# Tag Info

### What's the relevance of geometric rigidity/flexibility to physics?

Well, rigid structures (such as e.g. affine manifolds; think SR) and flexible structures (such as e.g. differential manifolds; think GR) both appear in physics. Canonical transformations on a ...
• 207k

### Question on special relativity

With some algebra, we can see eq. 1 and 2 are equivalent, \begin{align} &c\Delta t - \sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2} = 0 \;\;\;\; (1) \\ \Rightarrow\;\;\; &c\Delta t = \sqrt{(\...
• 1,910
Accepted

### is $LT$ a Lorentz invariant?

Consulting any text-book on special relativity, you will find the well-known fact that the four-dimensional volume element $d^4x = c \, dt \, dx \, dy \, dz$ is a Lorentz invariant as a consequence of ...
• 6,779

### Wormholes in general relativity

Yes, there's a long history of them, beginning with the original Einstein-Rosen bridge and the maximally extended Schwarzschild metric (white hole / black hole). Problems with this original "...
• 400
Accepted

### Wormholes in general relativity

There are solutions to the Einstein Field equations that describe a wormhole (i.e. a black hole connected to a white hole). But there is no evidence that these objects actually exist.
• 1,252

### Question on special relativity

No, there is no way to get a satisfactory theory using \tag1(c\Delta t)-\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}=(c\Delta t^\prime)-\sqrt{(\Delta x^\prime)^2+(\Delta y^\prime)^2+(\Delta z^\...

### Looking for papers that claim that spacetime is emergent

An influential modern classic is the essay Building up spacetime with quantum entanglement by Mark Van Raamsdonk. This is a good starting point to understand the mainstream of thought in this ...
1 vote
Accepted

### Spacetime coordinates 4-dimensional vs curvature of space time?

There is a difference, although it is a rather subtle one. Each point in spacetime (which we call an event) has a unique set of four spacetime co-ordinates. However, the values of those co-ordinates ...
• 56.8k
1 vote

### Spacetime coordinates 4-dimensional vs curvature of space time?

There is no difference. 4D spacetime coordinates are coming from that we see 3 space dimensions and 1 time dimensions. General relativity describes gravitation by that even this 4D spacetime is curved....
• 8,257
1 vote

### Is it possible that prior to the Big Bang, space and time were separate and were joined as a result of the Big Bang?

In classical and non-relativistic mechanics time is treated seperately from space. With the advent of relativity space and time are joined into spacetime. Both in special and general relativity it is ...
• 5,020
1 vote

### Boundary conditions on transition maps on general relativity

There's nothing fancy going on with transition maps. What a mathematician means by a "transition map", in the setting of general relativity, is nothing more or less than a coordinate change ...
• 291
1 vote

### Question on special relativity

Using $\Delta$anything is going to increase confusion. Relativity is about measuring the same events in different coordinates. So for light propagating a distance $L$, you have 2 events: Emission (Tx):...
• 35.9k
1 vote

### Question on spatiotemporal dimensionality about the contradictions of time being a dimension

There's a lot of misconceptions here. I will try to clear them all up one by one, but first we should review what a dimension is in the mathematical context of analytic geometry. A dimension in this ...
• 1,896

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