hanson wrote:
> […] Thomas 'PointedEars' Lahn" [insult] wrote:
>> hanson wrote:
>>> ds^2 = dx^2 + dy^2 + dz^2 - c^2dt^2 ..... [1].
>>>
>>> Some say ds^2 is "space-time", others say that
>>> ds is "space-time", other still insist that ds^2 or
>>> ds are "space-time intervals", while others are
>>> adamant that "s" happens to be "space-time"
>> Who, according to your research, says either one, and where?
>
> The 1-liner of yours above does show, off the bat,
> that you don't know what you are talking about […]
No, it shows instead that you make unsubstantiated claims.
>>> Just tell me the MLT dimensions of "space-time"
>>> as shown in [1]
>>
>> There are no “MLT dimensions of space-time”.
>
> So Space-time has no mass, no lenght, no area,
> no space and no time.
No, AISB it has three spatial dimensions (that can be compacted into one
dimension, space) and one temporal dimension (time). But those are
*mathematical* dimensions, ways of how the *coordinates* of an object can
change.
By contrast, mass and length, and by extension of length, area ([area] =
[length]²), are *physical* dimensions of *quantities*.
> but you say it exists.
It exists insofar as that we can indeed observe the effects that would
follow if the theories using it would be correct. IOW, the predictions of
the theories have been confirmed by observation again and again.
As you are probably aware, recently predictions that followed from assuming
the correctness of the general theory of relativity, in particular a curved
spacetime, curved according to the energy–momentum in a location, had been
confirmed once again by the experimental observation of gravitational waves.
> ROTFMAO!
Simple minds are easily amused.
> In [1] there is dx^2 + dy^2 + dz^2 which are ranges
> of x,y,z
No, they are not.
> that are ORDINARY **Length** items
Not really. “x”, “y”, and “z” in the referred equation are appropriately
chosen labels for the spatial *coordinates* of an event, a position, in
spacetime. “t” then is its one temporal coordinate, time.
The referred equation means that if you make the differences between
corresponding coordinates of two points infinitely small, you can arrive at
a way to measure distances between all possible two points in that flat
manifold.
> and x^2,y^2,z^2 are their respective AREAS;
Only in an overly simplified sense. “dx²” must be read “(dx)²”; _not_
“d(x²)”.
>> <snip> You must realize that there are
>> different definitions for the term “dimension”
>
> hansoon wrote
If you start quoting properly, as suggested by a proper newsreader, you will
probably not embarrass yourself again by failing to spell your own (nick)
name properly.
> So name some different definitions for length
> & name some different definitions for an area.
You misunderstand. I said that there are different definitions of the term
“dimension” in physics. One of them is borrowed from mathematics, from
geometry. The one you are referring to is not borrowed from mathematics,
and you are confusing it with the former.
>> there are different contexts in which it is used, if
>> you are going to understand “space-time” in physics.
>
> So, Lahn, show what those different contexts are
> and why they do need to be different for the one
> and same theory.
Because one (the mathematical one) concerns position only, and the other one
concerns all physical quantities. There are, of course, physical quantities
in the theories of relativity as well (they are physical theories after
all), and they do have dimensions there in the quantitative sense.
But spacetime *itself* does not have *that* kind of dimensions; it has the
mathematical kind instead. So your question regarding “the MLT dimensions”
of spacetime does not make sense; it betrays a fundamental lack of
understanding what spacetime is.
> Show what YOUR understanding of Space-time is,
My understanding, which is equal to what is being taught in mathematics and
physics classes since more than a century, is that spacetime is a 3+1-
dimensional manifold.
>> On the other hand there are dimensions in physics, of physical quantities
>> which can be described in terms of combinations of the quantities mass
>> (M),
>> length (L), and time (T).
>>
> hanson wrote:
> On the other hand you just said again that Space-time does
> NOT exist in the real world
No, I did not say that. I said that there are the dimensions with which
you determine position and distance, and there are dimensions which which
you *can* define the form of physical quantities. Those are *separate*
concepts. You are committing the fallacy of equivocation here.
> which makes it as USELESS to real physics
On the contrary. The mathematical dimensions of spacetime are fundamental
to describing how physical quantities change when objects are in motion
relative to one another.
Why? Well, one quantity important in motion is speed. Speed is
the magnitude of velocity, and velocity is the change of *position* per
unit time. A position has *coordinates*. Which coordinates determine
position is the subject of geometry, of mathematics.
If speed is measured relative to another object, it is important how
distances to that object and times on that object are measured. So
you see that there really is no contradiction in applying in physics
*both* definitions of “dimension”, but in different contexts.
<
https://en.wikipedia.org/wiki/Special_relativity#Physics_in_spacetime>
> So, tell why the motion of bodies _in_ space & -in_ time is
> not sufficient but needs […] space-time […]?
There are several ways to explain it. I prefer to start with the fact that
all experiments have shown that the speed of light is constant in all frames
of reference. Spacetime then provides a convenient mathematical framework
to describe the observed effects that follow from that.
> None of the agencies of the world's space faring nations
> do use SR or GR for determining the trajectories of their SVs
Because the speeds of those space vehicles (SV) are so low compared to the
mindbogglingly huge speed of light that (what we know since more than a
century) the *approximations* of classical mechanics suffice there:
lim γ(v) = lim 1∕√(1 − (v∕c)²) = 1
v→0 v→0
[γ(v) is the Lorentz factor for speed v which determines the degree of
length contraction and time dilation. As γ(v) approaches 1, it
becomes increasingly harder to observable any length contraction and
time dilation. If necessary, equations for both can be provided here
*again* to demonstrate this.]
However, SR and GR become important where electromagnetic signals are
involved, as those travel at the speed of light. One such kind of signals
are those of global navigation satellite systems (GNSSs). The trilaterated
position of the observer on the surface of this planet would be off if both
SR and GR would not have been considered in the design of the hardware and
the software of the satellites of those systems and the receivers on the
ground:
<
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html>
BTW, when do you think will you have learned to post in a civilized manner,
including *proper* quotation?
F'up2 sci.physics.relativity
--
PointedEars
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