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.
3
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1answer
88 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 ...
3
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1answer
368 views
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 ...
3
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3answers
523 views
How could spacetime become discretised at the Planck scale?
I didn't have much luck getting a response to this question before so I have tried to reword and expand it a little:
In early 2010 I attended this inaugural lecture by string theorist- Prof. ...
3
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2answers
86 views
Are all points in the universe connected?
Is it true that every point in the universe is connected or could be so theoretically? If so how is this mediated?
Is it through the quantum nature of the fabric of space or is it through the ...
3
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1answer
77 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
votes
1answer
97 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 ...
3
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1answer
257 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 ...
3
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1answer
131 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 ...
3
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2answers
84 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 ...
3
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0answers
78 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 ...
2
votes
3answers
235 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 ...
2
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4answers
1k 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 ...
2
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4answers
314 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 ...
2
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3answers
504 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 ...
2
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2answers
176 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.
2
votes
2answers
419 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 ...
2
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3answers
625 views
What are some approaches to discrete space-time used in modern physics?
This thought gave rise to some new questions in my mind.
What are the consequences for:
How would it affect duality i.e. particle, wave property of photons?
How does this statement affect the ...
2
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1answer
400 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 ...
2
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4answers
203 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 ...
2
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3answers
407 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 ...
2
votes
2answers
344 views
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 ...
2
votes
2answers
113 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 ...
2
votes
2answers
124 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 ...
2
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1answer
282 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 ...
2
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3answers
182 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 ...
2
votes
1answer
205 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 ...
2
votes
1answer
334 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 ...
2
votes
1answer
105 views
Questions about angular momentum and 3-dimensional(3D) space?
Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
2
votes
3answers
124 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 ...
2
votes
1answer
71 views
At the smallest level, how do things move?
When we see something moving on a screen it's usually just pixels being turned off at one location and turned on at another. For example:
This would render a dot moving from A to C.
Turn on pixel ...
2
votes
2answers
105 views
Does spacetime have momentum?
In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?
2
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2answers
634 views
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 ...
2
votes
1answer
137 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 ...
2
votes
1answer
206 views
What happens to string theory if spacetime is doomed?
What is expected to happen with string theory, if physics is reformulated according the lines hinted at by the twistor-uprising business discussed in this question and its answers for example and ...
2
votes
2answers
162 views
What's the difference between two Hydrogen atoms?
If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location ...
2
votes
2answers
174 views
What equations do I use to do basic time dilation problems?
I understand the concepts of relativity, but I don't know where to go to set up equations to do any actual calculations. For example, what equations would I use to find out the following:
A ship ...
2
votes
1answer
62 views
Why is that the space-time associated with the Earth is not shrinking?
If we apply the Friedmann Lemaître equation to the Universe, we find a critical density $\rho_c$ : if the actual density $\rho$ is under it, the Universe will continue to expand, if it is higher than ...
2
votes
4answers
339 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 ...
2
votes
1answer
318 views
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 ...
2
votes
1answer
201 views
Spacetime assumptions at OPERA
I would like to know what are the assumptions about the spacetime metric between the neutrinos emiter and detector, I mean, perhaps (just a stab in the dark) could be a mistake to asume the metric of ...
2
votes
3answers
72 views
What is the cause the light is affected by gravity? [duplicate]
I know that photons have no mass and that a photons exist only moving at the speed of light. So what is the cause that a massive astronomical object can bend a ray of light?
I have two thoughts, but I ...
2
votes
0answers
48 views
Naked singularity and extendable geodesics
I'm currently trying to understand the notion of a naked singularity. After consulting books by Wald and Choquet-Bruhat, it seems that for a naked singularity one must have that the causal curves can ...
2
votes
2answers
120 views
Does gravitational redshift imply gravitation time dilation?
The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in ...
2
votes
0answers
75 views
Car parking special-relavity puzzle
Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution?
Let's suppose a car is going to park to a garage and the garage is ...
2
votes
1answer
164 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 ...
2
votes
2answers
190 views
Did the universe always have 4 space time dimensions?
Is the dimensionality of spacetime in all usual models constant?
2
votes
3answers
173 views
In a very small static universe with only a particle, does it make sense to talk about time?
I am sorry if this question is silly; it′s just one of those things I wished I asked before leaving university.
If there were a static universe only as big as the size of two particles, say ...
2
votes
1answer
243 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 ...
2
votes
0answers
279 views
de Sitter and anti de Sitter metric
Is the following correct for the distance $d$ from the origin $(0,0)$ to point $(t,x)$ in the 2-dimensional
de-Sitter and anti de-Sitter spaces? Here, $t$ is time and the distance may be called the ...
2
votes
0answers
91 views
Does Spacetime have a “This Side Up” arrow? [duplicate]
Possible Duplicate:
Does the curvature of spacetime theory assume gravity?
Forgive my naivete as I am not schooled in Physics or Mathematics.
I was watching NOVA's "The Fabric of the ...
