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 it known what the necessary and sufficient conditions are for the existence of a “3+1 split” (by means of a foliation) of a (Lorentzian) manifold?

When trying to do physics on a more general pseudo-Riemannian manifold we want to require that there is a foliation of this manifold into three-dimensional subspaces. By this I mean we would like to ...
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5answers
3k 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 ...
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Why are objects at rest in motion through spacetime at the speed of light?

I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension ...
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3answers
6k views

Is it possible to stop time? [duplicate]

Assuming the spacetime principle, if the space is modified the time does too. So if the velocity in the space is increase, does the time slow down? What happens if the speed is the speed of light, ...
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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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3answers
489 views

Do objects with mass “suck in” spacetime?

I don't really understand the general theory of relativity (GTR) really deeply, but according to my understanding, the GTR say that gravitation is caused by the curvature of spacetime by objects with ...
7
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2answers
474 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
722 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 ...
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5answers
619 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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3answers
646 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 ...
7
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2answers
249 views

Is a spinor in some sense connected to space?

Spinors transform under the representation of $SL(2,\mathbb{C})$ which is the double cover of the Lorentz group $SO(1,3)$ - or in the non-relativistic case under $SU(2)$, the double cover of $SO(3)$. ...
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Is the universe finite and discrete?

Is the universe finite, both in the sense of being a closed spacetime manifold, as viewed from the macro level, but also in the sense of being fully discrete and finite in all of its intricate quantum ...
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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 ...
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2answers
237 views

How warped spacetime bends trajectories of light and moving objects?

I fail to see why the light follows something like the blue line and not the green line on the attached image. Figure 1 - light bends around warped spacetime Afaik. something similar happens ...
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5answers
977 views

Does (it make sense to say that ) the universe has a center?

I was reading this page: http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers and I found this sentence by Brian Cox: That seems to imply that everything is flying away ...
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5answers
1k views

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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2answers
806 views

Can special relativity distort the relative order in which events occur?

Pretend you are throwing darts at a dart board. You throw dart $d_1$ at time $t_1$. After you throw your first dart, you throw your second dart $d_2$ at time $t_2$. Given that $t_2 > t_1$ in a ...
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7answers
2k views

Surely space-time Curvature does not explain gravity, it just describe its effects?

In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ...
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9answers
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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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2answers
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What does “foliation” mean in the context of a “foliation of spacetime?”

I've seen foliation used in the context of "foliation of spacetime" here and elsewhere in papers and such. Generally defined in reference to a "sequence of spatial hypersurfaces." But I don't know ...
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4answers
209 views

Is light amplitude spacial?

In diagrams I often see light waves depicted as little sine waves that travel through space. And often when describing polarizers, the explainer will angle their hand to show the angle of ...
6
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3answers
721 views

Why do clocks measure arc-length?

Apologies in advance for the long question. My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
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8answers
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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
1k views

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon? If so, can quantum mechanics describe the universe at high energies where there is no ...
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3answers
391 views

Is my grandmother alive for some alien who is located on some place and is moving with some speed?

(I am science fiction writer. I had a goal in my novel to argue that time travel to past will not be available even in future. I asked here how to argue that. I collected answers and analyzed them and ...
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2k views

What does it mean for objects to follow the curvature of space?

In science documentaries that touch on general relativity, it is often said that gravitational pull isn't an actual a pull (as described by classical physics), but rather one body travelling in a ...
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7answers
270 views

If space is “expanding” in itself - why then is there redshift?

The "kid's" way of understanding the expanding universe is that: "space" is totally "ordinary", and all the galaxies are expanding through it (like an explosion). Of course, that's wrong. The usual ...
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2answers
336 views

What really is Spacetime?

What is a good definition on Space, Time and the most specific topic "Spacetime"? Because someone told me that spacetime is the foundation of the entire universe? And also, Is it possible to create ...
6
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2answers
340 views

Sewing together flat spacetime pieces = flat spacetime?

I'm trying to imagine the geometry "operations" here: Angular deficit and Conical spacetime of cosmic string If we sew flat spacetime pieces together, what is the requirement for the sewing to not ...
6
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3answers
469 views

“Warp-drive” thought experiment

Why wouldn't this "warp-drive" work? Assuming we can build a flywheel that can survive near light speed and have an onboard power storage or beamed energy that can spin it up to that speed and back ...
6
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2answers
166 views

Does expanding space cost energy?

