Questions tagged [spacetime]

As a consequence of the Lorentz transformations, time and space transform into each other when changing reference frame. This calls for a unified description: Minkowski spacetime.

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Can this describe an oscillating eternal universe without singularity?

Consider the FLRW metric. We pick a specific definition for the scale factor as suggested bellow. Suppose we have a hypothetical metric having the scale factor defined by $a(t)=\sin(t)(1+ \text{sgn}(\...
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What speed of light means? [closed]

speed of light means moving through space with the same speed you move through time? or to move "only" through space and not through time? Does this mean that you exist in two (or more) ...
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Small and large extra dimension(s) of the physical space

Trying to make sense of small and large extra dimension(s) of phyiscal space in a simple intuitive example. Consider a two dimensional manifold like $\mathbb{R}^2$ and we are trying to add a small and ...
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Aging when travelling at relativistic speeds

I have a twin. If I acquired a craft that travels at 10% of light speed and wanted to go to Proxima Centauri, it seems now like it would take me 42 years to get there. Would I be 42 years older when I ...
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Is Physics the ultimate "export field"? [closed]

According to Stephen Wolfram, the founder and creator of Mathematica and Wolfram Alpha, "export fields" are fields that when studied can be applied to work in any other field. Physics is the ...
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Is the spacetime at the singularity Euclidean? [closed]

Is the space-time at the baby universes created by singularity Euclidean? because at the singularity time stops due to time dilation which is remarkably similar to imaginary time, and at the ...
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Can we just use the uncertainty principle to explain something from nothing? [closed]

I have been following the argument related to the early universe and the emergence of matter-energy from nothing. They often refer to the notion of quantum fluctuations. But I wonder if a simple ...
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What IS the energy density of vacuum space (or spacetime)? [duplicate]

The question, even if similar to other questions here, pretends to clarify a subtle question: the identity of vacuum energy (or energy-density being more precise). Should we be confident in the ...
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Does the space curvature want it to become flat?

I've read that mass bends the fabric of space. So does space want this curvature to become flat? I know it's a different question. but I think some systems still want to come back to normal. Does this ...
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Is time-like separation transitive? [closed]

In other words, if events a and b are time-like separated, and events b and c are time-like separated, does it follow that events a and c are time-like separated? Is there a straightforward proof of ...
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Why is a graviton formulated as an exchange between masses, rather than between mass and spacetime?

In Sean Carroll's Lecture Notes on General Relativity he states: The gravitational interaction, meanwhile, can be thought of as due to exchange of a virtual graviton (a quantized perturbation of the ...
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What does the Einstein-Hilbert action look like in terms of Riemannian metric of positive signature?

For a 4-manifold to admit a Lorentzian metric is equivalent to that manifold having vanishing Euler characteristic. Any spacetime that admits a Lorentzian metric $g^{\mathcal{L}}$ can have that metric ...
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Why is gravity not a force? [duplicate]

Gravitation is the mutual attraction of masses, yet Einstein showed it is how spacetime is curved by mass and how mass moves in relation to this curvature. Why then do we still consider gravitation a &...
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Does dark energy cause the creation of spacetime?

The universe is expanding, in theory because of 'dark energy'. Does this mean that this dark energy is causing an increase in the amount of spacetime? I.e., does dark energy cause the creation of ...
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How can we have motion through time with Relativity?

How can anything actually move through time if Relativity is correct? It seems everything is just a Lorentz Transformation to a different reference frame and 4D spacetime keeps track of all of these ...
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Is it meaningful to draw $ct$ and $x$ axes by two lines intersecting at right angles?

In the Cartesian coordinate system, the x-axis is really perpendicular to the y-axis, by construction. Also, under a rotation of the coordinate system, the transformed coordinate axes $x',y'$ remain ...
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Spacelike separation vs timelike separation

In Witten's article, 'Light Rays, Singularities, and All That', he wrote "A spacelike geodesic in a spacetime of Lorentz signature is never a minimum or a maximum of the length function, since ...
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How to re-solve the Schwarzschild solution after inverting one of the assumptions?

The Schwarzschild solution is based on the following assumption: ...the geometry of the spacetime is unchanged under a time-reversal $t \rightarrow -t$. I’m interested in what the derivation and ...
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Does the ladder really fit inside the barn?

Does the ladder really fit inside the barn? If we could take a photo, would we see the ladder inside the barn?
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Integral Mass Formula

Shuang-Qing Wu, Di Wu's paper "​​​​​​​Thermodynamical hairs of the 4-dimensional Taub-Newman-Unti-Tamburino spacetimes" https://arxiv.org/abs/1909.07776 How do they get Eq. 11? Shouldn't ...
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How do we know the assumptions of the Schwarzschild solution are valid?

The Wikipedia article on the derivation of the Schwarzschild solution (https://en.wikipedia.org/wiki/Derivation_of_the_Schwarzschild_solution) lists 4 assumptions. The second of which is: A static ...
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What does it mean to say the universe is not locally real? [duplicate]

Pardon me if this is a naive question. What is difference between saying space-time is not locally real, and saying it is not real? The proposal that the universe is not locally real seems to imply ...
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Confusion about near-identical terms: gravity, gravitation, gravitational force - are they all the same?

As my other questions also point out, I study this for fun. I am in no university yet. as the title (hopefully summarizes), my question is this: is these words(or terms,) the same? gravity ...
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Have physicists ever consider the possibility that if spacetime can be crumpled the crumpling itself CREATES matter? (I'm not a physicist) [duplicate]

This following example explains my question. Let's take a spread out bed sheet, which represents spacetime. At the center of the bed sheet, I start to crumple/wrap the fabric of the bed sheet. The ...
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Need help with the proof to Proposition 4.5.12 in Hawking & Ellis

Proposition 4.5.12 in Large Scale Structure of Space-time by Hawking & Ellis is a proposition about varying a null geodesic with conjugate points to obtain a timelike curve. It states that If ...
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Would I not notice proper space in the same way that I don't notice proper time?

