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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Can two points always be joined by timelike curve?

I have asked this question on MSE but now I think it is better suited for the Physics Stack Exchange. Suppose $p$ and $q$ are connected by a causal (i.e. its tangent vectors have non-positive norm) ...
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Spacelike, Timelike and order of events [closed]

Hartle pg 60 The relativity of simulataneity means that it does not make sense in general to say that one event is later than another. An event can be later than another spacelike separated event in ...
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How is Lorentz invariance of $S$-matrix related to vanishing of Hamiltonian density commutator at spacelike separations?

In Section 5.1 of the book, 'Quantum Theory of fields Vol-1' by Steven Weinberg, he says that if the Hamiltonian density commutes with itself at spacelike separation then the $S$-Matrix satisfies ...
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Kallen-Lehmann + micro-causality do really imply equality of spectral densities for particles and anti-particles?

In Eq.10.7.11 of Weinberg's textbook on QFT vol.I, it is claimed that equality of spectral densities $\rho(\mu^2)$ for particles and $\bar{\rho}(\mu^2)$ for antiparticles (obtained by iserting ...
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Is momentum space "less physical" than position space?

In quantum mechanics and quantum field theory it is specially common to work in both position and momentum space. Passing the theory to momentum space is sometimes crucial, as one usually finds that ...
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Do Wightman axioms imply that the Wightman $n$-point functions have causal support?

Wightman axioms are one of the rigorous approach for quantum field theory. According to "PCT, Spin Statistics and All That", there is also a reconstruction theorem starting from Wightman $n$-...
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Why are inner horizons Cauchy horizons?

I know that RN black hole has two horizons, one outer one and one inner one. The outer one is the event horizon. As far as I know, a Cauchy horizon is the boundary of the domain of dependence of a ...
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Can the addition of two spacelike vectors ever null?

Consider $A^\mu = (a,b)$ and $B^\mu = (c,d)$ where $a<b$ and $c<d$ making them spacelike vectors with a metric of $\text{diag}(1,-1)$. Then, $A^\mu + B^\mu = (a+c,b+d)\equiv C^\mu$. For a vector ...
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Possible (Minor) Error in Original Lieb-Robinson Bound Paper

Introduction I was reading through Lieb and Robinson's original paper introducing their eponymous bounds, and I came upon the following statement: The task remains of corroborating our assertions ...
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Properties of the interior of the domain of dependence $D(A)$

I have been reading the book Semi-Riemannian Geometry With Applications to Relativity by Barrett O'Neil, but I have some problems understanding the properties of $int(D(A))$, where $D(A)$ denotes the ...
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What prevents two particles that made a black hole to unmake it?

Assume you have two high energy particles approaching each other and forming a black hole even before colliding (but before a singularity is formed, which I am not sure that is possible). If the laws ...
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Is there a proven causality that energy-matter causes curvature in spacetime?

I'm not very knowledgable in physics, sorry. I've read and (somewhat) understood that energy-matter causes space-time to curve but I was wondering about the causality in the statement. Is this ...
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Why Equal-time commutation relation?

Let $\phi(\bf{x},t)$ be a field, and $\pi(\bf{x},t)$ be the conjugate momentum field. A standard practice is to apply the equal time commutation relation: $$[\phi(\bf{x_1},t), \pi(\bf{x_2},t)] = i\...
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Why a past-inextendible causal curve can have a starting point?

I have some doubts about the notions of future and past-inextendible causal curves. The definitions of future and past inextendible causal curve that I have are the following: Let $\gamma$ be a ...
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Confusion on theorem 8.1.2 and corollary in Wald's GR book

In Wald's GR book theorem 8.1.2 says: Let $(M,g_{ab})$ be an arbitray spacetime, and let $p \in M$. Then there exists a convex normal neighborhood of $p$, i.e., an open set $U$ such that for all $q,r ...
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Electron fields does not anticommute at space-like points

In the end of page 804 and beginning of page 805 of Streater's paper Outline of axiomatic relativistic quantum field theory which can be find here https://iopscience.iop.org/article/10.1088/0034-4885/...
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How do we determine whether a surface is an event horizon? Exactly what to calculate to do this?

