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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1answer
49 views
Relationship between lightlike and spatial compactification
The compactification of a spatial dimension, say $x^1$ given by the identification $x \sim x^1 + 2\pi R$ is said to be related to the lightlike compactification
$$
\left(
\begin{array}{c}
x^0 ...
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2answers
72 views
What is the smallest increment of space and the smallest increment of time? [closed]
I believe that every point in space is a surface point. And if it was possible to break through or tear a point in space, it will create a black hole. I believe that's why a black hole can exist ...
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1answer
74 views
What does a point in space mean? What we humans think a point in space is in scientific term? (a broader picture)
I am a first year and general student. I Am just curious about the vacuum or space.
I just don't get what actually space is.
Well, I know our scientists are still working on it but still I just want ...
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1answer
69 views
How energy curves spacetime?
We know through General Relativity (GR) that matter curves spacetime (ST) like a "ball curves a trampoline" but then how energy curves spacetime? Is it just like matter curvature of ST?
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1answer
81 views
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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0answers
39 views
What about continuity of Space and possible discreteness of Time? [duplicate]
Is time continuous or discrete? Is even this question a valid question? If you say, it all depends on resolution then assume the best possible resolution achievable. If it is discrete, then what about ...
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0answers
52 views
Can we find a new spatial dimension in our space?
A 3d object looks like a 1d object when inspected from a large distance (the length of the object is larger than the width), looks like a 2d object when we come closer, and looks like a 3d object when ...
2
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1answer
59 views
Planck length implies lattice structure of space? [duplicate]
There is known to be a lower limit on space, which can be derived from the Planck units. It can describe the minimum distance resolvable between two points; but what then would the structure of space ...
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1answer
60 views
Time relative to pressure? [closed]
We all know the effects of speed on time, and we have a formula for that, but I have a hunch, that time also is relative to pressure, and that by increasing the pressure on matter, in fact time will ...
1
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2answers
139 views
In which direction do gravitons travel? Do they originate from mass or are they collected by masses?
This is a kind of silly question, that mostly goes unanswered: are gravitons detatched from the objects they act on, like photons in free space.
Maybe gravity or gravitons are collected by mass ...
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0answers
67 views
Can universe be a closed manifold?
I had a question at MSE which gave a rise to another question.
Maxwell equations can be written in form $$d\star F = J$$
Then by Stokes theorem we have
$$ \int_U J = \int_U d \star F = ...
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1answer
55 views
Is the universe we know just shaped due to time? [closed]
Call me a daydreamer, but I could not stop myself for asking this question.
I was idle when something ticked me and struck my head. I was thinking about universe, speed of light, and how time works. ...
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4answers
564 views
Is space “real”, or is it some sort of accepted postulate?
sorry for this very naive (layman) question.
What is space?
It seems to be every where in the equations of physics (as some sort of postulate or hidden hypothesis). We also have a direct experience ...
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1answer
48 views
Gravitational field strength and Horizon in Rindler coordinates
I came across the following statements in 't Hooft's black holes notes, but not being able to justify them.
The metric in the Rindler coordinates $x=\tilde{x}, y=\tilde{y}, z= \rho \cosh{\tau}, t= ...
3
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2answers
74 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 ...
1
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2answers
72 views
What is a geometrical object?
From the Wikipedia link for Geometry:
Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position ...
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0answers
39 views
Wick rotation and relativity
CMIIW, but as I understand it, Wick rotation replaces the Minkowski basis (t,x,y,z) with the Euclidean basis (it,x,y,z). Suppose that $t_2=t_1 cosh \beta+x_1 sinh \beta$ and $x_2=t_1 sinh \beta+x_1 ...
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1answer
80 views
How many dimensions are there in total? [duplicate]
I happened to get my hands on a string theory book where its been said that the universe's fundamental particle i.e. the string, takes about ten dimensions for specifying itself under symmetry. What ...
1
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1answer
170 views
Is time quantized? Is there a fundamental time unit that cannot be divided? [duplicate]
Is the present just a sharp line between the past and the future with no time at all, or is the present a short frozen unit of time?
Could time be quantized into a fundamental units? Like Planck ...
3
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1answer
49 views
Are there any restrictions on building the topology of spacetime out of the complement of open balls?
