As a consequence of the Lorentz transformations, time and space transform into each other when changing reference frame. This calls for a unified description: Minkowski spacetime.

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Is spacetime simply connected?

As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn. This falls into the ...
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0answers
380 views

Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...
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4answers
2k views

Does General Relativity imply loops in space?

Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. The analogy with a rubber sheet is popular. In ...
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2answers
845 views

How fast can time flow? A question of time dilation

(I would describe myself as an illiterate physics enthusiast, so I hope you'll forgive me if my ignorance is borderline offensive.) If I've understood anything of the concept of time dilation, your ...
11
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4answers
5k views

Why does Venus rotate the opposite direction as other planets?

Given: Law of Conservation of Angular Momentum. Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based). Surface same degree of aging all over. Hypothetical large ...
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6answers
4k views

What is our location relative to the Big Bang?

Given what we know about space, time and the movement of galaxies, have we or can we determine what our position is in relation to the projected location of the Big Bang? I've read some introductory ...
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4answers
642 views

Can physics get rid of the continuum?

Almost every physical equation I can think of (even though I don't actually feel comfortable beyond the scope of classical mechanics and macroscopic thermodynamics, as that's enough for dealing with ...
11
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6answers
630 views

More than one time dimension

We know that space-time dimensions are 3+1 macroscopically, but what if 2+2? Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two ...
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3answers
548 views

Space is expanding so what is time doing? [duplicate]

Space is expanding and as we know space and time are intrinsically linked to be now known as spacetime. What is happening to time during expansion? Is there more time, longer time or is the time part ...
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5answers
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Hubble's law and conservation of energy

If all distances are constantly increasing, as Hubble's law say, then lots of potential energies of form ~$\frac{1}{r}$ changes, so how is the total energy of the Universe conserved with Hubble's ...
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5answers
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Did spacetime start with the Big bang?

Did spacetime start with the Big Bang? I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before ...
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2answers
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Invariant spacetime - distance - Circular Motion

I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor. My question is, if something travels in a ...
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5answers
701 views

Is it possible for one black hole to pull an object out of another black hole?

Suppose we have a spacecraft just inside the event horizon of a black hole, struggling to escape, but slowly receding into it. Another (bigger) black hole expands until its event horizon includes the ...
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4answers
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Can spacetime exist in the absence of matter and energy?

I'm pretty sure Ernst Mach would have said that spacetime cannot exist without matter in it. But I'm also pretty sure that a black hole can be described as a self-sustaining gravitational field, ...
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1answer
450 views

Causal and Global structure of Penrose Diagrams

What kind of global and causal structures does a Penrose diagram reveal? How do I see (using a Penrose diagram) that two different spacetimes have a similar global and causal structure? Also, I ...
10
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1answer
453 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
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6answers
1k views

Is proper time a vector?

Proper time is identical with the spacetime interval of a timelike movement. A spacetime interval is the dot product of two vectors and thus a scalar. Proper time however is always pointing exactly ...
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4answers
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Minkowski spacetime: Is there a signature (+,+,+,+)?

In history there was an attempt to reach (+, +, +, +) by replacing "ct" with "ict", still employed today in form of the "Wick rotation". Wick rotation supposes that time is imaginary. I wonder if ...
9
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3answers
837 views

Is the edge of our Hubble Sphere within our Cosmic Event Horizon and why?

I was recently shown a pretty cool video about common cosmological misconceptions. It got me reviewing the different between event horizon (current distance within which we will see/interact), ...
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3answers
254 views

What is the exact meaning of homogeneity in cosmology?

I understand that, in general, homogeneity is the physical attribute of being uniform in composition (" of the same form at every point"), but I'm slightly confused when it is used in cosmology as ...
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Time travel outside of light cone without causality violation

If one is able to travel into the past but at a spatial distance that puts him outside of his own past light cone would this be considered a causality violating trip? Looking at a Minkoski diagram, it ...
9
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2answers
255 views

Rigorous definition of frame of reference

I'm looking for a mathematical definition of frame of reference. Most of the textbooks I have seen take it for granted and they just refer to some set of spacetime coordinates. A more mathematical ...
9
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2answers
453 views

Some questions regarding $n+m$-dimensional spacetime [duplicate]

Possible Duplicate: Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists? The following image: serves to aid the reader in ...
8
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3answers
159 views

Why doesn't $ds^2 = 0$ imply two distinct points $p$ and $p'$ on a manifold are the same point?

Let's suppose I have a spacetime manifold $M$. Let $p$ be a point on my manifold. Now I move from $p$ to some other point $p'$. Presumably I should have moved some "distance" right? How can I speak of ...
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570 views

Momentum and spacetime

My apologies up-front for the naive question and my rudimentary understanding, but I should be delighted if someone would enlighten me :) The question has to do with the application of the ...
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2answers
1k views

Does space curvature automatically imply extra dimensions?

