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jk22
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Since the metric is euclidean in coordinates ##(ict,x)## it can be drawn in a plane, but if the metric is ##diag(1,-1)##, can both axis still be drawn in a plane ?
vanhees71 said:I strongly discourage the use of the ##\mathrm{i} c t## convention in relativity. It's maybe a bit inconvenient first to introduce the Minkowski-pseudometric coefficients ##\eta_{\mu \nu}## and to deal with upper and lower indices for vector and tensor components, but it pays off. At the end at latest when it comes to general relativity the ##\mathrm{i} c t## convention doesn't make any sense anymore!
jk22 said:i comes too from taking squares when formulating the invariance of speed of light ##′x=ct\Leftrightarrow x'=A(x,t) ct'##, whereas taking plus minus for the A function treats cases separately and has free parameters (unwanted ?), but squaring leads to bilinear forms but also implies the price to pay as a singularity (BTW why is it not called the speed of light catastrophe ?) and imaginary numbers.
I would say it is sufficient to start writing down SR in general coordinate systems to make it no longer work.PeterDonis said:As @vanhees71 points out, once you move to general relativity, the ict convention no longer works
It might be there, but it is definitely in MTW... not a full chapter, just a few short paragraphs in a named section.pervect said:I think it was Taylor, in "Space-time physics" who has a chapter heading entitled "Farewell to ict".
jk22 said:Since the metric is euclidean in coordinates (ict,x)(ict,x)(ict,x) it can be drawn in a plane, but if the metric is diag(1,−1)diag(1,−1)diag(1,-1), can both axis still be drawn in a plane ?
A Minkowski diagram is a graphical representation of special relativity, where the horizontal axis represents space and the vertical axis represents time.
The time's imaginary unit, denoted by i, is a mathematical concept used to represent the imaginary part of time in a Minkowski diagram. It is used to simplify calculations and visualize complex numbers in the diagram.
The inclusion of the time's imaginary unit in a Minkowski diagram allows for a more accurate representation of the relationship between space and time in special relativity. It also simplifies calculations and makes it easier to visualize complex numbers.
In special relativity, the time's imaginary unit is used to represent the imaginary part of time, which is necessary to account for the effects of time dilation and length contraction. It is also used to calculate spacetime intervals and Lorentz transformations.
Yes, there are alternative representations of time in a Minkowski diagram, such as using a different imaginary unit or omitting the imaginary part altogether. However, using the time's imaginary unit is the most commonly accepted and widely used method in the scientific community.