Questions tagged [spacetime]
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 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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Confusion regarding bundle structure of Galilean spacetime in Penrose's The Road to Reality
I am reading Roger Penrose's The Road to Reality. In section 17.3, I encounter the following passage. To give a context, Penrose was explaining that even though an Aristotelian spacetime can be ...
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Are there null geodesics inside null infinity?
Looking at a Penrose diagram for Minkowski space, you would think that you could draw a null geodesic running from $i^0$, along $\mathscr{I}^+$, and ending up on $i^+$. In fact there would be many ...
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Why was pseudo-Euclidean geometry not enough for general relativity?
How would you explain to someone the change that Einstein needed in geometry for his new ideas about gravity and spacetime, what did he seek but could not be described by pseudo-Euclidean geometry?
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Does the derivation of the Lorentz transformation depend on space having at least two spatial dimensions?
Eisberg's 'Fundamentals of Modern Physics' derives the space contraction formula from a mirror experiment in which A reflects a light beam in a direction perpendicular to the motion of B, both ...
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Can an "absolute" frame of reference be determined by measuring the compression of light?
General relativity tells us that there is no absolute frame of reference (actually, it tells us that all frames are relative, which is close but not the same as there is no absolute frame).
Special ...
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Does kinetic energy of an object curve spacetime? [duplicate]
Based on general relativity mass and energy distribution curves spacetime. Thus, if an object with 1kg rest mass moves with constant speed and has a speed very close to speed of light, then it has an ...
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Common properties of all spacetime metrics
I understand that spacetime (in GR) has many possible metrics, all of which are calculated via the Einstein Field Equations. The Minkowski metric (from SR) is one solution of the EFEs; it is a ...
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Difference between coordinate time and proper time in general relativity
I was watching a video on relativity on YouTube that talked about the difference between coordinate time $t$ and proper time $\tau$ and I have a couple of questions.
As I understand it, the video said ...
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Is there any proof of why a charge is scalar?
I tried to prove it by contradiction as, if it was a vector then the isotropic space property that nature currently has now would not hold; But that proof eventually broke down. So, I was wondering if ...
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Closed timelike curves in the Kerr metric
I just read in Landau-Lifshitz that the Kerr metric admits closed timelike curves in the region $r \in (0, r_{hor})$ where $r_{hor}$ is the event-horizon ( I am talking about the case $|M|>|a|$ (...
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Why is spatial conformal infinity a point
One property of spatial infinity is that all spacelike geodesics end at it. Since spacelike geodesics can have different directions, I do not understand why spatial infinity is a point. It looks more ...
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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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How are spatial coordinate systems in physics defined?
Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
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What does this spacetime diagram mean?
I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about ...
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Proper time invariance and conformal symmetry group
Special relativity is based on the fact that the proper time is always the same in any inertial frame:
$$ds^2=(cdt)^2-dx^2=ds'^2=(cdt')^2 -dx'^2 $$
If I understand it correctly this is based on the ...
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How do we know that the space metric is expanding as opposed to objects moving relative to one another?
So we observe that the Universe is expanding. We observe galaxies moving away from us and the speed/red-shift is greater for galaxies that are further away.
How do we know that this observation is ...
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Intuitive explanation for the Lorentz transformation for time
I've recently started learning SR, and while the Lorentz transformation for space is pretty obvious, just the Galilean transformation combined with space contraction, I can't figure out the ...
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When is the value of spacetime interval $ds$ negative?
The spacetime interval in special relativity, $ds$, is defined as
$$
ds^2=c^2dt^2-dx^2-dy^2-dz^2
$$
with the $(+,-,-,-)$ Minkowski sign convention. The value of $ds^2$ can be positive, zero, or ...
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Is the Big Bang a naked spacelike singularity?
While reading some answers on similar topics, I was wondering about the nature of the Big Bang singularity in the standard cosmological model. I know it's a spacelike singularity that have a ...
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How can mass bend spacetime, if there's nothing to bend?
The Michelson-Morley experiment proved there was no aether, nothing that light moves through in space. Yet in GR, mass bends spacetime so that light travels in arcs around large masses. How can ...
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Is there such thing as curvature uncertainty?
I was trying to reason about how could quantum mechanics be related to the space-time curvature, and I have ended up in an apparent contradiction, which puzzles me. It would be nice if someone could ...
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Why are orbits around black holes stable?
Black hole theory involves space (or space-time), itself, being sucked into the black-hole, with the event horizon marking the point at which space/space-time is moving faster than the speed of light. ...
