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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106 views

Proof for impossibility of FTL Signals

Is there is formal proof for the fact that signals must always travel at a speed less than the speed of light in a vacuum? I understand that special relativity dictates that for massive particles to ...
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Global conservation + Lorentz invariance = local conservation?

On the page 83 of "Quantum Field Theory Lectures of Sidney Coleman", Coleman showed an interesting example: It seems that global conservation law and local conservation law can be related. ...
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What is the problem of higher-order time derivatives with causality?

I've heard that equations of motion with third- or higher-order time derivatives have problems with causality, but can't seem to find any proof or reasoning for this. Could anyone please help me? I ...
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Time-orderings for the time-like and light-like vectors cannot be altered

My question concerns the time-ordering for the time-like vector between two space-time points: $$ (t_1,\vec{x_1}) \text{ and } (t_2,\vec{x_2})$$ Is it correct to claim that: For a time-like vector, $(...
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Time-orderings for the space-like vector can be altered

My question concerns the time-ordering for the space-like vector between two space-time points in the Lorentz invariant theory: $$ (t_1,\vec{x_1}) \text{ and } (t_2,\vec{x_2})$$ Is it correct to claim ...
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Interpretation on a propagation amplitude in (3.93) of Peskin's QFT

From page. 55 and (3.93) of Peskin and Schroeder's An Introduction to Quantum Field Theory: First consider the propagation amplitude $\langle 0|\psi(x) \bar{\psi}(y)|0 \rangle$, which is to represent ...
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2answers
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Understanding Space-time intervals and its types

I am taking Introduction to Modern Physics class. There, we were studying spacetime intervals as a subsection of Lorentz's transformation. My professor said that $\Delta x^2-c^2\Delta t^2$ is ...
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Minkowski Space and the Expansion of the Universe

I was watching a video about Minkowski space. It stated that no past event, outside of the light cone in space can be a cause of an action inside the light cone. Is this due to the expansion of the ...
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4answers
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What is light cone? Explain to mathematicians who understand the Lorentz group but not light cone

Mathematically the Lorentz group is precisely the $O(1,3)$ is the 4-vector rotation preserving the inner product of 4-vector under this metric $$ \eta_{\mu \nu}=(+1,-1,-1,-1). $$ There are four ...
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If two hypersurfaces are conformally related and one of them is a Cauchy surface, is the other a Cauchy surface too?

I'm reading Wald's "General Relativity". In appendix D he states that conformal transformations preserve causal structure. Does this mean that they also preserve when a hypersurface is a ...
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Causality: Invariant Under Lorentz Transformation

I'll begin by stating that I have only studied a very small bit of special relativity: a couple of lectures or so around the end of the Physics course I took, intended just to "give us a taste&...
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Do commutators have to be spacelike, timelike, or light-like separated?

I am trying to compute commutators for the complex Klein Gordon field, which can be found in exercise 2 in chapter 2 of An Introduction to Quantum Field Theory by Peskin and Schroeder. For instance ...
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1answer
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Does indeterministic event imply the violation of causality?

In many cases, an indeterministic event were accompanied by the violation of causality in certain theory. However, does indeterminstic event in general imply the violation of causality in classical (...
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Would this equation for electromagnetic four force be valid when the energy of electromagnetic radiation is negligible?

The first piece of information I used in my derivation is that, with respect to electric charge, anti-matter is mathematically equivalent to ordinary matter traveling backwards in time, which means ...
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6answers
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If light and gravity travels in the same speed then why light cant escape the gravitational pull of black holes?

Speed of gravity is infinite? If fastest thing is light then how universe is spreading faster than the speed of light?
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Why would an FTL-drive imply time travel? (other answers and questions unsatisfactory)

I've been spending quite some time trying to understand why an FTL-drive would also imply time-travel, but every answer I can find seems to mainly be about semantics and perception. I will break it ...
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1answer
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For the future Cauchy development (or future domain of dependence), why is $D^+ (S) \subset \tilde{D}^+ (S)$?

