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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What happens if $ a^2 > M^2 $ in Kerr metric?

(Boyer-Lindquist coordinates and $ c = G =1 $ taken) As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
posfn0319's user avatar
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Do the Lorentz transformations contradict reality by implying time had no beginning? [closed]

Consider the following two points, or events as they are more commonly called, in SpaceTime: Event 1: $(x,t) = (0,0)$ Event 2: $(x,t) = (a,0)$ Take t=0 to correspond to the first moment in time. As ...
lee pappas's user avatar
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Is there a general methodology for causal nets of observables regardless of kinematics?

The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
Slereah's user avatar
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Could relativity be consistent if there are multiple light-like fields with different invariant speeds?

My understanding of real physical theory of electromagnetism goes like this: The Maxwell equations can be used to derive the speed of light; $$\nabla\cdot\textbf{E}=0$$ $$\nabla\cdot\textbf{B}=0$$ $$\...
spraff's user avatar
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Carter-Robinson Theorem

There are uniqueness theorems that classify Black holes according to its mass, angular momentum and charge. One of the theorem is Carter-Robinson theorem which has many assumptions and then it says ...
Talha Ahmed's user avatar
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How to generalize the (anti)commutation for spacelike separation to more than $2$ field operators?

Let $\phi_1$ and $\phi_2$ be quantum field operators of certain spin on $\mathbb{R}^4$. Then, the principle of locality dictates that if $x$ and $y$ are space-like separated, we have \begin{equation} \...
Keith's user avatar
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How to show causality for a Klein-Gordon field in 1+1 dimensions using field commutators?

For a non-interacting massive scalar field $\phi$ in an $n+1$ dimensional minkowskian spacetime, the field commutator between two event points is $$ [\phi(x),\phi(y)] = \int \frac{\mathrm{d}^n p}{(...
Gravifer's user avatar
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In Relativity theory, is chronological relation an order relation?

Let $(M,g)$ be a (Lorentz) spacetime, i.e a connected smooth manifold $M$ with a metric tensor field $g$ and a time orientation called future direction which is defined by a smooth timelike vector ...
PermQi's user avatar
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How does light know the destination?

According to Fermat's principle, light travels the fastest path from dot A to dot B. I wondered how light knows which path is the fastest, and found out that light actually goes all path, but non-...
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What is the meaning to the switch $dt^2\to-dt^2$ and $dr^2\to-dr^2$ in the Schwarzschild metric?

What is the meaning of the change $dt^2\to-dt^2$ and $dr^2\to-dr^2$ in the Schwarzschild metric, leading to: $$g=-c^{2}d\tau^{2}=(1-\frac{2GM}{c^{2}r})c^{2}dt^{2}-(1-\frac{2GM}{c^{2}r})^{-1}dr^{2}+r^{...
Manuel's user avatar
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Global Hyperbolicity and Timelike Boundary

I am trying to understand and show that asymptotically Anti-de Sitter spacetimes are not globally hyperbolic. Now, I have found papers that talk about global hyperbolic spacetimes with timelike ...
Octavius's user avatar
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Does it follow from Least Action Principle that particles do not go back in time, or do we stipulate this?

Consider the action integral, $S[\gamma] := \int L(\gamma(t),\dot{\gamma}(t),t)dt$. We can always re-write it in terms of an arbitrary curve parameter $\tau$ which need not coincide with time $t$: $$S[...
Rochelle's user avatar
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On the notion of Local Causality

In 1976, John Bell proved that any locally causal theory can't account for certain observed correlations, he formulated the local causality hypotesis in terms of "local beables". In ...
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About information transmission speed [duplicate]

Einstein says information cannot be transmitted faster than light. Say I set an alarm that ring at 9:00 am. I go to school, and wait until 9:00 am. Then I tell my friends that my alarm rang. If the ...
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Counterexample to the observable algebra of a region and its causal completion being the same

I was reading a paper by Ed Witten called "Algebras, Regions and Observers". It can be found here: https://arxiv.org/abs/2303.02837 A major theme is theorems relating the algebra of ...
Andreas Christophilopoulos's user avatar
4 votes
5 answers
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What can we accept in thought experiments in relativity?

Although title is more broad, and you are welcome to give examples, I will ask about why we accept certain things as acceptable in Einstein's thought experiments using a specific experiment: Consider ...
Mahammad Yusifov's user avatar
1 vote
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Conjugate points on manifolds

My question is: Why do conjugate points exist on globally hyperbolic manifolds, satisfying the strong energy condition? We define M to be globally hyperbolic if it posseses a cauchy surface and a pair ...
Tim2006's user avatar
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What does it mean that an observer can provide a quantitative temporal order only to the events on his worldline?