I assume that for a Lorentzian manifold (i.e. with Minkowski signature), the analog of an open ball is the interior of a light cone. My question is motivated by the observation that whereas any point ...
0
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0answers
61 views
Does a point exist in the real world [duplicate]
In mathematics we can have an infinite number of points between two integers.
This is really circular logic since a point is defined as infinitely small.
Does a point exist anywhere in the physical ...
5
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2answers
76 views
Which causal structures are absent from any “nice” patch of Minkowski space?
Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?,
where "causal separation structure" ($s$) should be ...
3
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1answer
79 views
Can the vanishing of the Riemann tensor be determined from causal relations?
Given a Lorentzian manifold and metric tensor, "$( M, g )$", the corresponding causal relations between its elements (events) may be derived; i.e. for every pair (in general) of distinct events in set ...
2
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1answer
52 views
Synchronization of clocks and observations of time in special relativity
I have thought up a situation that I cannot understand with my understanding of special relativity. I don't know general relativity, but as the situation doesn't involve gravity or acceleration, I'm ...
6
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2answers
177 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 ...
1
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2answers
92 views
Points in Spacetime
Assume there are two points in spacetime $a=(t,x,y,z)$ and $a'=(t',x',y',z')$. Let's say that the first one is in the origin of spacetime i.e. $a=(0,0,0,0)$. The point $a'$ has two possibilities
...
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4answers
129 views
How can the big bang occur mathematically?
As we know time began with the big bang. Before that there was no time, no laws, nothing. Mathematically how can an event take place when no time passes by? How did the big bang took place when there ...
3
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3answers
165 views
How does relativity explain gravity, without assuming gravity [duplicate]
I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first ...
4
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3answers
88 views
Does the expansion of the universe soon after the Big Bang affect the amount of time that light takes to reach us?
If faster than light travel is impossible, how is it that light emitted from matter so close together in the time soon after the Big Bang is only now just reaching us? I would assume that there would ...
1
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1answer
89 views
Killing vector argument gone awry?
What has gone wrong with this argument?!
The original question
A space-time such that $$ds^2=-dt^2+t^2dx^2$$
has Killing vectors $(0,1),(-\exp(x),\frac{\exp(x)}{t}), ...
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1answer
58 views
Does the actual curvature of spacetime hold energy?
My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
3
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2answers
194 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 ...
7
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1answer
162 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 ...
0
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0answers
34 views
metric extension outside the light cone
Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past ...
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2answers
75 views
Limit on velocity in Minkowski Spacetime geometry
Let A be a rocket moving with velocity v.
Then the slope of its worldline in a spacetime diagram is given by c/v.
Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90.
Does ...
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2answers
143 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
votes
1answer
98 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 (-+++) ...
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1answer
79 views
Spacetime and Timelike Intervals
The difference between a “timelike” spacetime interval and a “spacelike” spacetime interval can be understood in the following way: If the spacetime interval between two events is timelike, there ...
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0answers
41 views
Has Time in the Universe been found to be Discrete or Continuous? [duplicate]
I have a question, has the Universe been found to come in Discrete Quantum, like Quantum Physics or is it Continuous in Nature?
I was wondering if time was like a Continuum, like the fluid in a soft ...
1
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0answers
73 views
Do we expect that the universe is simply-connected? [duplicate]
I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe cannot be simply-connected, since the ...
3
votes
1answer
158 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
83 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 ...
1
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0answers
67 views
What were Feynman's objection(s) to a cubic lattice universe? [duplicate]
In this video of Feynman discussing the scientific method, starting at around eight minutes and 30 seconds, Feynman describes the proposition that space consists of a cubic lattice of points (as ...
6
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1answer
171 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 ...
0
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1answer
147 views
Multiverse theory and infinite individuals
I read an article about possibility of existence of multiverse and came up with a conflicting view with one of the sentences written in the article which goes as follows:
"If space-time goes on ...
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1answer
197 views
Did space and time exist before the Big Bang? [duplicate]
I accept the Big Bang theory. What I can't understand is how there can be a where or when to the Big Bang if space time did not exist prior to it. Did space and time exist prior to the Big Bang?
3
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1answer
147 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
3answers
139 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 ...
1
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0answers
53 views
When is spacetime homogenous and isotropic?
When is spacetime homogenous and isotropic?
For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric
$$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + ...
1
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0answers
58 views
Naked singularity and null coordinates
I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
