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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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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 ...
Talha Ahmed's user avatar
-3 votes
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Please tell me about "Action at a distance" in Electrodynamics [closed]

I am confused about how test charge informed about source charge. So I research on it. Web said me that it is "Action at a distance phenomenon". What is this? I am a first year Undergraduate ...
Arpan Purkait's user avatar
2 votes
3 answers
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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 ...
KDP's user avatar
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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 ...
Zee's user avatar
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1 answer
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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 ...
Ervand's user avatar
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Fundamental principles that govern all physical laws [duplicate]

Suppose a theoretical physicist wants to construct a theory to explain some newly discovered phenomenon. The new theory is expected to follow certain rules or fundamental principles. There are four ...
Mantu Das's user avatar
2 votes
1 answer
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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 ...
amansas's user avatar
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1 answer
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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 ...
Aidan Beecher's user avatar
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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 ...
Ratul Thakur's user avatar
6 votes
1 answer
127 views

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 ...
Fiter's user avatar
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How to Understand Negative Energy in the Ergoregion?

I am trying to understand the Penrose process and having trouble explaining negative energy in the ergoregion. How I interpret it is: Energy is the dot product between the four momentum of the object ...
Gene's user avatar
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Can wormhole inside a black hole become an escape?

I did not major in Physics so not sure if this is a proper question; but according to some Google search there do exist papers discussing wormhole inside black hole like this, which I am not able to ...
Luke Lee's user avatar
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If the speed of causality changes, could you go FTL?

In the middle of some research, I reached a sort of confusion that I’d like to sort out. In flat space FTL is impossible, because in a Minkowski metric, $$\mathrm{d}s^2=c^2 \mathrm{d}t^2-\mathrm{d}x^2-...
controlgroup's user avatar
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1 answer
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How is information defined when considering locality in quantum mechanics?

$\newcommand{\ket}[1]{|#1\rangle}$ My question is a follow-up from this discussion about the presence of non-local correlations in a theory that is deemed local. The first answer talks about the ...
UVcatastrophe's user avatar
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Is the spinning Cosmic String spacetime totally vicious?

The spacetime $(M,g)$ is given locally at each point by the metric: $$g= -(dt + a \, d \phi)^2 + d\rho^2 + \kappa^2 \rho^2 \, d\phi^2 + dz^2 \ \text{where} \ \ a > 0$$ This is the spacetime of a ...
Bastam Tajik's user avatar
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An interpretation for Propagator $D(x-y)$

When I learn QFT I always see that when we consider the causality problem in QFT, at first we may try to compute the propagator $D(x-y)$ for spacelike distance $(x-y)^2<0$, which is nonzero. An ...
Gao Minghao's user avatar
21 votes
5 answers
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Does an object approaching a black hole ever cross the combined event horizon of the black hole and itself?

Once you start studying black holes, one of the first things you'll probably hear is that from an outsider's perspective objects falling into the black hole take an infinite time to do so due to time ...
Giorgos G's user avatar
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2 votes
2 answers
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Particle Creation by a Classical Source (on-shell mass momenta)

It is noted in Peskin and Schroeder's QFT text that the momenta used in the evaluation of the field operator $\phi(x)$ are "on mass-shell": $p^2=m^2$. Specifically, this is in relation to ...
Albertus Magnus's user avatar
4 votes
1 answer
255 views

Quantum fields can leak out of the light cone? [duplicate]

So the transition amplitude for a free Klein-Gordon field for a space-like interval is finite and non-vanishing (decays exponentially). What does one make of this physically, i.e. what is the meaning ...
Albertus Magnus's user avatar
1 vote
2 answers
103 views

Determinism in relativity [closed]

We know that transitioning from classical mechanics to quantum mechanics, determinism breaks down. We also know that complexity and chaos theory have determinism in principle but we can't predict. My ...
physics's user avatar
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1 answer
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Are non-point spacetime events partially ordered?

When describing events in spacetime, we usually use points. We then phrase the relation between points as a trichotomy: either they are timelike, spacelike, or lightlike separated, based on the ...
Corbin's user avatar
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Is the causal structure completely determined by the Weyl tensor alone?

By causal/conformal structure I mean the context of Malament's 1977 theorem. If I understand correctly this means that any two spacetimes which agree about all of the future-directed continuous ...
Daniel Grimmer's user avatar
1 vote
2 answers
71 views

How do I interpret the time axis in a diagram with multiple light cones?

Light cones are often drawn on a spacetime diagram that has a directional time axis like the fourth one on this page: There is a time axis, and all of the light cones are align with it because this ...
Jim's user avatar
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Proof that commuting Dirac fields violate causality

What is the proof that commuting Dirac fields violate causality? All sources I could find just quote this result, but I couldn't find an explicit derivation anywhere. In particular, the case I am ...
pll04's user avatar
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2 votes
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Causality in Maxwell's equations

I have just read Jefimenko's notes on the causality violation it would pose to claim "varying electric fields give place to magnetic fields and viceversa" since both fields take place at the ...
Lagrangiano's user avatar
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2 answers
131 views

Can a non-local theory be consistent with special relativity?

If there was a non-local theory that explained quantum entanglement correlations, does it follow that it would violate special relativity?
Hume's user avatar
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0 answers
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Can you model relativistic interactions without locality?

Assume $c=1$ I've been doing relativity by myself so I may be making some assumptions here that I would not have if my learning had been more extensive. One such assumption is that you can model the ...
NaiDoeShacks's user avatar
3 votes
4 answers
364 views

Regarding the signature of special relativity

in special relativity we add time as a dimension and replace euclidean space $ \mathbb{R}^4 $ with a pseudo-euclidean space $ \mathbb{R}^{1,3} $ of signature $ (1,3) $ by defining a quadratic form $\...
Tomás's user avatar
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1 answer
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Exponential decay of propagator outside lightcone

In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator: $$D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
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How do you make self-consistent initial values?

In electrodynamics for each charge you need to have data for everything in its past light cone. But the union of all past light cones for all charges would be a spacetime volume rather than a ...
Emil's user avatar
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1 answer
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Why future infinity have no future end points?

I am studying Hawking's area theorem from the book the large scale structure of spacetime by Hawking and Ellis. At the end of page#318, it said: null geodesic generators of future infinity have no ...
Talha Ahmed's user avatar
1 vote
1 answer
166 views

How does null infinity differ from ordinary infinity?

Null infinity is the diagonal lines on the edge of a Penrose diagram. It seems to be the place where beams of light go if they never bump into anything, but only light can go there. It appears to be ...
Miss Understands's user avatar
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2 answers
65 views

Unidirectionality of Time in Spacetime

I have a question regarding the dimension of time. We all know that an event in spacetime is defined by a point $$ {x}^{u} = (ct, x, y, z) .$$ The only component that breaks the symmetry is $ct$, ...
Julián Oviedo's user avatar
2 votes
2 answers
136 views

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
-6 votes
2 answers
131 views

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
2 votes
0 answers
35 views

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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12 votes
5 answers
2k views

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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1 vote
1 answer
111 views

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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2 votes
1 answer
66 views

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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1 answer
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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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3 votes
5 answers
318 views

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-...
tneserp's user avatar
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1 vote
0 answers
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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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1 vote
0 answers
44 views

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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8 votes
1 answer
426 views

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
1 vote
2 answers
126 views

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 ...
Davyz2's user avatar
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0 answers
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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 ...
tneserp's user avatar
  • 49
3 votes
1 answer
45 views

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
647 views

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
2 votes
0 answers
63 views

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 ...
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