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The metric of world lines in Newtonian and Galilean spacetimes
Consider a flat Newtonian or a flat Galilean 2+1 spacetime. So, mainly a flat 2D Euclidean space, evolving over time, where each time-slice is connected with the next one by a world line. Like in this ...
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String Theory, understanding Einstein's Field Equations
Let me give some insight. I was researching about how Einstein-Field Equations arise from String Theory, and I came upon this post. It explains, mathematically, how you can arrive at the corrected ...
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Can we describe all forces as a curvature in space-time?
If we have Einstein's field equation
$$R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R=kT_{\mu\nu}$$
could we generalize it to
$$R_{\mu\nu} - \frac{1}{2}m_{\mu\nu}R=kS_{\mu\nu}$$
where $S_{\mu\nu}$ is the source ...
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Sewing together flat spacetime pieces = flat spacetime?
I'm trying to imagine the geometry "operations" here:
Angular deficit
and
Curvature of Conical spacetime
If we sew flat spacetime pieces together, what is the requirement for the sewing to not create ...
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Can one define a flow of spacetime?
One often reads things like, 'At the event horizon, the flow of spacetime exceeds the local speed of light.' But is this actually correct? Can you mathematically define some sort of spacetime flow ...
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Isotopy class of spacetime
We know that spacetime is an orientable manifold:
Can spacetime be non-orientable?
But supposing that spacetime is an orientable closed 2D surface, one might envision a variety of non-equivalent ...
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Conflicting definitions of reference frames in general relativity
I'm having trouble understanding what constitutes a reference frame in general relativity as there seem to be several contradictory definitions.
It is my understanding that, in special relativity, ...
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Einstein's initial clue that spacetime is curved [closed]
I did General Relatively years ago at Uni. I have revised a lot of the maths demo Dirac''s book. It is incredible the leap in thought to noting from the Bianchi identities that the curvature term's on ...
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Is light affected by space warping or time warping?
Gravity, according to the General Theory of Relativity, is simply the curvature of space-time. Objects in the universe move through space-time in geodesic paths. Also, the most interesting part is ...
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Why do light and masses (like planets) follow different paths through curved space?
It is often said that planets follow a "straight line" through space time. The argument goes that a star like our sun curves space, and the planets follow this path. The argument is also made that ...
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Physically what does warping (of space-time) mean?
So there's general relativity and Einstein's field equations that tell us "mass(or equivalently energy) warps space-time, and the warping tells mass how to move", but I'm still having trouble ...
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Regarding the possibility of Closed Timelike Curves
I've been looking a lot at Closed Timelike Curves, and how if a theory allows for these curves it doesn't respect causality. I understand that about the curves themselves (Grandfather Paradox), but ...
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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 (...
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Are there any Alcubierre Style metrics for sub-luminal speed warp drives?
In most literature I have found, research into the Alcubierre Metric, and Warp Drives seems to be highly focused on the plausibility of superluminal travel.
Today I was thinking to myself that maybe ...
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Can gravity be better described as buoyancy in spacetime than a pulling force?
Lately I've been contemplating this analogy to better explain the phenomena we call gravity to my children. Since I'm not a physicist or a mathematician, I'd like some input on the validity of my ...
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Is all energy quantised?
I'm wondering if all energy is quantized?
Can a particle with kinetic energy have any value of kinetic energy or is kinetic energy also quantized?
My reason for asking this is that if a particle is ...
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When is a circle not a circle?
Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle.
Now imagine the same ...
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"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 ...
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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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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. ...
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Spacetime has an infinite number of choices for differentiability. Coincidence?
Spacetime can be modelled using a four-dimensional topological manifold. Say we denote the manifold using $(M, \mathcal{O})$ where $\dim M =d$. The structure $(M,\mathcal{O})$ is not sufficient for ...
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Will an eventual discreteness of spacetime have consequences in the light of Noether's theorem?
No doubt Noether's theorem holds for the symmetry of translations in space and time. But what if we zoom in on very small lengths and times, and spacetime maybe becomes discrete? Will this have ...
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Why is time-evolution unitary (the sequel)?
One foundational postulate of QM is that a closed physical system at one instant of time, say $t$, is completely described by a wavefunction $\psi \in S^1\subset H$ (where $H$ is a Hilbert space and $...
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Electromagnetic radiation flux through null infinity
I encountered a problematic statement about electromagnetic radiation and I would be grateful if someone could shed some light on it.
The situation is the following:
Flat Minkowski space in 4D, with ...
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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 ...
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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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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 in ...
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