Event horizons play an important role in relativistic astrophysics, especially for black holes, but also for other spacetimes. It is fundamental to be able to determine whether a given surface is an ...
3 votes
1 answer
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Black hole metric of reflected shell of incoming light

At this point in Leonard Susskind's eighth lecture on general relativity, he begins a discussion about finding the metric of a black hole formed by an incoming, spherically symmetric shell of light. ...
2 votes
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Massive and massless modes in the Klein-Gordon equation

I am studying the massive Klein-Gordon equation in 3+1 dimensions with a given scalar source. The equation I am looking at is $$ (\Box +m^2)\phi(x)=J(x) \ , $$ and am interested in the following ...
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General Relativity via light cones curvature?

Is it possible to reformulate general relativity as curvature of objects' light cones instead of curvature of spacetime?
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How does the many-worlds interpretation solve spooky action at a distance?

If we take the classic example of two particles that are entangled with up spin and down spin, and we separate these particles a few light years apart and then observe them one after the other, they ...
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1 answer
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What is the fathest light from Earth can reach, given accelerating expansion?

At what current distance is the nearest point Q at which the photon sent from Earth right now never reaches it? There is the concept of a Hubble volume, which "is a spherical region of the ...
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Are Temporal Paradoxes possible within the Many Worlds Interpretation?

Are Temporal Paradoxes possible within the universe of the MWI, or is the idea not possible within this interpretation? I guess if one would alter something in the past within the MWI universe, they ...
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Prove there are not timelike vectors contained in the tangent bundle of a Cauchy surface

Intuitively, I do not visualize how could it can contain temporary vectors. I imagine that if there were a timelike vector tangent to a Cauchy hypersurface $S$, you could consider an integral curve ...
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What does the spacetime interval measure?

I know that the spacetime interval is the analog of the (square of the) Euclidean distance in spacetime. Also, I understand that it is an invariant quantity and determines spacetime's causal structure....
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Is superdeterminism just retrocausality?

I watched this YouTube video by Sabine Hossenfelder to try and better understand superdeterminism: https://www.youtube.com/watch?v=ytyjgIyegDI (Note: Physics begins around 8:12, before that she's ...
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Solving the Klein-Gordon Equation and Enforcing Causality

Perhaps this is too basic a question, but I am running into trouble attempting to solve the Klein-Gordon equation with a simple spherically symmetric source. Consider, for instance $$ \square \phi = A(...
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Closed time loops and causality in general relativity

I always read that GR does not seem to prevent closed time loops. This does not sound too crazy if you could somehow create a traversable wormhole (and move one of the ends fast and long to make the ...
2 votes
1 answer
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Is there something that violates "time locality"?

The way I understand locality is that for an object to influence another object away from it, it has to do so through the space that separates them. It can shoot out an EM wave to the other object, ...
4 votes
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Do spinor fields violate causality?

It is a theorem that spin structures on a spacetime $M$ exist iff the second Stiefel-Whitney class $w_2(M)=H^2(M, \mathbb{Z}_2)$ vanishes. I find this confusing for two reasons. First, it implies that ...
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Clarifications on proving lightlike vectors must be orthogonal with themselves

I'm trying to prove that lightlike vectors in Minkowski space must be orthogonal to themselves, and I have two questions about this. I tried two different approaches: If lightlike, $ds^2=0$ By ...
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Does light propagate at the speed of light in curved spacetime

There seems to be a lot of different ways to consider how one can describe electromagnetic waves in curved spacetime, and whether or not they go "at the speed of light" seems to be somewhat ...
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Splitting of general pseudo-Riemannian Manifolds

Under what conditions splitting (e.g. $m + p$ foliation of a $m + p$ dimensional manifold) of a general pseudo-Riemannian manifold (with any arbitrary signature) possible? If it is too general then I ...
1 vote
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Is causality a consequence or a constraint in physics?

