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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How does the curvature of spacetime induce gravitational attraction?

I don't know how to ask this more clearly than in the title.
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Can a huge gravitational force cause visible distortions on an object

In space, would it be possible to have an object generating such a huge gravitational force so it would be possible for an observer (not affected directly by gravitational force and the space time ...
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567 views

Does the Opera result hint to a discrete spacetime?

Could the Opera result be interpreted as some kind of hint to a discrete spacetime that is only seen for high enough energy neutrinos? I think I've read (some time ago) something like this in a ...
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486 views

Rotations in space-time

In Landau's Classical Theory of Fields, one finds the statement: Every rotation in the four-dimensional space can be resolved into six rotations, in the planes $xy,zy,xz,tx,ty,tz$ (just as every ...
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According to General Relativity, Does The Past “Exist”?

I'm curious about just what is meant by time being another dimension, like the three (observable) spatial dimensions. Does this imply, according to General Relativity, that the past and the future ...
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2k views

Gravitational time dilation at the earth's center

I would like to know what happens with time dilation (relative to surface) at earth's center . There is a way to calculate it? Is time going faster at center of earth? I've made other questions ...
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6answers
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How does velocity cause time dilation?

I've been trying to learn about the speed of light and time dilation, but I'm at an impasse. The presented facts say that if I travel around the solar system at 50% the speed of light and then come ...
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2answers
168 views

Why time is considered a dimension?

Why time is considered to be a dimension? And the other 7 (except the 3 dimensions of space, and the dimension of time) dimensions that string theory suggests, why can't they be realized?
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251 views

Is there an orthogonal time dimension in Minkowski spacetime?

Space dimensions are orthogonal one to each other. But what about time in the Minkowski diagram? At first sight, time seems to be orthogonal to space. But we have to consider that each Minkowski ...
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310 views

Excluding big bang itself, does spacetime have a boundary?

My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity). Does this mean that ...
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355 views

Time inside a Black hole

If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black ...
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308 views

About space-time and its four dimensions

I explained to someone I know about General Relativity (as much as I know). He said that he didn't see how it could be correct. He argued: How is 4-dimensional space-time space different to ...
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574 views

Universe Expansion as an absolute time reference

Why we call "constant" to the Hubble constant?, if the universe were really expanding then the Hubble "constant" should change, being variable, smaller and smaller..with "time". Other example/view ...
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908 views

Voyager local time dilation (caused by gravity)

Voyager I, as an example, taking account gravity and setting aside effects of speed as cause of time dilation. If it is very far away from earth and sun, so then there must be a difference in the ...
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479 views

Introductions to discrete space-time

It's comparatively easy (cum grano salis) to grasp the following concepts: Euclidean space-time (continous space and continuous time) classical mechanics (discretely distributed matter in continous ...
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394 views

The inner workings of the Olbers paradox

A long time ago I was told that the universe is finite. The provided "proof" (or reasoning), known as Olbers' paradox, was that on infinite universe there would be an infinite number of stars, and ...
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178 views

Element of area in 4-dimensional space-time

How would you proof that $$ \mathrm {Tr} (\mathbf{S\cdot \bar S })=0$$ where $\mathbf S$ is an element of area delimited for the 4-vectors $\mathbf u$ and $\mathbf v$ given by $$S^{\alpha \beta}\equiv ...
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539 views

Defining a Riemannian manifold - made easy?

In the context of GTR spacetime, I'm trying to get the basic idea of a Riemannian manifold clear in my mind. Apologies for the longwindedness. Question 1. Is this a reasonable, simplified summary of ...
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293 views

How is the complexification of spacetime justified?

As always the caveat is that I am a mathematician with very little knowledge of physics. I've started my quest for knowledge in this field, but am very very far from having a good grasp. General ...
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607 views

What bends fabric of space-time?

I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it? Other energy sources, forces ...
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172 views

How would be tv reception in a spaceship travelling close to speed of light?

My little brother has made me a tough question (specially for a computer science engineer). Imagine that there is a spaceship orbiting earth close at nearly speed of light (say 99%). Someone in earth ...
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543 views

Is the Portal feasible in real life?

Firstly, I assume prior knowledge/experience with the game Portal. Should it be possible that two openings (circles/unidentified-constructions) would work as interchangeable gates? With one opening ...
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291 views

Is spacetime all that exists?

Someone claiming to have studied physics is telling me that spacetime is all that exists and that this fact is the basis of modern physics. When I said matter/energy also exists in its various forms, ...
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1answer
664 views

Does electric charge affect space time fabric?

I am confused with this question. Does electric charge affect the space time fabric? If so, why? Also if electric charge does not affect the space time fabric, how can we interpret the origin of the ...
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Can you use a wormhole to travel through space not time?

I want to know if you could theoretically travel from your house to work via a wormhole but stay in the present day...without changing time. Kind of like teleportation but harnessing the energy of a ...
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Proof that Energy Momentum Tensor of Scalar Field Theory satisfies Weak Energy Condition

It's a question on Sean Carroll's Spacetime and Geometry, where we are supposed to prove that the energy momentum tensor of scalar field theory satisfies Weak Energy Condition (WEC). The energy ...
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Is there an absolute minimum scale to the universe? If so, why?