Total newbie with basically no physics knowledge here :) I would welcome any correction to the steps of my reasoning that lead to my question, which could easily turn out to be invalid :) My current ...
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2answers
2k views

What does it mean that the universe is “infinite”?

This question is about cosmology and general relativity. I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read ...
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2answers
561 views

A sketch of various combinations of numbers of space and time dimensions

I came across this picture/sketch on the internet, however there is no any explanation about it: What is "UNPREDICTIBLE"? "UNSTABLE"? "TOO SIMPLE"? "elliptic", "ultrahyperbolic"?? Some related ...
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3answers
663 views

Is anyone studying how the general topology of spacetime arises from more fundamental notions?

Stephen Wolfram in his book A New Kind of Science touches on a model of space itself based on automata theory. That it, he makes some suggestions about modelling not only the behaviour of matter ...
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3answers
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Is space infinitely divisible?

As a child I remember hearing the popular paradox presented by Zeno proposing that Achilles could never catch a tortoise in a race since he would have to traverse the infinite space between himself ...
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4answers
828 views

Why should one expect closed timelike curves to be impossible in quantum gravity?

From the Wikipedia article, it seems that physicists tend to view closed timelike curves as an undesirable attribute of a solution to the Einstein Field Equations. Hawking formulated the Chronology ...
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2answers
406 views

Energy balance of closed timelike curves in Gödel's universe

I recently read Palle Yourgrau's book "A World Without Time" about Gödel's contribution to the nature of time in general relativity. Gödel published his discovery of closed timelike curves in 1949. ...
8
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1answer
256 views

Plausible explanations for 3 local space dimensions

Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons). One such of course ...
8
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1answer
323 views

Our Universe Can't be Looped? [duplicate]

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
8
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1answer
101 views

Hamilton operator in absence of causal order?

I hope, this question isn't too broad or vague. In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a ...
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Why we don't see time dilation in stars orbiting black hole?

We have images of stars orbiting black holes or black holes destroying near stars, but why do we see the stars moving normally? I mean, if time dilation does exist, shouldn't we see that stars slow ...
7
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2answers
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What's the difference between space and time?

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time" but never explain what the difference is between the ...
7
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6answers
2k views

How to measure the curvature of the space-time?

I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ...
7
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5answers
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Naive visualization of space-time curvature

With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus: "If you throw a ball, it will move along a parabola. Initially its vertical ...
7
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2answers
998 views

How do I develop an intuitive model of spacetime?

I am your nightmare poster - a layman trying to learn special relativity. (I'm also a refugee from stackoverflow.com: trust me, it's only going to get worse). Apologies in advance if my question is ...
7
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2answers
4k views

What is imaginary time? [duplicate]

I am not professional physicist; but I am curious about Stephen Hawking's "imaginary time". It would be better to elaborate exactly what it is. I am not confused because of the word "imaginary" but I ...
7
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2answers
2k views

Does velocity or acceleration cause time dilation?

What causes time dilation? Acceleration or velocity? I've seen multiple comments on this forum that assert velocity is the cause, but that doesn't seem right to me. You can't have velocity without ...
7
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3answers
397 views

How does a rotating object cause frame dragging?

Frame dragging is a consequence of general relativity. But I don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if ...
7
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2answers
123 views

If photons don't “experience” time, how do they account for their gradual change in wavelength?

It is often said that photons do not experience time. From what I've read, this is because that when travelling at the speed of light, space is contracted to infinity, so while there is no time to ...
7
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2answers
109 views

What are the linear maps which preserve the time-like cone?

I'm looking at the set of time-like vectors: $\mathcal{T}_+ = \{ x \in \mathbb{R}^4 \mbox{ s.t. } x^T \eta x \geq 0 \:, x^0\geq 0\} $, where $\eta = \mbox{diag}(1, -1, -1, -1)$. I want to be able to ...
7
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2answers
347 views

Can we show that time is orthogonal to space?

It's easy to show that the time we measure is "in a different direction" from the space directions we measure. However, it's not immediately obvious to me that these directions are orthogonal. How do ...
7
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4answers
627 views

Hamiltonian and the space-time structure

I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian. Space-time structure dictates the form of ...
7
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3answers
461 views

How can I vizualize and understand curved spaces in general relativity?

I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle ...
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567 views

Getting back out of an Alcubierre warp bubble

Does the theory on paper provide a way for hypothetical travelers to get back out of the bubble that has gotten them close to their distant destination by compressing all the space in front of them ...
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Does the “Andromeda Paradox” (Rietdijk–Putnam-Penrose) imply a completely deterministic universe?

Wikipedia article: http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument Abstract of 1966 Rietdijk paper: A proof is given that there does not exist an event, that is not already in the past for ...