copy of ##\mathbb E^3##. The projection on the base space is the "universal time mapping" that...

Hey, if I take two objects for Example the Earth and Moon and treat them as a gravitational bound “system”. The Earth and Moon have their own local curves in spacetime. Can I use/treat the whole “system” as a curve in spacetime? For example, a curve that includes all objects of the “system”...

Here is the definition of spacetime? “In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.” But if space is literally the absence of matter or physical properties, and time has no...

Instead of a twin paradox, let’s just consider an inbound starship approaching Earth at relativistic speed. The traveler is on a flyby mission, he will never change speed or direction. We will disagree with the traveler on how much time will have elapsed when he passes Earth. The discrepancy can...

Do force carriers follow the curvature of spacetime, or do they travel in perfectly straight lines? With black holes, gravity of course exists, so I'm thinking the force carriers (at least gravitons) don't follow spacetime curvature, since they would never escape the event horizon. Sounds like...

The Wikipedia section below says that gravity is the earliest to appear out of the fundamental interactions, but wasn't high energy in every area already curving its local spacetime surroundings? https://en.m.wikipedia.org/wiki/Chronology_of_the_universe#The_very_early_universe

Reading this PDF from Professor Richard Conn Henry, I am confused by the multiplication by c on page 2. x, y and z are metres. t has units seconds. So I would think, "We can't subtract seconds from metres , we can't subtract dt from dx." To sidestep that, Einstein multiplied dt by c. c has...

What is the metric for a bag-of-gold spacetime?

Hi, Thanks for having me as a member. I've had a lifelong interest in science, all types of science but particularly in physics. It's the basis of everything isn't it? Biology is based on chemistry, chemistry is based on physics, physics is based on quantum physics and that is based...

Based on the current understanding of general relativity, it is possible that curving spacetime in the back of a spacecraft would allow for faster-than-light travel. In general relativity, the curvature of spacetime is determined by the universe's distribution of matter and energy. If a...

After trying to kinda get a picture of the field of play in quantum physics according to the standard model, a question came up. I tried to formulate the known bosons each as a particle transferring some property. 1. Photons transfer electric charge: the electromagnetic force gives attraction...

Can there be worldlines that are neither timelike, nor null, nor spacelike? They can Are there curves in spacetime that are neither timelike, nor null, nor spacelike? Why?

Exercise: My solutions: For events to be simultaneous, the invariant interval must be bigger than zero (spacelike). I got $$I = -c^2 \Delta t^2 + \Delta x^2 + \Delta y^2 + \Delta z^2 = -(0-1)^2 + (0-2)^2 + (0-0)^2 + (0-0)^2 = -1 + 4 = 3 >0$$. Which is indeed greater than zero, to find the...

Are there non-smooth metrics for spacetime (that don't involve singularities)? I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics: Lorentz invariance holds locally in GR, but you're right that it no longer applies globally when gravity...

Pseudo-Riemannian manifolds (such as spacetime) are locally Minkowskian and this is very important for relativity since even in a highly curved spacetime, one could locally approximate the spacetime into a flat minkowski one. However, this would be an approximation. Perhaps this is a naive...

I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned. There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify...

I have heard that some types of inhomogeneties and topological defects (like cosmic strings) in cosmology have been proposed to be able to break fundamental symmetries of nature such as the Poincaré, Lorentz, diffeomorphism CPT, spatial/time translational...etc symmetries... However, I have not...

Perhaps this is a stupid question but, if Lorentz symmetry and time translational symmetry are not global in an expanding universe, wouldn't that mean that is possible that other Hubble spheres outside our observable universe could have other symmetries or an absence of the Lorentz symmetry? I...

I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970) In the paper, the authors describe "spacetimes without symmetries". When I mentioned that, one of my friends said that no spacetime predicted or included in the theory of relativity...

In the context of the Theory of Relativity are there any spacetimes or metrics with a complete absence of symmetries? I mean, consider a type of space or metric where no symmetries would hold (at least not exactly, but approximately). A space or metric where the Poincaré invariance (including...