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.
71
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7answers
25k views
If you view the Earth from far enough away can you observe its past?
From my understanding of light, you are always looking into the past based on how much time it takes the light to reach you from what you are observing.
For example when you see a star burn out, if ...
31
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5answers
2k views
Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?
Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges.
Gauss's law implies that a the total flux through a ...
29
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6answers
1k views
What is known about the topological structure of spacetime?
General relativity says that spacetime is a Lorentzian 4-manifold $M$ whose metric satisfies Einstein's field equations. I have two questions:
What topological restrictions do Einstein's equations ...
22
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5answers
1k views
Is 3+1 spacetime as privileged as is claimed?
I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. ...
17
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7answers
737 views
What grounds the difference between space and time?
We experience space and time very differently. From the point of view of physics, what fundamentally grounds this difference?
Dimensionality (the fact that there are three spatial dimensions but only ...
15
votes
4answers
1k views
Einstein's postulates <==> Minkowski space. (In layman's terms)
What's the cleanest/quickest way to go between Einstein's postulates [1] of
Relativity: Physical laws are the same in all inertial reference frames.
Constant speed of light: "... light is always ...
15
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8answers
5k views
How exactly does curved space-time describe the force of gravity?
I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or ...
15
votes
3answers
740 views
What is the length of 1 second in meters
If time is treated as a fourth dimension of spacetime, what is relation between length and time units?
Or in other words, how can I convert time units to length units, for instance seconds to meters?
...
15
votes
7answers
1k views
Does Quantum Mechanics assume space and time are continuous?
I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics?
I can see the question is vague, but this is ...
14
votes
2answers
472 views
Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists?
The following image serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime.
The wikipedia article on spacetime, and the sub-article "The priveleged character of ...
14
votes
1answer
637 views
How does classical GR concept of space-time emerge from string theory?
First, I'll state some background that lead me to the question.
I was thinking about quantization of space-time on and off for a long time but I never really looked into it any deeper (mainly because ...
13
votes
3answers
506 views
Can light exists in $2+1$ or $1+1$ spacetime dimensions?
Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for ...
12
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3answers
104 views
What is meant when it is said that the universe is homogeneous and isotropic?
It is sometimes said that the universe is homogeneous and isotropic. What is meant by each of these descriptions? Are they mutually exclusive, or does one require the other? And what implications rise ...
12
votes
9answers
444 views
How to explain (pedagogically) why there is 4 spacetime dimensions while we see only the 3 spatial dimesions?
I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple ...
12
votes
3answers
1k views
If the universe were compressed into a super massive black hole, how big would it be?
I understand only a little of general relativity, but that's why I'm here! :)
Consider the hypothetical situation of some extra-terrestrial intelligence pushing all the mass in the universe, every ...
11
votes
3answers
549 views
Swimming in Spacetime - apparent conserved quantity violation
My question is about the article Swimming in Spacetime.
My gut reaction on first reading it was "this violates conservation of momentum, doesn't it?". I now realize, however, that this doesn't allow ...
10
votes
3answers
438 views
Space-time in String Theory
I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra ...
10
votes
4answers
342 views
The definition of an inertial reference frame in Einstein's relativity
I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
9
votes
5answers
785 views
Hubble's law and conservation of energy
If all distances are constantly increasing, as Hubble's law say, then lots of potential energies of form ~$\frac{1}{r}$ changes, so how is the total energy of the Universe conserved with Hubble's ...
9
votes
5answers
467 views
Is it possible for one black hole to pull an object out of another black hole?
Suppose we have a spacecraft just inside the event horizon of a black hole, struggling to escape, but slowly receding into it. Another (bigger) black hole expands until its event horizon includes the ...
9
votes
2answers
766 views
Invariant spacetime - distance - Circular Motion
I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor.
My question is, if something travels in a ...
8
votes
2answers
592 views
Can a non-euclidean space be descripted through an euclidean of higher dimension? so why use non-euclidean?
If you draw a big triangle in earth 2D surface you will have an aproximated spherical triangle, this will be a non euclidean geometry.
but from a 3D perspective, for example the same triangle from ...
8
votes
6answers
1k views
Experimental evidence of a fourth spatial dimension?
