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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Topology of spacetime

We know that spacetime is an orientable manifold: Can spacetime be non-orientable? But supposing that spacetime is an orientable closed 2D surface, one might envision a variety of non-equivalent ...
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Pole in the Barn Paradox

My professor recently gave us this paradox to solve as extra credit. The problem involves a runner moving at 4/5c holding a pole that has a proper length of 15 feet. They are moving towards a barn ...
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What is observed by Astronauts traveling from M at just under $c$, but proper distance increases at greater than $c$ due to spacetime expansion?

A rocket is traveling at a reasonable speed directly away from planet M at a large distance D. M is shaped like a coin and to the astronaut looking through a telescope directly out the back of the ...
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How to handle a lightlike metric with cross terms, and its corresponding proper time?

I understand that the metric of null-separated events is $\mathrm{d}s^2 = 0$. This would mean that the time component is equal to the spatial components, $\mathrm{d}t^2 = dl^2$. If there are cross ...
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Perception of simultaneous events

I have a two-fold question about the light-cone structure of spacetime, specifically about space-like separated events. As far as I understand it, any two events that happen at the same time in a ...
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Intuitive understanding of the spacetime interval

I have a low level understanding of the spacetime interval, which is the invariant distance between two points in spacetime as measured by two observers at both ends of Δs². However, the formulation ...
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Spacetime distances and perception

My question is about how things appear in human perception vs how things are in spacetime. Take as an example my perception of the laptop screen while I am writing this. As far as I understand it, ...
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How do 'locally Euclidean' and 'Lorentzian' requirements in manifolds reconcile?

In GR, we define our manifolds to be locally Euclidean. However, we also demand that our metric tensor have a Lorentzian signature. Since the metric tensor is a measure of curvature, doesn't the first ...
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Is the reason of that we can change $\partial_t$ and $\partial_i$ because of independent variable?

The reason of that we can change $\partial_t$ and $\partial_i$ is the two derivative is independent variable? If so, in General Relativity, It's impossible to change the two derivative? (Because in GR,...
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How to describe ‘when’ a black hole actually is? [closed]

If I look at any point in space I can think of it as being in the future because it takes me time to travel there. I can go there and an observer can watch me go there. When I look at a black hole I ...
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Clock synchronization and definition of simultaneity along a curve or contour in general relativity

What I understand so far Fix a point $A$ with coordinates $x^\alpha$ with respect to a frame $K$ with metric tensor $g_{\alpha\beta}$. Then take an arbitrary point $B$ infinitesimally close to it with ...
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Is there a dimension of time in M-theory or any version of String theory at all?

Are any of the curled-up dimensions in String theory a higher spatial dimension (as in a tesseract) or a temporal dimension?
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Gravitational Time Dilation and Equivalence Principle

My question relates to page 118 of these notes, which is reproduced below for your convenience. Specifically, I have difficulty understanding the line "This shows that time slows in a region of ...
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Is there a smooth, spherically symmetric, static, asymptotically de Sitter spacetime of constant scalar curvature?

...other than de Sitter space itself? Two clarifications: I am not talking about solutions of Einstein's equations, just spacetimes. So, general Lorentzian manifolds. I am not counting, for example,...
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Spacetimes where $R_{ij}\neq 0$ but $R_{ij}V^iV^j=0$ on a timelike and/or null geodesic?

Do there exist spacetimes with a timelike and/or null geodesic $\gamma$ with tangent vector $V$ for which $R_{ij}\neq 0$ on the geodesic, but $R_{ij}V^iV^j=0$ on it? If so, are there any general ...
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Can we have positively curved space within negatively curved spacetime?

Thinking about the universe as a whole. One could imagine that the three spatial dimensions each have the same, say positive, curvature, making space spherical, while time is negatively curved, making ...
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Are the “directions” of basis vectors in 4-wave vector basis same as those in spacetime basis?