Let $S \subset \mathcal{M}$ (where $\mathcal{M}$ is our manifold), the future Cauchy development of $S$ is defined as $$D^+ (S) := \{p \in \mathcal{M} |\ \text{every past inextendible causal curve ...
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Spacetime Diagram for Robertson-Walker Universe

For the Robertson Walker universe with metric $$ds^2 = -dt^2 +a(t)[dx^2+dy^2+dz^2]$$ where $a(t)=t^q$ and $0<q<1$, the light cones in the spacetime diagram are drawn as follow: From the diagram, ...
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ADM formalism, closed timelike curves and chronological protection conjecture

Is it correct that based on the premise of foliation by Cauchy surfaces the ADM fomalism restricts the set of solutions for general relativity to causal manifolds and therefore excludes closed ...
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1answer
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Relativistic particles and quantum fields and time like cone

Considering that a "classical" relativistic particle remains inside the time-like cone, does it guarantee that a quantum field must also do that for each of its path history? or it has to be ...
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1answer
85 views

What's the big deal with interacting tachyons?

I understand that any spacelike path appears to move backward in time from some reference frames, so e.g. a "reflected" tachyon can be absorbed before it was emitted. But I don't see how ...
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1answer
56 views

Does our past light-cone have some extension in three-dimensional space?

On spacetime diagrams cosmologists represent our past light-cone as a two-dimensional surface extending back in time, on which are situated all light-emitting events which we can observe today. This ...
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2answers
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If causality propagates at the speed of light, how could the Big Bang expand faster than that? [duplicate]

(I hope this question is a little more profound than the standard "if nothing can move faster than light..." question that pops up here regularly.) It has been said that the speed of light ...
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45 views

Tachyons as vector representations on the surfaces transitivity of Lorentz group?

In Wikipedia's surfaces of transitivity (of Lorentz group $G$, it says "Standard vectors on the one-sheeted hyperbolas would correspond to tachyons. Particles on the light cone are photons, and ...
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Time and causality at the beginning of the universe

I have been, quite a few times, been caught up in arguments on the internet, where my opponent posits causal events existed before the "singularity" at the "beginning" of the ...
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Two ships meeting in the distorted spacetime of a Krasnikov tube - what happens?

Given a Krasnikov Tube: a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an ...
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68 views

Electric fields existing everywhere in the universe, communication faster than speed of light?

If I take a charge and oscillate it, does that instantaneously create a field with magnitude, however small, at every point in the universe? If so, couldn't this fact be used to send messages faster ...
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59 views

Should time be a loop or a line?

It's interesting to see that torus was so popular in physics, that it worked so well. There was famous Gauss–Bonnet theorem which stated basically $$\oint_S K dS= 2\pi \chi(S)$$ where K was the ...
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1answer
70 views

Klein-Gordon equation on a compact, two dimensional domain

Consider the Klein-Gordon equation in two dimensions on any compact subset of $\mathbb{R}^2$ (that is, a Jordan domain). The equation is hyperbolic, and since the domain is compact it is not evident ...
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When do special relativity causally linked reference frames split into general relativity un-linked?

I'm looking for the "a-ha" moment in trying to understand how the super-luminal apparent speeds of the universe inflation theory are allowed. Specifically, the short explanation is that &...
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1answer
100 views

Objective direction of time in general relativity

In general relativity, the coordinates $x^\mu$ we put on the manifold are arbitrary and need not have any physical interpretation. For this reason, it is said there is no objective notion of time in ...
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1answer
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Lightning's tendency to find a tall point on the ground

Is lightning's tendency to connect to a high point on the ground due to probability in the colloquial sense, or is there some sort of electromagnetic stream of "information" exchanged ...
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Relation between Causality conditions and Energy conditions in Einstein's gravity

It is known that a general solution for Einstein's field equations $G_{\mu\nu}+\Lambda g_{\mu\nu}=kT_{\mu\nu}$ may not be always physically realizable. Energy conditions put restrictions on these ...
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1answer
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When can information escape from a black hole through a warp bubble-like spacetime?

