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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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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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 ...
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655 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 ...
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127 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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497 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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195 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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214 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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61 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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111 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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97 views

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 ...
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113 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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248 views

Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
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188 views

Can universal continuity be experimentally falsified?

It is an unresolved question whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Is the universe finite and discrete? How could spacetime become ...
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568 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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308 views

How to distinguish 4D and 3D vectors in handwriting?

Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting. In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
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499 views

Reducing General Relativity to Special Relativity in limiting case

I understand that general relativity is applicable to gravitational fields and special relativity is applicable to case when there is no gravity. But is there a derivation on how to reduce General ...
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731 views

Can Flow of time become still?

According to theory of time dilation, flow of time slows down significantly at the speed of light.Is there any conditions practically or theoretically when flow of time is reduced to zero means it ...
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575 views

Nature of spacetime 4-vector and tangent space?

An entry level confusion about spacetime. I understand that a 4-vector describes a point or event in spacetime. But I've also read (Bertschinger, 1999) that re spacetime "we are discussing tangent ...
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197 views

Is the assumption of space time to be a continuum is just a matter of mathematical taste?

Is the assumption of space time to be a continuum is just a matter of mathematical taste ? Isn't there any physical significance associated with it.
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Does time expand with space? (or contract)

Einstein's big revelation was that time and space are inseparable components of the same fabric. Physical observation tells us that distant galaxies are moving away from us at an accelerated rate, and ...
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223 views

Do we live in an integer dimension?

I have read that there exist non-integer fractal dimensions and the images generated from these dimensions look organic and they seem to provide a new way of describing the world around us, which ...
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Why does string theory require 9 dimensions of space and one dimension of time?

String theorists say that there are many more dimensions out there, but they are too small to be detected. However, I do not understand why there are ten dimensions and not just any other number? ...
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Does space have to be filled with charged particles to carry electromagnetic waves?

I'm a newbie here so have mercy. I'm studying electromagnetic waves. This is the propagation of energy via the vibration of charged particles, as I understand it. A charged particle could be like ...
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108 views

How can space be euclidean when light bends?

I have read people arguing that tridimensional space sections of space time continuum (whatever its number of dimensions) appears to be euclidean from empirical evidence. I cannot reconcile it with my ...
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39 views

Creating a 3-D object from 2-D objects

I'm reading a book, 'Warped Passges' by Lisa Randall. In it she mentions how we can envision higher dimensions by explaning how higher dimension ojects can be created from lower dimension objects. So ...
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114 views

How is time distributed through space?

I was greatly confused when I saw video saying that if two wormholes were separated by time instead of distance, it would allow time travel. My question is what did they mean by this statement? What ...
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Deriving formula for time dilation

Last week in class we derived the formula for time dilation using light clocks and got $$t=\gamma t_0\quad \gamma=\left(1+\left(\frac vc\right)^2\right)^{-1/2}$$ So far so good. However, after class I ...
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138 views

Pseudo-Riemannian Manifolds with multiple temporal dimensions

Consider a Pseudo-Riemannian Manifold with signature $$ (\underbrace{+,\cdots,+}_p,\underbrace{-,\cdots,-}_q) $$ For any positive integers $p$ and $q$. Can this kind of manifold contain closed ...
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299 views

Curvature of Spacetime

I have been exploring for some time both the Special and General Relativity, hoping to glean at least a conceptual grasp of their basic tenets. In reading the book "Gravitation" by Misner, Thorne and ...
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148 views

When it is said that the Higgs field is a scalar, do they mean Lorentz scalar?

We often hear that Higgs boson is a scalar boson, and that Higgs field is a scalar field. I was always thinking that this means "4-scalar". In other words, it is space-time invariant, .i.e. it's ...
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414 views

Planck time & length

Why is Planck time the shortest possible duration ever? It's defined as the duration needed by light to travel Planck's length, but surely, give me any number, I can give you a lower number than that? ...
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202 views

Curved space or curved spacetime?

As I understand it, you can have time + flat space = curved spacetime. So, when one is trying to emphasise that there is a curvature to the space, is it more technically correct to say curved space ...
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865 views

$\pi$ and the Curvature of Space

If one draws a circle on a sphere and measures the ratio of the diameter to the circumference, that value varies depending on the diameter of the circle compared to the diameter of the sphere it is ...
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338 views

What does a closed time-like curve look like?

I want to see a plot of closed time-like curve in $(t,x)$. $t$ - vertical axis $x$ horizontal axis (the usual setting just neglect $y$ and $z$ components of $(t,x,y,z)$). What does it look like?
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404 views

Orientability of spacetime

In many theoretical setups it is implicitly assumed that the underlying manifold (i.e. spacetime) is orientable. Then our analysis depends on this implicit assumption. For example, Stokes' theorem ...
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104 views

If two events separated by a spacetime interval of zero, can they both be said to be happening “now”?

Can the concept of c be validly expressed as "the rate at which an event propagates through space"? There was a television program last year featuring Prof Brian Cox. The presenter asked him "Is it ...
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114 views

Quantum Field Theory with (2,2) metric

Does someone know some reference which treats QFT in a space with the following non-Lorentzian signature: $g_{\mu\nu}=\text{diag}(-1,-1,1,1)$. I'm interested in basic stuff like the shape of the ...
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125 views

If Space is continuous, why can't we go below Planck Length?

I am not talking about any other attributes of particles, vacuum etc ruling out Uncertainty Principle thing. If talking about pure Space (which is continuous, not discrete, cf. e.g. this Phys.SE ...
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146 views

What is the meaning of space-time curvature?

What is the difference between the Space-time curvature and Space curvature?
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149 views

How much faster would a Clock without gravity run?

Pardon the misleading title. It is to my understanding that moving/heavy clocks run slow. The Earth itself is under gravitational influence from many sources, and is moving. Is there a way to know ...
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208 views

Why are black holes special?

A black hole is where it's mass is great enough that light can't escape at a radius above the surface of the mass? I've been told that strange things happen inside the event horizon such as ...
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158 views

Why can certain functions be absorbed into the Schwarzschild metric, while others can't?

Another question about the Schwarzschild solution of General Relativity: In the derivation (shown below) of the Schwarzschild metric from the vacuum Einstein Equation, at the step marked "HERE," we ...
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488 views

Are the principles of space-time homogeneity and Isotropy independent of one another?

Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
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83 views

Is it best to look at light as a particle when trying to understand special relativity?

So my course about special relativity explains time dilation using a moving train, where one sends up (i.e. perpendicular to the direction of movement) a light pulse which gets reflected etc. (a ...
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2k views

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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96 views

How exactly and WHY does matter affect space-time? [closed]

According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) ...
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48 views

The equivalence of two worlds related by T-duality

T-duality in string theory relates a world containing open and closed strings with a D$p$-brane with a compact dimension with radius $R$ with a dual world with a D$(p-1)$-brane with a radius ...
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197 views

Can the compactified dimensions of M-Theory/String Theory become uncurled?

Is it possible for the curled dimensions described in superstring theories to become uncurled and open up. I have read that the big bang could have been the uncurling over 3 dimensions through ...
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Does negative energy density (i.e. weak energy condition violation) create closed timelike curves?

I remember reading something about Stephen Hawking denying the fact you can't make CTC's (Closed Timelike Curves) without weak energy condition violation. If this is true, where do the light cones ...