Questions tagged [causality]
The influence one event, process, or state, has on another event, process, or state, whereby the latter is at least partly dependent on the former.
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When are the different choices of spacelike hypersurfaces equivalent for the quantisation of a field theory?
Suppose we have a field theory with a Lagrangian density $L$ on a Lorentzian manifold $(M,g)$. For the specific case of Minkowski spacetime, we can impose the equal-$t$ quantisation CCR:
$$[\phi (x), \...
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Wald theorem 8.1.2 and the proceeding corollary
I am currently confused on the corollary of theorem 8.1.2 in Wald's book, specifically the paragraph separating the two. I've attached a screenshot below.
Why does Wald say that using theorem 8.1.2 ...
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Multiple time dimensions and understanding ultrahyperbolic differential equations
On article "On the dimensionality of spacetime (https://space.mit.edu/home/tegmark/dimensions.pdf) Max Tegmark writes about ultrahyperbolic differential equations leading to unpredictability:
&...
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Prove that Cauchy hypersurface is closed
Witten in https://arxiv.org/abs/1901.03928 at page#18 proved that Cauchy hypersurface S is closed hypersurface by contradiction. He wrote
suppose that p ∈ M is in the closure of S but not in S. Let γ ...
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Intersection between causal future and causal past
I am trying to show that for a closed, achronal surface $S$ the intersection of its causal past $J^-(S)$ and causal future $J^+(S)$ is the surface itself, i.e.
$$S = J^+(S) \cap J^-(S)$$
Note that I ...
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Entanglement collapse and relative order of events
According to QM (and many confirming experiments) outcomes (e.g. spin) of entangled particles measurement are non-locally correlated (i.e. can’t be pre-configured for such correlations).
It seems that ...
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How curve is inextendible?
I am reading a literature arXiv:1901.03928v6 [hep-th] 12 Jul 2023 and it says :
In Minkowski space, the timelike geodesic $(t(s),x(s))=(s,0)$ is inextendible if $s$ is regarded as a real variable.
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Strongly Future asymptotically predictable space
Consider a spacetime $(\mathcal{M},g)$ which is a weakly asymptotically empty and simple spacetime and partial Cauchy surface, $\mathcal{P}$ in $\mathcal{M}$. $(\mathcal{M},g)$ is called strongly ...
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Change of simultaneity with speed and direction
I am a physics enthusiast. I was watching a video by Professor Brian Greene on YouTube. He said that when an alien in a distant galaxy is at rest relative to Earth, he will see the present of earth. ...
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Future inextendible curve
The definition of future inextendible curve is as follows:
A causal curve $\gamma$ is called future inextendible if it is impossible to find an event p $\in \mathcal{M}$ such that for all $U \subset \...
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Order of events is invariant in timelike intervals
I thought that the order of events could be something that changes with a boost. But recently, I read in a book that for time-like separated events, the order of events is invariant.
If I think about ...
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Can the nonlocal Aharonov–Bohm effect be used for instantaneous transfer of information? [duplicate]
This famous effect and experiment is considered being nonlocal in the sense that it cannot be explained by classical causality and also being "instantaneous action at a distance". However, ...
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Can something escape from inside of a black hole's event horizon by putting a sufficiently large mass next to it?
As far as I know, a lot of the maths surrounding black holes basically assumes that the black hole is the only mass in the entire universe. But what if something has fallen into the event horizon of a ...
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What exactly is the role of the Lorentzian metric within spacetime? [closed]
I learned that twodimensional spacetime diagrams and fourdimensional spacetime manifolds are provided with Lorentzian (pseudo-Riemannian) metric. However, regarding a spacetime diagram with a light ...
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How can a theory of gravitons produce a metric that shortens spatial distances?
Consider the two principles:
A QFT of spin-2 particles (gravitons) cannot transmit information faster than the speed of light by special relativity. (Let's make an assumption that such a theory can ...
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Time-like separated and Space-like separated events
I am trying to get an intuition about Time-like separated and Space-like separated events. I understand the definition of these terms, but I lack intuitive understanding of what these concepts ...