Let us assume an arbitrary 4-vector $\vec{A}(\vec{x})$ where $\vec{x}$ is event. $\vec{k}$ be 4-wave vector such that $\vec{B}(\vec{k})$ is the Fourier transform of $\vec{A}(\vec{x})$ in $\vec{k}$ ...
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Is the conformal group in $2+0$D isomorphic to the Lorentz group $SO(3,1)$ in $3+1$D?

In the Wikipedia article on conformal field theory, it is said the following: The conformal group is locally isomorphic to $SO(1,d+1)$ (Euclidean) or $SO(2,d)$ (Minkowski). Does that mean that the ...
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How much does light curve due to gravity compared to what Newtonian mechanics predicts [duplicate]

I've heard that it curves twice as much is this correct?
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According to general relativity planets and Sun bend the spacetime (explaining gravity), but does this hold true for smaller objects?

According to general relativity planets and the sun bend spacetime, and that is the explanation of gravity. However, does this hold true for smaller objects, like toys, pens, etc.? Do they also bend ...
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Why didn't the CMB clump into denser parts like the matter in galaxies with voids inbetween since the photons exert gravitational pull on each other?

There are other questions on this site about the CMB, but none of them answer my question specifically. I am not asking about fluctuations in the CMB. How could inflation affect the CMB? Now as far as ...
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Why not $\frac{x}{c}$ instead of $ct$?

The moral of the parable in special relativity is that: The same units should be used for all distances. The (squared) distance is invariant. Different frames are related by rotations. Now what we ...
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What would happen to a long ruler in a strong gravitational field?

So, let's say that we have an incredibly long, virtually indestructible ruler. We have advanced enough to move it wherever we want. Let's also say that we have another, identical ruler of the same ...
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Is there any mathematical meaning to words like: Event or Cause or Effect etc [duplicate]

If you read any text on Physics then you would reorganize after enough time that Yes language of physics (Nature) is mathematics. I'm letting this discussion to opinion-based nor some philosophy of ...
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Can flat spacetime have curvature?

Hi I am new and I hope this can make sense. Is it true that flat spacetime can curve? For example, you have a flat piece of spacetime that curves at a constant rate of pi/2. the flat spacetime would ...
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If a light beam is sent tangent across earth would it curve at 9.8 $\rm m/s^2$? [closed]

Just to see if my understanding of the curvature of light is correct.
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Can civilizations orbiting black holes keep time with their interstellar travellers?

Due to relativistic-velocity interstellar travel time dilation, travellers would return in the far future of any civilization launching such an effort. A chart from wikipedia indicates typical time ...
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Can a cosmological constant model inhomogeneities?

Consider the following zero-order approximation to the universe: Spacetime is perfectly homogeneous, and The cosmological constant is exactly zero. This doesn't quite work. Neither assumption is ...
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Why does time 'change' when gravity increases?

I was doing some research on gravitational time-dilation, my topic for the Breakthrough Junior Challenge (a science video contest where contestants have to explain a hard science/math topic in 3 min ...
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What are physical evidence that we are living in affine space?

An affine space of dimension n on $\mathbb R$ is defined to be a non-empty set $E$ such that there exists a vector space $V$ of dimension n on $\mathbb R$ and a mapping $\phi:E \times E \rightarrow V,\...
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Could torus spaces (defined by Planck length) exist?

Let $\epsilon_c$ denote critical energy density, $\epsilon_t$ energy mass density at time $t$, $c$ the speed of light, $G$ the gravitational constant, $H=\dot a/ a$ the Hubble constant, $\Lambda$ the ...
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On the spacetime significance of Feynman diagrams (and Witten diagrams)

This post is just a thought about Feynman diagrams and their interpretation. When I draw a FD, my intention is to provide a direct way to calculate terms in a series expansion. Now, from what I ...
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As one moves with uniform speed in de Sitter space, does he experience blueshift of the de Sitter radiation?