It is well known that nothing can escape a black hole, including gravitational radiation. Many questions have been asked here about this topic, such as: Can gravitational waves escape a black hole? ...
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Where's the rest of it? - Schrödinger equation for a free particle whose position is known

Assumptions I will be working in one spatial dimension throughout. It should be possible to generalise to three dimension with relative ease but doing so adds little to the conversation, only serving ...
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2answers
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Moving a 2x2 the length of the solar system [duplicate]

If we were able to push a 2x2 piece of wood that is the length of our solar system, how would it behave? My colleague says since its all part of the same molecular structure, the whole piece of wood ...
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Can information travel faster than speed of light in this situation?

I know the answer is no but I have a thought experiment that seem to be violating that. Imagine two persons living on two different planets namely A and C which are 10 light years apart. There is a ...
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Another speed of light: how to test it? [duplicate]

Suppose there are ANOTHER time-like dimension with another speed of light $$C>>c$$ Would we notice that huge speed of light? How to test the existence of such a huge constant or speed of light?...
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What is the meaning of synchronization in special relativity?

Suppose there are two observers $A$ and $B$ (or reference frames if you will), let us label their time coordinates by $t_A$ and $t_B$ respectively. When we say we synchronize the clocks of $A$ and $B$...
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Chronology Protection Conjecture with a wormhole time machine-Mechanisms in layman's terms

I remember hearing about Steven Hawking making a Chronology Protection Conjecture back a couple of decades ago. He seemed to be arguing that the properties of the universe would conspire to prevent a ...
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Sabine Hossenfelder's argument to rule FTL paradoxes out

I have recently seen Sabine Hossenfelder's video on faster-than-light travel, in which she argues no paradoxes would arise if we had something like a FTL warp device, because the trajectories leading ...
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1answer
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What would happen if a black hole disappeared? [closed]

Imagine if a black hole disappeared. Would spacetime act like a rubber band and propel objects that used to be caught in its gravitational field outwards - i.e. some kind of space time explosion? How ...
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1answer
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Can Einstein's action at a distance be action into the past?

This youtube video is about how it is not measurable or of any consequence what the one way speed of light is, only that a two way trip has an average speed of $c$. An example is moving ...
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1answer
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How to show causality is preserved in path integral approach?

I am struggling to find a good way to show causality is conserved using the path integral approach. In the operator approach one can show that $[\hat{\phi}(x),\hat{\phi}(y)]=0$ if $x$ and $y$ are ...
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Are unreachable parts of the universe 100% unreachable or do we just say so?

In Kurzgesagt's video TRUE limits of Humanity is it stated that most of the universe will be forever unreachable because the universe is expanding faster than the speed of light. This is possible ...
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How is momentum conserved in this situation?

Let’s say we have two inactive electromagnets spaced one light-minute apart, with north poles pointing toward each other. One of the electromagnets is turned on for ten seconds, and then turned off ...
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Probability of finding a particle outside it's light cone

Say we just created a particle (high probability of one-particle state), is the probability of a very far away detector getting triggered at the time of creation (probability of finding a particle ...
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Which force came first in Newtonian gravity? Force A on B or force B on A?

Can a body $X$ apply a gravitational force on a body $Y$ without itself being acted on by a gravitational force from $Y$? Just per intuition, we deduce from Newton's third law that if $A$ applies ...
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Causality and wave configurations in dispersive media

As motivation, consider if I handed you two photographs of a ball at two different times, and asked you if it were possible for the ball to have traveled as far as it did in a certain time. In the ...
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In the context of condensed matter physics, what does it mean for time to have two dimensions?

In an online article that describes condensed matter physics for laypersons, the author describes various so-called "designer materials" that have exotic properties, including one in which ...

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