# All Questions

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### Lorentz Factor from Minkowski's Original Paper 'Space and Time'

Consider the following figure: Minkowski, in his paper 'Space and Time', derives the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ from considerations of this figure. He ...
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### Lorentz-transformation

I don't understand how to derive the matrix representing the Lorentz-transformation given two systems S and S': $$x' = \Lambda x$$ these transformations do not leave the differences $\Delta x^\mu$ ...
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### Spacelike and timelike intervals confusion

I'm confused about this, specifically the spacetime interval. A timelike interval is one in which 2 events can be related to each other in a given reference frame within its light cone, that is, it ...
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### Paradox are all 4D distances zero?

The 4 dimension distance from the origin of a point is $\sqrt{x^2+y^2+z^2-t^2}$. Which means the 4 dimensional distance on the light-cone is zero. Take a point A and a point B in the future at ...
179 views

### Invariance of the relativistic interval

Imagine we have two events, $E_1, E_2$ in the coordinate systems $K, K'$ (with coordinates $(x,y,z,t),\ (x',y',z',t')$), whilst $K'$ ist moving with the speed $\vec v$ in regard to $K$. From the ...
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### Minimum separation from the spacetime interval

I've been working through invariant spacetime interval questions recently, and I came across a question in my lecture notes where; $$\Delta s^2=\Delta x^2 -(c\Delta t)^2 > 0$$ Now it is clear to ...
192 views

### The derivation of the Lorentz transformation: addition of distances

In the derivation of the Lorentz transformation, one has a reference frame, $S$, at rest and another, $S'$, moving away at constant speed $v$. At time $t$ there is an event at a point $x$ in $S$. The ...
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### Invariance of spacetime interval in special relativity: linearity

I'm trying to understand which assumption are necessary to prove the invariance of the spacetime interval $$\Delta s^2=c^2\Delta t^2-\Delta \mathbf{x}^2$$ in special relativity. The postulates of ...
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### Clearing up a discrepancy when deriving the Lorentz transformation from length contraction

I've been working through the Feynman Lectures on Physics. I'm currently on lecture 15: The Special Theory of Relativity, specifically 15-5, the section on the deriving the Lorentz Transformation ...
129 views

### Lorentz Velocity Transform With Tensor Notation [closed]

So I'm attempting to prove the Lorentz Velocity tranform: $${v_x}' =\frac{v_x-u}{1-v_xu/c^2}$$ using tensor notation. In this case obviously $\beta = u/c$ and $\gamma=(1-\beta^2)^{-1/2}$. The ...
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### Hyperbolic rotation of spacetime and Lorentz transformation

My question is: What is the motivation behind deriving Lorentz transformation using hyperbolic functions? Is it because the formulation in such way offers a handy mathematical tool? Or is there ...
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### How to derive the spacetime interval from the Lorentz transformation?

I've seen plenty of derivations of the Lorentz transformation from the spacetime interval. Can this process be reversed, to derive the spacetime interval from the Lorentz transformation and the two ...
60 views

### What is the physical significance of locally Minkowskian but not necessarily geodesic coordinates?

Consider an event $P$ in spacetime and a coordinate system $x_\mu$ such that at $P$: $g_{\mu\nu}=\eta_{\mu\nu}$ $g_{\mu\nu,\sigma}=0$, or equivalently the Christoffel symbols vanish at $P$. $x_\mu$ ...
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37 views

### Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
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### Definition of the Lorentz transformations [closed]

Until very recently I believed that the Lorentz transformations were defined as "the transformations that carry one inertial reference frame into another". In Wikipedia's page we find something along ...
620 views

### Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
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### Schutz's geometrical proof that spacetime interval is invariant

I'm trying to understand the proof that spacetime interval is invariant under for any two inertial observers. I know it's easy to arrive at the result using Lorentz transformation but I'm trying to ...
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### How to motivate this approach on Special Relativity?

One of the most common approaches to Special Relativity is that based on the two Einstein's postulates: The laws of Physics are invariant in every inertial reference frame The speed of light ...
901 views

### Spacelike to timelike four vectors

First at all, let me just say that I'm not a Physicist, I study mathematics. So, I have this question. If you have a spacelike four vector, is there any transformation that could change it to be a ...
3k views

### Are Lorentz transformations linear transformations? [duplicate]

My textbook says that Lorentz transformations are linear transformations and present them as matrices. Lorentz transformations relate different coordinate systems with each other. It seems that ...
1k views

### Minkowski metric — why does it follow from the constancy of the speed of light? [duplicate]

In all the sources I’ve been able to find, the Minkowski metric appears ad hoc, or is defined analogously to the euclidean metric. I’d love to see an argument why this metric (time coordinates ...
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### Homogeneity of space implies linearity of Lorentz transformations

In the derivation of Lorentz transformations, the Wikipedia article mentions a couple of times that the linearity comes from the homogeneity of space. I am looking for a thorough explanation on this.
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### Deriving the Lorentz Transformation

I have been trying to understand a more or less geometric derivation of the Lorentz transformation, and I'm getting stuck at one spot. The wikipedia article for the Lorentz transformation for frames ...