All objects in de Sitter space experience de Sitter radiation from the space boundary (which is spherical). What happens if one moves uniformly in one direction? Logic says, de Sitter radiation should ...
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If gravity is spacetime curvature, and spacetime doesn't show any discreteness, then gravity doesn't show any discreteness and can't be quantized?

I am not asking about why or how gravity should be quantized, or what the problem with renormalization is, or what the discrepancy is between QM and GR is. Those are beautifully described in other ...
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Is the set of spacetime manifold a set of event?

In general relativity spacetime is defined as manifold. Is this manifold the set of events? For example if our universe is constituted of only one non-interacting particle, should our manifold be a ...
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Is it possible we live in a white hole?

Is it possible we live in a white hole? We live in a universe that is expanding at an accelerating rate – does this not seem similar to a white hole? Could a living organism interpret a black hole as ...
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“Different reality” inside a black hole

why does our perception of space and time entirely change inside a black hole? And why does time not stop inside it from the perspective of the inside observer, however, extremely slows down for the ...
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Is gravity a force? Can there be a new BETTER theory for it? [closed]

what I'm asking is simple in look, but actually, it goes into depth and is complicated. Can there be a new better theory for gravity? and how and why is it not a force? it seems like the theory's the ...
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Can you conformally map the Lorentzian cylinder to the Lorentzian plane?

When studying CFT in Euclidean signature, for the purpose of radial quantization, we conformally map the Euclidean cylinder to the Euclidean plane (minus the origin, which I ignore). Can one also ...
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Understanding the general metric of a stationary spacetime

Wikipedia says the metric for any stationary spacetime, when made independent of $t$, has the form $ds^2 = \lambda(dt - \omega_i\ dy^i)^2 - \lambda^{-1}\ h_{ij}\ dy^i\ dy^j$ with the Killing vector $\...
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Intuition as to why a constant four-acceleration must be zero

In a tutorial, it was derived that a constant proper acceleration must be zero: $$ u \cdot a = 0 $$ Taking the time derivative of both sides: $$ a \cdot a + u \cdot \dot{a} = a^2 = 0$$ And so $a^\mu = ...
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Photon Created Traveling “Directly Away” from center of BlackHole just inside and perpendicular to Schwarzchild Radius

An object traveling directly toward the center of a black hole crosses the Schwarzschild Radius, and then emits a photon pointing "directly away" from the center of the Black Hole about a ...
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Does the invariance of interval hold only for events that occur in inertial reference frames?

For example, if we have two frames that have constant relative velocity, would the interval be the same between any two events? Or should we impose the condition that the particle must not accelerate ...
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Lower limit to the distance between two mouths of a wormhole?

This is more like a conceptual question. Wormholes are tunnels connecting two different parts of the same universe or connecting two parts in different universes. Taking the former one as an example; ...
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How many numbers are required to describe attitude or orientation in $n$-dimensions?

In general, the attitude or orientation of a rigid object is described by three numbers. For an aircraft, these might be the pitch, roll, and yaw with respect to the direction of motion. For a ...
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Was the universe cold before the Big Bang? [closed]

I think matter cause something to be hot or cold. So before Big Bang there was no matter in the space so what would have been the temperature of space at that time (if time was even there before Big ...
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Topology - The space of time [duplicate]

In physics, one of the ways to solve problems is to find a similar mathematical model which describes the problem, and that leads to my question: By experiments we familiar with the space of time, we ...
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Common properties of all spacetime metrics

I understand that spacetime (in GR) has many possible metrics, all of which are calculated via the Einstein Field Equations. The Minkowski metric (from SR) is one solution of the EFEs; it is a ...
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Is it a postulate that light travels on a geodesics?

In arbitrary spacetime, light travels on geodesics. Is this a postulate or can it be derived from a more fundamental principle?
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How does relativity explains time-dependent behaviour for objects not experiencing time? [duplicate]

A variable electrical field produces a variable magnetic field, which in turn produces a variable electrical field, and so on, leading to an electro-magnetic wave, which is eventually what light is ...

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