What is the space-time interval?
To describe it, mathematically, and not semantically,
because it may be an abstract construction requiring a complex number,
we use the formula ds²=dl²-dt².
That doesn't make the "thing" much clearer.
We can then set ds²=dl²+i²dt²
But that doesn't make things any less clear.
I suggested setting fire to all that, not to bother with it anymore, to
leave the student alone for a while, and to never again use this
ridiculous, heavy and cumbersome notion in special relativity.
We don't have it, and that's also what's terrible, despite the cries of
some aficionados who have no need for it.
So why this stupid fanaticism?
Stockholm syndrome? The persecuted ends up adoring and glorifying his tormentor?
What's the point of all this?
On 2024-08-12 09:27:04 +0000, Richard Hachel said:
What is the space-time interval?
To describe it, mathematically, and not semantically,
because it may be an abstract construction requiring a complex number,
we use the formula ds²=dl²-dt².
That doesn't make the "thing" much clearer.
In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz².
If ds² = 0 the line element is light-like. If ds² > 0 the line element
is time-like and √(ds²) is proper time. If ds² < 0 the line element
is space-like and √(-ds²) is proper distance.
Although the formula refers to a particular coordinate system any other orthogonal isometric coordinate system can be used instead and ds² is
the same.
What is the space-time interval?
To describe it, mathematically, and not semantically,
because it may be an abstract construction requiring a complex number,
we use the formula ds²=dl²-dt².
That doesn't make the "thing" much clearer.
In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz².
Le 13/08/2024 à 13:42, Python a écrit :
Le 13/08/2024 à 13:38, Mikko a écrit :
Until very very recently (you can check on fr.sci.physique) he firmly
believed that ds^2 is always zero, go figure!
That's not what I actually said.
I was talking about an event occurring in a frame of reference
and whose information reached any observer present in this frame of reference.
For example, a terrestrial observer who observes the explosion of a supernova.
If the explosion took place 15,000 years ago, the observer will note (dl,dt)=(15,000,-15,000)
and therefore ds²=0
Le 13/08/2024 à 13:38, Mikko a écrit :
Until very very recently (you can check on fr.sci.physique) he firmly believed that ds^2 is always zero, go figure!
Le 13/08/2024 à 15:31, M.D. Richard "Hachel" Lengrand a écrit :
Le 13/08/2024 à 13:42, Python a écrit :
Le 13/08/2024 à 13:38, Mikko a écrit :
Until very very recently (you can check on fr.sci.physique) he firmly
believed that ds^2 is always zero, go figure!
That's not what I actually said.
I was talking about an event occurring in a frame of reference
and whose information reached any observer present in this frame of
reference.
For example, a terrestrial observer who observes the explosion of a
supernova.
If the explosion took place 15,000 years ago, the observer will note
(dl,dt)=(15,000,-15,000)
and therefore ds²=0
This utterly idiotic! A space-time interval is about TWO events, there
is only one event here.
I thought you had, at least, understand that an interval is between two events. I notice that you didn't even understand that.
You are getting more and more silly every single day old man.
Le 13/08/2024 à 15:35, Python a écrit :
Le 13/08/2024 à 15:31, M.D. Richard "Hachel" Lengrand a écrit :
Le 13/08/2024 à 13:42, Python a écrit :
Le 13/08/2024 à 13:38, Mikko a écrit :
Until very very recently (you can check on fr.sci.physique) he firmly
believed that ds^2 is always zero, go figure!
That's not what I actually said.
I was talking about an event occurring in a frame of reference
and whose information reached any observer present in this frame of
reference.
For example, a terrestrial observer who observes the explosion of a
supernova.
If the explosion took place 15,000 years ago, the observer will note
(dl,dt)=(15,000,-15,000)
and therefore ds²=0
This utterly idiotic! A space-time interval is about TWO events, there
is only one event here.
I thought you had, at least, understand that an interval is between two
events. I notice that you didn't even understand that.
You are getting more and more silly every single day old man.
And the shock of the photons on my retina, is that not an event?
Le 14/08/2024 à 12:21, Python a écrit :
And the shock of the photons on my retina, is that not an event?
This is utterly irrelevant.
Guignol!
And the shock of the photons on my retina, is that not an event?
This is utterly irrelevant.
Le 13/08/2024 à 13:38, Mikko a écrit :
In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz².
Not really.
ds² = dx²+dy²+dz²-dt²
But this formulation has little interest in special relativity, and I
find it useless to teach it as is to students and high school students.
Physicists start from this formula, which is a little more complex than Hachel's, which is:
To²=Tr²+Et²
There is little more to do than to place the units of measurement, and
the whole theory holds up much more easily than the dogma of "the
invariance of the space-time interval".
Hachel replaces with "invariance of proper time", which is pure
evidence, like a swallow is a swallow.
On 2024-08-13 13:10:33 +0000, Richard Hachel said:
Le 13/08/2024 à 13:38, Mikko a écrit :
In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz².
Not really.
ds² = dx²+dy²+dz²-dt²
Both sign conventions are used. It doesn't matter as long as one knows
which one is used. The information content is the same anyway.
If you represent vectors and position defferences with quaternions then
the real part of the square of the quaternion is ds² according to the
sign convetion that I used. But quaternions are rarely used in this
context so that is not important.
Am Donnerstag000015, 15.08.2024 um 11:26 schrieb Mikko:
On 2024-08-13 13:10:33 +0000, Richard Hachel said:
Le 13/08/2024 à 13:38, Mikko a écrit :
In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz². >>>Not really.
ds² = dx²+dy²+dz²-dt²
Both sign conventions are used. It doesn't matter as long as one knows
which one is used. The information content is the same anyway.
If you represent vectors and position defferences with quaternions then
the real part of the square of the quaternion is ds² according to the
sign convetion that I used. But quaternions are rarely used in this
context so that is not important.
Yes, becaause quaternions are the wrong construct, but quite close.
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