I'm currently reading the introduction to Naber's The Geometry of Minkowski Spacetime, and in this post I'm writing down a few silly questions that keep popping into my head. I have near-zero formal ...
GeometriaDifferenziale's user avatar
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2 answers
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Are all events along a Cauchy surface always space-like separated?

I'm new to relativity. Are all events along a Cauchy surface always space-like separated? I know that a necessary condition of a Cauchy surface is that every inextendible causal curve intersects the ...
John Smith's user avatar
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Do events very far away happen in a different timeline?

I am not sure how to ask this question in a concise manner so I am sure somebody out there explained it but I cannot seem to find it. So I recently watched some videos explaining that $c$ not only ...
VJZ's user avatar
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If I were to drop my phone into a black hole, would I be able to catch it?

Say, for the sake of argument, I am outside the event horizon of a black hole and accidentally drop my phone (or some other object) into the hole. If I were to enter the black hole, would I ever be ...
guninvalid's user avatar
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How to choose contour of integration prescription Klein- Gordon Propagator? [duplicate]

I am going through the complex integral in peskin & Schroeder's intro to QFT (equation 2.54, deriving the Free Klein-Gordon Propagator): $$\langle0|[\phi(x),\phi(y)]|0\rangle=\int \frac{d^3p}{(2\...
Nick Heumann's user avatar
2 votes
2 answers
127 views

Does causality forbid time travel?

If causality is an axiom or a fundamental law in physics, would the existence of causality be a reason which forbids time travel? Because time travel could break causality so we see first the effect ...
Jose Perez's user avatar
3 votes
2 answers
551 views

Null infinity reachable by timelike worldlines?

Usually, Penrose diagrams are marked with points and segments being named past/future timelike infinity $i^{-,+}$, past/future null infinity $\mathscr{I}^{-,+}$ and spacelike infinity $i^0$ -- see for ...
Octavius's user avatar
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Same curvature but different orientation of light cones? [duplicate]

Can there be two regions of spacetime which have the same curvature, but with their light cones oriented in different directions? In the Stack Exchange question "General Relativity via light ...
Anuj Manoj Shah's user avatar
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Does inflation theory assume a finite universe?

Inflation theory has it that the early universe was causally connected, and could “mix”, hence explaining relative homogeneity of the CMB. The universe then rapidly expanded and became causally ...
Captain Chicky's user avatar
2 votes
2 answers
230 views

Non-vanishing amplitude outside light cone doesn't violate causality? [duplicate]

I am following Peskin & Schroeder's QFT book. And on equation 2.51, we get an expression for the free Klein-Gordon propagator for timelike intervals $x^0-y^0=t$, $x-y=0$: $$D(x-y) \sim e^{-imt}\...
Nick Heumann's user avatar
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Why is Quantum entanglement spooky? And is it really exclusive to quantum physics? [duplicate]

In School (15 years ago) quantum physics really fascinated me. The implications on reality, what we know, and how the world behaves is amazing. In school it was mainly about how we change stuff just ...
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3 answers
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Causality in formulas in general physics

Follow-up on this question about causality for Newton's second law. In $F=ma$, the $=$ sign signifies proportionality, not causality. It makes sense, as the equal sign is invertible, whereas causality ...
Mauro Giliberti's user avatar
1 vote
1 answer
155 views

Does a geodesic exist that will take someone across the event horizon?

I saw the movie "Interstellar" a few years back, and was amazed that Cooper was able to fall from 1 AU into a black hole before his daughter turned 110. Intuitively, I would think that there ...
The Shepard's user avatar
4 votes
5 answers
444 views

Is the speed of causality slower in water?

I've recently read that what most people learned to think of as the 'speed of light' is actually the 'speed of causality', and that light just happens to travel at that speed (through free-space.) I'...
Cognitive Hazard's user avatar
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10 answers
2k views

Cause-effect definition of fictitious forces

I'm currently teaching a general-physics-for-engineers class, and we approached fictitious forces. As I was explaining them, students asked me how to discriminate "real" forces from ...
Mauro Giliberti's user avatar
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0 answers
92 views

Questions regarding action at a distance

There seems to be two concepts in action at a distance The existence of an mediating medium (energy or matter) through which action is transmitted The finiteness of the speed at which the action is ...
Hans's user avatar
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2 votes
1 answer
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How to interpret Poisson bracket of fields in terms of causality?

In quantum field theory, the fact that space-like separated observables commute, i.e. $[\hat {\phi (x)}, \hat{\phi(y)}]=0$, is taken as the test for causality. The equivalent statement for classical ...
Rain Deer's user avatar
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1 answer
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What does hypersurface of simultaneity exactly mean?