Based on my rather circumscribed understanding of modern physics, one of the key insights of quantum mechanics over previous scientific theories is the prediction that there exists an absolute limit ...
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is there a metatime required for space-time to change

Space-time is thought to curve and ripple. Is a kind of metatime required in or during which such events take place?
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Is space-time a Kantian concept - just a concept of the working mind? [closed]

Is space time a Kantian concept – that is, just a concept of the mind at work? That is that there is no ‘out there’ – it’s in the ‘mind’? Relativity might work but it certainly requires a stretch of ...
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96 views

If we say the universe is expanding, shouldn't it be expanding relative to something?

I don't understand, if everything in this world is relative to something else, then cannot we essentially say that nothing exists independently? We say that the universe is considered to be the ...
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132 views

Index raising and lowering - how does it work?

In the context of four-dimensional spacetime, how does the metric turn a tangent vector into a gradient, and vice versa? By this I mean that I know the metric can be used to raise and lower indices: ...
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76 views

Are there any restrictions on building the topology of spacetime out of the complement of open balls?

I assume that for a Lorentzian manifold (i.e. with Minkowski signature), the analog of an open ball is the interior of a light cone. My question is motivated by the observation that whereas any point ...
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191 views

Space time a function of itself, objects in it, or both?

Is spacetime a function of itself, objects within it, or both? I am struggling to understand just what is spacetime without objects in it (or theoretical reference points) and thus no frame of ...
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196 views

Negative energy and large-scale spacetime structure

I was reading an essay from Stephen Hawking's on the Space and Time warps and I was trying to make sense on some statements referring to the Casimir effect such as: The energy density of empty ...
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108 views

Is GPS time measuring the proper time on the mean sea level or the GPS station itself?

LeapSecond.com states: Global Positioning System time is the atomic time scale implemented by the atomic clocks in the GPS ground control stations and the GPS satellites themselves. Does GPS ...
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Can a curvature in time (and not space) cause acceleration?

I realize that the curvature of space-time causes acceleration (gravity). Is it possible to have a curvature only of space, or a curvature only of time? If so, would a curvature only of space, or a ...
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84 views

Is the concept of space-time curvature a recursive one? [duplicate]

A way some people explain (or try to explain) how gravity works is using space-time curvature: an object with high mass distorts the surrounding space-time plane like a bowling ball distorts a sheet ...
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85 views

Is force the unique possible relation between particles? [closed]

Is force the unique possible relation between particles? It was requested to further specify my question. The followings paragraphs contain some of my thoughts and confusions. Historical ...
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1answer
178 views

Proper time along path in Minkowski Space

Consider the path $x^\mu(u)$ in Minkowski space; such that: $$t = \frac{a}{c} \sinh(u) , \quad x = a \cosh(u) ,\quad y = 0 ,\quad z = 0 $$ where $a$ is a positive constant and $u$ is a parameter ...
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Restriction of a Lagrangian

I'm wondering if anyone could help me with the following questions. Let $M$ be the Minkowski spacetime, given $f\in C^{\infty}(M) ; f(m)=x^{0}(m)$, with $\{x^{\mu}\}$ being a global Cartesian ...
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995 views

Is time quantized? Is there a fundamental time unit that cannot be divided? [duplicate]

Is the present just a sharp line between the past and the future with no time at all, or is the present a short frozen unit of time? Could time be quantized into a fundamental units? Like Planck ...
3
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1answer
230 views

The most general form of the metric for a homogeneous, isotropic and static space-time

What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
3
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1answer
603 views

Why does the universe exhibit three large-scale spatial dimensions? [duplicate]

Possible Duplicate: Is 3+1 spacetime as privileged as is claimed? Regardless of your favorite theory of how many dimensions the universe has in total, the universe seems to have a deep ...
3
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1answer
125 views

An issue about the compactness and the existence of CTCs

There is a well known fact that a compact spacetime necessarily contains a closed timelike curve (CTC). Proof can be found in several books on GR (e.g. Hawking, Ellis, Proposition 6.4.2), and in ...
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483 views

Problem with convergent geodesics at 2D sphere

There is a chapter on general relativity in the book Spacetime Physics Introduction To Special Relativity by Taylor and Wheeler, which qualitatively explains how attractive gravitational force can be ...
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182 views

How would an observer perceive movement on a train that's travelling near the speed of light?

Person A is on Earth and a train (or whatever you want to imagine) travels past him at near the speed of light. How would person A perceive movement on the ship? If time is slowed on the ship from the ...
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1answer
207 views

Hamiltonians and Lagrangians, Euclidean and Hyperbolic: Are they related?

The Lagrangian of a system is the difference between its kinetic energy $T$ and potential energy $V$, and is relativistically invariant: $L = T - V$ The Hamiltonian of the same system is the sum ...
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60 views

What Would Negative Mass Do To Spacetime?

It's known that positive mass bends space-time to create a curvature. But if something had negative mass what would it do? Make it flat or like a crest?
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1answer
105 views

Is it possible that the universe in its entirety is discrete rather than continuous? [duplicate]

Since electric charge is comprised of discrete units and and mass is formed by discrete units is it possible that space-time itself is discrete as well?
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Why doesn't everything expand when the universe expands? [duplicate]

Everybody has been taught at one point, "oh the universe expands, but that doesn't mean that everything is expanding uniformly, since that means we can't detect the expansion, but only that huge ...