Space-time interval...

[Richard Hachel]

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?

R.H.

[Python]

Post by Richard Hachel
What is the space-time interval?
To describe it, mathematically, and not semantically,
because it may be an abstract construction requiring a complex number,

You do have issues with complex numbers too (and linear equations, and
differential calculus, etc.) I know.

Anyway complex numbers are useless here. For once your are right on
something. But that stops there.

Post by Richard Hachel
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.

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/24%3A_The_Theory_of_Special_Relativity/24.06%3A_Lorentz_transformations_and_space-time

Post by Richard Hachel
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?

You fail to understand because you are 1) an imbecile and 2) a stuffed
shirt, a pompous infatuated cretin.

[Mikko]

Post by Richard Hachel
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.

[Python]

Post by Mikko

Post by Richard Hachel
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.

Richard never understood what a coordinate system is.

Until very very recently (you can check on fr.sci.physique) he firmly
believed that ds^2 is always zero, go figure!

[Richard Hachel]

Post by Python
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

I can go further, and ask for a more precise notation than dl.

I then set E=(x,y,z,To,t) in Hachel notation that I do not explain,
because those who read me are intelligent enough to decode me easily
without me giving them the bottle.

So, for example, we have E=(12000, 9000, 0, -15000.0)

I said that the space-time interval will be noted ds²=0 for all the joint
observers who will cross the solar system at this precise moment, whatever
their speed and direction.

This is very obvious, and it even becomes ridiculous to talk about it too
much.

Let's take a single case: a rocket passes on the Earth's Ox axis, at two
hundred and forty thousand km/s (Vo=0.8c).

A well-understood Lorentz transformation immediately gives me.
E'=(40000, 9000, 0, -41000, 0)

We see that here again ds²=0

This is trivial.

Although it allows me to emphasize a remark that I have often made: If one
or more observers are conjoined,
whatever their relativistic speeds or their direction, they all observe
the same present universe.

Very deformed in x (Poincaré-Lorentz transformation)
x'=(x+Vo.To)/sqrt(1-Vo²/c²)
but always with t"=t'=t=0.

Do you understand these things better than the buffoon Python, who says
anything and everything.

R.H.

[Python]

Post by Richard Hachel

Post by Python
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.

[Richard Hachel]

Post by Python

Post by Richard Hachel

Post by Python
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?
You're a buffoon.
A guignol.

R.H.

[Python]

Post by Richard Hachel

Post by Python

Post by Richard Hachel

Post by Python
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?

This is utterly irrelevant.

You are a crook Richard.

[Richard Hachel]

Post by Python

Post by Richard Hachel
And the shock of the photons on my retina, is that not an event?

This is utterly irrelevant.

Guignol!

<http://news2.nemoweb.net/jntp?***@jntp/Data.Media:1>

R.H.

[Python]

Le 14/08/2024 à 14:05, M.D. Richard "stuffed-shirt Hachel" Lengrand a

Post by Python

Post by Richard Hachel
And the shock of the photons on my retina, is that not an event?

This is utterly irrelevant.

 Guignol!

It is so irrelevant that you didn't event mention it.

Face it Richard: physics is not your thing. Live with it.

[Richard Hachel]

Post by Mikko
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.

This does not even need to be discussed or demonstrated.

We can have fun (uselessly) by posing:
To²=Tr²+Et²
then Tr²=To²-Et²
then if Tr²=-ds²/c then ds²=dl²-To²c²

But all this complicates things.

Let's just talk about the invariance of proper time (which cannot be
unique, we cannot have two proper times) and all this will be much simpler
and much truer.

Simpler, you understand. No more need for a puzzle with complex notions
(i²=-1).

But above all, more fair in the end.

You have noticed that Paul B. Andersen has carried out a small study on
the Tau Ceti traveler, where Bella is an astronaut who evolves in
accelerated mode (10m/s²) on the 12 ly to cross.

Paul easily finds (a=1.052ly/y²) that in the terrestrial frame of
reference Bella will take 12.9156 years since:
To=(x/c).sqrt(1+2c²/ax).

He is right.

But then he gets bogged down in complex considerations, and proposes a
proper time for the rocket of about 3.5 years while Tr=4.776 years.

The complexity of the concepts then leads to dramatically false results.

R.H.

[Mikko]

Post by Richard Hachel

Post by Mikko
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.

Post by Richard Hachel
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.

The useful concepts are proper duration and proper distance. They are
related to ds², which therefore is at least interesting.

Post by Richard Hachel
Physicists start from this formula, which is a little more complex than
To²=Tr²+Et²

Physicists don't start. They started when they were students. Now they
continue from what they and others have already achieved.

Post by Richard Hachel
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".

Units of measurement are not needed for the theory.

In the usual formulation the invariance of the space-time interval is proven
from empirically validated postulates.

Post by Richard Hachel
Hachel replaces with "invariance of proper time", which is pure
evidence, like a swallow is a swallow.

It is not really a replacement. Proper duration and proper distance are
just terms used in certain situations for the more general concept.

[Thomas Heger]

Post by Mikko

Post by Mikko
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.

The 'real deal' is something called 'complex four-vectors' (aka
'Bi-quaternions').

This construct seems to mimic spacetime in the correct way.

It could be understood as certain type of 'geometric algebra', with such
bi-quaternions as 'elements' and so called 'Pauli algebra' as conncetion.


A guy named Jonathan Scott had written about this construct and how to
use it in the context of SRT (and others).

I took the idea and enhanced it to 'structured spacetime'.

My concept assumes, that spacetime of GR is real and composed from
elements, which behave like bi-quaternions.

This idea works without particles as real lasting entities, but regards
matter as internal structure of spacetime.

(This spacetime could also be called 'active vacuum', 'relativistic
ether' or similar.)

The main idea is, that the background (spacetime, 'active vacuum') acts
like a real physical system, which has internal structure, to which
matter (and we ourself) belong.

I have written kind of 'book' about this idea, which can be found here:

https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing

TH

...

[Mikko]

Post by Thomas Heger

Post by Mikko

Post by Mikko
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.

They are not wrong but 4-vectors are better for purpose.