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$i\epsilon$ prescription for 4D massless Green's function in position space
The Green's function for the d'Alembertian operator with Feynman boundary conditions is given in many QFT textbooks as (in four-dimensions and $(+,-,-,-)$ signature)
$$
\Box G(x)=\delta^4(x)\\
G(x)=\...
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How does the theory of relativity point to a block universe? [closed]
Please explain in layman's terms how Einstein's theory of relativity points to a universe that is eternal and non moving, where past, present and future all coexist simultaneously.
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Example of super-luminal phase velocity and why wave front velocity as opposed to phase/group velocity pertains to causality
As the title suggests, I have heard that phase velocity of a wave traveling in media could exceed the speed of light and become super-luminal, whereas some people claim that group velocity cannot. ...
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Cause-Effect Events in accelerated frames
How can we be sure that timelike events maintain their cause-effect relationship in accelerating reference frames, given that the definition of time ordering in special relativity is based on inertial ...
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What is the quantum mechanical root of causality?
Consider the following 3 premises.
Premise 1) Quantum mechanics has an inherent randomness.
Premise 2) Objects in the world appear to obey causality. For example, I can push a book on a table, and it ...
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If we imagine tachyonic particles do exist, then can they travel slower than the speed of light $c$ from a reference frame traveling slower than $c$?
If we imagine a tachyonic particle travelling faster than the speed of light, can there be any reference frame which perceives a tachyon as travelling slower than $c$ by applying Lorentz contraction? ...
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Non-Local Causality - The Piston
A free particle is inside a box of length $L$ with a movable piston at the end. The piston is attached to two plates facing each other and a ball is fired at the first plate.
Now assume that all ...
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"Negative time evidence" in the news - are they really observing causation backward in time?
There are many news about recent https://arxiv.org/abs/2409.03680 by Aephraim M. Steinberg group, e.g.:
https://www.scientificamerican.com/article/evidence-of-negative-time-found-in-quantum-physics-...
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Why Peskin and Schroeder speak about Causality for Not-Observable Fields?
On p. 28 in Chapter 2 of Peskin & Schroeder the concept of causality is discussed. Specifically, it considers two fields at two different point and then it considers a space-like separation. ...
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Spacetime point in forward light-cone [closed]
Consider the transformation of massless free scalar field $\phi$ under inversion of spacetime point, which is defined as,
$$I: x \to -\frac{x}{x^2}. \tag{3.2.27}$$
The two-point function of massless ...
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How can you safely enter a black hole? [duplicate]
In a hard science fiction novel, suppose we want our heroes to enter a black hole. What laws of physics could we tweak to make it theoretically possible, albeit a technological feat?
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Do quantum entangled particle pairs actually interact? [duplicate]
I believe this question could help simplify the accepted understanding of quantum entanglement for myself and others with little to no real physics background.
So my understanding of one way to create ...
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Is it possible to transmit information from within a black hole via the momentum of a rocket activated after passing the event horizon?
Imagine a simple, non-rotating black hole and a massive rocket that is free-falling past the event horizon of the black hole, linearly towards the singularity. The rocket is massive enough that it ...
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What exactly is Gödel referring to when he says "world lines of matter" in his 1949 article about his solution to Einstein Field Equations?
I am writing my college thesis about Gödel's article A New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation.
As far as I had understood, there are important geometric ...
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How can I measure the space time interval between two events?
This is my last resort for a frustrating problem that I am certainly overcomplicating, but I don't have enough understanding to complete alone.
The problem goes like this:
Consider a space station ...
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If information can't move outwards the singularity then how does the event horizon "know" it has to expand simultaneously along the whole surface?
I have read this question:
When matter is added, carefully and radially to make sure it does not add angular momentum, the horizon radius increases proportionately to the amount of mass added (but ...
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Time-independence dependent on time-function
I am having trouble understanding time-functions in Schwarzschild spacetime when one coordinate is null. By definition, a function $f$ is called time-function if its gradient $\nabla f$ is timelike ...
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Why is AdS-boundary considered timelike?