I wonder if causality is a constraint that we must add to physical models (if needed), or is it a consequence of Lorentz invariance and locality (or something else). In other words, which properties ...
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Characterizing compactness of the Alexandrov topology in a spacetime

This is perhaps more of a soft question and on the mathematical side of things, but I'm struggling to find references and to formulate a precise argument. There's of course the chance that what I'm ...
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Local algebra of AQFT vs Bisognano Wichmann Theorem

Maybe I am misunderstanding something really stupid, but I am finding it hard to think of local algebras in terms of wedge algebras. One of the claims (see, e.g., Section 3 and 4 of this paper) is ...
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12 votes
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If the escape velocity at the event horizon is the speed of light does it mean that slower bodies won't move away at all?

If we say that the escape velocity from a planet is say 10 km/s we think that a slower body will move away from that planet but will be eventually forced to fall back on the planet. In simple words we ...
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How do Lieb-Robinson Bounds talk about locality without the position operator?

So we know when one goes from QM to QFT Lieb Robinson bounds become micro causality. But micro causality is a statement on the commutators assuming they are space-like, time-like or light-like. ...
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How is the singularity of Schwarzschild space-like if a one can take a time like path to it?

It is known that when one crosses the event horizon of a Schwarzschild black hole, one cannot return and is destined to hit the $r=0$ horizon. My understanding is that this can be seen from the ...
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Normal to the hypersurface

I have a given metric and I want to choose a spacelike hypersurface and find the normal to that hypersurface. I know that if the hypersurface is spacelike, then the normal is timelike. The given ...
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Can a causal relationship ever be established with absolute certainty (in principle)? [closed]

Is it possible in principle to ever establish or prove a causal relationship exists between two variables or events?
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Could the speed of causality be (significantly) faster than $c$?

The other day my son (13) asked me whether it was possible that light went very slightly slower than our best measured $c$, and at the same time had a very tiny mass, but we aren't able to measure ...
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1 answer
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Is anything in the universe instantaneous? [closed]

By my logic, there should be some time lag between the action and the reaction, however small the lag.So can we say that an effect to a reaction happens instantaneously in our universe?
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Invariant of time-order in lightlike interval

I'm trying to prove that the time order is invariant in a lightlike interval, I have this $$P_1=(X_1^0, X_1^1,0,0)$$ $$P_2=(X_2^0, X_2^1,0,0)$$ Two lightlike events in a inertial frame where $t_2>...
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What are Time Capsules in Julian Barbour's theory of a Timeless Universe?

Barbour (The End of Time, The Janus Point) describes Time Capsules as Nows (instants of the universe) with awareness of other instants. That we experience time because we 'live in a Time Capsule'. I ...
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1 answer
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Self-coupling of gravity and gravitation escaping a black hole - contradiction?

The field equations are non-linear, that can be interpreted as gravity is coupling with itself, see for example here: Non-linearity and self-coupling of gravity I'm trying to understand what that ...
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1 answer
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Reconciling special relativity and quantum mechanics

I have been referring to QFT for the gifted amateur, p. 75. To evaluate whether a particle can exist beyond its forward light cone, we check if it has a non-zero amplitude. The amplitude being ...
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Is the set of reachable arrangements of an indeterministic universe (of a given material substrate) sensitive to its initial arrangement?

Suppose two equally massive universes have an identical material substrate of the same fundamental particles. Suppose then that these two universes initially have different arrangements of these same ...
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Is the set of reachable states of an indeterministic universe sensitive to its initial conditions?

Suppose two universes with the same amount of mass-energy and evolving according to the same natural laws, but having different initial conditions. Is the set of states that are reachable by the ...
12 votes
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Why does an Alcubierre drive, travelling FTL, violate causality, if the universe expanding FTL doesn't?

An Alcubierre drive seems to be plausible as a means to travel faster than light, because it doesn't move the object itself, but the space around it. it's said that matter and information can't move ...
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