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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34 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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2answers
67 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 ...
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0answers
56 views
Im a layman trying to understand the 4th and 5th dimension someone please explain! [closed]
If in the 3rd dimension we have height, length and width what axis (axes) could we possibly add? From my limited research I have read that the 4th isn't time but rather another spatial dimension. My ...
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1answer
143 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 ...
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2answers
56 views
Mental and mathematical representation of the space-time concept [closed]
How can I imagine the space-time in my mind? And also is there a mathematical representation of it, and of its modifications? Can the Einstein tensor be the answer under this aspect?
$$
G_{\mu \nu} = ...
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1answer
43 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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0answers
58 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 ...
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2answers
72 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 ...
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1answer
69 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
47 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 ...
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2answers
164 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 ...
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2answers
87 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
122 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
158 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 ...
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3answers
75 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 ...
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1answer
88 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
47 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 ...
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2answers
182 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 ...
6
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1answer
155 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 ...
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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
69 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
103 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
91 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
76 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
39 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 ...
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0answers
69 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 ...
2
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1answer
129 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
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3answers
75 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 ...
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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
165 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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1answer
136 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
147 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?
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1answer
143 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
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3answers
132 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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0answers
49 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} + ...
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0answers
52 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 ...
2
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0answers
65 views
Naked singularity and extendable geodesics [duplicate]
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 ...
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0answers
45 views
When spacetime expands to the point where galaxy clusters are not observable, will there by any interaction?
It's my understanding that in a few billion years, clusters of galaxies won't be able to directly observe one another due to the expansion of spacetime overcoming gravity between those clusters. ...
2
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1answer
74 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 ...
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4answers
208 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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1answer
91 views
Space time curvature real or theoretical (mathematical)?
Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could ...
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2answers
115 views
Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass? [duplicate]
The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't ...
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3answers
142 views
About gravity through space time curvature
Is it possible to produce virtual gravity? I mean gravity without the help of mass by curving spacetime with other effects like fast rotating objects?
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1answer
72 views
Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?
In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime.
If I ...
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2answers
83 views
If inherent randomness exist in quantum mechanics, what then of eternalism implied by relativity?
I am nothing but a curious layman so don't go too technical on me.
First of all, I am well aware that a lot of people consider the question of determinism vs indeterminism to be unsolved and others ...
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2answers
133 views
If the universe is 3D, how is space-time like a “fabric”? [duplicate]
I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures ...
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2answers
154 views
How do Doppler Effect and Time Dilation differ?
Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B).
Edit: I am adding a relativistic ...
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2answers
139 views
How to find a curvature of the space-time by having $g^{\alpha \beta}$ in the following case without cumbersome calculations?
The metric tensor for Fock-Lorentz space-time,
$$
\mathbf r_{||}{'} = \frac{\gamma (u)(\mathbf r_{||} - \mathbf u t)}{\lambda \gamma (u) (\mathbf u \cdot \mathbf r) + \lambda c^{2} (1 - \gamma (u))t + ...
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0answers
164 views
Spacetime around a Black Hole
If we consider the sun, then space-time is curve around it. My question is that what is the kind of curvature of space and time around the black hole. Is that space and time more curved around the ...
3
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1answer
98 views
How much time has passed for Voyager I since it left the Earth, 34 years ago?
34 years have passed since Voyager I took off and it's just crossing the solar system, being approximately at 16.4 light-hours away. How much time have passed for itself, though?