Does the cosmic inflation reduce the energy density (inversely) proportional to the volume, or does the inflation "cost" energy? Is space itself "something" created at the expense of energy?
6
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3answers
677 views

The Big Bang in an infinite universe

If the universe is spatially infinite (and assuming, if it makes a difference, that we don't have eternal inflation), what actually happened 13.7 billion years ago? Was the energy density infinite (or ...
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1answer
234 views

A Game Of The Number Of Space-Time Dimensions

Holger Bech Nielsen, one of the founders of string theory, has apparently just played some sort of game between different potential dimensions for space-time and reached the conclusion that D4 wins in ...
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198 views

Equilibrium for a rope hanging in a Schwarzschild spacetime

Update: Trimok and MBN helped me solve most of my confusion. However, there is still an extra term $-(2/r)T$ in the final result. Brown doesn't write this term, and it seems physically wrong. Update ...
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1answer
179 views

If a fundamental theory exibits e.g. a mirror symmetry, in what sense it the underlying geometry real?

Are the more recently discovered symmetries in string theory such that the theories based on mirroring geometries are absolutely the same from an observable point of view? I have mirror symmetry ...
6
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1answer
145 views

Could dark energy make a large black hole less black?

Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying ...
6
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1answer
616 views

Is there any uncertainty between mass and proper length or time?

I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
6
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1answer
465 views

Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?

The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
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5answers
2k views

What is the extent of the universe?

Is there any realistic, understandable, provable (even in some extent) explanation/model for the extent of the universe? What is its shape? and Why? I mean physical explanations not philosophical ...
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4answers
10k views

If gravity is a bend in Space-time then what is magnetism?

Einstein postulated that gravity bends the geometry of space-time then what does magnetism do in to the geometry of space-time, or is there even a correlation between space-time geometry and ...
5
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1answer
694 views

Gravity is curved geometry: A fact of nature or model-dependent interpretation?

We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by ...
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2answers
2k views

Is my interpretation of how a gravitational wave is formed correct?

I'm sure many here are familiar with the following image showing the 2D representation of how the fabric of spacetime is warped by the presence of mass:- Can this fabric be interpreted as an ...
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4answers
2k views

Does a moving object curve space-time as its velocity increases?

We always hear how gravity bends space-time; why shouldn't velocity? Consider a spaceship traveling through space at a reasonable fraction of the speed of light. If this spaceship, according to ...
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717 views

How to prove that we are living in a 3D world?

Is there any scientific experiment that can lead us to conclude we live in 3 dimensions without the premise of the conception of limited dimensions? Thank you all who helped in the improvement of ...
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4answers
2k views

Measuring the speed of light and defining the metre - absolute or relative?

If the metre is now defined as the distance light travels in vacuum in 1⁄299,792,458th of a second and the speed of light is accepted to be ...
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5answers
635 views

What distinguishes time from space in Quantum Field Theory?

Consider the following expression for a general QFT action: $$ S ~=~ \int_0^t\mathrm dt~L ~=~\int_0^t\mathrm dt\int_\mathbb {R^3}\mathrm d^3x~\mathcal L ~=~\int\mathrm d^4x~\mathcal L.$$ Here we ...
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4answers
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Expansion of the Universe, will light from some galaxies never reach us?

Is it true that the light from some galaxies will never reach us? The explanation for that is that the Universe expanding faster than the speed of light. But, if the speed of light is constant in ...
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4answers
2k views

ALL “forces” as manifestations of properties of space-time

I apologize if this seems like a quack question, but I need some insights by those who know much more than me in Physics. Anyway, the gravitational "force" (not really a force) is a manifestation of ...
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2answers
773 views

Why is time special?

In Special Relativity, the spacetime interval between two events is $s^2 = -(c{\Delta}t)^2+({\Delta}x)^2+({\Delta}y)^2+({\Delta}z)^2$ giving the Minkowski metric $\eta_{\mu\nu}=\text{diag}(-1, 1, 1, ...
5
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2answers
332 views

Is the assumption that space-time has to be a continuum just a matter of mathematical taste?

Is the assumption that space-time has to be a continuum just a matter of mathematical taste? Isn't there any physical significance associated with it?