I was wondering why the conformal boundary of (compactified) AdS is said to be timelike. Consider the conformal compactification of AdS spacetime with metric
$$g = (- dt^2 + dx^2 + \sin^2 x \ d\Omega^...
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Does retarded Newtonian gravity predict apsidal precession and gravitational radiation?
This is a question that have troubled me for a while, beginning with the historical fact that the apsidal precession of Mercury as noted by Urbain Le Verrier was one of the motivating issues behind ...
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Reflection positivity and $i\epsilon$ in Green's function
There are several ways to tell you why there is $i\epsilon$ in physical Green function, like from direct derivation of $\langle\Omega|\text{T}{\phi(x)\phi(y)}|]\Omega\rangle$, or from path integral ...
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Geodesics in the Schwarzschild Penrose diagrams
I drew the Penrose diagram for the Schwarzschild spacetime the coordinate transformation (actually a series of transformations):
$$ \widetilde{T} = \arctan(T+R) + \arctan(T-R)$$
$$\widetilde{R} = \...
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What is the difference between "maximal Cauchy development" and "maximal global hyperbolic development" within General Relativity?
Following the theorem of Choquet-Bruhat and Geroch, we can define the maximal Cauchy development of initial data (see Theorem 10.2.2 of Wald's 1984 GR book, herewith attached). However, in the ...
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When Does a Singularity Become Naked in Space-Time?
A singularity within a space-time 𝑀 is typically hidden behind an event horizon, preventing any information from the singularity from reaching distant observers. However, a singularity may be "...
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Why would time distorsion be greater than space distorsion? [closed]
So, I'm reading The Hidden Reality by Brian Greene, and on page 31, he does state in a note that time distorsion has a bigger influence than space distorsion? I have trouble understanding that, since ...
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Prove a four-velocity vector lies inside of the light cone; do I just need to prove that the four-velocity is a timelike vector?
New to relativity; and I'm reading the Hartle books, on page 144;
The questions asks to show that, at every point along the curve $x_s(t)$, the four-velocity of the ship lies inside the forward light ...
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Hawking and Ellis Lemma 4.3.1 Proof
I have a few questions about Hawking and Ellis' proof of this lemma (pages 92-93):
Write the $(2, 0)$ stress-energy tensor in coordinates as
$\mathbf{T} = T^{ab} \partial_a \otimes \partial_b$ and ...
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End points of event horizon
I am reading The Nature of Space and Time by S. W. Hawking. In the last paragraph on page 16 he said that:
event horizon may have past end points but don't have any future end points
I understand ...
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Can a light signal from Earth reach a galaxy outside the Hubble Horizon?
Is this video on the FLRW metric (timestamp 29:00 minutes) mistaken in its claim that a light signal from Earth cannot catch up with a galaxy outside the Hubble horizon, due to the horizon receding at ...
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How does loop quantum gravity handle spacetimes which aren't globally hyperbolic, like the Kerr metric?
Loop quantum gravity assumes spacetime is globally hyperbolic. However, the interior of a Kerr black hole isn't globally hyperbolic, containing closed timelike curves. So, how are Kerr black holes ...
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Causality for gauge dependent operators in quantum field theories
Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
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A few doubts regarding the geometry and representations of spacetime diagrams [closed]
I had a couple questions regarding the geometry of space-time diagrams, and I believe that this specific example in Hartle's book will help me understand.
However, I am unable to wrap my head around ...
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Confusion about timelike spatial coordinates
I'm pretty new to general relativity, and I'm self-studying it using Sean M. Carroll's text on the subject. In Section 2.7, he introduces the notion of closed timelike curves. He gives the example of ...
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Canonical commutation relations of quantum fields in null coordinates
To quantize a scalar field, we impose the equal time commutation relations
$$
[\Phi(t,\mathbf{x}),\partial_t\Phi(t,\mathbf{x}')] = i\hbar\delta^{(3)}(\mathbf{x-x'}).
$$
This can also be generalized to ...
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Understanding Causality for Relativistic Schrödinger Equations
I would like to understand precisely in what sense are relativistic Schrödinger equations (Klein-Gordon,Dirac etc) causal. I'm not referring to the second quantized field or any field theory for that ...
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