HSS - "Hyper Surface of Simultaneity" Listening to different sources online I understood that HSS for a observer represents the points that are at same moment of time. Consider a 1d world. ...
D Star Let's Explore's user avatar
12 votes
10 answers
5k views

Does force cause acceleration or acceleration cause force?

I am currently studying advanced mechanics (meaning I do have an introduction in mechanics). I know the question is a bit weird (actually a lot). My question is: "Is it the acceleration which ...
Charu _Bamble's user avatar
1 vote
0 answers
104 views

Timelike Directions

I'm trying to understand timelike directions. $$\gamma[e_0+\beta(\cos\theta e_1+\sin\theta e_2)]=k^\mu\partial_\mu$$ My questions: is $\beta$ the velocity of the massive particle as described by its ...
user345249's user avatar
3 votes
1 answer
178 views

Cosmological understanding from Penrose diagram of de Sitter spacetime

The conformal diagram of de Sitter spacetime looks like this I think I understand the causal properties of this diagram. Someone who is static in the south pole can send messages only to the upper ...
P. C. Spaniel's user avatar
0 votes
2 answers
105 views

Light-like vector in Schwarzschild metric

If I shoot a light ray radially, assuming the Schwarzschild metric, what vector would I plug in to the metric tensor to get a relationship between the $t$ and $r$ coordinates? That is what vector do I ...
Shaashaank's user avatar
0 votes
2 answers
103 views

If a photon is absorbed, does the associated wave function disappear instantaneously, or at the speed of light?

I came to this question while thinking about light with extreme wavelengths. Say we had light (em radiation) with a wavelength of 100's of thousands of kilometres and we absorbed a photon of it on ...
John Hobson's user avatar
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Domain of dependence in Causal structure for spacetimes that are not globally hyperbolic

I'm trying to prove an implication of a surface $S$ embedded inside a manifold M not being its Cauchy surface. The literature and problems available for these topics are already pretty less hence I'm ...
Math boi's user avatar
6 votes
2 answers
2k views

Do the Einstein Field Equations force the metric to be Lorentzian?

In GR, we are working with Lorentzian metrics, which are examples of a pseudo-Riemannian metrics. That is, we are trying to find pseudo-Riemannian $g_{\mu\nu}$ that are solutions to the field equation ...
Buddha Buck's user avatar
0 votes
1 answer
104 views

Newton's second law - local laws and non-local laws

What are local laws? I was reading this line in a book... Newtons second law is a local law. This means that it applies to a particle at a particular instant without taking into consideration any ...
Aditi Bansal's user avatar
2 votes
1 answer
80 views

Find an example of a closed, achronal set $S$ in Minkowski spacetime such that $J^+(S)$ is not closed

This is one of the exercises on Wald's General Relativity: Chapter 8, Problem 8.b Find an example of a closed, achronal set $S$ in Minkowski spacetime such that $J^+(S)$ is not closed. (Hint: ...
Níckolas Alves's user avatar
2 votes
2 answers
138 views

Relationship between spacelike and timelike distances in General Relativity vs. Special Relativity

In Minkowski spacetime, the distance $d_S$ between two space-like separated events $x$ and $y$ can (up to constant) be given by a distance between the two time-like separated events $z$ and $w$ where $...
Werner Einstein's user avatar
1 vote
0 answers
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Spatial separation in analogy to time separation in Lorentzian geometry?

O'Neill (Semi-Riemannian Geometry With Applications to Relativity, 1983, p. 409) defines time separation between two events as follows: "If $p, q \in M$, the time separation $\tau(p, q)$ from $p$...
Werner Einstein's user avatar
2 votes
2 answers
147 views

Can a body escape a black hole by being thrusted? [duplicate]

I am told many time that nothing can escape black-hole because black-holes escape velocity is more than speed of light. But we know object don't necessarily have to exceed speed of light to escape a ...
Zeesan's user avatar
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-1 votes
1 answer
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Since we observe stars, galaxies, etc in their past - is it correct to say that our present is only present for us but is in the past from afar? [closed]

So - I know that when we observe galaxies, we are observing their past. And that if the same past-them were to be looking at us, they would see our past. But when we look at their past - that is a ...
Mars Xoxo's user avatar
-1 votes
1 answer
120 views

According the theory of general relativity, what is the role of causality in the changes of the curvature of spacetime? [closed]

In Einstein's equations the curvature of spacetime and energy-momentum-pressure density are correlated. Is it clear when changes in matter energy density affect causally to curvature and when changes ...
Eusa's user avatar
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1 vote
0 answers
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Physics model for my tub of water demo

I want to setup a demo to show people an intuitive example of causal inference (Pearl 2009) using a simple experiment. I have a tub of water with two accelerometers floating on the surface. In the ...
Galen's user avatar
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