As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist.
Is there any direct or indirect evidence ...
8
votes
3answers
809 views
Can spacetime be non-orientable?
This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
8
votes
1answer
504 views
Is String Theory formulated in flat or curved spacetime?
String Theory is formulated in 10 or 11 (or 26?) dimensions where it is assumed that all of the space dimensions except for 3 (large) space dimensions and 1 time dimension are a compact manifold with ...
8
votes
2answers
393 views
Is spacetime simply connected?
As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn.
This falls into the ...
8
votes
5answers
1k views
Why is gravitation force always attractive?
Why is the gravitation force always attractive? Is there a way to explain this other than the curvature of space time?
PS: If the simple answer to this question is that mass makes space-time curve ...
8
votes
1answer
86 views
Hamilton operator in absence of causal order?
I hope, this question isn't too broad or vague.
In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a ...
7
votes
7answers
1k views
Why are extra dimensions necessary?
Some theories have more than 4 dimensions of spacetime. But we only observe 4 spacetime dimensions in the real world, cf. e.g. this Phys.SE post.
Why are the theories (e.g. string theory) that ...
7
votes
2answers
1k views
Is reality discrete at the quantum level? (…and what does it imply not only mathematically?)
On a quantum scale the smallest unit is the Planck scale, which is a discrete measure.
There several question that come to mind:
Does that mean that particles can only live in a discrete grid-like ...
7
votes
3answers
479 views
Is anyone studying how the topology of space arises from more fundamental notions?
Stephen Wolfram in his book "A New Kind of Science" touches on a model of space itself based on automata theory. That it, he makes some suggestions about modelling not only the behaviour of matter ...
7
votes
3answers
706 views
Does the curvature of spacetime theory assume gravity?
Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are ...
7
votes
1answer
155 views
Is spacetime flat inside a spherical shell?
In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
7
votes
4answers
348 views
Hamiltonian and the space-time structure
I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian.
Space-time structure dictates the form of ...
7
votes
2answers
2k views
Why does Venus rotate the opposite direction as other planets?
Given: Law of Conservation of Angular Momentum.
Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).
Surface same degree of aging all over.
Theoretical large ...
7
votes
4answers
504 views
Does the “Andromeda Paradox” (Rietdijk–Putnam-Penrose) imply a completely deterministic universe?
Wikipedia article: http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument
Abstract of 1966 Rietdijk paper:
A proof is given that there does not exist an event, that is not already in the past for ...
6
votes
1answer
160 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 ...
6
votes
5answers
358 views
More than one time dimension
We know that space-time dimensions are 3+1 macroscopically, but what if 2+2?
Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two ...
6
votes
1answer
146 views
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 ...
6
votes
1answer
136 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 ...
6
votes
1answer
282 views
Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?
The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
6
votes
2answers
366 views
Some questions regarding $n+m$-dimensional spacetime [duplicate]
Possible Duplicate:
Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists?
The following image:
serves to aid the reader in ...
5
votes
2answers
377 views
What's the difference between space and time?
I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time" but never explain what the difference is between the ...
5
votes
4answers
816 views
Did spacetime start with the Big bang?
Did spacetime start with the Big Bang? I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before ...
5
votes
2answers
399 views
Why do objects follow geodesics in spacetime?
Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation ...
5
votes
2answers
182 views
Do objects with mass “suck in” spacetime?
I don't really understand the general theory of relativity (GTR) really deeply, but according to my understanding, the GTR say that gravitation is caused by the curvature of spacetime by objects with ...
5
votes
4answers
604 views
Alternate layman's metaphors for illustrating curved space-time
The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as ...
5
votes
1answer
329 views
Intuition for multiple temporal dimensions
It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with ...
5
votes
1answer
222 views
What does scalar phi represent in spacetime?
Trying to understand one-forms and vectors via Schutz's A First Course In General Relativity.
His example uses a spacetime diagram, a scalar field phi, a curve (worldline) parametrized using proper ...
5
votes
2answers
252 views
What really is Spacetime?
What is a good definition on Space, Time and the most specific topic "Spacetime"? Because someone told me that spacetime is the foundation of the entire universe?
And also, Is it possible to create ...
