XPost: sci.astro
From: PointedEars@web.de
Bill Sloman wrote:
> On 6/02/2026 11:10 pm, Jan Panteltje wrote:
>> I think I did read somewhere gravity moves at the speed of light.
>
> Gravity waves seem to.
_Gravitational_ waves
> LIGO apparently picked up an incipient binary neutron star fusion
> early enough for optical telescopes to be pointed at the right spot
> to see the optical output.
ISTM that this is insufficient observational evidence that the phase speed
of GWs is equal to c because we do not know when before the merger (this is
not called "fusion") the first GWs were emitted: They could have been
emitted long enough before that the light that was emitted later was still
not able to catch up with them.
More convincing evidence is that it definitely took ∆t ≈ 10 ms for the
first
detected GW (of GW150914) to propagate from LIGO Livingston, Louisiana to
LIGO Hanford, Washington, which is ∆x ≈ 3000 km *Euclidean* distance away
from the former (this means a phase speed of ∆x/∆t ≈ 300 000 km/s):
>> I do not need the Nobel prize, that is all corrupt anyways,
>> but really the probability that it would be different particles with
exactly the same speed is not very high.
>
> Einstein's general relativity theory that makes space-time four
> dimensional,
_Spacetime_ has been _four-dmensional_ since special relativity; the concept
was introduced by Minkowski in 1908, not Einstein in 1905 (but Einstein,
after some hesitation, made extensive use of it as it enabled him to
formulate general relativity *after* 1908).
> with time as the imaginary fourth dimension,
Time is NOT an "imaginary dimension" of spacetime; it is a *real(-valued)*
coordinate, e.g. (c t, x, y, z)^T for a position four-vector.
You are confusing the time in the pseudo-Euclidean/-Lorentzian manifold that
is vanilla SR/GR spacetime with Euclidean ("imaginary") time; perhaps
because of a popular-scientific book or two by Hawking who did not explain
the origin of his "imaginary time" concept (a Wick rotation) very well
(probably because the maths would have gone way over the heads of most of
the readers; IIRC he once joked that "Someone told me that each equation I
included in the book would halve the sales.")
What happens is that (for simplicity the Minkowski) spacetime metric can be
written
ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2
= -(dx^0)^2 + (dx^1)^2 + (dx^2)^2 + (dx^3)^2,
where the first identity can be derived from a simple geometric idea how to
measure the distance traveled by a light pulse in vacuum, and the
superscripts in parentheses on the last line mean indices, not exponents.
We can then make use of the fact that i^2 = -1, where i is the imaginary
unit, and define the Euclidean or ("imaginary") time
x^4 := i c t ==> dx^4 = i c dt ==> (dx^4)^2 = -c^2 dt^2,
so that the metric can be written
ds^2 = (dx^4)^2 + (dx^1)^2 + (dx^2)^2 + (dx^3)^2
which looks Euclidean. This coordinate transformation is called
*Wick rotation* and turns out to be very useful in quantum field theories.
> means that every point in the universe is effectively in contact with an
> ever-enlarging sphere whose surface is sufficiently far away that the
> sum of the squares of the normal space separation is exactly cancelled
> by the sum of the square of the time-axis separation.
This applies in some sense to events connected by *light* and other effects
that propagate at the same speed.
--
PointedEars
Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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