I'm working to understand the metric tensor in spacetime (including 4 dimension lengths and 6 angles). I know that if I'm carrying a clock near a black hole I won't notice that my proper time is any ...
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Why can infinite quantities not be shown in an experiment or observed in physics?

To modern physicists knowledge, there are no truly infinite quantities that can be shown with an experiment or observation. Time is not infinite, it had a beginning. Matter and energy is finite (...
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Understanding consequences of spacetime relativity

If I understood right, time flows slower where there is more gravitational force, compared to where there is less: that means that if we put a first timer in a point A in which there is more gravity, ...
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Can the QED action be expressed using geometric algebra?

Hestenes et al. have been able to rewrite the Dirac equation in terms of the "spacetime algebra" (Clifford algebra over Minkowski space), as laid out here. I was wondering if the same can ...
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Curvature of the space-time in a presence of multiple gravitation sources

how can we measure the curvature of the space-time in a presence of multiple gravitation sources when the photon travels through a space populated by closely packed stars?
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Particles and string theory

In string theory, how are specific string states associated with specific particle species? How in particular is the photon described as a string?
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When mass bends space time, why does it cause acceleration? [duplicate]

I have the impression that the idea was: mass doesn't cause gravitational force; it merely bends space time, and that's why an apple falls towards the center of Earth: and some people think: oh, if a ...
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What is concept of left region of rindler space-time?

A accelerated object follow a hyperbolic path in a Minkowski spacetime diagram. Minkowski spacetime has two regions: left (I) and right (II) regions of Rindler spacetime, as it is shown in the picture ...
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Does Shapiro time delay apply to massive objects? [closed]

The diagram below I have borrowed from another question about Shapiro Time Delay: Impossible dilemma about Shapiro delay and momentum conservation My question is if Shapiro time delay applies to ...
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Quantum Theory and Time [closed]

I read somewhere that quantum theory requires absolute time and not a dynamic time as described in relativity. Can anyone confirm this and further describe in laymen's terms what quantum theorists ...
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A doubt on penrose process and efficiency

Accordingly this paper $[1]$, the efficiency of the so called Magnetic Penrose Process (MPP) is, for supermassive black holes of mass $M∼10^{10} M_{\odot}$, immersed in the magnetic field having $B∼10^...
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Ultrastatic spacetime and cosmological constant

A spacetime $(\mathcal{M},g)$ is called "ultrastatic", if it admits a set of coordinates such that $$g=-\mathrm{d}t^{2}+h$$ where $h$ is a Riemannian metric, which does not depend on time. ...
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What is the Minkowski vacuum state?

I am reading about the Unruh effect in General Relativity. I encounter very often the term Minkowski vacuum state. A typical phrase may be, "observer accelerating in the Minkowski vacuum". ...
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The temporal extent of matter

In most branches of physics an object such as a particle is assumed to follow a trajectory in spacetime (or in space and time in the case of non-relativistic physics), and therefore at any instant it ...
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What is the formal criteria that the spacetime is curved?

We suppose we have three scenarios. We are far away from mass and energy in a spot in the universe. We put in free movement a small object $m$, for example, an apple. At the same time, we send a ...
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Static Spacetime = no cosmological constant?

I stumbled over a strange result, which cannot be true: In the (3+1)-formulation of general relativity, one considers a metric of the type $$g_{\mu\nu}\mathrm{d}x^{\mu}\mathrm{d}x^{\nu}=(-\alpha^{2}+\...
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Rindler Observers

In the process of transition from STR to GR, I'm trying to understand what Rindler observers actually are. Here is how one of the questions from our assignment defines them: If the distance between B ...
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Does the dating of the formation of the world take into account the effect of space-time curvature? [duplicate]

For example, when we calculated that the age of the universe is about 13.8 billion years, did we take into account the difference between the flow of time back at the early universe, where mass was ...
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How do we make an observation of a 4D spacetime trajectory if we, observers, have only access to a 3D world?

So far, I know that a trajectory in general relativity is a 4-vector, and a force-free particle follows a geodesic which is in 4D as well. My question is: how do we make an observation of such a ...
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Showing the ADM-Mass of Schwarzschild-Spacetime

Can someone show that the ADM-Mass of Schwarzschild is identical with the Mass-Parameter?
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Simultaneity of events

Apologies, this thought has been bugging me and I am... Simple Consider two observers. One on Earth (stationery) One travelling away from Earth at some appreciable % of c If the spaceship sent a ...
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Gabriel's horn and General Relativity

Is there anything in GR that involves Gabriel's Horn? This idea came to me when I met Flamm's paraboloid. If we take Schwarzschild metric at constant time and $\theta=\pi/2$, we get $$ds^2=\left(1-\...
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How does a field $\phi(x,t)$ have infinite degrees of freedom and why are its inputs labels not variables?

Consider a classical Lagrangian $L(q, \dot{q})$, which by definition has a discrete number of degrees of freedom. Now suppose we have a quantum field (or any field) which we denote by $\phi(x,t)$. It ...
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Is energy "equal" to the curvature of spacetime?

When you are solving the Einstein field equations (EFE), you basically have to input a stress–energy tensor and solve for the metric. $$ R_{\mu \nu} - \frac{1}{2}R g_{\mu \nu} = 8 \pi T_{\mu \nu} $$ ...
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Relation between mass and spacetime

I am trying to understand whether spacetime possesses an intrinsic "elasticity" that is acting as a sort of counter-force to mass trying to bend it.

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